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!
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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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January Focus: Numeracy Talks
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.
“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.
“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.
“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.
“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!