In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 31, 2024.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

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Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

**Pam **00:00

Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam Harris.

**Kim **00:06

And I'm Kim Montague.

**Pam **00:07

And this episode is a MathStratChat episode, where we chat about our math strategies. Every Wednesday evening, I throw out a math problem on social media and people from around the world chat about the strategies they use and comment on other's thinking.

**Kim **00:21

Alright, so this Wednesday, our math problem was 16% of 22. How would you solve this problem? Pause the podcast. Solve it however you want. Remember, the problem was 16% of 22. Solve it, and then come on back to here how we solve it.

**Pam **00:37

Bam! Alright.

**Kim **00:40

You want to go first or you want me to?

**Pam **00:42

You go first.

**Kim **00:43

Okay, 16%. I got my pencil. 16% of 22.

**Pam **00:46

I got my pen. I got my pen.

**Kim **00:49

I'm going to go with 10% of 22 is 2.2, 2 and 2/10. And 5% would then... Because it's half of 10%, 5% would be 1 and 1/10. So, 1%. Okay, so 10% was 2.2. So, 1% would be 22/100. like $0.22.

**Pam **01:16

Okay.

**Kim **01:17

So, when I put those together, I've got 3.3 and $0.22. So, I'm thinking about that like $3.30, the 3.3. And $0.22. So, that's 3 and 52/100.

**Pam **01:34

For 16%.

**Kim **01:35

16%.

**Pam **01:36

Nice. So, you found 10%, 5%, 1%. Added those together to get the 16%.

**Kim **01:42

Yep.

**Pam **01:43

Nice. So, a little Five is Half of Ten strategy. You can find 16 times anything or 16% of anything. Nicely done. Cool. Okay, so I am going to play a little bit with the communitive property. If 16% of 22 is going to be equivalent to 22% of 16. And I'm not going to develop that right now. But I've learned that, and I know I can use it. So, now, I'm going to find 22% of 16. So, I'm thinking about 16s. And I'm going to find 2% of 16s. Am I? Is that what I'm going to do? Actually, I'm going to find 10% of 16. So, 10% of 16 is 1.6 or 1 and 6/10. To help me think about 20% of 16. And 20% is double 10%, so double 1.6 is 3.2.

**Kim **02:36

Mmhm.

**Pam **02:37

Now, that I have 20%, I'm going to scale that down to get 2%. And so, if 20% was 3.2, 2% is divided by 10 of that. So, divide 3.2 by 10 is 0.32 or 32/100s

**Kim **02:53

Yep.

**Pam **02:54

No.

**Kim **02:54

Yep.

**Pam **02:55

Yes. So, now I've got 20% is 3.2, and 2% is 0.32. I add those together to get 22%, and I end up with 3 and 52/100 or 3.52.

**Kim **03:08

Hey, so I know this is a short episode. Nicely done by the way. You and I both said "point" and people have massive problems with us saying "point". Do you want to comment on that for just a second?

**Pam **03:17

Yeah. I mean, so I think we both said both. I said 32/100 and 0.32. I don't know that I said 3 and 2/10. Anyway. So, we like to say both. Is it correct that 3.2 is actually 3 and 2/10? Sure. And I think it's important that kids hear that, do that, mess with it more than just hear it. I had the experience of as a student, where I had a teacher all year long made me say 3.2 as 3 and 2/10. And it did nothing for me. Just the saying of it did nothing. Now, if we would have... Dived. Dove. I never know what the past tense is. Dived in. I don't know. If we would have gone into it more, and actually developed like place value and why it was called that, maybe it would have done a little bit more for me. But just the naming of it that way did nothing for my place value. I just memorized how to say it. I said it that way. So, we're good. Say it both. In common speak, people talk about $3.2 million in debt or whatever.

**Kim **04:20

All the time.

**Pam **04:21

Yeah, all the time. And so, I think we need both, so we need both. There you go.

**Kim **04:25

Alright.

**Pam **04:25

That's why we say both. Whoo!

**Kim **04:27

Well, we can't wait to hear everyone else's strategies. Maybe it's like one of ours. Represent your thinking. It's super fun to see you like sketch out your thinking, rather than just type out some numbers, so take a picture of your work and tell the world on social media. And while you're there, comment on other people's thinking. It's super fun to get props or ask questions of what other people did.

**Pam **04:48

Yeah and learn! Learn through that. And tag me when you're there on social media and use the hashtag MathStratChat. And make sure you check out our next MathStratChat problem that we'll post the next Wednesday around 7pm central time. And then, pop back here to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement! Let's keep spreading the word that Math is Figure-Out-Able!