Episodes 311-312

**Focus: **311: Match Equations to 10-Frames / 312: 10-Frames Different Ways

**“I Can” statement:** I can match equations to 10-frames. / I can fill 10-frames in different ways.

**Extension Activity: **Represent the Equation with 10-Frames / 10-Frame Shake

In Kindergarten, we start with our Mystery Math Mistake, which features a delicious word problem about a plate of cookies. If there were 6 cookies on the tray, and someone ate 2, how many were left? You’ll have to be a detective to see if you can figure out where Mrs. Gray made an error while solving this. I bet Jordan and Carly, the two kids on this show, are going to help steer her right!

As we start getting into the main part of the lesson, we do a lot with those great phrases: *What do you notice? What do you wonder?* We show kids three different modalities of numbers put together to match equations. There are 10-frames, but we also have snap-cube towers, as well as the Counting Buddy Jr. that has five beads of one color, and five of another. We start off with what students notice within these three different types of models that they’re seeing. At the end of the day, all of the models equal 10, but they are composed of different numbers – 7 and 3 on the 10-frame, 8 and 2 on the snap-cubes, and 5 and 5 on the Counting Buddy.

We then start working with students being able to see an equation and see if they can match it to the 10-frame. We can do a process of elimination for students, but they see the equation with 10 = 7 + 3 and they have to decide if that 10-frame matches. This really helps students with their part-part-whole understanding, getting them to understand that 10 is the total, and it’s made up of two parts that are denoted by red or yellow counters.

We then flip over to a different tool by using our Counting Buddy Sr., which is one of my favorite tools that you can use to show different parts to numbers. Some people clear it by pushing the beads up to the Counting Buddy’s head. But another option is to put half the beads towards his head (10 beads) and half of the beads towards his feet (10 beads). This way you can pull the beads into the middle to come up with different combinations, which we do in this episode. Then, you can draw in the two parts of the 10.

We’ll show different equations on the Counting Buddy Sr. – 6 + 4, 3 + 7, and so forth. In the end, we want kids to talk about what they see is similar or different about the tools that we’re using in the show compared to a 10-frame, or even a Counting Buddy.

For the extension activity, it’s the students’ turn to represent the equation with the Counting Buddy Sr., so we actually have a spot on the extension page where students can fill in their different combinations as they’re looking at it, and then matching the Counting Buddy to the equation that they’re working on.

In show 312, we’re also leading with a Mystery Math Mistake. This time, however, we take a story problem that’s very similar to the one in the previous show about cookies. In this problem, there were 4 cookies on the tray and 2 more came out of the oven and were added to the tray. How many cookies are there now? I wonder if you can see where Mrs Gray’s mistake is…Did she add or subtract to find out the answer? Our friends on the show, Jordan and Carly, are going to be a great help for that.

Our “I can” statement is I can fill 10-frames in different ways. We have four different pictures (A, B, C and D) that we’ll show students to ask them which one doesn’t belong. These all are different structures of 10-frames with a different variety of red and yellow counters, some filling the whole 10 frame, some not. Kids will talk about which one doesn’t belong.

The best part of this activity is that each 10-frame, as they look at it deeply, might not belong for one reason or another. We pay particular attention to a 10-frame that looks like a 10-frame, but is actually two 5-frames. Students should be able to see how two five frames really does represent seeing 10, even though it’s two separate parts.

We then play a really fun game called the 10-Frame Shake. Students are going to shake 10 two-sided counters and spill them onto the table. They have their 10-frame mat and a really great recording sheet where students can write in their 10-frame, write in their number sentence and then write in their number bond.

In the last portion of show 312 for Kindergarten, we work on* how many more* counters are needed to fill the 10-frame. So we show 7 on the 10-frame and students can see that there are three empty. They get to match it to the equation 10 = 7 + 3, 10 = 8 + 2, or 10 = 5 + 5. As students work through this with Mrs Gray, they’ll start to see that they can look at the empty spaces to help them to be successful with this concept.

**Focus: **311: Compare Lengths / 312: Compare Indirect Lengths

**“I Can” statement:** I can compare and order objects by length. / I can use a third object to find longer and shorter objects.

**Extension Activity:** Compare the lengths of objects / Create comparison statements

We start episode 311 by working on the Mystery Math Mistake, but in first grade, we’ll look at it a little differently than in Kindergarten. For this problem, we’ll be revisiting a topic from a previous show (310) where we added 10s and 10s and 1s and 1s. Value Pak is helping with this problem, but is all upside down, confused and turned around, so he solves incorrectly. Students have to use their magnifying glasses to study the problem and see if they can figure out where Value Pak has gone wrong.

As we begin this length unit, students are going to be presented with three different pencils. The pencils are actually the same length, but they are positioned to start at different places. By asking students what they wonder and what they notice about the pencils, we give them a taste of what the lesson will be about. The students in our show, Dennis and Han, talk about why they think the pencils might be different lengths based on how they look. We also ask which pencil they think is the longest (trick question, remember!). This leads into a conversation about measuring things from endpoint to endpoint, and why that will help you be more accurate when you measure.

Next, we look at a pencil and a crayon and we create comparison statements about the two objects. Students will learn to use phrases like “longer than” or “shorter than” to describe different objects of length. Then, we add in a highlighter and snap cubes to spark even more conversation. For example, “Comparing the highlighter to nine connecting cubes, which one is shorter?”

We had so much fun comparing things that there’s a deleted scene from this part of the show! You can watch it here to see even more examples, show it in your class to let someone else do the talking for a few minutes, or even send let students watch it at home for extra practice! In the scene, Mrs. Markavich talks about how we can look or think about the size of your foot and your pointer finger and make comparison statements about objects that are shorter or longer.

In the episode, we continue to look at different objects, like scissors and a hole punch and a stapler, and decide if we can order them from shortest to longest. Then we take fettuccine noodles, a straw, and one base 10 block, and see if we can order it from longest to shortest. We also talk about those words of “taller” and “shorter” as we turn things around differently, and it helps us to think about those descriptors that show length.

Mrs Markavich does a great job talking about the idea of a starting line, like you’re going to start a race, but you’re going to start at the endpoints and everyone is going to begin in the same place.

For the extension activity, it’s the student’s turn to compare the length of different objects, just like we did in the show.

As we move on to episode 312, we do another Mystery Math Mistake, again with Value Pak. This is similar to the previous episode, but we want to see if kids can apply the strategy of Valu Pak to find errors.

Continuing our unit on length, we show two sets of objects, and ask *What do you notice? and What do you wonder?* The same green pencil is used in both comparisons as that length to measure. Students talk about the pencils being different lengths and that they’re lined up by endpoint, but they have lots of wonders about those objects. We want to hear statements like “The purple pencil is longer than the green pencil, but the blue pencil is shorter than the green pencil.” or “The blue pencil is shorter than the purple pencil.” These types of statements that can compare to a third object are really important.

Then start to compare objects that we might not be able to measure or physically put next to each other, but we can use with yarn or string to help us compare these large objects. For example, we figure out the length and width of the dry erase board we use on the show, and ask *which is longer?* By using the string to measure one of the sides, we can compare it to the other to see which is shorter or longer based on the comparison piece, which is the string.

This idea can apply on a larger scale too. We talk about different ways that kids get to school – bus, riding in a car, walking, etc. So, using this idea of a third object to compare, by looking at the map, we try to decide if Clare or Maya’s house is closer to school. By using the same string to help us measure the distances, we can figure it out.

We do a lot with the extension activity, where students can compare objects using yarn or string to help them to figure out how to create some of those comparison statements that we talked about in the show.

**Focus: **311: Halves, Thirds, and Fourths / 312: Fractions with a Whole

**“I Can” statement:** I can partition circles and rectangles into halves, thirds and fourths. / I can make halves, thirds, and fourths different ways, and discover a whole.

**Extension Activity: **Split the Shape / Split the Shape, Version 2

In episode 311 for second grade, we also do a Mystery Math Mistake, bringing in an upside down, all turned around D.C. He’s really struggling with decomposing numbers to make a friendly number, and so we want to see if students can look at this in an inquiry-based way and discover the error. Shaunda and Kelly are the students on this show that help us to see where that error might be.

This show begins our look at fractions! As we’ve done in different episodes before, students will look at four different images and decide which one doesn’t belong. The important part to notice here is that the shapes are partitioned in different ways, but they’re not always in equal ways. As we introduce fractions, we want kids to understand the idea of equal parts. In the show, we take a rectangle and fold it into two equal parts. We take that same rectangle and show how we could fold it into thirds. Then, we also do a non-example of thirds, which I think is really important for students see. As you’re folding something, especially into thirds, students’ spatial awareness skills are really a struggle, and so even if they’re folding something like a letter, it might not be into equal parts. Then we talk about folding something into fourths.

The second grade standards want kids to know that halves represent two equal parts, thirds represent three equal parts, and fourths represent four equal parts (which we can call quarters, another vocab word to work on!).

Then, we take this idea into circles and talk about which circles are not examples of halves. Students will see three different pictures of circles that are fractions, and students have to decide which ones are not examples of halves, fourths, or thirds. Kids must be able to look at the way things are divided and decide if they are equal. In the show, Clare and Diego are asked to divide a circle into three parts, and we have to evaluate whether their circles are partitioned equally.

Split the Shape is the extension activity for students to play with a friend. They’ll have a spinner and rectangles, squares and circles that must be partitioned into halves, thirds, and fourths, depending on what the player rolls.

As we move on to 312, you guessed it – another Mystery Math Mistake! Our friend D.C. has gone wrong in his arithmetic, and Shonda and Kelly have to find his problem!

The show begins with two rectangles and the request for them to be partitioned into quarters, or fourths. Then we ask students to shade in 1/4. The girls in the show are thinking of partitioning the rectangles in two different ways, so we talk about the different ways that you could partition a rectangle that would still be equal, but would be able to allow 1/4 to be shaded. We go through the same process with squares – looking at how to partition and shade one half of a square in different ways. The goal is to get kids to really understand why equal parts are important, especially as we look at fair shares.

We try to give scenarios to help students understand that, even though the size of the piece looks different, iit still could be equivalent or equal to the fraction that we’re talking about. In our scenario, Diego’s dad makes two square pans of cornbread and slices it up for the family. Diego’s little brother feels that his piece is smaller than his brothers’ – his brother has a perfect square, where Diego has a long strip. It’s still divided into fourths, but the size of the piece looks a little bit different.

Of course, you can’t really talk about fractions and dividing things equally without dividing up a pizza! If you have a pizza, and you have friends over, how many pieces is each person going to get? Obviously, we have to know how many friends there are. If we were to have a pizza and share it with three friends, with each person getting a slice, they would get ⅓ of the pizza or the pizza would be cut into three equal parts. We would do the same thing if we had four friends coming over. We might cut the pizza into four slices and each friend would get 1/4.

Pies are another classic fractions visual, and in this episode, we match word problems to pies. Some of the pies are full and cut, some parts of the pie are empty where somebody has eaten part of it. If Noah ate most of the pie, but he left a quarter of the pie for Diego, can we find the pie which represents the problem to apply what we’re learning in the show?

For the extension activity, we play Split the Shape, Version 2! In this version, students are going to partition circles, rectangles and squares into different parts, based on the spinner that they’re using, and see who can get their parts shaded first.

**Focus: **311: Fraction Number Lines / 312: Locate Unit Fractions

**“I Can” statement:** I can learn about fractions using a number line. / I can partition number lines to locate unit fractions.

**Extension Activity: **Create and partition number lines / Partition, locate, label fractions

Episode 311 for third grade begins with a Mystery Math Mistake on a concept students have studied in a previous show. D.C. is looking at 18 x 9 and is a bit confused with his decomposing and composing as he’s making his area model with partial parts of partial products. Trevor and Marcus are going to help Mrs. Askew figure out where the mistake is and get D.C. back on his feet!

For this episode, we’ll continue our work with fractions that we began a few episodes ago. In fact, we have 16 shows on fractions for third grade because it’s such an integral part of the students’ success as they move on to fourth grade.

Our “I Can” statement for this episode is: I can learn about fractions using a number line. For the next four shows, we’ll have two number lines for students to look at. One of the number lines is partitioned starting at zero and then going to 10, and the other one begins at zero and goes to 1, with a tick mark in the middle. Students notice different things about these two number lines – one of the big things we want them to see is that the quantity of the number line differs based on how it’s partitioned. We look at what we think that tick mark might represent as it’s halfway in between zero and 10 and the other one is halfway between zero and one.

We then take different number lines, and find different ways that we can sort them. This just gets kids comfortable with the idea of taking a number line and separating it into fractional pieces. One student says that the number lines have tick marks at the whole numbers, so they might look at sorting those where they see a number line start at zero and end at six, and there’s no actual fractional parts in the middle but they’re actually looking at just whole numbers. The other ones are a fraction number lines that have just fractions in them at the tick marks.

A common point of confusion for third graders is being able to make a number line proportional. It goes back to the spatial awareness thing! So we spend time in the episode looking at how students can create their own number lines. We look at where half should be labeled on a number line, or how a person might think of half as a number line divided into two half parts, just like you would with fraction strips. Many of the common misconceptions are addressed while we’re creating number lines in this segment.

We spend the rest of the show really looking at number lines and figuring out how to fold them so we can make different number lines. we make a number line that’s in halves, fourths, eight, thirds and sixths. Then we compare those to the fraction number strips that we made in the previous show.

For their extension activity, students are going to create and partition number lines. It’s really important to make sure that kids go slow here to make sure they understand the parts. many students, if they’re trying to divide a number line into fourths, will put in four tick marks. In the show, we stress that the fourth tick mark is usually on the whole number, depending on how you’re dividing it. So, if you want to partition your line into fourths, you would only need to add three lines. This helps them make that connection that’s needed.

In show 312, we get another Mystery Math Mistake! We’re doing 15 x 3, and D.C. just cannot seem to get it right. The boys help set him straight to make sure he has all the parts in his area model to do his multiplication.

Our “I Can” statement is: I can partition number lines to locate unit fractions.

Unit fractions? What are those?? Often, math books talk about unit fractions, but students don’t really understand what they are. We know that a unit fraction always has one in the numerator, and then it has a denominator. Think of a unit fraction as a fraction that describes the pieces that we’re talking about. If I have something divided into thirds, the unit fraction we’re talking about would be ⅓. If I had something divided into six parts, the unit fraction would be 1/6.

To get students thinking about this, we start with four images to figure out which doesn’t belong. Students have to look carefully at the number lines and fraction strips to see where things are labeled and have them pay attention to the details in these. We really want to make sure that students can clearly locate and label fractions on a number line, because there are important things to include: partitions of equal parts, a dot, a label for the fraction.

To apply this concept, we have three friends that create a number line – Clare, Andre and Diego. We want to have the number line partitioned into fourths. It is really helpful when kids can look at things that maybe aren’t perfect and bring their reasoning to why they agree or disagree with the way somebody has partitioned the number line. We have some people that feel that the number lines are done exactly right. A lot of these number lines are no longer ending at one but they’re extending to two. And so we go through and kind of have an evaluative look to see how these number lines are really created.

We then start practicing partitioning number lines, locating and labeling the fractions. We label 1/3, we label one 1/2, we label ⅛. Sometimes, a fractions number line might end at four, not just at one. Students should know where 1/8 is and how you’re not going to find 1/8 appearing between one and two, and two and three, because 1/8 is only between zero and one. This will help the kids to get that relationship.

Since we represent fractions three different ways – fraction strips, area models, and number lines – we want to ask students *which way do you like to look at fractions?*

Of course, the extension activity is to partition, locate and label fractions on the number line, so that students will have lots of great practice with their new skill!

I think your students are really going to like our Mystery Math Mistake! It’s a really fun spin on math that helps kids really get interested in trying to find the error. If you want to take it a step further in your classroom, have the students create their own Mystery Math Mistake! If you want to check out more on Mystery Math Mistakes, visit our SIS4Students page to see a whole week’s worth of problems that we did during the beginning parts of COVID. See if you can spot the mistake and let us know!

M³ Members, don’t forget to download the PowerPoints and get your very own Mystery Math Mistake animation!

