Explaining Mathematical Reasoning

Question 1

Jenna has 7 red blocks and 5 blue blocks. She wants to find how many blocks she has in total by using the “make a ten first” strategy. Which explanation correctly shows the steps she should take?

Accepted Answer

I added 3 to the 7 to make 10, then I added the remaining 2 from the 5, so the total is 12.

Answer

I added 3 to the 7 to make 10, then I added the whole 5, so the total is 15.

Answer

I added the whole 5 to the 7 to get 12, saying I made ten first.

Answer

I added 3 to the 5 to make 8, then I added the whole 7, getting 15.

Question 2

Sam solved the addition problem 8 + 5 and wrote the answer as 12. Which explanation correctly shows the error in Sam’s work?

Accepted Answer

Sam counted one too few when adding, so the correct sum should be 13.

Answer

Sam added the numbers correctly; 8 + 5 really equals 12.

Answer

Sam should have subtracted instead of adding, because the problem asked for a difference.

Answer

Sam wrote the numbers in the wrong order, which changes the answer.

Question 3

Liam has 7 red marbles. He then gets 8 blue marbles and says the total is 15. Which explanation correctly shows another way to see that the total is 15?

Accepted Answer

Liam can make a ten first: add 3 to the 7 to get 10, then add the remaining 5 (because 8‑3 = 5) to get 10 + 5 = 15.

Answer

Liam adds the two groups directly: 7 + 8 = 14, so the total would be 14.

Answer

Liam makes a ten by adding 2 to the 7 to get 9, then adds the remaining 6 to get 9 + 6 = 15.

Answer

Liam counts up from 7 by eight steps: 8, 9, 10, 11, 12, 13, 14, 15, so the total is 14.

Try three questions

Jenna has 7 red blocks and 5 blue blocks. She wants to find how many blocks she has in total by using the “make a ten first” strategy. Which explanation correctly shows the steps she should take?

Sam solved the addition problem 8 + 5 and wrote the answer as 12. Which explanation correctly shows the error in Sam’s work?

Liam has 7 red marbles. He then gets 8 blue marbles and says the total is 15. Which explanation correctly shows another way to see that the total is 15?

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