It’s a great week in Mathville! Get the inside scoop on episodes 315-316!

# Teacher's Guide

Episodes 315-316

**April Focus: Mystery Math Mistake**

In the Mystery Math Mistake, our warm up for April, 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!

### Kindergarten

**Focus:** 315: Counting Groups 11-20 / 316: Count Groups Up to 20

**“I Can” statement: **I can figure out how many objects are in our collection. / I can answer questions about how many are in groups up to 20.

**Extension Activity: **Race and Trace / Build the Tower

We start off kindergarten with a Mystery Math Mistake, and D.C. is all confused! He’s created number bonds for 10-frames, but somewhere he found an error. Eric and Maki help set D.C. straight in this Mystery Math Mistake.

The “I Can” statement is: I can figure out how many objects are in our collection.

We know that Kindergarten students often struggle with one-to-one counting if things are not presented in an organized way because they often recount. So, we start the show by talking about how to count a collection of clear counters. There are different ways to go about counting – we could line up the objects, we could make sure we touch and count each one. We also use a new tool that you can download, called My Counting Mat, which helps students slow down and count more carefully. They can put all of their items on one side of the mat, and then, as they cross over the line on the My Counting Mat, they can count it so they won’t lose track.

Our Math Might friend Value Pak appears in this episode because we want to be able to set up our collections in a way that helps us see the value of 10s and 1s. We also use a different mat, the Double 10-Frame Mat, which helps students see the value of 10s and 1s by creating a set of 10, and then some more. So students will count in three different ways and then they can match up with Value Pak, seeing the red Value Pak in a 10, and the white Value Pak in three, and then when you put that together it makes the number 13.

It’s really important when we’re looking at teen numbers, like 16, to make sure that students don’t just say “one, six.” We want them to know the value of what they’re saying. The one in the number 16 is really a 10, and the six is six. You could think of a teen number as 10 six.

We then play a game called Race and Trace (watch the deleted scene!), and that’s the extension activity that the students will be playing in show 315.

As we move into show 316, we’re going to be doing a Mystery Math Mistake very similar to the one on the previous show, but this time instead of number bonds, D.C. is making number sentences to go with his 10-frame, and he is all turned around and confused!

The “I Can” statement is: I can answer questions about how many are in groups up to 20.

We open the episode with a pile of unifix cubes, asking *What do you notice?* and *What do you wonder? *Obviously, we can’t really count that pile of cubes, but we can look at them and maybe estimate the amount by looking at how many we see. We might be able to ask questions as we wonder, like, “Are there more red cubes or yellow cubes?” I think this opportunity to investigate through inquiry is really important for Kindergarteners to set them up for what we’ll be doing during this lesson. As we did in the previous lesson, we use the Double-10 Frame Mat here to begin to organize the cubes and we also use Value Pak to help us see the value of our collection.

We then have a collection of cubes and each student says there is a different amount – one says it is 15, another says 17, another says 16. They can’t all be right! So we have to investigate to see who is correct. We bring out the My Counting Mat again to make sure that we’re not counting too fast, which can lead to errors in counting.

We then look at scatters and different arrangements of an amount (12). We want to find out which arrangement of objects is easier for counting? A circle? Probably not because, when you start off counting in a circle, you might forget where you start if you don’t make a mark. It might be easier to line it up in a 10-frame where we have a row of five, and a row of five, and a row of two. Maybe we could line the objects up and skip count by twos. So we talk about the different ways that to arrange objects, and then we have different objects that we can arrange – buttons, snowflakes and even popsicle sticks.

For the extension activity, we do a game called Build the Tower. Students are going to roll a connecting cube onto a number mat with the numbers 0 – 9 and add that number to their tower. The first person to get to 20 in their tower is the winner.

### First Grade

**Focus:** 315: Measuring Lengths Longer than 100 / 316: Story Problems with Length

**“I Can” statement: **I can measure lengths longer than 100. / I can solve story problems with measurement and compare length

**Extension Activity: **Match-Up with Value Pak / Problem Solving with Professor Barble

We start off episode 315 with a Mystery Math Mistake, but this time we have Professor Barble who is upside down and all confused. We solve a problem that says *Rocco had 12 bags of fruit snacks. Jack gave him three more. How many did Rocco have in all? *It’s an addition problem, and we go through the Professor Barble process, but we might do the wrong operations. Can Nora and Laila help us?

Our “I Can” statement is: I can measure lengths longer than 100.

We are going to be measuring the students’ bodies in this episode! If you’re in the classroom, you could trace the students’ bodies on a large piece of butcher paper. In the show, Clare uses a piece of string to measure the length of her body and she discovered that it was 112 cubes long. When we have that many cubes, what is the best way to count them? We bring this back around to base-10 understanding with base-10 blocks. That’s a lot of cubes to count individually, but we can have 11 groups of 10 and 2 single cubes to make 112.