(valid M³ Membership login required)

Thanks for joining us for our last blog from our featured guest blogger, Kristin Marczak, who is teaching in the trenches in the Upper Peninsula in Michigan. I’ve worked with Kristin for the last several years as a Molding Math Mindset teacher who has gone through our training, and has implemented so many of the great things we’ve been doing in the area of math. She’s an expert at doing numeracy talks, being able to really look at students in her classroom and figure out where their needs are best met by bringing in concrete, pictorial, and abstract means.

In fact, I was just visiting her two weeks ago in her classroom and we were modeling some different things, and I’m so impressed with the work that they’ve done at her elementary school, C.J. Sullivan Elementary, and I can’t wait to share her interview with you!

To narrow it down to the one biggest challenge has become nearly impossible even though I have thought about this question so many times over the last year. I believe each teacher faced their own challenges depending on what life is like outside of the school building. The ripple effect of one challenge to the next truly tested me as an educator, as well as a parent guiding my own children through their online learning. We experienced many growing pains, but we adjusted and made it through somehow!

I have two children of my own in elementary school. At times, I would be teaching my own class and have two children on their own Google Meets. It was a challenge to have so many devices on our wifi! That is something I was not prepared for or had even considered when this world of online learning began a year ago. Many times, my Meets would freeze and students would have to shut their cameras off in order for me to just get through the lesson. Teaching first grade and not being unable to see their faces and make that eye contact definitely took the wind out of my sails many times. Being virtual and not being able to have the face-to-face connection during teaching made me feel like I was failing as a teacher. At times I felt the Meets were chaotic and I would end them earlier than anticipated just to ensure I kept my composure and didn’t break down in front of my students.

We all know the “teacher look” and after 14 years of teaching, I have perfected mine! Once we moved to completely online learning the “teacher look” was no longer something that worked as classroom management strategy. I had to come up with new ways to keep students engaged. Whether this meant wearing funny hats, changing outfits between Meets, or just sharing a funny video clip or meme, I had to be flexible and allow room for change.

At the beginning of virtual learning it felt like complete chaos, and I truly felt defeated. I was not sure how I was going to be while teaching through Google Meets and Google Classroom. I think at some point, most (if not all!) teachers felt the same way. Teachers have this gift of adapting and making split second decisions to better their lessons and give their students what they need. The last year has been something none of us could have anticipated, but teachers and students alike are resilient, and by staying the course we were able to dig ourselves out of the trenches and make it to the other side – hopefully!

Without moving to virtual and hybrid classrooms, I would not have used Google Classroom. I now feel quite confident in it and would be able to move to completely online easily. I am happy my district provided PD to support and help to make us feel much more competent and effective. At the beginning of this school year, we had a hybrid model. At any given time the amount of face-to-face or virtual students could fluctuate. I had to not only keep up with my face-to-face students, but also keep a Google Classroom updated daily and have students join Meets. It was a draining cycle of working all day in the classroom, and then working the evenings on Google Classroom, but the knowledge and experience using Google Classroom will definitely be beneficial in the future.

During one of my Google Meets, my dog, Daisy, joined and completely stole the show! My students were way too excited to return to the lesson and continue. We spent the rest of the Meet asking Daisy to do tricks and be on camera. It was hard for me to let the lesson go, but it gave me a chance to laugh with my students and just enjoy the moment.

When we moved to virtual learning, we were teaching from home without a document camera – which was a challenge! Through Google searches, Pinterest, and scanning social media, I found a great app called iDocCam that uses your iPhone as a document camera. I would set up my iPhone on top of books and pots and pans to reach the right height and use that during our Google Meets. It made my teaching much better and the students were more engaged.

I will always be in favor of in-person learning. I feel that in-person learning offers students so much more than an online classroom can. Being in-person allows me to connect with my students and build trust that I was unable to build while being virtual. There is no better feeling than working with students and seeing them get that smile on their face when they make progress and are full of pride.

Besides personally loving the connection with my student, the students need each other too. First graders are learning how to build friendships and follow rules and schedules. In the classroom, we create a community that not only builds on academic skills, but also on social and emotional skills.

While teaching in the trenches it is very easy to get “stuck” or “lost.” I strongly suggest, first and foremost, to take care of yourself. I know that is easier said than done, but coming from my own experience, when I was not taking time to rest and recharge, all areas of my life were negatively affected. Trying to balance all the different types of classrooms and your own personal life can be too much, for even the most ambitious person. Put the computer away, put the work away, and rest!

Allow yourself to “let go” and try something fun. I run a tight ship and thrive on schedules and routine. I had to loosen the reins once virtual learning happened! It was not easy, but I was reminded that learning can take place in many different forms.

**“If you can stay positive in a negative situation, you win.” **

Kristin Marczak is a Michigan native who studied elementary education at Northern Michigan University, and has a Master’s Degree in Curriculum and Instruction from Western Governors University. She began teaching at L’Anse Area Schools in the summer of 2007, and is now in her 14th year at C.J. Sullivan. Aside from 1.25 years in Kindergarten, the rest of her teaching has been in first grade, which she loves because she gets to watch her students develop so many skills.

Kristin’s dream job would be working with schools on developing and improving curriculum and being a coach for teachers to improve their instruction styles.

Currently, Kristin lives in L’Anse, MI with her two children, Landon and Avery. She loves sports, especially the Detroit Lions, reading, spending time with her two children, and dog, Daisy.

If you’ve watched any of the 1st grade Math Mights shows, then you’ve seen Tiffany at work! She is an amazing teacher! I’ve had such fun working with her on the show, but I also know she is a rockstar in her classroom as well.

I met Tiffany several years back while working on our Molding Math Mindsets project in Romulus Public Schools. She was a first grade teacher, and still is in the first grade classroom today! We worked a lot together in the area of math. In fact, Tiffany was one of the math leaders as she has great leadership skills in her school district, and she has spearheaded a lot of the curricular work that we’ve done in math in first grade.

I’m so excited to have her tell us about her experience with teaching in the trenches.

Obviously, it’s new for all of us, which was a humongous challenge. I would say, on the teaching level, teachers went into this with zero training. No one really had any idea of how to do it, how to be successful, where to start, who to go to – there was just no training.

Additionally, what I’ve found to be *really* challenging is, when I have students in the classroom, I can control that environment. If they’re not prepared and they don’t have a pencil, I can get them a pencil. If they don’t have their homework, I can get a new sheet of homework. If they don’t have something they need or need help, it’s within my control to help them. When they are at home, I can’t control what’s going on. If they don’t have a pencil that day, I can’t just hand them one. I can’t control that their parent is sitting in the room next to them and the TV is on at volume 1000 so they can’t hear the lesson. I can’t control that they have three or four brothers and sisters and, while their parents have done their best at putting them all at the table to learn, my student can hear what’s going on in their sister’s classroom and their brother’s classroom. They can hear the other teachers. *I* can hear the other teachers. I think it’s just really hard, and it made it really hard for kids to focus.

And then thirdly, I would say, you kind of have two different kinds of parents, both of which are challenging. There’s the “too much support” parent who is just a helicopter. They’re not leaving their child to do anything independently – they’re doing all the cutting, they’re doing all the gluing, they’re doing all the clicking on the computer. They’re hovering over their student’s work so you don’t really know if the student is learning anything, you don’t know if the student needs additional support. Even though you’ve gently told the parents “Let them go, I’ve got this,” they don’t want to. And then you have that other extreme, the parent who you’ve never seen one time all year, and it’s obvious that they haven’t been involved at all.

The teachers in my district are teaching in-person and virtual simultaneously. So, in my classroom, I have 12 students in-person, and I have five students that are virtual. It’s really hard on your heart. That first day back, those virtual students were crying. They were super sad because they weren’t at school with their friends, and they want to be there, but for whatever reasons, their parents have chosen to keep them home. It’s particularly hard on the virtual students because they may be feeling like they’re being left out or not able to participate as much because now that I’m managing everything that’s going on. Before, when we were all virtual, I just managed what was going on in front of the screen, but now, I have kids that are needing to keep their masks on, needing to stay in their chairs, needing help with assignments. There’s a lot that goes on in class that the virtual students aren’t a part of.

However, I think the most glaring challenge is that, while I knew that kids were going to be low when they came back and I knew that they weren’t getting everything that they needed, I never realized the severity of it until they came back into the classroom. I have a student who cannot write any letters in her name. She doesn’t know how to form any letters. The severity of what has happened over this last year leaves me not really sure where we go from here or how to adjust to get these children to the next point so that they can be successful and this doesn’t damage them forever.

I have always known that six-year-olds could achieve whatever task you set forth for them. But what I learned going 100% virtual is just how true that is. I was thinking, *how can I teach kids how to manipulate Google Classroom virtually on day one at six years old*? But it can be done! I think that that made me just grow exponentially. The kids did an amazing job with just repeated instructions every day. Everything in my Google Classroom is by date, so every single day there is the topic is by date, Monday, March, 15, and then their assignments for the day are posted under that topic. There’s an icon next to each one, so they know that their red dot is what they do the first thing in the morning, the green heart is for reading, the plus sign is their math assignment, etc. They learned, almost immediately, how to manipulate those assignments, turn those assignments in, get feedback on the assignment and be in a Google document with me at the same time. They learned, when they needed help on something, if they clicked in the box to let me know,, I knew exactly where they needed help instead of them having to present their screen, I can be right in there with them working. I just think that this group of kids, for this whole past year, are going to be amazing at technology because the little ones have just nailed it.

With kids being virtual, you sometimes just can’t get to your mute button fast enough. I have a student who is extremely quiet. She basically didn’t say two words in Kindergarten, and she doesn’t talk a whole lot in first grade. She was very nervous, so anytime that she wants to talk, of course I encourage it. One day, we came back from lunch and she said, “Mrs Markavich, can I tell you something really funny?” Of course, I said yes because I was so excited that she wanted to talk! She said, “During lunch, I was going through my mom’s camera roll on her phone, and I saw a picture of her boobs!” The rest of the class started laughing. I muted her as quickly as I could and then I just said, “Oh, we don’t share that kind of personal information with the rest of the class.” But that was probably the funniest thing that happened to me, all school year while the kids were virtual.

I did 95% of my teaching in my classroom, even though it was an empty classroom. I started the year not having a clue what I was doing, like everyone else. So I have a smartboard, a computer, and I had a Chromebook. I propped my Chromebook in front of my smartboard and I logged in every day to my Google Meet, where I could see my students all day long. They were basically looking through the Chromebook onto my smartboard, and anything that I needed them to see they could see on my smartboard. I could use my document camera that way, I could present videos that way, or anything else that I needed them to see. They saw through my smartboard but then I could see them the entire day as well, and not have to wonder what they were doing.

Another thing that I did, like probably 1 million other virtual teachers, was occasionally create different Bitmoji classrooms or dashboards, where the students could click on different links to get to the materials that they needed for the day. This might be something that some people think first graders, or six-year-olds can’t work with the Bitmoji classrooms, but my kids were pretty successful at it.

I would 100% go back to the classroom.

Of course I would want to teach all day, every day, anywhere that I could, but kids need to be in the classroom. I think that’s where they learn the most, I think that’s where they can show their independence, and I think they can be successful. I think that they need the social aspects of it and how to be in society. While I think I’ve done a pretty good job virtually, being physically in the classroom is where I would pick to spend all day, any day.

**Have grace and be kind to your colleagues.** That has been emotionally draining. It has beaten us down. I’ve had to scrape myself up off the floor and say, *I can go to school today and I can do thi*s when I thought I couldn’t. And so I think if you have grace with your colleagues, and know that they could be going through exactly the same thing that you’re going through or feeling the exact same way you feel. I know that I had never done this before.

I love change and I embrace change, but not in this manner. I knew that I was going to fail.** I knew that there would be days where something would fail.** And that’s okay. The kids will grow from my mistakes and learn, “Oh, even our teacher isn’t perfect! She makes mistakes, or this didn’t go the way she planned.” Don’t dwell on it, and just move on. If it doesn’t work, if you failed, let the kids know that you failed, and just say, “Okay, we’re going to try again tomorrow and hopefully tomorrow is going to be a better day for me as a teacher, and for you as students, based on my mistakes!”

Tiffany Markavich has a B.S. in Education from Eastern Michigan University and a Master’s Degree from the University of Michigan Dearborn in the area of Education. Throughout her 22 years in Romulus Community Schools, Tiffany has taught 1st and 2nd grade and served as the Reading First Literacy Coach. Currently, Tiffany is the Co- School Improvement Facilitator for Halecreek Elementary and the District Wide 1st Grade – Grade Level Leader.

Tiffany is passionate about making every day in her classroom an amazing educational experience, doing numeracy talks, and having her kiddos “kiss their brain”!!

As I have the opportunity to work with schools all over the country, I am privileged to interact with all kinds of incredible educators, especially this year, as our profession has really had to level up in the face of adversity during COVID! We, in education, have definitely had to pivot. We’ve had to adapt to new, and ever-changing, situations, and now, we’re having to deal with the aftermath. We all have stories of how this past year has changed or grown us, and in this blog series, I want to highlight a few of those stories. I hope you can identify with and be encouraged by the teachers in our series as they share challenges, victories, and the tips and tricks they’ve learned along the way.

**Sara Katt is one of those teachers you want your kids to have.** As an all-virtual teacher of 5th grade math, she’s worked tirelessly over the past year to shift and perfect her craft in response to the demands of the pandemic. Through all the change and uncertainty, however, Sara has embraced the virtual teaching platform and continues to fulfill her calling as an educator, even if it looks a little different these days.

I have yet to decide if this is a challenge or a blessing, but **I do not do any live lessons.** I can only offer live one-on-one meetings for support. In some ways, this has been very nice, because my lessons can be fairly well-scripted, prepared ahead of time, and available at any time to students. All of my assignments are released for the week on Monday morning and kids have the whole week to complete them. That has been really nice for our district, since many families only have internet through hot spots on parent cell phones. Many of my students work at odd times due to limited internet, shared computers, and other home-based needs. Having recorded lessons allows them the flexibility they need and keeps them moving at a pace that works for their home.

While recorded lessons have been a great solution to student problems, it has made teaching more challenging; especially in math. **I can no longer rely on visual cues, raised hands, and questions from the class to guide my instruction.** Thankfully, I have 10 years of experience to help guide me in my videos. I generally know what questions, confusions, etc, will come up. However, despite my best efforts, I’m certain there are things I miss. I also have no control over when the kids complete their lessons. While I encourage them to follow an agenda I’ve posted, not all students do. Some of them like to do math on days they have help (normally a parent’s day off), and they complete a week’s worth of math in one or two days. That puts very large amounts of time between lessons. I have yet to decide if that has been helpful (forced retention) or hurtful (loss of long term memory opportunities).

The math series we use has also been a struggle for me as a virtual teacher. The book comes with a virtual platform, but work can’t be shared between the teacher and students. To accommodate this, I have had to create assignments for them from scratch through Google Forms and other Google platforms. **I have had to get very creative in analyzing the answers they submit** to see if they truly understand a concept. When it is clear they don’t, I have to try to decide what errors they are making, often without seeing their work to support the answer. I have become an expert at error analysis this year!

As mentioned earlier, I have become very good at deciphering where errors are coming from in a student’s work and being able to create personalized lessons/support for them. When I am “in person” teaching, there are so many other things going on that it can be difficult to find time to really analyze work and find the small errors students make. However, that is now my only outlet to find out how they are really doing in math. It is forcing me to stay on top of their work far more than I needed to when I could just glance at their work and do a spot scan for understanding.

I also feel like I’ve improved in the way I present material. In a classroom, students are forced to at least hear me, no matter how much I talked. In a video, if they get bored, they just turn me off. That forced me to really consider how much I was saying and if everything I was saying was meaningful. I’ve learned to really condense my thoughts.

If I kept a blooper reel of film, this would be a very long blog. I don’t even want to count all the times I’ve gotten part way into a video and sneezed, flubbed words, gotten totally lost in what I was doing, had commercials start playing – you name it, I’ve lived it.

