Thanks for joining us for our blog this week for our Math Mights recap on shows 317 and 318!
This week’s shows will be the last of the 300 level shows. As you know from the 200 level shows, we stopped at 217 and 218, giving you eighteen shows per quarter. And so, next week, we’ll start talking about shows 401 and 402. Don’t worry! there won’t be any big gap in the instruction when we start the 400 level shows, it’ll just be a continuation of where we left off.
This will also be our last two shows featuring a Mystery Math Mistake. Look for a new type of warm-up when we start the 400 level episodes!
300 Series Focus: Mystery Math Mistake
In the Mystery Math Mistake, our warm up for the 300 level series, the Math Mights get their strategies all mixed up! Students have to be detectives to see if they can find the mathematical error as we work through the problem. You’ll have great fun watching the shows as students start to look with a critical eye to see if they can spot the Mystery Math Mistake!
“I Can” Statement: I can count pictures with 10 and some more, and answer the question how many? / I can represent numbers 11 through 19 in more than one way.
Extension Activity: Guess Then Count / Cover Up
In Kindergarten, we’re going to be working on counting with 10 and some more. In our Mystery Math Mistake, D.C. definitely needs your help! He’s come up with different number bonds by decomposing the number seven, but students will have to look carefully to see if they can find his mistake. At this point in the year, having Kindergarteners practice analytical thinking is such a great exercise! They always think their teacher is right, so this lets them back up a little bit and see if they can find the error.
The “I Can” Statement is: I can count pictures with 10 and some more, and answer the question how many?
At the beginning of the show, we have a variety of different cubes. This is the first time we’re having Kindergarteners do a little bit of estimation! We want them to figure out what’s too low, about right, or too high. Of course, our students could touch and count the collection of cubes, but we really want them to get the basic idea of what a good guess would be. Guessing two cubes would be “too low,” because we can obviously see there are way more than two cubes. “Too high” for a Kindergartener might be 50 cubes because, even if we were to look at 50 on an abacus, we could see that there are way less than 50. A “just right” guessitmate might be about 10.
When we rearrange the cubes into an organized 10 and some more, like we’ve always talked about in Kindergarten, we can easily and quickly see that there’s 14. Now, we also know how students might want to revise their estimations after they see the orientation of the objects set up a little bit differently. Instead of saying that two would be too low, we know that a good estimate for “too low” would be 10. Obviously we didn’t fill a full double 10-frame, so it would be “too high” to estimate 20. We know the “about right” answer is 14. It’s really great to provide that opportunity for kids to do their own thinking through this process!
Then we visit with our friend the Counting Buddy Sr. to see if we can figure out how many beads are showing! The Counting Buddy Sr. has 10 of one color beads and 10 of another color. It’s really important to mix up the modalities of numbers for Kindergarten kids so they aren’t just seeing that double 10-frame. So, in this episode, we’ll match a lot of different numbers with 10 and some more with the Counting Buddy. If you don’t have Counting Buddies in your classroom, check them out here!
Of course, we still want to be practicing with the double 10-frame, so we ask students to match the double 10-frame mat with a teen number, making sure to ask how they know which number it is.
The estimation portion of the show comes back in the extension activity, called Guess Then Count. Kids will grab a handful of counters or small objects and guess about how many they have. It’s a really great way for them to understand the idea of something that’s too low, that’s just right, or something that’s too high.
In episode 318, we’re continuing on this journey of teen numbers. D.C. gets mixed up again in our Mystery Math Mistake. He does number bonds again, but this time he decides to do them with missing addends. He has a total of eight, and then he has five, but does he end up putting the other missing addend in correctly? Can you use your analytical thinking to find D.C.’s error and help turn him around?
The “I Can” Statement is: I can represent numbers 11 through 19 in more than one way. As we said before, in Kindergarten it is really important to not just show numbers in one modality. In the previous show, we mixed up the double 10-frame with the Counting Buddy Sr. In this show, we bring in the third modality of a rekenrek.