And so we have a variety of students in our pretend classroom that measure their body length in cubes and we talk about how we can count the cubes. For example, one person has 10 groups of 10 and 4 singles, so we know that that is 104.

We then transition into matching up a number over 100 with unifix cubes so students can see the representation together. Then, we talk about measuring different animals. We have the length, in cubes, of each animal on posters and students have to read that number. A red fox is 11 groups of 10 and 5 singles, how long is it? If a raccoon is 10 groups of 10, or the dog was 11 groups of 10, how long are these animals?

We then use Value Pak to talk about how a lot of kids say numbers incorrectly. When they’re counting in the English language, sometimes kids will say “twelveteen, thirteen, fourteen.” Mrs. Markavich had this happen a lot in her classroom! If a student is trying to read the number for the dog, which was 11 groups of 10, they might say eleven-d-ten (which isn’t really a number!). So, we talk about being really careful with numbers and how to honor the place value when we say the numbers.

For the extension activity, they’re going to do a match up with Value Pak. We usually see Value Pak in just red and white, representing just the 10s and the 1s, but we had our artist work on expanding him to 100s, which are orange! Students will be matching up numbers that are higher (in the 100s) with base-10 blocks. The idea of measurement is wrapped in with the idea of numbers higher than 100.

In show 316, our Mystery Math Mistake has Professor Barble upside down again! He should maybe be showing a subtraction visual model, but might get confused and so Nora and Laila help set him straight.

In the “I Can” statement, we can solve story problems with measurement and compare length. This episode is all about bringing length into real life situations and being able to use it to compare. Naturally, Professor Barble is the star of this show! Some of the problems ended up on the cutting room floor (check our deleted scene page to see them!), but we are talking about things like which paper clip is longer? How many cubes longer is the math book than the reading book?

This kind of problem is known as additive comparison, which can be quite difficult for first graders. As a result, I think it is really important to use Professor Barble’s step-by-step process to help students solve this type of problem.

And then it’s their turn! The students get to do a comparison problem with Professor Barble, walking through the step-by-step visual model process. They’re going to be using a non-proportional bar and adding in some of the pieces of information from the problem themselves.

### Second Grade

**Focus:** 315: Coins and Values / 316: Coin Combinations

**“I Can” statement: **I can learn about coins and values.** / **I can learn about quarters and find the values of different sets of coins.

**Extension Activity:** Coin Compare: Levels 1 and 2

Show 315 opens with a Mystery Math Mistake featuring T-Pops! He is solving 78 + 14, but as the kids in the show contribute their thoughts about where the error was, you’ll see how you can look at an addition problem and actually end up doing the inverse operation! Nora, in the show, realizes that the answer can’t be 82 because 82 – 14 isn’t 78. It’s important for kids to realize how to look at the error, and we have to dig deeper to find out where T-Pops went wrong.

The “I Can” statement is: I can learn about coins and values. We talk about coins and value some in first grade, so this show touches a bit on some of the first grade standards. We don’t really count combinations anymore in first grade, but this is a nice review show to really help look at the attributes of coins. To begin, we ask our kids on the show to brainstorm on chart paper what they know about money.

In this show, we focus on dimes, pennies, and nickels, and their values. We also do combinations where we’re adding nickels and pennies together, or dimes and pennies, or dimes and nickels. We aren’t getting to quarters just yet, as I think it’s really important for kids, when they study coins, to practice skip-counting by 10s, then 5s, and then 1s.

An abacus is a really great tool to use with counting coins. If you’re counting by dimes first, then nickels, then pennies, you can use the abacus to help slow down your counting. We also talk a lot about how you go about counting money if you have a picture of coins, and you can’t rearrange them from greatest to least. Maybe you want to count or touch the dimes first, then the nickels, then the pennies to make your counting a little bit easier.

On the extension activity, students are going to be doing an activity called Coin Compare: Level 1, where students are going to be comparing coin sets with their partner to see who has the greatest total.

As we move into show 316, our Mystery Math Mistake is very similar to the previous show so that, in the first show, students could learn or be introduced to an idea or concept, and in the second show, we do a similar problem but students are able to be more independently involved to figure out where the error is.

The “I Can” statement is” I can learn about quarters and find the values of different sets of coins. There’s a new coin in town in this show – it’s the quarter! We’re looking at ways you can create a quarter or combine the values of coins in different ways. We present students with three quarters and ask *What is the value, in cents, and then how can you create that same value with different coins?* Could you have two quarters, two dimes, and then a nickel? Would that still equals 75 cents?

We have different combinations of coins – quarters, dimes, nickels, and pennies – that students will study. In second grade, one of the standards asks students to be able to make a certain amount using the fewest coins possible. If we wanted students to make 66 cents, they might do six dimes and six pennies, but how would we make that same total with the fewest number of coins?

For the extension activity, students play Coin Compare again, but this time they’re playing level two! We’re going to be mixing in quarters to make this a little bit more challenging for students as they’re counting and comparing with a partner.

