
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!
Math is Figure-Out-Able!
#MathStratChat - October 15 , 2025
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 15, 2025.
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
Pam 0:00
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.
Kim 0:09
And I'm here. I'm Kim.
Pam 0:10
And this episode is a MathStratChat episode. Where it's going to go well today. Where we chat about our math strategies. Every Wednesday evening, I throw out a math problem on social media. People from around the world, when they're alive and awake, chat about the strategies they use and comment on each other's thinking.
Kim 0:26
Okay.
Pam 0:26
Hey, Kim!
Kim 0:27
This Wednesday, our math problem was another which is more orangey? 12 ounces of orange mix in 15 ounces of water or 20 ounces of mix in 23 ounces of water? How would you solve this problem? Pause the podcast, solve it however you'd like, and then come on back to hear how we're going to solve it.
Pam 0:45
Bam. Okay, you go first.
Kim 0:52
Okay.
Pam 0:53
Can I command that? That's not very nice. Kim, would you like to go first?
Kim 0:56
Sure, that's
Kim 0:57
fine. Okay, the numbers are not brilliant here. I don't like the 23 ounces of water, so...
Pam 1:05
Rude.
Kim 1:05
What I'm going to notice is that in the 12 ounces of mix to 15 ounces of water.
Pam 1:11
Mmhm.
Kim 1:12
That if they had equivalent amounts, that would be 12 for 12. But there's 3 extra ounces of water in that mix.
Pam 1:19
Okay.
Kim 1:20
And the same thing is true in the 20 to 23. That also has 3 extra ounces of water.
Pam 1:29
Mmhm.
Kim 1:29
So, if they have the same amount of extra water, then I have that 3 extra ounces of water to share within the 20... How do I say this? I've got 3 extra ounces of water for the entire mix. Which is a bigger mixture. Did I say that
Kim 1:52
well?
Pam 1:52
I think so. Are you saying in the 12 to 15, you've got this 3 extra ounces of water for the 12 cups of mix?
Kim 2:03
Yeah.
Pam 2:03
And in the 23, you've got 3 extra cups of water, but you got 20 cups of mix.
Kim 2:09
Yeah.
Pam 2:10
You got more cups of mix to spread out in
Pam 2:12
the...
Kim 2:12
Yeah, in the extra. Yeah.
Pam 2:14
Which one's more orangey then?
Kim 2:16
So, I think that the more orangey is the 12 to 15.
Pam 2:21
Because... Wait, are you sure? I just heard it the other way. If it's 3 cups of water for 12 cups of mix, and then 3 cups of water for 20 cups of... Oh, right. No, okay, I had to say it. More mix in only 3 cups of water.
Pam 2:40
Yeah, more mix in only 3 cups of water, so... Wait, so that's more orangey.
Kim 2:45
So, they both have 1. It's a 1 to 1 ounce. And there's 3 extra ounces of water.
Pam 2:52
Right?
Kim 2:52
What did I say? Do I even know what I said?
Pam 2:56
Well, I thought you said that 12 to 15 was more orangey. But I'm thinking the 23 is more orangey.
Kim 3:02
Yeah, I think I meant the 20 to 23. Because that extra ounces of water is going to dilute the 20 ounces of mix
Kim 3:09
less.
Pam 3:10
Less. That's the important part.
Pam 3:12
Yeah.
Kim 3:12
Yeah, we thought this would be a good one. Whoo!
Pam 3:14
Okay,
Pam 3:14
I'm going to do it slightly differently.
Kim 3:16
Okay.
Pam 3:17
So, you kind of focused on that extra 3 ounces of water. I'm going to focus on getting a common amount of mix.
Kim 3:24
Okay.
Pam 3:25
So, the 12 to 15, the 12 cups of mix or whatever, I'm going to scale that up to 60 cups of mix.
Kim 3:32
Okay.
Pam 3:33
So, 12 to 15 is equivalent to having 60 cups of mix to 75 cups of water. Did I do that right? Times 5 times 5?
Kim 3:41
Mmhm.
Pam 3:42
Yeah. The 20 cups of mix would scale up to also 60 cups of mix. The 23 would scale up to 66 cups of water. So, now I've got the same amount of mix in different
Pam 3:56
amounts of water.
Kim 3:57
Wait, did you say you're scaling it up? Oh, just by 3 on this one. Yeah, okay.
Pam 4:01
Yeah.
Pam 4:01
So, 60 to 60 cups of mix to 75 cups of water. And 60 cups of mix to 66 cups of water. So, I've got the same amount of mix with different amounts of water.
Kim 4:12
Yeah, nice.
Pam 4:13
So, the same amount of mix with 75 cups of water is going to be diluted more than the same amount of mix with 66 cups of water, so it's stronger, the 60 to 66 or the
Pam 4:24
20 to 23.
Kim 4:25
Very nice. Alright, I hadn't thought about that. Great
Kim 4:28
job.
Pam 4:28
So, that was easier for me to think about the same amount of mix per water than it was for me to think about the same amount of water per mix.
Kim 4:37
Yeah.
Pam 4:37
That's interesting.
Kim 4:38
It's super good. Listeners, you think we've solved these problems before we get on. We totally don't.
Pam 4:43
Bam.
Kim 4:43
We can't wait to see what you do every week. Join us on MathStratChat and let us know how you think about the problems and comment on each other's thinking.
Pam 4:50
Yeah, we'll post the problems on Wednesdays around 7:00 p.m. Central. When you answer, tag me and use the hashtag MathStratChat. Then join us to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement! Math is Figure-Out-Able!