It has become a running joke amongst the kids and I to listen for my pets in the background of videos. I often end up recording lessons at home because there are far fewer interruptions there. However, there is also a cat there. This particular cat is apparently fascinated with 5th grade curriculum because she joins most of our videos. At least once or twice a week you can hear a small meow in the background of a film; always at the most inopportune time. I used to try to edit around them, but now I leave the quiet ones in for their enjoyment. **Plus, as a teacher bonus, it entices the students to listen closely! **

Over the last year, I have slowly developed a system that works for me at home. **I am fortunate to have dual monitors at home, which make my life SO much easier!** They are, without a doubt, one of the best things I did for myself. I find it very helpful to have multiple documents open while recording. I can have my documents all lined up on one screen and record from another. It helps me keep my videos paced well, and it keeps me from having awkward screen/program jumping while I record.

At the beginning of my virtual teaching attempts, I was having a hard time teaching math without being able to record myself working on paper. **I found a “hack” that was an excellent replacement for my document camera.** I had seen another teacher who made use of their cell phone and a locker shelf (milk crates work too). For live lessons, I could log my computer in as the teacher and my cell phone in as a muted student. By placing the camera in a grate opening, I could then present a lesson like I was using a document camera. For recorded lessons, I would film it with my camera and upload the video to YouTube for the kids to view. I’ve since upgraded to an actual document camera at home, but, in a pinch, I still make use of my shelf.

I choose teaching. When I was in the college, my professors always told us we’d never be bored with teaching if we were doing it correctly. Right now, I find that to be more true than ever before. Virtual teaching has forced me to be flexible (not my strong suit) and creative in the ways I present material. I have really enjoyed the challenge.

In-person teaching allows me to spend time with some of my favorite humans every day; something I love and cherish. While I’ve worked hard to form those same relationships with my virtual students, it will never be quite the same. I think we can all agree that teaching is a trying profession, but every time I consider doing anything else, my heart won’t let me. **No matter what teaching looks like, I think it will always call to me.** I think my new favorite t-shirt sums it up best, “I will teach you in a room, I will teach you now on Zoom. I will teach you in a house, I will teach you with my mouse. I will teach you here or there. I will teach because I care!”

Here are the top five things I’ve learned this year:

Being strictly virtual, it has been really easy for me to let the lines blur between home life and school life. When we went home last March, it was nearly impossible for me to separate myself from school. My email is connected to my phone, so any notifications pop up instantly and pull me back in. Now, I’ve learned that it is important for myself, my family, and my team, for me to take time for myself. Whatever self-care looks like for you, make time for it!

I’ve found a lot of virtual groups through social media that have saved me more than a few times. There are countless teachers trying to support each other out there. I’ve gotten lesson plan ideas, technology support, and advice from teachers all over the world in the last year (all for free). It is amazing what we can do when we come together!

One thing I enjoy about virtual learning is that it frees up some time for my students. I can offer them art projects we would never get to do. Last spring, my co-teacher and I taught kids to cook. I’ve dressed up in funny costumes, recorded things in odd voices, had a bad joke competition, and countless other fun times with my kids. Yes, they took up time. Yes, the Zoom meetings weren’t overly structured. Yes, I wanted to pull my hair out more than once. But, looking back at the last year, those are the things I remember, and I’m certain it’s what my kids will recall in future years too.

If the last year has taught me anything, it’s that some things are just out of my control. I have had to learn to let the little things go. All that does is create tension that I have no room for in my life. Every day, I work hard to see the good in things in any situation. I’m not always successful, but my stress level goes way down when I am!

I like routine. I have favorite lessons that I teach every year. I have books I like to read to the class because I know the reactions they generate. For me, while those things are my favorites, I was getting to the point in my career where things were becoming too routine. Sometimes, it’s nice (even necessary) to shake things up. Try a new kind of assignment. Read a different book. Wear the silly costume. You won’t regret it!

Sara Katt has a Bachelor’s degree from Saginaw Valley State University and a Master’s Degree from Concordia University in STEM Curriculum Design and Development. She is actively teaching 5th grade with Standish-Sterling Central Elementary. Throughout her 10 years in education, Sara has experience with nearly all grade levels both as a paraprofessional and teacher. Sara is passionate about teaching in general, but especially loves teaching math!

It’s hard to believe that we have 64 Math Might shows released and almost another 48 that are almost done being written, edited, produced, and soon to be sent off! For the month of March, we’re going to take a break from Math Might Teacher’s Guides as we prepare for the Stay tuned for more fun with the Math Mights as we start a new challenge: Mystery Math Mistake! Students will have to play detective and figure out where we made the error in our math!

In the mean time, be sure to check out your grade level to see which of the 16 shows and extension activities you could use in your classroom next week!

Although we’ve done a lot of remote training during COVID, as we complete more Math Mights shows, I’m starting to work with schools in-person a little bit more! I absolutely love being back in classrooms, but one of the biggest things we’re seeing in schools now are the ramifications of the COVID slide (read more about the COVID slide in this article from NWEA). Reading and math are subjects that build on themselves, and when we have large gaps of skills in students, we *have* to fill in those holes.

At SIS4Teachers, pre-COVID, we regularly worked with at-risk students, students that might need a little bit more think time or maybe haven’t covered a standard as fast as another student. Through systematic instruction and lots of dedication, we had schools that had made incredible catch-up growth with their at-risk kids, and now, looking at the effects of COVID on education, it feels a little like somebody plowed over all that hard work.

In one particular school district that I work with, we started our M³: Molding Math Mindsets training and coaching series with a group of Kindergarteners several years ago. They started with our numeracy foundation training, went through the foundations of number sense, doing visual models, being able to do number talks, and last year, those Kindergarteners were in fourth grade. They scored higher than the national average on our test that shows growth, the NWEA, and they were an amazing example of the success that can happen as we work to build a solid foundation of math skills.

Now, imagine those 4th grade kids who were completely on top of it lose a large chunk of their fourth grade instruction at the end of the year due to COVID. They missed the fraction instruction, the higher level of multiplication and division, they lost out on some of the area, perimeter, and volume things they were supposed to learn. Then, we start their 5th grade school year, a little bumpy, a little bit of hybrid instruction, taking a break in November and December, back in a hybrid situation, just doing our best to get kids in school every day, all day. Let’s just be honest, there are gaps.

It’s not anybody’s fault. There’s nothing we can do about it. But the switch to virtual learning, coupled with the lack of consistency in learning models that has been necessary over the past year, has damaged everything we’ve worked towards in education. And I’m sure the school districts I’m working with aren’t the only ones experiencing these struggles.

Well, first we have to figure out where we are. What amount of instruction was missed? What was gained? What concepts were learned well enough so that students can apply that knowledge to something new? How can we analyze what students should have learned to see where they are now?

Then we have to decide what to do. Do we continue to plow through our material, even if we know the success rate of students is not where we want it to be? Do we continue to give chapter tests or unit summative tests as we have in the past?

**The answers to these questions depend on your school’s situation.** I can’t believe all the combinations of classroom activities I’ve seen in the schools I’ve visited. We have one school that goes in-person every day, and has for most of COVID. We have other schools that are hybrid, where they’re teaching their class in-person, but have a group of kids entirely online in a Google Classroom. These teachers have to sit at their table, working under a document camera or at a smartboard so students at home can see the instruction. Can you imagine trying to manage math instruction when you can’t walk around to look at your other students??

We have schools where students check in live every day, attendance is taken, and they have class on Zoom or Google Meet. At least, in that situation, you know instruction is happening and you might have a little better idea of where kids are because you can see them every day.

We also have school districts that are so rural that their internet isn’t strong enough for live teaching. Instead, teachers have to record all their instruction and upload it, hoping that kids are able to access the content in their homes, and never knowing if they actually understand the material.

Teachers around the world are in the trenches, experiencing the effects of COVID and the pandemic on their instruction, and many are left wondering where their kids actually are in their understanding.

I think it’s really important to take a step back for a second. Before we can decide what to do, we have to get an accurate picture of where we are. Over half of our year is completed. In fact, we don’t have much school left; we’re already in March! We have a lot of schools, in January, that collect data on students about the standards that they should have learned from the beginning of school this year until where they are today. With some of our schools, we sifted through the curriculum and did some careful planning on what standards we hoped that students would have learned by the end of January, and created interim assessments so we could see exactly where the students were.

These interim assessments were based on standards and DOK, or depth of knowledge. Some of the questions were DOK 1, which is simply asking for the information, but we wanted to look at DOK 2 and 3 as well, asking if a child could actually apply that information. I want you to picture an assessment that has four corners on it, and each square in that assessment is going to address a standard to see where a kid is. It might not go into the depth of asking them all the application things, but do they know how to take a fraction and add it to another fraction with an uncommon denominator? And, can they apply that in a scenario in a story problem?

Teachers do all kinds of informal assessments in the classroom, but this assessment was a little bit different.The goal of these assessments was not to give it, find out that a lot of my results were red, so I’ll go back, reteach tomorrow, and give the test again. We wanted to collect data to see what has been lost in the storm, in the COVID slide.

The best part of the whole process was being able to have data review meetings with each teacher. The data is all color-coded to show how well students are doing based on grade level expectation – green is good, yellow, orange, and then red, which means really far below grade level. We wanted to help teachers understand exactly where they were in this situation with their students, and make a decision based on the data in their classroom to either continue to plow through material with kids that are failing, but have a *Congratulations! *letter for finishing the material, or do something different.

If we see that 20 out of 28 students are failing a particular standard, we might initiate a “clean up on aisle five.”

The results of the assessment were very interesting. As you look at the younger grades – Kindergarten, first grade, and even second grade – the data that we collected wasn’t as strongly red as it was as we started to get into older grades. This is because a lot of kids can have what’s called “catch-up growth” in their K-2 years because their brain is actually able to learn *more* than a year’s worth of content in a year’s worth of time.

For a lot of these younger kids, we were able to say, *Hey, we’re really on track with these kids! We got this going! But, kids are still struggling with writing numbers, and with the idea of starting at 45 and counting on, so I’m going to make sure I’m working on that. Also, I noticed that their conservation to 10 is not quite where I want it to be, so we’ll keep working on that too.*

But as we looked into third grade, fourth grade, and fifth grade, where you talk about concepts that needed to be built on the foundation of what students learned the year before, we saw 88% of the kids falling in the red, which is our “far below basic” category, 8% of the kids were “below basic,” 4% were “at basic” and zero of 26 kids were proficient or advanced. This was a running theme with classes we studied, and these were the kids that had the data to show that they were really excelling in fourth grade. As a teacher who worked so hard over an extended period of time, this data is so disheartening.

**This is the reality of where our kids are based on the aftermath of the storm. Now, we have a decision to make: Am I going to now just keep going, even if kids don’t have the foundation? Or am I going to revamp the way I lay out my curriculum for the rest of the year? **

I think you could pick either option, and I’m not sure that anyone really understands which one is better. I can tell you that, once we create holes in learning with math, those holes continue to get bigger. Think about the layers of an onion. If you have a layer that’s rotting, you might not know because there are other layers over it. We’re going to see this group of kids impacted by COVID continue to go up with holes missing in their instruction.

In our districts, based on our data, we decided not to just keep going. **We decided to pause delivery of new content** for two weeks, maybe three weeks, and at the most, four weeks so we could go back and attack some of these areas where kids are completely falling apart.

So, with a fifth grade group having 88% of their kids in the red on the standards that were taught from September to January, we decided to take this month of March, and really go back and pick out the pieces and the core concepts that we want kids to master. We’ll revamp our year where we can look at a deep dive into fractions, and then look at different ways that we can implement some of these other standards.

Now, not every classroom in your school district might have 88% of the kids as “far below basic,” but you can certainly see, when you go through your data, that it’s the opposite of what we usually look for. Usually, if I see that about 80% of my kids are getting a concept, I move forward with instruction. But now, I only see that about 20% of the kids are getting it, so I need to work to improve proficiency.

To be quite honest, some of the data that we collect is skewed, especially with virtual learners and well-meaning parents. As we were analyzing the data, we saw a few students in the green. I wondered if those students were virtual learners, and the teachers confirmed that. They said they knew for a fact that the student was not at that level. So, some of those students that we thought were green, really might be more of an orange or even a yellow.

I think one of the hardest parts for schools experiencing the COVID slide is we are still having to give state testing which causes a great deal of anxiety for teachers because in many schools it is part of their evaluation. I suppose there are two different ways you could think about 1) it is very expensive and is only going to give us data on students we already know aren’t up to standard. Or 2.), we can look at it as a way to take a collective, national look at the damage COVID has done to educational performance. No one should be suprised by that the data but it might be a hard reality of how we are going to rebound from the aftermath,

So let’s give ourselves a chance. Let’s give ourselves a gift, as teachers, to look and see where the gaps are with our students. Let’s do a “clean up on aisle five” after this COVID storm, and see if we can effectively get kids to master these standards.

** They’re not going to be where they’re supposed to be.** Each educational situation across the United States and different countries is very unique. But you and I both know that math builds on itself. So I think we have to look at this realistically and objectively. We’ve seen data in younger grade levels that support the idea that students can catch up. With that in mind, we can pause new learning, be intentional about our efforts and set forth on the other tasks, and we just might be able to bridge some of these gaps in our students’ learning so they can continue to move forward.

I would love to hear what you’re doing in your school district. How is your district responding to the “cleanup on aisle five” after the COVID storm? Of course, the storm isn’t completely over, but with the vaccine and all the things we have going, we’re hopeful that we’re moving in the right direction to have some normalcy back. I would love to chat with you, and have conversations about how you’re going about this!

- Teaching during COVID, white paper by Jo Boaler
- The COVID-19 Slide: What summer learning loss can tell us about the potential impact of school closures on student academic achievement, article published by NWEA

Episodes 307-308

**February Focus: Word Problems**

In these warm-ups, we’ll use a step-by-step visual model process, which will vary slightly depending on the grade level and what type of problem that we’re working on. Professor Barble helps students slow down, think about what the word problem is asking, and organize the information it conatins before they jump right into solving it. Yes, we even do this in Kindergarten! See sections below for more specific information about how word problems and model drawings are used in each grade.

**Focus: **307: Break Apart Numbers / 308: Label Story Problems

**“I Can” Statement: **I can find all the ways to break apart numbers. /I can show what happens in a story problem and solve.

**Extension Activity:** Make or Break Numbers / Label Story Problems

In episode 307, students will use their journal template that we’ve featured in past episodes, however, in this episode, we’re going to be really focusing on subtraction. We want to show kids that they can do subtraction with concrete tools, show it in a quick draw, use a 10 frame to show subtraction, and then see how you go about creating a number bond with subtraction and the computation that goes with it. Students should have a good understanding of this, as we’ve done it in past shows, so, at this point, we are fluidly using all of those processes with subtraction.

The “I Can” statement is: I can find all the ways to break apart numbers. We’re going to use D.C. here and see if kids can notice if one of the combinations is missing from a set. Obviously you could look at this in an expression and see if I came up with all the combinations for nine. Another way that I like to do it is for students to see the combinations within a number bond. They can look at the collection of number bonds and see if one is missing. In the show, we analyze a student that thinks they’ve come up with all the combinations to nine, but we use the process of elimination to discover that they’re actually missing one.

This also looks at that idea of the flip flop fact, if you will, where kids can see that 9 = 1 + 8, but also, 9 = 8 + 1. We want kids to include all of those facts, so we use D.C. and the Counting Buddy Sr. to show this. A great way to use the Counting Buddy Sr. is to push 10 beads towards his head and 10 beads towards his feet. This way, when you draw the beads into the middle, the colors will match the combinations. If I want to show nine, I could pull four beads to the middle and then five beads of another color. When kids look at it, they will see four and five equals nine.

We continue with combinations by playing a game called Make or Break Numbers, where students draw a card, and then have to put their counter on two number scatters that would total that number. If they drew the number seven, they have to be able to look at different configurations – five frames, dice pattern, or a domino format – and figure out which two numbers would end up making the seven. They might put a counter on a two that looks a lot like a dice, and maybe the five that’s also arranged like the dice.

We want students to really understand and see the patterns, which will help them create combinations more easily. If I have 0 + 7, 1 + 6, 2 + 5, 3 + 4, etc. you can see on one side, the numbers are counting up. On the other side, they’re counting down. We use a really great visual on the show to help kids understand this pattern, and then they get an opportunity to play Make or Break Numbers in the extension activity.

In Kindergarten 308, we continue with Professor Barble and another subtraction problem. Pro Tip: Have your students watch the first show (307) early in the week, then, they can try working through the problem in 308 a little bit more independently.

