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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 - March 26, 2025
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 26, 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
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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 mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.
Kim 00:06
And I'm Kim.
Pam 00:07
And this is a... What are you laughing about?
Kim 00:09
I'm laughing because you say, "Let's go!" "Like, wait. Where? Wait! Wait for me!"
Pam 00:14
"Where are we going?!" 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 each other's thinking.
Kim 00:25
Okay, so this week, our problem was... Good gravy. 48 times 52. How would you solve this problem? Pause the podcast. Solve it yourself however you'd like. The problem is 48 times 52.
Pam 00:41
You know, we actually do believe in that. The more that you mess around with relationships, the better our strategies will hang on what you've already been thinking about. So, just to throw that out there.
Kim 00:51
And it's super fun when somebody will say, "I did it like you!" So, you know, there's this idea that you thought about it first, and then when you read other people's thinking, then you can honestly say, "I did it like you!"
Pam 01:07
Yeah. Yeah, that's kind of cool.
Kim 01:09
Alright, I'm going to first.
Pam 01:12
What are you doing?
Kim 01:13
48 makes me think of 50, which makes me think of 100, so I am going to write down 100 times. 52 is 5200. Half of that is 2600. And that would be fifty 52s. And then I'm going to subtract two 52s, which is 104. So, I've got 2600 minus 104. So, 2496.
Pam 01:38
Nice. I like it. Would you ever consider doing fifty 48s, and then adding on two more 48s.
Kim 01:48
Say it again? Fifty 48s.
Pam 01:50
Mmhm. And then... So, fifty 48s, you could do kind of similar to what you did.
Kim 01:55
Yeah, if I did a hundred 48s and fifty 48s.
Pam 01:57
Yeah.
Kim 01:57
Sure, sure.
Pam 01:58
And then you would just subtract two 48s. No, sorry. Add two 48s. And the two 48s is that 96 sitting there in that 2,496.
Kim 02:08
I like it.
Pam 02:09
Okay cool.
Kim 02:09
Is that what you did?
Pam 02:10
No!
Kim 02:11
Oh. Okay.
Pam 02:11
No, I was just playing with. But we could have.
Kim 02:14
Sure.
Pam 02:15
But I didn't. No, so I'm still playing around with the idea that these problems are... What? There's a number right in the middle of them. 50. So, 48, 52. 50 is right in the middle.
Kim 02:27
Mmhm.
Pam 02:27
So, I could think about 48 as 50 minus 2, and I could think about 50 as 50 plus 2, and I could multiply all those parts together. So, 50 times 50 is 2500 or 2,500. The -2 times 50 and the positive 2 times 50 add to 0. -2 times -2 is 4, so I have to subtract 4. 2,500 subtract 4 is 2,400 and there's that 96. Da dum dum. So, I could have said to myself, "The number in between them is 50, so it's just going to be 50^2 minus the difference 2^2." I could have done that. Because if I have a minus b times a plus b, that's always going to be a^2 minus b^2. So, if I can figure out what the a and the b are, in this case 50 and 2, then I could do that. Do I want to do that? It's good question.
Kim 03:22
Well, what's really nice is, if you think about it like 50^2, you can actually draw the square.
Pam 03:28
That's true.
Kim 03:29
And then you can find...
Pam 03:32
That overlapping...
Kim 03:33
Yeah.
Pam 03:34
...b^2 that has to be taken off?
Kim 03:36
Yeah.
Pam 03:37
That is pretty cool. Nice spatial representation.
Kim 03:40
Mmhm. Okay, well, we can't wait to see every week what you do. Join us on MathStratChat and let us know how you think about the problems. Comment on each other's strategies.
Pam 03:49
We'll post the problems on Wednesday around 7:00 pm Central. And when you answer, tag me and use the hashtag MathStratChat. Then join us here to hear how we're thinking about the problem. Thanks for being part of the Math is Figure-Out-Able movement! Math is Figure-Out-Able!