### Third Grade

**Focus:** 315: Equivalent Fractions / 316: Equivalent Whole Numbers as Fractions

**“I Can” statement: **I can identify, generate, and locate equivalent fractions. / I can find fractions, and whole numbers that are equivalent.

**Extension Activity:** Equivalent Fraction Roll / Same, But Different

As we move into 315 for third grade, we do a Mystery Math Mistake with Springling, where she is using the strategy of multiplying up. We’ve covered this strategy extensively in previous shows, but now, we want kids to look with a more critical eye to see where Ms. Askew maybe went wrong. The problem is 48 ÷ 4 and so we’re asking the question *How many groups of 4 go into 48?* We have to find out where the error is in what we’re doing. We also introduce the idea of using the inverse operation here when one of the students says, “I know that 14 x 4 = 56 and we’re trying to get to 48.” I think it’s important for kids to know about that concept as they’re analyzing to see if an answer is correct.

The “I Can” statement is: I can identify, generate, and locate equivalent fractions. We’re spending a lot of time here looking at equivalent fractions in different ways – fraction tiles, fraction strips, area model papers, as well as shading in different bars – to demonstrate how we can tell if a fraction is equivalent.

I think it’s really important, when teaching equivalent fractions, NOT to teach students the “butterfly method” or other really quick tricks because, you don’t want to teach them a procedure with a concept they don’t understand. So give the example of a person that ran 3/6 of a mile and somebody else that ran 1/2 of a mile, asking *who ran further on the track?* Well, really looking at the equivalencies on a number line is really important to be able to compare those fractions.

The number line work that we do in third grade is such an integral piece. Kids really struggle here, and so we give them a variety of fractions such as ½, 3/8, 6/8, 7/8 and so forth, and we want them to be able to locate and label them on the number line. Then, once we have these plotted, we look at having a number line that’s in fourths and then another long number line in eighths. Can we find one that is equivalent on the number line because we’re looking at the same point?

In the extension activity, we play an equivalent fraction roll, where students play different rounds and create fractions, trying to find an equivalent fraction to the one that they created.

In show 316 in third grade, we do another Mystery Math Mistake. Again, it is a very similar problem that uses multiplying up – 63 ÷ 3 – and Springling has made an error somewhere in the groups. Maybe she didn’t count all the groups of three? Let’s see if we can discover where her error is!

The “I Can” statement is: I can find fractions, and whole numbers that are equivalent. We spend a lot of time on this show talking about fractions that are larger than one. A lot of times, we call those improper fractions, but I always say, *If I wanted to eat three halves of a pizza, and I was super hungry, does it mean that it’s improper?* Not necessarily. We still have to use the word “improper” because we do see it on tests, but it’s really important to make sure that, when you say improper, you make sure third graders know what that means. Ask them! A lot of kids will say it means the numerator is larger than the denominator, but we want them to say that an improper fraction is a fraction larger than one. This make sure that we’re always going back to the number sense within fractions.

Most kids know that we label one on a fraction number line. We know it’s 3/3, we know that equals one. But what happens if a fraction number line doesn’t have any fractional parts in it? How else would you label one? Well, the fraction for a one would be 1/1. If you have a fraction number line that just goes to two, it would be 2/1. So we talk about the idea of looking at what fraction might be equivalent to the whole. If you have 3/1 and 4/1 are all equivalent to a whole number, but so is 3/3, and so we want kids to look at that in depth.

Then we look at different number lines and decide what fractions are equivalent to whole numbers. We have a variety of fraction number lines that are in halves, fourths, and thirds, so that kids can look and say things like, *I know that half is not equal to a whole, two halves is equal to a whole. Three halves is not, but four halves is equal to a whole number – it’s two.* We want kids to look beyond just what a whole number is.

Then, we want to bring in D.C. I love using D.C.’s strategies to show fractions that are larger than one! He smashes with his hammer to decompose and pull out the whole! When you and I were younger and we had 12/6, we always said *how many groups of 6 go into 12*? But a lot of times, this is difficult for kids. So, instead, we can take a fraction and decompose it by pulling out the whole. If I have 12/6, I can pull out 6/6, and another 6/6, and almost make a number bond.

We do that with several examples, especially when it isn’t a nice and even decomposition, like 12/8. In that example, D.C. is going to smash that and pull out 8/8, and then 4/8 so we know that it is 1 4/ 8. If DC were to have 10/3, he’s going to pull out 3/3, 3/3 and 3/3, which is going to total 9/3, and then he’s going to have an additional third. That makes it easy for kids to look at the wholes and say, okay that is 3 1/3. It’s really awesome, I think, to use D.C.’s strategy here and I really love the idea of that in this show!

In the extension activity, they’re going to play a game that’s called Same, But Different. In this game, students are first going to choose the denominator (in third grade, we want to use halves, thirds, fourths, sixths, and eighths), then they spin a spinner to find out what the numerator will be. Then, students will work on finding equivalent fractions, like we do in the show.

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!

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