The I can statement is: I can show what happens in a story problem and solve. We give a scenario of a market, and Elena is shopping at the market with her grandfather. She chooses to buy some mangoes, and her grandfather chooses to buy some pineapples. How many pieces of fruit did they buy? A lot of times kids just appeal and ask for your help to get the idea of how to do word problems before they even think about it. We want them to slow down and pay attention to details! *What do you notice and what do you wonder about that story problem?? *We didn’t give any quantities! How are we going to solve it without quantities?? This gets students’ inquiry-based thinking going and then we give them an actual story to go with that scenario. Elena chooses four mangoes, her grandfather chooses two pineapples. NOW, How many pieces of fruit did they buy?

We also focus on drawings in this episode to see what else can we add to a drawing to give more detail. So, for our initial scenario, if I were to show four counters, draw a partition line, and have two more counters, does that depict the story enough? What if I drew four circles, a partition line and then two more, but above the four I wrote an *M* to represent the mangoes, and a *P* above the two to represent the pineapples? We want kids to be able to add more details to their organized drawings. We do a couple different examples with a bear eating blueberries and raspberries. We add more details to the drawing by labeling the *B* above the blueberries, adding that partition line, and then putting an *R* above the raspberries.

Giving kids the opportunity to really look at how to label that organized drawing is really important! In our extension activity, we have a few problems that someone can read to the students and they can pick out which drawing with the label matches that word problem. This really helps kindergarteners to attend to detail and slow down a little bit as they’re starting to look at different word problems.

**Focus:** 307: Make Sense of Equations / 308: Write Equations to Match the Strategy

**“I Can” statement: **I can add one-digit, and two-digit numbers to make an equation. / I can add one digit, and two digit numbers, and an equation.

**Extension Activity: **Closest to 95 / Closest to 95 (lower starting number)

In episode 307, we are continuing with a Professor Barble warm-up, but we’re using a non-proportional manipulative. You’ll also notice that we’re starting to scaffold away by not always including that sentence form. We’ll have more blanks in the sentence forms, and we’re also using a little bit higher numbers to continue to challenge our first graders.

In this subtraction problem, we don’t want kids to just guess and check. You’ll see that we use a number word instead of the actual numbers so that kids have to really pay attention to the details. They couldn’t just grab the two numbers and add or subtract.

The “I Can” statement is: I can add one-digit, and two-digit numbers to make an equation. 45 + ? = 50. At the beginning, we use 10 frames to get kids to understand this. We build 45 on 10 frames, which gives us four full 10 frames with five in another. How many more would it be to get to 50? The idea here is to give kids a visualization of 45. Instead of counting up by ones to get to 50, could I visualize five 10 frames with only 45 in it? It makes it a lot easier to figure out how to make that equation true by adding in the five. We do another example with 38 + ? = 40. Again, we build 38. We use 10 frames in the show, but you could also use an abacus to help kids see that it only takes two more for them to get to 40.

We also talk about the idea of decomposing using the 10 frames again. We have 34+ 9 and D.C. comes into play again to help us decompose and add by making the friendly decade number. This is something that students just will need a lot of practice with!

We play a game called Closest to 95, where students start at 55, they take turns drawing cards and adding that amount on, and try to see who can get to 95 first. In the extension activity, kids get to play this game with a partner. This really helps because, as you’re adding on numbers, can you decompose and make that next decade, and then add on a bit more to make it easier? Kids start to be able to do some of these strategies a little bit more independently as they start to have more practice with it.

In show 308, Professor Barble helps us look at the idea of missing addends. If we have a total and a part, can we figure out the other part? We have a visual model written out, but we have more pieces missing from the sentence form, so kids have to really pay attention and put in those details and label correctly.

The “I Can” statement is: I can add one digit, and two digit numbers, and an equation. We give them four equations to look at, 7 + 9, 22 + 5, 32 + 8, and 44 + 8, and we ask *which one doesn’t belong*? We want kids to do an analysis of each of those four problems, and maybe figure out a reason why one of them, or all of them, might not belong. Maybe only one problem is adding a single digit plus a single digit, so 7 + 9 might not belong. Another student might say, when you’re adding these together, everything has to make a new 10 except for 22 plus five. This kind of inquiry is a really great way to get kids to attend to precision and come up with their own formulations of why a certain problem might not belong.

The focus in this show is seeing, when we’re adding a single digit plus a double digit, does it make a new 10 or not? Not necessarily *do we regroup?* as you think of with T-Pops. For example, if I’m going to add 9 + 63, am I going to make a new 10? Well yes, nine is one away from 10. And if I’m adding it to 63, it’s going to make a new 10. But what about if I added 26 + 3? Is that going to make a new 10? Well no, because I’m not going to cross over into that decade of 30. This helps kids start to think about when they’re making a 10. I think sometimes kids use D.C.’s strategy and they just decompose numbers for the sake of breaking it apart. However, we don’t want to forget the other part of D.C. – he likes friendly numbers! We want students to remember to see if they’re going to make a new 10 or not.

The other thing that happens in the show is we have an algorithm where water has been spilled on one part of the problem! This game of Splat! really requires kids to use their number sense. I have 32 + *SPLAT!* There’s a splat over the second number so we can’t see what it was! But I can tell you it was a one-digit number and it made a new 10. There are multiple possibilities here – it could be an eight or nine in order for it to make a new 10. It can’t be a one because 32 + 1 doesn’t make a new 10. It couldn’t be a 2, because 32 + 2 doesn’t make a new 10. I love this activity to get kids to extend their thinking and apply their number sense.

In the extension activity, we played Closest to 95 again, But in this case, the kids start at a lower number of 25, and they get to decide when they pull that card, do they want to add 10s, or do they want to add ones when they do it? That’s a really great way for kids to apply that concept of place value as well.

**Focus:** 307: Sort and Name Shapes/ 308: Draw Shapes

**“I Can” statement: **I can sort and name shapes based on their sides and corners. **/ **I can find and draw shapes with specific sides and lengths

**Extension Activity: **What Shape Am I? / Draw Shapes with Attributes

In episode 307, we do a word problem with Professor Barble where students look at pennies. We do an additive comparison problem, solving with a little bit higher numbers, as we have 37 pennies, and Blake has 55 more pennies.

After the warm-up, however, we completely switch gears in this set of shows away from place value and into shapes. The “I Can” statement is: I can sort and name shapes based on their sides and corners. We get the kids engaged by looking at two sets of shapes, one that has three corners and three sides, where the other set of shapes has multiple attributes. We want kids to notice those attributes by studying a non-triangle versus a triangle.

We do a really fun sort in this episode. Based on what they learned in first grade, I think a lot of second graders think a triangle always looks the same, a pentagon always looks the same, a hexagon always looks the same. In this sort, we focus on the attributes of shapes to help kids realize that, while a triangle has three sides and three corners, it doesn’t always look like a perfect triangle. A quadrilateral has four sides and four corners, but it can be a square, a rectangle or any other shape with four sides and four corners. The same goes for pentagons and hexagons. We play a game called Penta-What? to help kids understand this idea. In the game, we have a secret shape they have to guess and they can ask yes or no questions to narrow it down.

We also talk about shapes that are not shapes, and the idea of a “closed” shape. Or when we have things that don’t necessarily create either a triangle, a quadrilateral, pentagon or a hexagon. For the extension activity, kids are given more irregular-looking shapes and have to decide if it is one of the four shapes that we’ve been working on.

As we move into show 308, we’re going to do a Professor Barble problem again, where students are going to see if they can figure out a part-part-total problem that is worded a little bit differently. Mr. Arnold has a box of pencils. He passes out 27, and has 45 left. How many pencils did he start with? Some kids might think that they’re starting with 45 and subtracting, but they really have to listen to the details and look at the way that this visual model is described to be able to solve it correctly.

We continue with shapes and the “I Can” statement: I can find and draw shapes with specific sides and lengths. Getting kids to draw shapes, as you know, is quite difficult, and it’s a bit hard to show that in our show because we don’t have actual students, but we’ll give you the elements to work on!

We begin with a “Which One Doesn’t Belong?” exercise to get kids into the mindset of shapes. We want them to estimate, based on a description, what shape someone drew. Diego drew a shape that has fewer than five sides, two sides are three centimeters long, which shape could Diego have used? There’s a picture of a rectangle, a triangle, a hexagon, and a square. Students can think through the elimination process – *If it only has five sides I can eliminate the hexagon* and then bring back in some of the parts of measurement.

If we had been doing these shows throughout the entire school year, kids would have already done centimeters and meters, so we bring in some rulers here to get kids to look at the attributes of different shapes. How many sides? How many corners? How many inches are the side lengths? We also talk about the idea of square corners, not necessarily about making a 90 degree angle yet, but the idea that some corners are perfectly square and some aren’t.

We have fun drawing different shapes in an activity where they have a table with a certain number of sides to pick from: three sides, four sides, five sides, six sides. We can create corners of three, four, five and six. We can describe the length – do you want one side to be two inches, two sides to be two inches? And then how many square corners – zero square corners, one square corner, two square corners, or all square corners?

The fun discovery here is that, when you don’t have an even number or the same number of sides and corners, you might make a shape that isn’t a shape! We kind of talk about that concept a bit, and then for the extension activity, kids have to figure out What Shape Am I? They’re given the attributes of a shape, and they have to figure out what shape is being described.

**Focus:** 307: Name the Parts of Fractions / 308: Describe Parts of Fractions

**“I Can” statement: ** I can name parts of a whole. / I can use fractions to describe parts.

**Extension Activity: **Name the Parts of Fractions / Describe the Parts of Fractions

In episode 307, students here are working with Professor Barble again with a problem where we’re using division. In these division problems, if you pay close attention, we’re going to be using kind of this “…” or “groups unknown”. Students are looking at someone having 36 balloons and they want to give each person four balloons. Well I don’t know how many people will be, so there’s a “…”, meaning that they’re going to take that bar, which is a total of 36 and chop it so that each person gets four. This kind of problem is a little bit harder for third graders sometimes, because we don’t give the number of groups. I didn’t say we want to take 36 balloons and divide them among a certain number of people. Instead, you have to figure out that result unknown.

In third grade, we’re now moving into fractions! We spend quite a few shows on fractions, which I’m really excited about. The “I Can” statement is: I can name parts of a whole. To get kids thinking, we give four options and they have to figure out which one doesn’t belong. Again with this kind of activity, there’s a descriptor for each of the four images as to why they might not belong, depending on the reasoning the child uses. Some of them are not partitioned equally, and so we talk about this new word *partitioning* which really means to split into parts. Yes, things can be partitioned, but are they always partitioned into equal parts? Kids are given a variety of images to sort based on how they are partitioned, some are non-equal parts, and some are equal parts, and this also helps give kids that language to use. And then, of the shapes that are partitioned, even if they aren’t equally partitioned, we sort them into the number of parts, two parts, three parts, and four parts.

Then we give kids the opportunity to partition rectangles. We wanted this to be hands on, so kids could do this at home with a post-it or a 3×5 card and see if they can partition a rectangle four different ways.

The main focus in third grade is to be able to understand that three equal parts equals thirds, four equal parts equals fourths, six equal parts equals sixths, and then eight equal parts equals eighths. Kids really practice with this idea in the extension by reading and writing fractions based on how many equal parts they have in order to apply this concept.

In episode 308, we continue with Professor Barble doing our visual model warm-up. In this one, we have 24 people lined up to go in canoes. Each canoe will have three people in it. How many canoes will they need? Again this is the “groups unknown.” The total bar is going to equal those 24 people, we’re going to break that bar into groups of three, but we don’t know how many groups of three are in 24. so we kind of put that “…” there. There are some really great examples in these visual models to help third graders with this idea!

The “I Can” statement is: I can use fractions to describe parts. We have another Which One Doesn’t Belong activity looking at parts that are divided equally vs not, and we have students look at horizontal partitions versus vertical partitions. We want students to see things in different ways to see how fractional parts are made up.

In this particular episode, we make fractions strips, which are a really great tool that anyone can use. It’s just pieces of paper that we encourage kids to keep in an envelope to pull out during this unit.

Remember that the fraction strips are labeled with the actual unit on them, and so in some ways kids might guess and check with this. We take a whole and split it in half. If you fold the halves in half, it’s going to make fourths. If you fold the fourths in half, it’s going to make eighths. Same thing if you took a piece of paper and a strip and fold it into thirds, and then folded it in half again, it’s going to make sixths.

As the extension activity here, students are going to make those fractions strips on their own to keep. This tool will be GREAT for students to have available to help them during this fractions unit!

M³ Members, want your very own animated Professor Barble to use in your warm-ups? Don’t forget, to download the PowerPoints and save them! He pushes his button, the bar pops out, and your students will be ready to go! Plus, all the work of drawing the visual models is already done for you!

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Episodes 305-306

**February Focus: Word Problems**

In these warm-ups, we’ll use a step-by-step visual model process, which will vary slightly depending on the grade level and what type of problem that we’re working on. Professor Barble helps students slow down, think about what the word problem is asking, and organize the information it conatins before they jump right into solving it. Yes, we even do this in Kindergarten! See sections below for more specific information about how word problems and model drawings are used in each grade.

**Focus:** 305: Break Apart Pattern Block Designs/ 306: Compose and Decompose Numbers to 9

**“I Can” statement: **I can compose and decompose numbers to nine. / I can compose and decompose numbers up to nine with towers.

**Extension Activity:** Matching Expressions / Two Parts to Make Seven

In the Kindergarten 305 episode, we’re going to continue with word problems with Professor Barble. This time we look at some different types of problems, still not going higher than sums of 10. For example, John has a paperclip chain. He has five large paper clips and puts on three small paper clips, how many paper clips does he have? Students are modeling this out with the Math Work Mat, showing that organized quick draw, modeling in the 10 frame, a number bond, and then filling in the computation statement to match. The “I Can” statement is: I can compose and decompose numbers to nine.

We invite students to the lesson by having them look at different pattern blocks, orange squares and purple diamonds. There are four combinations labelled A, B, C and D, and we want to see what things kids notice about which one wouldn’t belong.

In Kindergarten, we typically only have one thing that doesn’t belong, but this show stretches kids’ thinking a little bit to see if they can find reasons to argue that each one of the choices doesn’t belong in some way. One student might say one of them has seven shapes and the rest have six shapes, so that one doesn’t belong. Someone else might say that one of them doesn’t have any squares, and it doesn’t belong because it’s all diamonds. We want kids to pay attention to the part and the part and the total, or the way things are organized, but this concept will also allow all students to contribute to the lesson in some way.

We do a fun activity with pattern blocks to see if students can create something with only seven pattern blocks in a combination of green triangles and orange squares. We can create a house or we might create a castle, and we can use our creation to relate to the sums of numbers. I used three triangles and four squares to create my house, which total seven pattern blocks. In your castle, you used two triangles for the peak and five squares for the base. It’s all about approaching things in different ways, being given a quantity and seeing the part-part-total.

We continue this by looking at combining trapezoids and triangles and using a total of eight pattern blocks to see what we can make. Someone creates a boat, one student creates a star, and we also have a rocket. If we wrote the statement 5 + 3, is that true of all three of these pictures? Here, we want to get Kindergarteners to see that their opinion matters and that they can apply their thought process. They might disagree with that statement, and so then we go through and figure out which one of the designs doesn’t match.

For the extension activity, kids see a set of pattern block designs and have to determine which expression goes with which design, based on the part-part-total composition of the design. This is a fun way for kids to engage in this concept with a different type of manipulative – We don’t have to always use unifix cubes for kids to get that idea of part-part-total!

In show 306, we continue with word problems and helping students to do adding with two different numbers. Hopefully, by now, students are becoming a bit more fluid with this problem solving process that we have outlined in the Kindergarten Journal, as we’ve focused on it quite a bit in the shows this month. With continued practice, problem solving should be becoming easier and more natural for Kindergarteners.

Our objective here is very similar to the previous show: I can compose and decompose numbers up to nine with towers. As you know, we can’t give students enough practice with this concept. Whether we do pattern blocks or we use the counting buddy or we use towers, kids need repetition with this concept of decomposing and composing numbers.

To invite kids into this lesson, we lay out different trains of unifix cubes and ask students what they notice and what they wonder. What’s the same? What’s different? All of the trains total six, as students will discover, but we have one broken into three and three, one broken into four and two, and one broken into one and five.