A rekenrek is similar to the top two rows of an abacus, 10 on each row, five of one color and five of another. We want kids to become familiar with this math tool! If you haven’t used a rekenrek in your classroom, we have several videos on how to use it. The big thing to remember, which you’ll see in this episode, is that you clear to the right. I say “white right” or if you push the beads to the right, I say “clear to the right, red in the lead.” To help your students remember, you can put a smiley face in the upper right-hand corner to show how it is cleared. It does feel a bit awkward at first when you push beads to the left because you’re thinking wait, I read from left to right! However, once you push the beads to the left, maybe showing a row of 10 and then two more, you’ll actually read it from left to right.
Then, we use two different modalities – the double 10-frame and the rekenrek. And we end the show by bringing in all three tools and practicing conservation to 20 with the rekenrek, the double 10-frame, and the Counting Buddy Sr.
I really like this extension activity for this episode! It’s a little complicated for some students, but I think they’ll like it once they get the hang of it. It’s called Cover Up. Students will grab a teen number and try to match the double 10-frame and the rekenrek that represent the number. If you do this activity with your Kinder kiddos, make sure you have a double 10-frame mat and a rekenrek nearby so they can see exactly what the quantity is! You want them to make the connection of 10 and some more, but not memorize it in just one way.
“I Can” Statement: I can solve story problems with unknowns in all positions. / I can think about story problems and write equations.
Extension Activity: Problem Solving with Professor Barble / Professor Barble Puzzles
In episode 317 for first grade, our Mystery Math Mistake is bringing back something we talked about in a previous episode – decomposing & composing with addition This can be a hard concept for first grade and so we want to see if they can look deeper into a problem to figure out where D.C. is making his mistake. He is going to decompose the numbers and we’re going to see if Rocco and Aiden can help him figure out where the mistake is.
Our “I Can” Statement is: I can solve story problems with unknowns in all positions.
If you heard me say “story problems,” you know what character we’re using in this show – it’s Professor Barble! We are bringing back this concept of a visual model, but in a little less scaffolded manner than we have before. We have different problems that have unknowns in different positions. For example, Elena bought a bag of beads to make a bracelet, she takes out nine beads to make a bracelet. There are 11 beads left in the bag, how many beads were in the bag when Elena bought it? These types of missing addend problems can sometimes be complicated for first graders, just because of how they read. So, we want to make sure that we’re really walking through Professor Barble’s step-by-step process – rewriting our sentence in question form, figuring out who our who and what is, chunking and checking the problem, putting in our bars – all of those great things that we’ve taught in the past so students can understand this problem.
Then, we want to find out which equation matches the story, in this case the story of Elena and her beads. She has some beads in a box. She uses five of them to make a bracelet. She has 10 beads left. How many beads were in Elena’s box? What should our number sentence, or equation say? 5 + 10 = ____? Maybe ____ – 10 = 5? Or 10 – 5 = ____?
I really like this episode because a lot of students guess when it comes to word problems – do we add, or do we subtract? When they’re having to actually see the mathematical statement, it really gets them to think about whether it’s going to be an addition or a subtraction, or maybe even a missing addend that we might be using.
The extension activity is for students to do a missing addend problem on their own with Professor Barble and his step-by-step visual model process.
As we move into show 318, this Mystery Math Mistake brings you a showdown between D.C. and Value Pak! Our problem is: 29 + 14. Students can decompose and make the 29 into a friendly decade number, or they can solve with Value Pak by decomposing the 29 into 20 and 9, and the 14 into 10 and 4, and then adding the 10s and then the 1s. Can you figure out where the error is that one of our characters made?
The “I Can” Statement is: I can think about story problems and write equations. Again, we’re keeping consistent by using Professor Barble and his step-by-step visual model process. One of our problems says Mia made nine paper frogs. Diego made 15 paper frogs. How many fewer frogs did Mia have then Diego? This is an additive comparison problem, which is usually quite complicated for first graders.
We don’t often get to every problem that we have planned when we’re shooting the shows, so some of this episode might be on the cutting room floor, which means bonus examples for you! Check the deleted scenes page as we’re posting new clips all the time!
At the end of the show, we really want to make sure again that students are understanding which equation matches the story. Kids need a lot of practice with this concept and so for the extension activity, they’re going to be doing Professor Barble puzzles! These are really fun puzzles where students have to match an equation and a visual model together with the story problem to see if it all makes sense together.
