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

Answer

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

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

Answer

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

Answer

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

Question 3

Noah has 6 blue beads and 8 red beads. He wants to find how many beads he has in total by using the “make a ten first” strategy. Which explanation shows the correct way to solve it?

Accepted Answer

I added 4 to the 6 to make 10, then added the remaining 4 from the 8, so 10 + 4 = 14.

Answer

I added 2 to the 8 to make 10, then added the remaining 6, so 10 + 6 = 16.

Answer

I added 4 to the 6 to make 10, then added the whole 8, so 10 + 8 = 18.

Answer

I added the two numbers straight away and got 14, but I didn’t use the make‑a‑ten method.

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?

Noah has 6 blue beads and 8 red beads. He wants to find how many beads he has in total by using the “make a ten first” strategy. Which explanation shows the correct way to solve it?

Keep going on this shelf