Math is Figure-Out-Able!

Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what? Join them for ~15-30 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able. See www.MathisFigureOutAble.com for more great resources!

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Math is Figure-Out-Able!

#MathStratChat - June 7, 2023

June 07, 2023 • Pam Harris

0:00 | 5:47

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 7, 2023.

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

Instagram: Pam Harris_math

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 00:07

And I'm Kim Montague.

Pam 00:08

And this is a MathStratChat episode. What is MathStratChat? Well, every Wednesday evening, I throw out a math problem on social media, and people from around the world chat about the strategies they use. We love seeing everyone's thinking.

Kim 00:22

Okay, so this Wednesday, our math problem was 14 is 35% of blank? How would you solve this problem? Pause the podcast, solve a problem however you want. The problem is 14 is 35% of what? Solve it, and then come on back to here how we solved it.

Pam 00:41

Alright, percent problems. Bam! This is fun. Okay, so here's what I was thinking about. I've got a download bar, like a percent bar. You might call it a... Now, my mind is blinking the other. There's a... Blinking? My mind is blanking. Blinking and blanking at the same time. Tape measure or tape diagram. Tape measure, wow. Okay, so on that percent bar, I put on the top 14, and on the bottom I put 35%. And I didn't actually take the time to put 0% and 100%, but I could have on the bottom. And then, my goal is to find out what the 100% is. What correlates to the 100%? So, I've done these a few times and I've kind of started to think, "What can I scale that 35%, in such a way, that I can also scale the 14, so that I can get up to 100?" Like, right now I'm thinking 35 times what is 100%." Eh, it's not doing it for me. But if I could get down to say like 5%. Oh, that I can I can mess with because then 5% can get up to 100%. So, I'm going to go ahead and scale from 35%, down by 7. So, I'm going to divide by 7 to get 5%. Which means I'm going to divide the 14 by that 7. And 14 divided by 7 is 2. So, now I know that 2 correlates to 5%. Two is 5% of whatever that number is, of whatever the same number 14 is 35% of. Once I know something is 5%, well that's sweet because now 5% scales up nicely to 100%. Because 5 times 20 is 100%. So, I would take that corresponding 2 times 20, and I would end up with 40, corresponding to the 100%. So, I'm saying 14 is 35% of 40.

Kim 02:29

Yeah, nice.

Pam 02:31

Can I tell you a little check I'm doing just real quick?

Kim 02:33

Sure, yeah.

Pam 02:34

I had not done that problem before I talked about it at all. So, I was in my head, I was like, "Half of 40 is 20. Yes, 14 is less than that. That feels about right because 50% would be 20. So, 14, 35% of... Yeah, that feels about right." Yep.

Kim 02:48

Yeah, that's nice. I mean, I love that you did that. And I actually made the same moves that you did. But you know what, it's funny because you started by saying you put it on a percent bar. And I did not draw a percent bar. Even though I made the same moves that you did, I actually sketched out a ratio table.

Pam 03:08

What?

Kim 03:10

So, I drew a line, horizontal line. And I wrote in the first kind of entry on a ratio table, I put 14 on top then 35% on the bottom. So, basically, the relationship of 14 and 35% I was going to maintain. But same idea. I wanted to know what would the relationship be if I got up to 100%.

Pam 03:37

Huh.

Kim 03:37

So, I also did scaled down by divided by 7 and get 2 to 5%. And then, I scaled immediately to 40 to 100%.

Pam 03:49

Interesting. I have to think about that a little bit. So, I might say that if I was working with students, I would want to start on a percent bar...

Kim 04:00

Yeah.

Pam 04:01

...to make sure we're feeling the relationships. Percent bar is a little more limited because you actually have to keep. Like, on your ratio table, you could kind of go where you wanted to go as you moved across the ratio table. And I had to actually go backwards on the percent bar. When I divided by 7, I actually literally, you know, put the 5% where it would belong on that download bar and put the 2 where it would belong. Whereas you just kind of kept going entries in the ratio table, right? So, where your model is a little more versatile.

Kim 04:32

But yours connects to things that kids know, which is downloads. It gives an understanding to percentages more than mine. Mine keeps things very like numerical.

Pam 04:46

And you're maintaining the equivalent ratios, so that's why it works. So, eventually I would think we would want to get to kids using the ratio table as a tool, but we would want to start with percent bars. Would you agree?

Kim 04:58

Yeah, I do.

Pam 04:59

Awesome. Alright.

Kim 05:00

Alright. Okay, so we are interested to hear about your strategy. I wonder if it was like ours. Represent your thinking and take a picture of your work or screenshot on your phone, and tell the world on social media. And while you're there posting your strategy, check out what other people did and comment on their thinking.

Pam 05:18

And tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. And on Facebook, Math is Figure-Out-Able. And use the hashtag MathStratChat. And check out the MathStratChat problems that we post every Wednesday around 7pm Central Time, and then hop back here to hear how we're thinking about the problem. Ya'll, thanks for joining the Math is Figure-Out-Able movement. Let's keep spreading the word that Math is Figure-Out-Able.