D.C. definitely appears in this show! Even though Kindergarteners aren’t necessarily using D.C. to decompose and make a 10, they’re still learning to break apart cubes, which is the premise of our game called Snap the Cubes. D.C. has a row of nine cubes, and he uses his hammer to smash it. Player One decomposes the cubes in a certain way. Player Two has to describe how the cubes are broken up. There’s a nice recording sheet that helps students create different combinations as they’re breaking the cubes apart to see the expressions that match.

Through this activity, we hope that kids will see the pattern that emerges if I do one and eight, and then two and seven, and then three and six, etc. If we were adding to eight, it could be two and six, three and five, four and four, etc. As they build with the unifix cubes and record their combinations, they’ll be able to see the progression of the two parts.

And so as the extension activity, kids play Two Parts to Make Seven. Given a set of seven unifix cubes in a drawing, kids get to select which two parts they’re going to color in and create that expression. Ultimately, we want kids to be really flexible in their understanding for these concepts so that they’re able to apply them as they’re starting to learn more about part-part-total.

**Focus:** 305: Add 2-Digit Numbers & Write Equations / 306: Decompose/Compose to Add

**“I Can” statement: **I can add numbers, and write equations to show my work. /** **I can add two-digit numbers to a one-digit number by decomposing and composing.

**Extension Activity:** Adding with Value Pak / Solving with D.C.

In show 305, we’re continuing to work with Professor Barble at the beginning, this time using a non-proportional approach for part-whole addition. Our journal page is similar to what we’ve used in the past, but instead of the unit bar being labelled with individual units, it’s open. Kids have to figure out where to put the marks to represent quantities in the problem. If someone has six green apples and three red apples, I’m not going to put that line directly in the middle of the bar, because six doesn’t represent an equal half of the total. Instead, I’m going to move it over a bit to the right because six is larger than three. This warmup problem gets kids to start to understand the idea of proportioning a bar out, and so we go through the whole step-by-step process just a little bit differently.

A lot of first grade teachers want to continue putting that individual unit into the drawing. However, soon, someone’s going to have 16 apples and 12 apples, and that’s going to be too many individual units to write in. So, at that first grade level, we really encourage students to make the unit bar match what they’re using by writing in their own unit quantities.

The I Can statement is: I can add numbers, and write equations to show my work. And so we have Molly and Han, who are trying to find the sum of 24 + 63. Molly starts off with 20 plus 60. Can we figure out what her next step should be? Students are going to solve these problems in different ways. In this case, Molly is solving with Value Pak, adding the 10s first and then she will need to do the ones. Han takes a different approach for 24 + 63. Han decides to start with 63 and then add 20 to get a total of 83. What does he have to do next? This strategy shows a different approach. Han is taking the whole number 63 and then just adding in the 10s, so eventually he has to do the ones as well. Obviously, we want students to be able to create the methods and the equations that are easiest for them, but we also want them to distinguish how students are adding in different ways. We have students try to match the expression they see to which expressions you might use to find the sum.

Another example would be 24 + 32. We show six different expressions and students have to determine, *could you use this?* Well, obviously someone could do 30 + 20, and then 4 + 2. Somebody else could have taken 32 and then added 20 and then added four. This is a bit of a harder task, but helps students become a bit more analytical, as they have to look at the six expressions and decide which two were used to solve the problem.

And so students get to solve with Value Pack for two digit plus two digit numbers. Now again, students can decompose and solve by adding 10s and 10s and then ones and ones, But they also could take the larger number, and then count up if they chose.

As we move on to show 306, students are again working with Professor Barble. This time, we are solving a part-whole missing addend with a non-proportional bar. We have students label the total with a part that has a quantity and a part that doesn’t, it’s unknown. There were 12 coats on a rack. Seven of them were pink, the rest were blue. How many blue coats were there?

The important thing is to make sure students get really good at labelling what they’re adding to their drawing. Pay close attention to how Mrs. Markavich labels what each quantity means so she can go back and chunk and check those parts of the problem as she’s adding it.

The I Can statement is: I can add two-digit numbers to a one-digit number by decomposing and composing. The introductory part of this is similar to a previous number talk where we ask kids to look at how many they see and add on more. So we see three 10-frames filled and then we add on some more. How can students look at the groupings of 10 and quickly determine the quantity without counting? This takes the idea of a numeracy talk a little bit further.

Then, we ask what might be the most efficient way to add if we have a problem like 8 + 47. One student decides to put 47 in their head, and do +1, +1, +1, 48, 49, 50, 51, etc. That works, but for first graders, is that the most efficient strategy?? Maybe not. Maybe we should use D.C.! D.C. has a big part of this show to help students understand how to decompose to create that new 10. So if I’m doing 8+ 47, I might want that 47 to become a 50. I’m going to decompose 8 into 5 + 3, and make that next decade number.

Don’t forget that students really need visual assistance for this! On the show, I have a mat with six 10-frames on one big sheet (you could print it on legal paper and have kids fill it in). You could also use an abacus to help them see how to decompose numbers in order to add.

I really like the extension activity here because it’s Solving with D.C. For each problem, students have five empty 10 frames because I really want students to be able to build the first number on the 10 frames, and then start a fresh 10 frame to build the second number so they can see how to decompose to make that decade number.

**Focus:** 305: Compare 3-Digit Numbers: Part 2 / 306: Order 3-Digit Numbers

**“I Can” statement:** I can use place value to compare 3-digit numbers.** / **I can order three-digit numbers using place value understanding.

**Extension Activity:** Make the Greater Number / Help Value Pak Get In Order

In episode 305, we are using Professor Barble, but we’re actually doing a full problem with him! I chose to do additive comparisons here because I think that second graders really struggle with this concept. It’s harder than the more simplistic part-whole addition, part-whole subtraction, or part-whole missing addend kinds of problem. Doing an additive comparison helps students learn to put in a value for each person as they’re creating their visual model. For example, Mallory has 36 crayons and Nolan has 4 more crayons than Mallory. How many crayons does Nolan have? Oftentimes, kids are taught to circle the numbers and underline the important words, so most kids would come up with 36 + 4 = 40. However, we want kids to have more of a sense of what the words are asking by putting in a unit bar for each character and then adding in and adding the values. You’ll see how it makes this kind of problem a lot easier for kids to solve.

As we move on, we continue with place value and looking at using three-digit numbers to compare. We play a fun game where students get to decide if the statement is true or false. The catch is that the statements are not just going to be two different numbers, but they involve addition! For example, 330 < 300 + 3. Kids are required to solve the addition problem before they decide if the statement is true or false. For the example, kids have to be careful to attend to place value in order to see that the statement is false.

In previous shows, we’ve talked about all these different ways to compare. In this show, students have to decide which one they want to use. If you had 521, and you were going to compare it to 523, would you use Value Pak and build it looking at the hundreds, 10s and ones? Would you use base-10 blocks like we have in the past? Would you use discs? Or would you use the number line? Students can pick a strategy that best works for them! One student might find the place value discs are easier to use, where another student might find using the number line is easier. We want kids to have this freedom!

The last activity in this show is giving kids three numbers that could potentially fit into a statement more than once. They have to figure out which numbers go into which statements. And so we have different blanks for greater than or less than, and kids kind of have to use their thinking caps a little bit here to figure out which number will fit into which statement.

For the extension activities, we have Make the Greater Number. In this game, kids will spin the wheel and combine digits to apply the ideas we’ve been talking about with place value and make a greater number than their partner.

As we move on to 306, we’re going to continue with the Professor Barble warm-up, and I do another additive comparison problem. I really want kids to slow down to read the problem! Diego read 15 more pages than Jaida. Well, if we don’t have that unit bar for each student, that could be a really difficult problem to solve!

The I Can statement is: I can order three-digit numbers using place value understanding. Up to this point, we’ve done a lot with greater than, less than, and equal to, but can students now put them in order?

I love the idea of posing a problem that might be incorrect and having students become detectives, instead of having the teacher always being the person that’s telling them right from wrong. In this show, we have a list of numbers that Kiran and Andre order from smallest to largest and they have to decide if they think that both students’ orders are correct. We get different feedback – someone uses a number line to tell why a number isn’t in order, somebody else uses the Value Pak to get the idea.

There’s a valuable realization for students here as to the efficiency of strategies. If I give you five numbers ranging from 700 to 850 and asked you to put them in order from least to greatest, and you started using a number line to plot them, the work is already done for you because it’s in order from least to greatest! Another student might start ordering by place value and start with all the numbers in the 700s, then move to the 10s, then the ones, then go back to the numbers that are in the 800s, then look at the 10s and the ones, and then finally plotting the numbers. That takes time. Maybe another student prefers base-10 blocks. Well, gosh, that would take kind of a while to build five different numbers with base-10 blocks in order to compare. Is it easier for us to look at the digits like Value Pak? Or is it easier to look at the number line? Again, the idea we want to communicate is that there can be more than one way and that my way doesn’t have to be the same as my partner’s.

In our extension activity, Value Pak needs some help! They’re all mixed up, and students have to help get them into the right order again.

**Focus:** 305: Representing Division: Part 2 / 306: Dividing with Even Larger Numbers

**“I Can” statement:** I can divide using the multiplying up strategy. / I can divide within 100 where the quotient, and the divisor is more than 20.

**Extension Activity:** Divide with Mutliplying Up / Compare and Estimate Quotients

In Episode 305, we continue with Professor Barble, now actually doing a word problem with multiplication. We want kids to understand how we can divide the bar into equal sections to represent groups – for example, there were five crates of milk with nine milk cartons in each, how many milk cartons are there in all? Having students draw a visual model to make sure they understand this concept is really important.

We spend a little bit more time on this with the I Can statement of “I can divide using the multiplying up strategy.” We’ve touched on it in two previous shows, but this is something that kids need repeated practice with, so we spend some time looking at that multiplying up strategy for division in this show.

We present the problem of 52 ÷ 4. It’s great to start by building the total of 52 with place value discs or base-10 blocks so you can model pulling out 40 or 4 groups of 10, showing that there are only 12 left, then seeing that 4 x 3 is 12. We really model the idea of seeing that focus number using the multiplying up strategy to help us, but also showing the repeated subtraction that’s happening when students are going through this process.

They are given four problems that are a little bit higher. We have 56 ÷ 14, can we use the multiplying up strategy? Well, maybe kids only know what 2 x 14 is, because they can do their doubles. The idea is to let them multiply up with the friendly numbers that make the most sense to that student.

As we move into show 306, students are again using Professor Barble with a multiplication problem so students can understand how to look at a visual model and create it. In 305, we learned how to do it, in 306, they’ll do it a bit more independently.

The I Can statement is: I can divide within 100, where the quotient or the divisor is more than 20. We’re working with higher numbers here! We want kids to see that they have a better, hopefully more solid, understanding for division. So if I looked at something like 84 ÷ 4, could I do an estimate to see what would be too low of an answer, about right, or too high? Instead of rushing into a procedure, we want kids to actually think: What if I had 84 of something? What would be the reasoning? Why might something look that way?

We do another example problem of 78 ÷ 3 to show the concept of division with fair shares, but also how to do it with multiplying up. We practice with larger numbers like 96 ÷ 4. And we ask students which way they like to solve division problems: Do they like using the base-10 blocks? Or do they like using the idea of multiplying up?

Students do an activity that involves understanding division to estimate and compare quotients. If kids are really just guessing or don’t have an understanding for what division is, this is where you’re really going to see that they have a lack of understanding because it’s going to be hard for them to estimate if they don’t know what it looks like.

If you’re an M³: Molding Math Mindset member, remember that you can download these presentations! How great would it be to have visual models all mapped our, ready to show in your virtual or face-to-face classroom? Maybe you show the actual show, or maybe you just want to download the PowerPoint and alter the numbers in the problems to fit what you’re doing – either way, they’re all yours to file and use!

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Month Two of the Math Mights Show!

For the first four weeks, number talks were the focus of the warm-up for the shows. As we move into shows 303 and 304, we’re switching our focus, and introducing Professor Barble, a Mathville citizen that loves to solve story problems, to help us warm up our math brains. In fact, Professor Barble really helps students conquer word problems by using visual models. The goal of visual models, also known as model drawings, unit bars, tape diagrams, and lots of other names, is to create a picture that helps students understand word problems. It helps them go slow to go fast!

We’ve talked about word problems with visual models in many different blogs and have so many resources available (check them out here!), and so it is wonderful to see all that come to fruition in the warm-ups for these episodes that you can use right in your lesson!

Episodes 303-304

**February Focus: Word Problems**

In these warm-ups, we’ll use a step-by-step visual model process, which will vary slightly depending on the grade level and what type of problem that we’re working on. Professor Barble helps students slow down, think about what the word problem is asking, and organize the information it conatins before they jump right into solving it. Yes, we even do this in Kindergarten! See sections below for more specific information about how word problems and model drawings are used in each grade.

**Focus:** 303: Break Apart Numbers to 5 / 304: 2 Parts of Expressions

**“I Can” statement: **I can compose and decompose numbers to five. / I can compose and decompose numbers and show 2 parts with an expression.

**Extension Activity:** 5-Frame Shake / Shake Those Discs!

In Kindergarten show 303, we’re going to be working with the “I Can” statement: “I can compose and decompose numbers to five.” In our warm-up for this show, we’re going to be using Professor Barble and our Kindergarten journal template, to do a part-whole addition problem. On their Math Work Mat, students will actually act out the word problem with Mrs. Gray, create that quick draw that we’ve been practicing in the previous episodes, but also show it in different modalities by doing a quick model on the 10-frame, showing a number bond, and finally doing the computation.

It’s important here to notice that at the bottom of the page, we did not put in the addition sign or subtraction sign. We want students to go through that process of determining the operation on their own. We still do the chunking and reading the problem, and create that sentence form as kids understand it, however, it’s very scaffolded so that Kindergarten students can be successful with this.

Then, we invite students into this lesson by looking at two pictures of diamonds in different arrangements. Asking students, *What do you notice? What do you wonder?* really helps kids activate their understanding of what we’re trying to accomplish in the lesson. Students can notice different layouts of the diamonds, seeing five together, but also seeing five spread out into three and two. They can wonder why the shapes are laid out that way. And we create an addition sentence like 5 + 0 = 5 or 3 + 2 = 5 to match the pictures.

We start off the main part of the lesson using linking cubes for a train activity where we have a bowl, and students put some of the cubes in the bowl, then we have to figure out how many cubes are in the bowl. We used a bowl because we don’t have actual students in our studio, so you could certainly play this game where a student puts a few of the cubes behind their back instead! If I have three unifix cubes in front of me, and there was a total of five, how many of them are in the bowl? This helps kids understand the part-part-total of decomposing the number of five, seeing it in an algorithm, as well as being able to do it in a number bond. By playing this game, we show that you can create five in multiple ways. If 5 is the total, maybe 2 and 3 are the parts, or maybe 5 is the total with 4 and 1 as the parts. You’ll hear how our fictitious students in the show are thinking as they decompose the number 5.

Towards the end of the show we play one of my favorite games, called 5-Frame Shake. This is a fun activity where students put five two-sided counters in a cup or bowl, shake them out, and then make the different combinations of five on a five-frame mat, again, using the number bond and number sentence to go with it. If you’re at home, you could do this with pennies and use heads and tails instead of the red and yellow of the counters. This game is also the extension activity so students can play at home with parents or in a classroom in a Math with Someone station.

As we move into show 304, the objective is for students to take what they learned in the previous show and apply it: “I can compose and decompose numbers and show 2 parts with an expression.” We use Professor Barble as a warm-up in a very similar problem, this time using lamps to get kids to understand the part-part-total, but more so using all the components of the kindergarten journal: a quick draw, the 10-frames, the number bond and then the computation.

In the warm-up, we do a little bit of a numeracy talk by showing kids sets of two-sided counters and asking them *How many do you see?* *How do you see them?* We’re using a total of six here, but we want kids to see this in an unstructured way, where it’s not always in the 10-frame. They might see a scatter or a dice/Domino pattern. Using two-sided (red/yellow) counters, we show three and three, equaling six, we show four counters that are red and two counters that are yellow where the set of four looks a lot like a dice pattern, and then we do another one with five and one. We’re having students use their numeracy to apply this concept of part-part-total, but also asking them to see what is the same and what is different. All of those pictures equal six, but they’re composed in different ways.