“I Can” Statement: I can find coin combinations to make 100 cents. / I can solve addition and subtraction story problems in the context of money.
Extension Activity: Handful of Coins / The Toy Store
As we move into second grade and show 317, T-Pops gets to make an appearance in this Mystery Math Mistake! He’s all upside down and confused trying to solve 62 – 36. I wonder if T-Pops made a common error that many second graders make at this time of the year when they’re thinking about regrouping! Landon and Miles are on the show to help set us straight.
In these two episodes, we get to talk more about coins! The “I Can” Statement is: I can find coin combinations to make 100 cents. We start with a What do you notice? What do you wonder? where we present students with a variety of different coin combinations that they can look at, including a dollar bill, which is new on the show.
Kids might make the connection that it takes double the amount of nickels to make a dime. We also present them with a picture where they see the $1 bill, but they also see two quarters and five dimes. We want kids, without any prompting, to get the idea of what we’re talking about in the show by asking our famous questions.
We then start counting nickels. We need 20 nickels, we know, to make $1. Then, we look at how you can make a collection using only dimes to make that same value. We want kids to see how you can exchange the coins in this situation. Sometimes, counting nickels can be hard, but if students can point to two nickels at a time, they can start skip counting by 10s if they realize the exchange value.
Then, we take a lot of the show’s time to talk about how four quarters equals $1, three quarters equals 75 cents, and two equals 50 cents. We want kids to have the idea of how they can add up different combinations, so we’ll bring in the idea of adding quarters, nickels, dimes and pennies and being able to represent it in different ways.
The application at the end of the show presents a child having $1.10 in her pocket. Can we represent that with coins? What about with a paper dollar? The activity is called Handful of Coins, and students are going to do just that! They grab a handful of coins, draw a picture to represent the amount of coins, and then they’re going to add it up to see what their total is.
In Episode 318 for second grade, our Mystery Math Mistake again features our friend T-Pops. Since students did so well catching the mistake in episode 317, this one should be easy! We purposefully make the warm-ups similar in each set of shows to help students really get great practice with a concept and hopefully take their learning deeper in the second show as they approach a familiar concept/problem.
The “I Can” Statement is: I can solve addition and subtraction story problems in the context of money. This is helping kids to be able to stretch their thinking a little bit to see if they can apply their knowledge of coins and money. The first step is asking: How many coins do you see? And How do you see them? The really interesting fact is in this picture, there’s actually pennies, nickels and dimes. There is a total of eight of each coin. We talked about the idea that, even though the actual quantity of the physical coins might be the same, their values are certainly very different.
Then, it’s time to go shopping! Kids get a list of items they might need to buy – a pack of pencils or a pencil sharpener, an eraser or a pen – and they’re going to the school supply shop with a certain amount of money. These problems involve addition AND subtraction, as we have to add the total of items that we have, and then we’re going to have to subtract it from what we have. We may even use a Math Might character to help us solve some of these!
We give a variety of examples here where students are buying different things and we want to highlight where we need to add and subtract. We know sometimes when we’re counting money, a really great character to use is Springling. We also can use D.C. when we’re adding.
The independent extension activity is a trip to the toy store! Students have to figure out how much different items cost, and then figure out how much money they have, how much is spent, and then, if they have money left!
“I Can” Statement: I can represent and compare fractions. / I can compare two fractions with the same numerator.
Extension Activity: Fractions take Action /
In episode 317 for third grade, our Mystery Math Mistake features the multiplying up strategy. Springling has gone wrong in counting up for the problem 84 ÷ 7. Somewhere there’s an error and our friends Nora and Layla are going to help find it!
We’re continuing our journey through fractions in these two shows, first with the “I Can” statement: I can represent and compare fractions.
We ask students to look at two fractions strips, but one of them has a cloud covering part of it. We ask What do you notice? What do you wonder? Even though the cloud is covering a portion of the fraction strip, we hope that kids can still compare them by looking at the amount that they see shaded. Then, we ask Are these fractions equivalent? If I was looking at 1/2 and 1/3, are they equivalent? One of our friends says no! If I look at those two fractions on the number line, I can see that they’re not equivalent. We use some of the tools that kids have learned about throughout previous shows to help them determine their answer – area model papers, fraction tiles, or maybe even a number line. Students are also asked to compare 4/6 and 5/6. This one is a bit more simple because of the common denominator, so students can decide if those two fractions are equivalent by looking at how many pieces there are.
