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!
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.
“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.
“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.
“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.
“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!
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