In this episode, we play a game called Shake Those Discs, which is really similar to the 5-Frame Shake, but with more counters. We want students to be able to have the expression and represent it in a drawing. So, if we put seven counters in a cup, shook it, and then got two yellow and five red discs, could we do the drawing? The students would draw the first two circles, and then put the partition line before drawing the additional five to show that *two and then five would equal seven*. Obviously, students could use colors (the yellow and the red) to show the two parts of the expression, but we want kids to understand how that drawing might be created.

We go through several different examples of Shake Those Discs, and we play a round with eight counters. Maybe I have three red and five yellow, and I write down the expression 3 + 5 to match it.

We also talk a lot about how two expressions can be represented with the same amount of counters. If I have three yellow and five red, I could also show five red and three yellow. In first grade, we call this “flip flop backs” because the numbers are just changing spaces, but the total is the same and the numbers are the same. We want kids to understand the commonalities between part-part-total as they look at it.

We don’t always have room for everything we plan in our PowerPoint to be in our final show, and this is one of those times! Members, download the PowerPoint for this show because we talk about different ways to make seven with the discs.

As an extension activity, kids can play Shake Those Discs. We suggest playing with nine counters, but this game is easily differentiated so that any student can play. Ultimately, we want students to create the expression to match the discs they shake out!

**Focus:** 303: Add 10s and 1s / 304: Add 2-Digit Numbers

**“I Can” statement: **I can add tens and ones to two-digit numbers. / I can add two-digit numbers and find matching equations.

**Extension Activity: **What Did I Add? / Four-in-a-Row

Professor Barble kicks off episode 303 for first grade! We start with a scaffolded journal for first graders. Obviously, we’re presenting this in the second half of the school year, so if students were doing visual models, hopefully they’ve been doing them with both proportional and non-proportional models. In this show, however, we decided to introduce visual models as we might do for students seeing it for the first time. We do a part-whole missing addend problem with proportional manipulatives or proportional bar so you can see the individual units.

I think the most important thing here is to get kids to NOT solve on the visual model! We see that happen so often in first grade! It seems like first graders also like to guess *I think we should add! *Or *I think we should subtract!* But we want them to actually look at the model, fill in the information that’s needed and put the question mark above the section we’re looking at. We want them to play close attention to the visual model checklist (download one here – in English AND Spanish!) which outlines the seven steps of the visual model process that we use in grades 2-5. This checklist breaks down that process to be more developmentally appropriate for a first grader to follow the steps with the teacher.

We go through checking and chunking, making sure that we have these pieces of information in the word problem that are chunked out, checking those off and putting them into the visual model BEFORE we compute and just jump to solving. As always, we provide the sentence form as well.

In the meat of the lesson, the engagement looks a little bit like a numeracy talk, where we have 10 frames showing 30 – three 10 frames that are filled completely with red counters. We ask students *How many do you see? How do you see them?* Obviously, you see 30 and you see full 10-frames, but as we change the image, we leave that 30, and then we add more on. You could think of this as an extension of the numeracy talks, but working with higher numbers here. If kids understand that conservation to 10 within a 10-frame, can we now extend that knowledge to see three full 10-frames and another 10-frame with three red counters and two yellow counters and know instantaneously that it’s 35? Or 30 + 3 + 2?

We then extend that further where kids see three full 10-frames, and then a 10-frame with five red counters and four yellow counters. Can they tell us how many we see? Enter Value Pak, the character that clicks together and shows their values on their belly. If I do see three full 10-frames, it’s three groups of 10, but the value of that is really 30. And then if I were to see another 10-frame with nine in it, I know that total is 39.

I think the visualization of the quantity is a really important connection for students to make, and then to also relate that back to what it looks like in the actual number form. So, seeing 30 + 9 in the digits will really create that number 39.

We play a game called What Did I Add? This game can be a little bit complex when you first look at it, but it’s a great game to play with kids! Partner A flips over a number made with place value strips – say, 54. Partner B draws a secret number to add to the original number. But the catch is that the secret number can be 10s or 1s! Partner B draws a 3 and can decide to add three 10s or three ones to 54, and then tells Partner A what was added. *54 + ? = 84* And then Partner A has to figure out what was added. It’s a great inquiry-based game to play for students to apply this concept of adding 10s and 1s.

For the extension activity, students get to play a spinner version of What Did I Add? to practice applying the concepts we learned in this episode.

In episode 304, we continue to work with Professor Barble and proportional bars at the beginning of the show, doing part-whole subtraction. In the later shows, we will eventually use a non-proportional bar, so this will be a springboard for students to understand this concept.

Posing an inquiry-based question that gets kids to think differently about how other students solve problems is a great way to point their attention toward what we’re focusing on in the lesson. In this particular warm-up we start off with Ming and Keshawn sharing their answers for 5 + 34. One student thinks it equals 39. Another student thinks it equals 84. This student made a common error when solving this type of problem – they stacked up the problem and lined up the five in the 10s column. Instead of adding 5, they actually added 50. We want kids to discover that the placement, or the place value, of numbers actually makes a difference when you’re adding.

In this show, we look at different ways that you could add two-digit numbers. Pay close attention to our sample problems, for example 23 + 45. Students often start with the number that begins the number sentence instead of actually thinking about which number is more or less. When we’re solving these problems, we show it with both place value blocks and then place value strips. One student starts with 23, adding in the 10s and then the 1s, where another student looks at it from the perspective of starting with the larger number. We can see that it’s less work to actually add by starting with 45 and adding two 10s and then three ones. We want students to notice the efficiency of these methods and equations, and explore what is the same and different about them. We also have students look at base-10 ways of seeing numbers so they can discover which equations match.

Finally, we do a somewhat complicated activity with drawing where a student adds two numbers together and has to analyze which equations actually match. In this particular problem, they’re adding together 63 + 25 – what are all the different equations that they could make with that one problem? You could do 63 + 20 = 83, and then add in the rest by adding 83 + 5 to get 88. This helps kids to analyze how they’re going about solving the problem, and really be able to break down the equation.

The extension activity for first graders to work on adding two-digit numbers is a Four-in-a-Row game. The kids will apply their understanding of how they can add two two-digit numbers and then apply their learning to see if they can get four in a row before their partner.

**Focus:** 303: Comparing Numbers on a Number Line / 304: Compare 3-Digit Numbers

**“I Can” statement: **I can locate, represent and compare three-digit numbers on a number line. / I can use place value to compare three-digit numbers.

**Extension Activity:** Plot and Compare / Compare with Value Pak

In Episode 303 for second grade, we’re working specifically on helping students understand model drawings or visual models with Professor Barble. At the beginning, we’re not necessarily solving a problem, but we’ll have a picture of Professor Barble with a word problem already drawn out in a visual model and students will guess what word problem goes with the visual model.

I can’t stress enough the importance of kids having lots of fluid practice with this! Yes, everyone can break down a story problem, but can they look at a drawing and create the story problem it was based on?

For this warm-up, we do a several missing addend problems where students have to look at how Professor Barble created his visual model, and then come up with what that visual model says. For students who haven’t used visual models, this is a great introduction to help them understand why visual models are important.

Our “I Can” statement is “to locate, represent and compare three-digit numbers on a number line.” When we look at place value, we often just look at 100s, 10s and 1s, but kids use number lines for so many other things (fractions and higher level concepts), that we need to be sure to include number lines for place value.

We have three different number lines in the opening activity to get kids interested. There’s the number line written from zero to 10, another number line that ends at 100, and another number line that ends at 1000. All the number lines are the same length and the tick marks all match up, but really the values of those really depend on the total number that is at the end of it. We ask *What do you notice? What do you wonder? *about the number lines and see if students can locate the number three, the number 30, and the number 300. To do that, you have to look and analyze each of those number lines to see what each tick mark is actually worth. The first number line, the tick marks are worth one, in the second number line, the tick marks are each worth 10. And the third number line has tick marks worth 100 each.

We look at different number lines where we have located points on the number line. One number line might start at 620 and end at 630. Students have to understand that it is going up by one, and try to figure out where the number would be located on the line.

We end the show by comparing numbers. We build them with base-10 blocks and plot them on the number line so kids can put those two pieces together. When using the number line to compare numbers like 371 and 317, we can gauge which number is greater by looking down the number line – numbers to the right are higher numbers. This is a step further than just using the base-10 blocks like we have in the past.

So we have several different examples where kids are going to do that, and in the extension activity, students will plot and compare three-digit numbers to see if they can apply what they’ve learned in the show.

In Episode 304, the word problems with Professor Barble are similar to the previous episode, with the drawings presented to see if kids can come up with what the word problem actually said. This time, we’re focusing on additive comparisons, trying to really make sense of what those types of word problems are asking. This is quite tricky for students because they often don’t understand that the algebraic *X* is the same value. Even though a line in a drawing might be longer than the other, students may not realize that the *X* represents a constant value in additive comparison problems.

We’re continuing our learning about place value in this episode with the “I Can” statement of “I can use place value to compare three-digit numbers.” We have two people who have a quantity of base-10 blocks, and we’re trying to decide *Who has more, and how do they know? *We want students to look at the quantity of place value blocks in each place to see how many there are, which really helps break down what the number is. We look at the hundreds, at the 10s and then at the ones. Oftentimes, kids look at quantity over value. So, if they were to see two hundred blocks, two 10 blocks and then see some ones, versus seeing one hundred block, four ones and a variety of 10s, a kid is instantaneously going to think that the number with two hundred blocks in it is larger. This show takes into consideration that we can rename numbers different ways and that it’s not okay just to look at a quantity, especially just the hundreds blocks, because, in this case, there might be more than ten 10 bocks and so kids need to see that maybe those numbers are actually the same when they compare their values.

We also use the place value discs to address this concept, looking at it in a non-proportional way, which is important in second grade. As we go across, when the hundreds are the same in the discs, the 10s are the same, but the ones are different, they can break down those numbers in that way. Of course, we use Value Pak as a way to help students understand that we’re looking at the values of numbers.

As an extension, students get to play a comparison game with Value Pak, where they build different numbers and find out which one is greater and which one is less.

**Focus:** 303: Dividing with Larger Quotients / 304: Representing Division: Part 1

**“I Can” statement: **I can divide with larger numbers within story problems. / I can make sense of representations of division.

**Extension Activity: **Division Problem Journal / Representing Division Problems with Base-10 Blocks

In the third grade episode 303, Professor Barble presents a visual model for students to try and guess. The warm-ups will be on the topics that we’ll use in the next segments of the show, so it’s really just getting students’ feet wet by looking at a visual model. These problems in the warm-ups for third grade are focused on multiplication visual models. Professor Barble will have his drawing, out from his starting line, looking at a diamond collection, and there will be bags with seven diamonds in each. We want to see: *Can a student construct a word problem based on that picture?* We give them a couple of opportunities here to start to get that language of what word problems are looking at, which will eventually help them to actually do visual models. The “I Can” statement here is “I can divide with larger numbers within story problems.”

Anytime you can set the scene for a word problem for students, whether it’s with a small video or even a picture, it really helps for students to understand it. This one starts off with Maria’s class splitting up into groups to go on a field trip to the aquarium. *What do you notice? What do you wonder?* I’ve been to the aquarium before! So, what are things that you’re thinking about? I see that they’re splitting up into groups. I wonder how many kids are going in each group? So, we pose the question: There are 48 students going on a field trip to the aquarium, they’re put into four groups. How many students are in each group?

We ended up being able to integrate the step-by-step visual model process for what Professor barble is doing with this idea and topic, even though we’re just in the introductory part of word problems with our show. It really fit nicely to have students go through the steps with this story problem, and then get at the concept of how to divide. We end up having 48 students, and there would be 12 in each group.

We use place value discs here to help students use the “multiplying up” strategy to figure this out. How many groups of four are there in 48? We can start off with the idea of at least five groups of four are in 48, which gives us 20. We want to build up to get to that 48, so we put in another group of five groups of four, to get another 20. Now we’re up to 40, with 10 sets of 4. We’re almost up to that 48!. We do two groups of four to give us eight, which gives us that target number 48. Then, it’s easy for kids to see: add up the five and the five and the two to get 12 groups of four.

We originally wanted to focus on three different ways to divide, but obviously we didn’t have enough time! (M³ Members – don’t forget to download the PowerPoint!) Shows sometimes get cut short, and so the big take home for this show is that they can use place value discs to find fair shares with division. Also, we wanted kids to start to understand that strategy of multiplying up.

In order to do a division word problem for the extension activity, we gave the students a journal, similar to what we use in the show, which walks them through the step-by-step process we want them to use.

In episode 304, we again do a visual model with Professor Barble, who already has the problem ready to go and ready for students to guess the word problem that goes with it. This time, we also do a little bit of multiplication and division to see if kids can pick out those parts. Our “I Can” statement is “I can make sense of representations of division.”

We have blocks to show how someone’s already solved the problem. So I can see three equal groups built with base-10 blocks, and in those three groups, I see 13. The key here is *Can a student tell me what the division problem was based on the way I’ve separated it?* This gets kids to look at the total, to see that there’s 39 altogether, and then how we put them into three equal groups. It’s the opposite of how we would look at it in a different way.

Next we practice doing 55 ÷ 5 with base-10 blocks where students can actually see 55 base-10 blocks and ask, *how we could go about dividing those*? Obviously we can do that with fair shares, like kids are used to doing, and we can even extend that knowledge as we start to look at 65 ÷ 5, by doing those fair shares.

In this show we want students to connect how you can break blocks apart, but that eventually doing fair shares almost becomes inefficient. We even take a hundred block and divide it by five, where kids figure out how to cash in that 100 block for 10 10s and are still able to divide. But then as we start to realize, when we get to something like 90 ÷ 15, this becomes less efficient. It’s not like I’m going to take one 10 and then break a 10 into five ones and continue to do this.

This is why we want students to focus on the idea that we introduced of “multiplying up.” We have this target number of 90. We’re trying to figure out how many groups of 15 are in 90. Students that don’t know their multiplication facts well can always use this strategy because you can anchor to lower numbers. Do they know what 15 + 15 is? Well if I know that, I know I can get two groups of 15 to make 30. Another two groups of 15 is another 30, and I’m at 60. I’m trying to get to 90. Another two groups of 15 is another 30. So if I add that up – two groups, two groups, and two groups – I know that six groups of 15 equal 90.

We want students to explore this idea and represent division, so some of the problems we know will work well with fair shares, But, as a third grader, when is it time to start to use multiplying up as a strategy? Not every book uses this particular strategy, but I find it really beneficial to help students understand the concept of multiplying up, because oftentimes, kids go into that traditional algorithm and are taught that really quickly, and don’t really fully understand that concept.

If you’re an M³: Molding Math Mindset member, remember that you can download these presentations! How great would it be to have visual models all mapped our, ready to show in your virtual or face-to-face classroom? Maybe you show the actual show, or maybe you just want to download the PowerPoint and alter the numbers in the problems to fit what you’re doing – either way, they’re all yours to file and use!

(valid M³ Membership login required)

Wow! It’s been a month since Math Mights launched! Four full weeks, two shows from four grade levels (K-3)…Wait, can we do the math for that? Eight shows in four weeks means we have released **32 Math Might shows** to date!

I must say, January was filled with so many different new things! It’s still hard for me to believe that we produced and launched 32 different shows in the first month that provide outreach to parents, to caregivers, to teachers, to students all over Michigan, and even our nation, because you can tap into michiganlearning.org or mathmights.org.

These episodes are 301 and 302, and you might be wondering *what happened to 219, 220, 230*? We’re planning to release 18 shows per 10 weeks, and the numbering system for the episodes just refers to the quarter of instruction. Don’t get overwhelmed by the episode numbers – they just help us know that we’re going into the third quarter of instruction with this week’s episodes.

Hopefully, as we are going through the thought process of how we designed these shows, you can see that it’s all about getting kids to see the importance for all of these different skills that we want them to be able to learn!

Episodes 301-302

**January Focus: Numeracy/Number Talks**

We continue with Math Practice 3 in this week’s numeracy/number talks, where students are going to solve the problems wrong – that’s what happens in your classroom, after all! Helping students learn to respond with “I politely disagree with your answer because…” is a really great way to help students to connect with this practice.