Once we determine that 4/6 and 5/6 aren’t equivalent, we can use that concept to get kids to look at things a little differently. One child might say that 4/6 is less than 5/6, and show their work on a number line. But another student says no, 4/5 is greater than 5/6, and they show their number line. Who is right?
One of the most important takeaways from this show as we’re comparing fractions and looking for equivalent fractions or comparing fractions is that the length of the number lines we’re using must be the same. Unless the number lines match exactly, we can’t really compare apples to apples. In the show, we prompt kids to come to that realization as we talk about what they’ve noticed and make some connections to what we already know about fractions that can help us when we’re comparing.
The independent activity is called Fractions take Action. Students will decide if the problem is going to have a common numerator or a common denominator, and then figure out the best way to determine if the fractions are equivalent.
In show 318 for third grade, our Mystery Math Mistake is the second one to showcase the multiplying up strategy. Springling is trying to solve 96 ÷ 6. Can students find the error this time?
For this show, we’re going to take what we’ve learned about equivalent fractions and add to it with the “I Can” Statement: I can compare two fractions with the same numerator. We often hear people talk about a “common denominator,” but we don’t often talk about a common numerator. On the show, Priya says that 5/6 is greater than 5/8, but Taylor says 5/8 is greater than ⅚. Let’s look at how students are really thinking about this kind of comparison. We know that sixths are larger than eighths.
So 5/6 is greater than 5/8. When you’re looking at a fraction that has a common numerator, we know we’re talking about the exact same amount of pieces, so we’re going to have five pieces out of the six or five pieces out of the eight. It might help if kids can relate this to eating something – do you think you’d get a bigger slice if a pie was cut into eighths or if the pie was cut into sixths? Once we have a good idea of the size of the pieces, we know we’re talking about the same amount of pieces. So obviously, 5/6 are a lot larger than 5/8.
We use this same strategy as we start to look at comparing other fractions, like 3/4 and 3/8. Again, kids often have a fear of fractions, and they don’t really want to think about them. But, wait a minute! Those fractions have a common numerator! If I thought about taking a brownie pan, and I cut it into four pieces, would I want a piece that size? Or would I get a bigger piece if I cut the brownies into eight slices? I only get three pieces, so which size would I like to have? Students can use this common numerator process to help them understand that 3/4 is larger than 3/8.
As we move on, we want to make sure kids are careful looking at common numerators, 5/3 or 5/6. Well someone thinks thirds are larger, but they also have to remember that 5/3 is a fraction larger than one (you might call it an improper fraction in your classroom). It’s okay to let kids say improper fractions. In fact, many of the tests will label it like that. But I always ask third, fourth and fifth graders, what is an improper fraction? Their answer is usually when the numerator is larger than the denominator. But, we want to tie it back to number sense. Help your kids get in the habit of calling it a fraction larger than one whenever they see a fraction where the numerator is larger than the denominator. We spend a lot of time on the show looking at this common numerator idea. I think it’s a really great way to get your third graders to think about fractions.
Our really fun game that we’re going to play is called Spin to Win. We’re going to look at it with either the same numerator or the same denominator.
I hope you’re having as much fun as we with all these Math Might shows! Remember if you’ve already taught a concept in your class this year, file these episodes away for next year!
Also, remember, If you’re an M3: Molding Math Mindsets member, you have all of the footage that we use to create these videos – the PowerPoints that I made with the instructional videos, number talks, Mystery Math Mistakes, Professor Barble’s problems. It’s already put together and ready to use with a click of a button on our M3 dashboard. We have a separate Math Mights page created just for members, so you can go use those problems! So many of our schools are using the Math Might shows for summer school instruction! Great idea because the work is already done for you, even the extension/independent activity that goes with it!
M³ Members, don’t forget to download the PowerPoints and get your very own Mystery Math Mistake animation!
(valid M³ Membership login required)