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**5. Which is greater, 79 x 25 or 75 x 29?**

*Mike Lawler shares a post and videos of his two sons doing this same problem*.

**Student 1**

- 79 x 25 is greater. I remember a strategy that was shared last week, and that’s what I did:
- 79 x 25 = (75 x 25) + (4 x 25)
- 75 x 29 = (75 x 25) + (75 x 4)
- So, clearly 75 x 4 is greater than 25 x 4.

*The student realized that he meant to say 75 x 29 is bigger based on strategy that he’d used.*

**Student 2**

- 79 x 25 is greater. I rounded the numbers.
- 79 x 25 –> 80 x 20 = 160 (I multiplied 8 times 2, then added a 0.)
- 75 x 29 –> 70 x 30 = 120 (I multiplied 7 times 3 to get… oh, wait, that’s 21… it should be 210)

*Other students pointed out to Student 2 that she didn't add enough zeros to her answers.*

**Student 3**

- 75 x 29 is greater because…
- 75 x 29 –> 75 x 30 = 2250 (I multiplied 75 and 3, added a 0.)
- 79 x 25 –> 80 x 25 = 2000 (I know 4 times 25 is 100, so 8 times 25 is 200, then I added a 0.)
- I’m 99% confident my answer is correct.

**Student 4**

- I think they’re both equal because…
- 75 x 29 = (70 x 20) + (5 x 9)
- 79 x 25 = (70 x 20) + (9 x 5)

A student reminded Student 4 that many students last week did break the problem down as she did, but they were wrong. Because of this recurring mistake, I explained to the class why breakdown of the product does not work or is insufficient via this rectangular model below.

A student reminded Student 4 that many students last week did break the problem down as she did, but they were wrong. Because of this recurring mistake, I explained to the class why breakdown of the product does not work or is insufficient via this rectangular model below.

**6. What is 0.48 x 921?**

**Student 1**

- 1/2 of 920 is 460. Then I tried doing .02 times 921 but didn’t get too far.

**Student 2**

- 1/2 of 921 is 460.5, and I just stopped there.

**Student 3**

- 1/2 of 920 = 460
- 2% of 1000 = 20
- 460 – 20 = 440

Student 4

Student 4

- 1/2 of 921 = 460.5
- .02 of 921 = 18.42 (I did 2 times 921, then added the decimal)
- To subtract 18.42 from 460.5, I did how many is 18 from 60, that’s 42. Then 50 minus 42 is 8, so I got 442.08.

Student 5

Student 5

- I did similar to what Student 4 did, but instead of finding .02 of 921, I found…
- .01 x 921 = 9.21
- 460.5 – 9.21 = 451.29
- 451.29 – 9.21 = 442.08

**7. Which is greater, 13/19 or 2/3?**

**Student 1**

- I changed 13/19 to about 13/18 and 2/3 is equal to 12/18, and I’m about 70% confident that 13/19 is greater.

**Student 2**

- The fractions were small enough that I can do mental math and change them into common denominators, so 13/19 is 39/57 and 2/3 is 38/57, therefore 13/19 is greater.

**Student 3**

- I changed 13/19 to 14/20, then I thought of a pizza, and that’s a lot of little pieces. So I’m about 70% confident that 2/3 is bigger than 13/19.

**Student 4**

- I know 2/3 is 12/18 if I multiply top and bottom by 6. 12/18 is bigger than 13/19 because I imagine a pizza. I’m 90% confident.

**Student 5**

- I cross-multiplied: 13 times 3 is 39 and 19 times 2 is 38, so 13/19 is bigger. I’m 100% confident.

**8. What is 0.4 × 58.6 × 5 × 3?**

**Student 1**

- 1/2 of 58.6 = 29.8, round this up to 30
- 30 x 5 = 150
- 150 x 3 = 450

Student 2

Student 2

- 1/2 of 60 = 30
- 5 x 3 = 15
- 30 x 15 = 450

Student 3

Student 3

- 5 x 3 = 15
- 60 x 15 = 900
- 50% of 900 = 450

Student 4

Student 4

- 5 x 3 = 15
- 15 x 0.4 = 6.0 (I did 15 times 4, then place in the decimal)
- 58.6 x 6 = (50 x 6) + (8 x 6) + (0.6 x 6) = 300 + 48 + 3.6 = 351.6

Student 5

Student 5

- 5 x 3 = 15
- 15 x 60 = 900
- 900 (0.4) = 360