**Kindergarten**

**Focus: **301: Addition and Subtraction Expressions / 302: Matching Expressions to Drawings

**“I Can” statement:** I can figure out how expressions go with story problems. / I can match expressions to drawings.

**Extension Activity:** Match the Expression / Match ‘Em Up!

For numeracy talks in both our Kindergarten shows this week, we are still using the Counting Buddy, but extending it a little bit higher by asking kids to show *one less *or *one more*. Again, we did this with the 10 frame, but the linear nature of the Counting Buddy (with five of one color and five of another) requires the students to think a little differently. They need to instantly recognize how many they see, but also be able to visually manipulate the beads by taking away or adding on.

In episode 301, we’re going to be focusing on figuring out how expressions go with story problems. We did a lot of work in Kindergarten this month with story problems and drawing the pictures that go with them, but now we’re looking at it the other way. Students will look at a series of four different drawings or algorithms (some addition, some subtraction), and they have to figure out which one doesn’t belong. We want kids to understand that, when they see an algorithm with an amount that is crossed off, that represents subtraction. If they see a drawing with some and some, that represents addition.

Like last week, we use some pretty fun videos that I like to help kids get into the story problem so they can better act it out. We’re doing that again this week because I love using videos, and I encourage you to do the same! These are 21st century students, and the more we can help them visualize, the better!

In one sample problem, there are 10 students on the bus. Six students get off the bus. How many students are on the bus now? We act this out now on a math work mat.

One of the things I want you to pay close attention to is we’re no longer using a mat that depicts the scene of the story. Now, we’re using a blank math work mat. If you’ve been doing story problems pretty religiously with your **Kindergarteners, at this point in the school year, they should now be able to visualize that story pretty well and be able to act it out on a blank piece of paper.** You do not have to use my math work mat! Use a purple piece of paper if that’s what you have in your classroom! A lot of kids build on dry erase boards. However, whatever you decide to use, I do want to urge you to have a designated place for students to act out word problems because, as you know, we’re asking CPA, concrete pictorial abstract. If kids have built the problem with their counters on top of the paper they’re using for the problem, it’s going to get in the way as they start to do their picture and their algorithms.

We bring in some other great story problems here to see if kids can match the language of the problem to the expression. We have a video of students playing hopscotch. There were eight kids playing hopscotch. Three of the kids left to go jump rope. How many kids are left? Without even solving it, we want the kids to look at that problem and start to assess the possible expressions. Does 8 + 5 match? 3 – 3? 8 – 3? We take kids through the process of acting it out because we’re looking specifically at the expression to see which one goes with the problem. A little bit of deductive reasoning for our small little Kindergarteners to do, but they will do a great job on this if you set it up in the right way.

Another story problem that we do involves a student in a video putting things in his backpack. Again, a story that kids can relate to – getting help in the morning packing in their backpack! There are two books in Nathan’s backpack. Nathan puts four more books in his backpack. Which expression matches that: three plus three, six minus two, two minus four? Again, you want to go through that idea of CPA to help students really understand this.

The extension activity goes right along with what we’re teaching in the show, and in this one, there’s a story problem so that they can practice matching the expression to the word problem that they’re reading to see which one goes together.

In show 302, in the meat of the lesson, we’re starting now to match expressions to drawings. Before, in 301, we were looking at word problems and trying to figure out which expression would match. This time, we want to see if they can do the opposite, but also extend it a little bit more.

We look at a drawing of four red circles and two yellow circles. A student says, “I think that means six minus two.” As we get kids to engage in the lesson, to ask questions about what the students said, I’m asking them: Do you agree or do you disagree? Together, we act out the drawing of circles and know that, if we were to see a drawing of a subtraction problem, it would have had a diagonal slash through some of the circles, and in this case, that’s not what we see.

We want to help kids understand that the picture is going to help them match the expression. To do that, we play a really fun memory game together: “Match the Picture to the Expression.” In this game, we have different drawings – some with two-sided counters, some with just circles to show “some and then some more”, some with circles crossed off. We want to see if students can look only at that drawing and then match it up to the expression. This game can also be played as an extension, if students would like.

Students become detectives in our next activity, where we ask them to put on their magnifying glasses and find the opposite of what they have. If we give them the expression, can they make a drawing that matches? If we give them a drawing, can they show us an expression that matches? This is part of the extension activity where kids can play that memory game.

**Focus: **301: Decompose/Compose Numbers Different Ways / 302: Comparing Numbers Different Ways

**“I Can” statement:** I can decompose and compose two-digit numbers in different ways using 10s and 1s. / I can compare two-digit numbers decomposed and represented in different ways.

**Extension Activity: **Place Value Riddles / 10-Frame Compare

In first grade, we’re still using the Counting Buddy Senior for our numeracy talks, but to make it more challenging, we’re asking *What is two less? What is two more?* Again, being able to look at 10 and 10 on the Counting Buddy and connect it with the double 10-frame is huge! Our third modality for these numeracy talks, if we were to continue this, would be a rekenrek. It’s so important for students to understand this concept of numeracy using the different modalities!

In episode 301, we’re helping students learn to decompose and compose two-digit numbers in different ways, using 10s and ones. To begin, we have a pile of cubes that we’re going to use to get kids to engage with the lesson. We have two 10s and a large, almost impossible-to-count pile of ones, and we ask kids to estimate the quantity that they see. The goal is to help students see that, if we started to group things in 10s, that our estimate would probably become more exact. By organizing our 10s and ones, we’re able to better understand our mathematical understanding.

For the show, we are building different ways to see 94. We bring in Value Pak again, sporting their values on their bellies to represent the number 94. We know that 94 can be renamed 90 and 4, but is that the only way we can break apart the number? It is really fun for students to play around with this number using the place value strips and the base-10 blocks to see how they can divide the number in different ways.

One of my personal favorite place value boards is included in this particular show. It has 10s on the left side, on the right side, for the ones, there are three empty 10-frames. For first graders, who can be overwhelmed sometimes by looking at renaming numbers, this place value board is gold! As I start to look at eight 10s and 14 ones, I can put the 1’s in the ten frame to represent 14 ones, and I’m going to go ahead and build it. The students are so familiar with that base-10 system and the 10-frames, that using this mat with these types of lessons gives them a great visual picture of what’s going on.

We want students to be able to look at a number and realize how many different ways we can break it down. If we did 94, it could be 70 and 24, we could do different addition statements and say different amounts of 10s and 1s, but at the end of the day, it still equals 94.

In the latter part of the show, we play a game with number riddles, which is kind of fun because it really helps kids think. You’re really using the Eight Math Practices for kids to attend to precision and to be able to think through what they’re doing. For example, one riddle says: *I have four 10s and 25 ones, who am I?* If kids need to use that mat to help them solve that problem, that’s perfect! Another example says: *I’m the number 49. If you represent me with 29 ones, how many 10s?* Doing these kinds of riddles stretches the 1st graders’ thinking and takes the level of math to a deeper place. It’s very different from how you and I learned it, but we’re going a mile deep, not a mile long. If first graders can have this kind of number sense with the scaffolded tools that are needed, they are going to be set up for success.

For their extension activity, students get to be able to do some different riddles where they can take those home or to school and solve those different problems, while applying this higher level thinking.

In show 302, our more/less numeracy talk with the Counting Buddy Senior is working through the same goal. In the show we are comparing two-digit numbers by decomposing and representing them in different ways. Now, we want kids to decide *is the amount I’ve built greater or less than? *For example, if one person has five tens and 32 ones, and another person has seven 10s and two ones, who has more? We bring back in Allie the Alligator and Al the Alligator and they battle it out over the compared representations.

What you’ll notice about the representations we use is that they connect to the previous show we just did, where kids are going to see two 10s and 12 ones compared with three 10s and two ones. They may not realize it right away, but those are equal! As you share your thought process solving the problem, kids will be able to apply this concept. A lot of times kids just look at the number of 10s, so they see that and think, *I see three 10 sticks, obviously 32 is larger than the other because it only has two 10s. *

We also bring back the mat we used in the previous show, but we’re doing it now for more of a comparison.

We also can look at quantities within Value Pak. If I had 20 + 13 and 13 + 30 in an actual algorithm, we can ask Value Pak to help us to solve and figure out that 20 + 13 = 33. And if I have 13 + 30, which is the same idea of 13 ones and three 10s, we can put that together.

For our extension activity, we have a game where kids can see the base-10 blocks in a lot of different ways, but the quantity actually all equals the same. There’s also a fun game to play with this one called Base-10 Compare, where kids can really apply their thinking and what they’re learning in this show.

**Focus: **301: Expanded Form / 302: Numbers Represented Different Ways

**“I Can” statement:** I can read, write and represent three-digit numbers using numbers and expanded form. / I can read, write and represent three-digit numbers, including number names.

**Extension Activity:** 3-Digit Dash / 5 Way Challenge

In second grade, we are working hard this month to help kids really understand the concept of number talks. We do a lot with solving different ways and showing how we’re doing this. For second graders, this should be second nature! As the students understand Springling, we want to move them away from dry erase boards and let them do the problems mentally.

For episode 301, the “I Can” statement is “I can read, write and represent three-digit numbers using numbers and expanded form.” You guessed it! We’re going to use my friend Value Pak, because I’m kind of obsessed with them! The idea is that kids can use the hide-zero cards and these place value strips to really start to understand if a statement is true or false.

If I have 800 plus 90 plus 7, does it equal 894? If I have 407, and I add 70 plus 400, is it true or false? We go through lots of different statements and have students think about this idea.

The examples are done in both proportional manipulatives and non-proportional. **I can’t stress enough how important it is to use both. **Sometimes, kids fail to apply their knowledge when using proportional manipulatives or they might find the non-proportional easier – either way, the goal is to help kids learn to reason. In this episode, we build different numbers with base-10 blocks – three 100s, five 10s and seven ones – and then we want kids to think about the equations they’re looking at. We also do the same thing with place value discs. So, what is the sum of the 100s, 10s and 1s? What is the three-digit number it makes?

A simple, but fun, dice game comes up towards the end. We roll the dice and try to create the largest number, in expanded form, so kids can see the 100s, the 10s and the ones.

We want kids to be able to apply their thinking to three-digit numbers, regardless of the modality in which they see it (base-10 blocks, place value discs, place value strips, etc.).

We play a game called Three Digit Dash, where students roll those dice, create a number in expanded form, then show the three digit number, and finally, decide who is the winner! The winner may be the person with the largest, but it could also be the person who has the least amount. Lots of options to extend this game!

In episode 302, our “I Can” statement says “I can read, write and represent three-digit numbers, including their names.” This is a really hard concept for a lot of second graders because, as you’re writing numbers and the word form, it becomes tricky.

To engage our second graders, we’re going to start by looking at four pictures. One has just the numbers, one is in base-10 blocks, one tells how many 100s, 10s, and ones, and then it’s written out in the word form. To help kids understand this idea of word form, we really spend time talking about all the different forms.

I threw something in here that I hear kids say all the time. And even though our example might be exaggerated in the show, I hear adults say this too. If we have the number 588, we often hear people say five hundred AND eighty-eight, do you agree or disagree? Value Pak stops by to visit and I go a little father into fourth and fifth grade to show students that, when you’re saying 5 AND 88, that’s like saying $5.88. We really want kids to see that “and” really means a decimal point. When we’re writing numbers in word form and we’re saying them out loud, we should be saying the numbers and their value without saying “and.”

A really important tip here is to give kids a sentence form for this. You’ll see it in the show. ____ hundred, ____- ____. This is so your kids can see 627 and say 6 hundred twenty-seven. Giving kids a number name chart for this concept is also really helpful because these are really big words to spell!

Then, we look at base-10 blocks, and apply this whole concept with what they’ve been learning in place value with a game called the Five Way Challenge. Can students take a number and only show it in 10s and ones? Can they only write it in word form? Can they compose it in a different way? In expanded form? Can they show it in a base-10 form?

As we go through this show, we take the number 273 and have students show it different ways. Of course, things like the expanded form, or maybe the base-10 form, might be easy, but to be able to show it in ones and 10s when it’s a number in the hundreds, and then to have to compose it a different way – those two will be a challenge for your second graders!

For the extension activity, students get to do the Five Way Challenge with a friend. They might also do it at home, or even for homework.

**Focus: **301: Multiply with Multiples of 10 / 302: Multiply with Larger Numbers

**“I Can” statement:** I can multiply any one-digit whole number by a multiple of 10. / I can multiply numbers that are larger than 20.

**Extension Activity: ** 4 in a Row: Multiples of 10 / Close to 100

Rounding out this number talk for third grade for the month, we’re just focusing on subtraction and making sure kids understand the concept, not just with Springling, but also D.C. Of course, we also get a visit from T-Pops.

You want to ask yourself: *do your third graders really understand how to subtract*? *Do they understand D.C.’s connection to subtraction? Do they understand how T-Pops does subtraction, especially with two-digit minus two-digit numbers with a non regroup?*

The concept for episode 301 is to multiply any one digit number by a multiple of 10. So, 6 x 90 or 4 x 30. This is also a really great show to help kids visualize what you’re talking about.

I have heard this statement about multiplying more times than I care to remember: “If it’s 4 x 30, boys and girls, just do 4 x 3, and then add the zero.” AH! Don’t ever say that! Because it doesn’t make sense! Kids are thinking *What do you mean – 4 x 3 and then add a zero…why?* To which we usually respond, “Don’t ask why. Just do it.” At least that’s how I learned! This show really takes you step-by-step to help you get this concept across in your instruction. We want kids to understand the *why* before the *how.*

Let’s start by having kids look at what we mean by 3 x 40. I have base-10 blocks that might be laid out as 12 sticks, but I’m going to organize them so I have three groups of four. There are 12 total blocks, but the value of each of those blocks is 10, not one, so 12 times 10 equals 120.

As we start to work through this concept, we’ve got to bring in our friend T-Pops. T-Pops is going to help students really understand this, and, I have to be honest, I love doing this with the place value discs! I know you’re probably not surprised because I’m always using those! But we want kids to be able to see what’s going on. If I have 8 x 30, let’s figure out how many total discs we have. I have 8 groups of 3, and so kids can visualize and look at those discs. We’re not talking about their value of 10, but for 8 x 3, how many total disks are there? Oh, I see that we have 8 groups of 3, so I know there’s 24 total disks. Okay, but the value of each of those disks is worth 10. Oh, that’s why it’s 24 times 10! It’s not about memorizing “just add the zero”!

We do lots of different examples to solidify kids’ understanding of this concept. There’s nothing wrong with using base-10 blocks to do this, but I would urge you, if you don’t have place value discs in your classroom or available to send home, go ahead and use them virtually. They are a really great non-proportional tool to help students with this concept.

We have a really fun game for students to play called Four in a Row Multiples of 10. Students are going to roll a die, and they’re going to answer different problems to see who can get their four in a row first.

In episode 302, our “I Can” statement is “I can multiply numbers that are larger than 20.” This is where kids get to go on an Estimation Exploration, another way to invite students to the lesson! We present a problem – 3 x 26 – and ask: What would be your estimate for this? What’s too low? What’s just right? What’s too high? Well, as we look at this problem, we want kids to start to process, so we go through the reasoning as to why kids would estimate an answer that’s too low or about right. So often, kids are just spoon fed multiplication and don’t get to actually think about what’s going on. For example, *Oh, if I thought about 26, it’s kind of like quarters that are worth 25. If I had three quarters, it would be about 75.*

We know our kids hate estimating because they want to be exactly right. We bring D.C. back into the show, where he is doing what they learned with the teen numbers, but now we’re decomposing that two-digit number to break down the multiplication. If I had 2 x 37, D.C. helps us to decompose it into 30 and 7. And so we can easily do that 30 x 2, and 7 x 2 to put it together.

Of course you want kids to see this in an area model as they’re solving, so they’re actually seeing the value of what they’re creating. Oftentimes in multiplication, kids are learning that traditional method, and it’s 7 x 2, and then it’s 2 x 3, but it’s not actually 2 x 3, it’s 2 x 30.

We also have the place value discs in the initial part of this episode, if you feel students might still need to visualize that idea of the 4 groups of 22, let’s say, that they’re going to solve. You can look at those discs and help at-risk learners work through the process: *I see 4 groups of 20. Oh my gosh, I can figure that out! Now I see 4 groups of 2. *We solve this out with many different examples in this show, hoping that students will become efficient in their understanding.

We really want to lean third graders away from this idea that the most efficient way to solve multiplication is repeated addition. We have other strategies that we can be using at this point!

For the extension activity, we have a really great game for you to use for your students for multiplying larger numbers called Close to 100. Students get to decide the values of the numbers they’re going to be multiplying, and they’re able to use this strategy that they learned today.

I hope that you have as much fun watching these shows as I’ve had creating them. It has truly been a rewarding experience and I cannot wait for what’s coming in the month of February! We’ll continue to work on standards that you’re actually teaching, and we’ll have a special visit from my friend Professor Barble who will help you teach word problems a totally different way than you and I learned!

If you’re with our M³: molding math mindset membership, make sure you’re taking advantage of your backstage pass to exclusive Math Mights content by tagging and downloading the PowerPoints to use on a daily basis – both this year, and for years to come!

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It’s the third week of the Math Mights show, and we’re here to give you the information that you need to help you be successful – tips and tricks from Shannon to help you out!

Don’t forget, on every single Math Mights show, we include links to virtual manipulatives! If we use place value discs in the show, you can use the virtual discs to do the lesson right along with the show! You could even use the virtual manipulatives online with your virtual students!

Make sure you go in and download that PowerPoint that goes along with each show! Maybe you haven’t gotten to the lesson yet depending on your pacing. Maybe you’re getting ready to teach it, or you’re not quite there yet. Either way, save the PowerPoints in a folder and you’ll have a library of interactive lessons ready to go for in-person teaching, virtual/online learning, or a hybrid situation!

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Episodes 217-218

This week, we focus on presenting different modalities to increase application of quantity.

Look for specifics about number talks by grade level in the corresponding section below.

**Focus: **217: Subtraction Word Problems: Part 2 / 218: Addition Word Problems with Quick Draw

**“I Can” statement:** I can use objects or drawings to show that I can solve subtraction word problems up to 10. / I can figure out what’s the same and different about story problems.

**Extension Activity: **Trash Can Subtraction / Visual Model Puzzles

Dotson, our Subitizing Superhero from Deck o’ Dots, is the star of the show once again in our numeracy talks, but this time, we’re switching it up. Instead of the 10-frame, we’re using the Counting Buddy, Jr., which is a linear manipulative with five beads of one color and five beads of another. You could also think of it as the top row of a rekenrek. Our goal is to introduce this new idea of quantity and help kids get away from one-to-one counting to figure out how many beads there are. As you know, many kids eventually just memorize the 10-frame, and so they don’t take time to really apply their knowledge of quantity to a different modality.

In the numearcy talks this week, we have our different friends that have different thoughts on the answer, and as always, we’re trying to bring in Math Practice 3. A friend might say, “I politely disagree with your answer. I think it is…” and we want students to be able to prove or defend their answer to each other. We really want kids to experience this process of thinking and feel comfortable giving their ideas: Do I actually agree or disagree? How do I react when a friend doesn’t have the same answer as me? What if I think that I’m really right?

In episode 217, we’re working on using objects and drawings to understand the idea of subtraction word problems. We start off with some really delicious donuts on a plate that are getting eaten, and we get to play one of my favorite games that I created called Trash Can Subtraction. (You can check our website for a tutorial video!) As we know, when you start to teach subtraction in Kindergarten, it’s like they’re stunned. Kindergarteners don’t usually get the idea of *taking away*, that you have an amount and then you take some away. Oftentimes, they revert to what they understand with addition. So, in Trash Can Subtraction, we use a mat where there’s physically a trash can on it to help them understand that we’re going to *take away* that amount.

To play, students pull a card and build that amount on the mat. The amounts that we have students build here, 7, 8, 9, or 10, are intentional. Students are going to roll a die and subtract the amount on it, so we want to make sure the number they build is more than 6 or you would end up with a negative number. Once they build their number, and then roll, students will physically remove that amount into the trash can to show that they’re *taking away*. There’s a nice recording sheet that is the extension activity for this episode to help kids get that idea of subtraction.

Next, we move into the idea of subtraction word problems using a bucket of apples. We have, another mat that you can use that has a bucket on it, and we can show how many apples were in the bucket. If there were seven apples in there and someone bought three, now how many are left? It’s all about** physically acting out the ideas on a mat with a depicted story that matches the word problem.** This will help Kindergarteners really visualize what we’re doing. Of course, we’ll draw a picture – an organized drawing, not real apples or haphazard circles – and put a diagonal slash through some to show that we took those away. Then we do a number sentence. We follow that process with a variety of problems, really helping students understand how that picture that we draw should really represent what’s happening in the story.

For episode 218, we have the same concepts for our numeracy talk, but for the concept we’re working on figuring out what is the same and different about story problems. We bring in addition and subtraction word problems so we can help kids see the connection between them.

Anytime we can start with a video clip, we know it will grab their attention! So we start this word problem with a video of penguins to help them visualize their quantitative picture more than a static image would. Let’s compare: There are 5 penguins on the shore, and then 4 more swim in from the ocean. How many are there? We act that out with a nice organized drawing that has a partition line between the 5 penguins and 4 more. And then we switch the story problem up. There were 9 penguins on the shore, and then 4 of them jumped in the ocean. In my picture, I start with 9 circles and cross out the 4 to get 5.

But the most important part is the comparison! Look at the drawings we created for each problem – what do you notice is the same? What is different?

I often find that we’re spoon-feeding word problems to our Kindergarten kids. We tell them exactly what to do, and they do it, just like parrots, but they never get time to internalize what they’re learning. This is one of the reasons I love this exercise of comparison!

We do another fun story with some jellyfish where we’re acting it out, and talking about the differences in the way that the drawings look to show that one is taking away and one is adding.

The extension activities is one that we modified from the visual model puzzles we created for our SIS4Students Virtual Math series that we did this summer. Kids cut out a story, a picture, and the number sentence to see if they can match them all. Again it’s getting kids to understand that word problems can really come alive! They’re not just words on a page telling you what to do.

**Focus: **217: Comparing Numbers / 218: Greater Than / Less Than

**“I Can” statement:** I can compare two-digit numbers using <, =, > because I understand tens and ones.

**Extension Activity:** Greater Than/Less Than game, True/False Sort

First grade also gets a linear look for our numeracy talks, but we use the Counting Buddy Sr., which has 10 beads of one color and 10 of another. This doesn’t work with a rekenrek, but you could certainly make a linear representation with pipe cleaners and pony beads if you wanted. The goal is to get the kids acclimated to seeing an amount in a different way. For example, they might see 14 – a group of 10 and 4 more. Are your students able to transfer their knowledge from the double 10-frame to a linear representation? We also have some incorrect answers to help students practice saying “I politely disagree with your answer and the reason is…”

In episode 217, we’re comparing two-digit numbers using greater than, less than, and equal to, which we can do because students now understand 10s and 1s. We’re primarily using the base 10 blocks in this episode, and we start by showing two quantities built with the base 10 blocks and asking what kids notice or wonder. When students first see the base 10 blocks and are starting to compare, they often look at the quantity of blocks, not necessarily the value. Here, one student says they think 26 is greater than 32 because there are more blocks on that side. This is a big misconception for first graders.

We spend time helping students build the language for greater than, less than, and equal to using a balance scale. We rarely see seesaws or teeter totters anymore where kids would understand the idea of balance and greater than or less than, so we talk about apples on a scale and either side of the scale being greater than, less than or equal to.

Our friend Value Pak stops in to help us look at numbers and compare them to see what is greater than or less than. We don’t introduce the traditional symbol with the “alligator” eating the number because I feel like that’s a procedure that students just memorize without understanding the concept. They think I’ll just eat the larger number because the alligator is hungry, without taking time to consider the value of each of the numbers.

We designed the sample problems to require students to slow down and pay attention. For example: 64 and 44. Well, those 1s are the same, but the 10s are different. Look at: 54 and 59. Wait, the 10s are the same, but the 1s are different. We also do have a few that are equal to, such as 35 and 35.

The extension activity is a fun game where students spin a wheel, and each player decides which number is greater than or less than.

Episode 218 continues with the Counting Buddy Sr. as we did before. We’re now comparing numbers, but we’re bringing in the greater than/less than symbol. We have Allie the alligator and Al the alligator, which Mrs. Markavich does a great job of describing how the wider part of the symbol is pointed towards the larger number, and the point is pointed at the smaller number.

This is kind of confusing for first graders. To help kids really understand the concept, we present statements like *34 > 54* and *54 > 34* and they have to determine which one is true. Then we switch the numbers and keep the symbol the same. We want students to be able to apply the ideas by giving them statements and letting them decide: 17 < 47 True or false? How do you know? 58 = 53. How can we make that statement true? The extension activity is a sort where students are going to cut out different statements and sort them in the correct columns of true or false.

**Focus: **217: Representing 100s Different Ways / 218: Compose 3-Digit Numbers

**“I Can” statement:** I can represent 100 in different ways. / I can compose 3-digit numbers using place value understanding.

**Extension Activity: **Base 10 Compare / Who Am I?

Episode 217 takes the students’ knowledge of subtraction and starts with a number talk with Springling. (We started the Math Mights show in January, which is towards the end of most subtraction units, so this is more of a review as we move into our place value unit in these two shows.) In this number talk, we do a two-digit minus a single-digit, and use the idea of Springling. Students agree with the way someone solved it, but we’re still showing different ways that you might get there.

In 217, we’re starting off with representing 100 in different ways using base 10 blocks. When you look at base 10 blocks, we were always taught to think: *how many 10s?* *how many ones?* But no one ever told me that there could be 16 ones! I was always told there only could be 10 ones and then you have to trade them in for a 10. We want kids in the 21st century to be able to look at this abstracted understanding and reason.

We have a number displayed with 8 10s, and 16 1s. Kids see that different ways. They might see that there are 96, because there are 9 10s and 6 1s, but somebody else could say it’s still equal to 8 10s and 16 1s. Often, our second grades will say no, 8 10s and 16 1s does not equal 9 10s and 6 ones. We want to encourage this kind of flexible thinking, however!

We build our way up to be able to create the number 100 with 8 10s and 20 1s, which is another way to show that we have 100. We then want to be able to rename 100. How many 10s is 100? How many 1s is 100? We use my favorite math tool, the abacus, to show how many different ways we can create 100. Kids need to see that 100 can be broken up into a bunch of different ways. You can start with a number, say 35, on the abacus, and then count the rest – 10, 20, 30, 40, 50, 60, 65, to get the other part of the 100.

Proportional vs non-proportional manipulatives make an appearance in these shows. It might be a little over a second grader’s head, but it’s helpful for the teacher or parent watching to understand that unifix cubes and base 10 blocks aren’t the only tools for recognizing place value. By second grade, though, the brain is ready to understand the idea of non-proportional manipulatives.

I use the example of dimes and nickels in U.S. currency. A dime is smaller, but worth more. A nickel is larger, but the value is less. This helps us start to grasp the idea of place value discs. Let’s build 90, asking kids how many 10s is that? Now build 110. How many 10s? We want kids to be really flexible with this concept of being able to see quantities in different ways and know that it might not be exactly all the 10s and all the 1s, but truly understanding the value of the discs.

For an extension activity, we play a game called Base 10 Compare, where students look at the quantity, but we trick them and we put in 10 1s in for a 10. So kids really have to use their understanding from the show and apply it in the extension activity, which is a lot of fun.

In show 218, we did the same thing with our number talks – showing subtraction in different ways. For the concept in the show, we move into the idea of composing three-digit numbers using place value understanding. We use a bucket of base 10 blocks and have kids figure out how they can figure out the value of what I have. How many hundreds are there? How many 10s are there? How many ones? Well, as you can imagine, I don’t make this equal the exact amount! We try two hundreds, but I have 28 10s, and I have 15 1s. So it’s not just so simple for students to look at those base 10 blocks, as we have in the past. We’re really trying to apply that thinking! Kids have to understand that, once we look at those blocks and kind of group them by like values, we end up having 4 100s, 9 10s and 5 1s, which is the value of 495.

Then we call on our friend Value Pak because we’re now talking about the value of numbers. Value Pak wears their values on their belly, so if we look at 495, we know it can be decomposed by place value, which is really great.

Non-proportional and proportional manipulatives come into play here too. We use the place value discs, where students have to figure out what the value is using the fewest number of disks. I have 1 100, 7 10s and 18 1s – that’s a whole lot of disks! Kids have to apply their thinking to reduce the number of discs. This is a really hands-on activity to have our students do. I only have 16 minutes in the show, but you can have your student do these day after day in your classroom to give them more time to connect this understanding.

We do a really fun game where kids try to guess the value of the numbers, which is called Who Am I? Giving kids characteristics of quantities will really help students to be able to apply their understanding in this show, to be able to name different values, regardless of the 10s and the 1s that they’re seeing, but they’re looking at the total value represented.

**Focus: **217: Multiply with Teen Numbers / 218: Multiply Teen Numbers with Larger Groups

**“I Can” statement:** I can make sense of different ways to solve multiplication of teen numbers.

**Extension Activity: **Multiplication with D.C. Practice Problems

Number talks continue with subtraction for third grade. However, we’re encouraging third graders to think outside the box and show it another way besides Springling.

We have a surprise visit from our friend D.C , and Miss Askew does a great job showing the distance between the two numbers, but really trying to understand why, when you have a regroup when it’s 86 minus 48, a student might decompose that 86 into 70 and 16. Ultimately it’s the same thing that we’re doing in T-Pops.

The I Can statement is about making sense of different ways to solve multiplication of teen numbers. I have to be honest is one of my top favorite shows because it really seems to resonate with third graders to understand that, when we group things together, we can see that amount as we look at it.

For example: 3 x 14. We could tell kids the procedure – do 10 x 3 and then 4 x 3 and you’ll get the answer. But often, kids can’t visualize exactly what that means. I think building this problem with the place value discs is brilliant as it creates a great pictorial representation to help students understand D.C.’s strategy. As I look at 3 times 14, I’m now decomposing it into 10 and 4, and really looking at the values of those numbers. Then, I can make 3 groups of 10, and 3 groups of 4 with discs, and see the whole problem more clearly. It helps make multiplication of teen numbers less intimidating.

Many students are still thinking of multiplication as repeated addition in this stage but this stretches their thinking to know there are higher level strategies we can use. If we spend really good time on getting students to develop the skill of decomposing by place value to solve multiplication with teen numbers it will help them apply their thinking in the next show on the use of the area model.

As an extension activity, we have four problems to be solved with D.C., like 5 x 13, or 3 x 16, to see if students can apply this new concept.

In 218, the number talks look the same, and we get T-Pops, and Springling, and even D.C. involved. In the show, this time we’re working on solving multiplication problems with teen numbers with larger numbers. Sometimes students are thrown into the procedure of doing an area model – “put the number here, then put the number here” – but they don’t really understand what it means. For the invitation to this lesson, kids look at different statements where they have four different pictures and have to figure out which one doesn’t belong. For some of the problems, you might look at it and see they all actually don’t belong in some way, shape, or form based on how we describe it, but the goal is to help students stop, think and be able to apply the concept based on their understanding.

The area model would be a new concept here for students. A couple of the questions in this show are actually asking students to solve for the area. If you had a whole year of Math Mights, students would have already learned length and width. But, depending on your pacing, you might need to review some of those concepts with your students.

We want students to be able to create an organized area model by applying their understanding of multiplying teen numbers. D.C. comes into play, helping us decompose those numbers, and then put them into an area box so kids can see how we’re solving. We do use a variety of story problems to bring this concept to life with a fence story, a hallway, and even some peaches.

Now, you might ask why I’m not using Professor Barble and our problem solving process. We’re going to spend most of February looking at that. Here, we just want to show real life scenarios that would require us to multiply numbers that high.

There’s a really great activity at the end with D.C. which gives four problems, along with the area box drawn in. We’re taking multiplication a step further with multiplying teen numbers by getting students to plant that in an area box so they can really start to apply their thinking.

Hearing the feedback for Math Mights from administrators and teachers and parents has really been awesome! I hope that you’re finding this to be a valuable resource as well! If you are, let us know with a quick message!