Addition and subtraction strategies (age 7+)

Question 1

When adding 34 + 27, a student adds the tens (30 + 20) to get 50 and the ones (4 + 7) to get 11, then combines 50 and 11 to write 61. Which explanation best describes why this addition strategy works?

Accepted Answer

Because the tens and ones each represent separate values, adding the tens gives the total number of tens and adding the ones gives the total number of ones; then combining those totals gives the correct sum.

Answer

Because adding the tens first automatically adds the ones as well, so the ones addition is unnecessary.

Answer

Because breaking the numbers into tens and ones makes the total larger than either original number, which is why the method works.

Answer

Because when the ones add to a two‑digit number we can ignore the extra ten and just keep the ones digit.

Question 2

When adding 27 + 38 using the standard algorithm, a student adds the ones digits 7 + 8 = 15, writes 5 in the ones place and carries 1 ten, then adds the tens digits 2 + 3 plus the carried 1 to get 6 tens, producing 65. Which statement best explains why this procedure always gives the correct total?

Accepted Answer

We add the ones (7+8=15), write the 5 in the ones place and carry the 1 ten because ten ones make a ten; then we add the tens (2+3) plus the carried 1 to get 6 tens, giving 65.

Answer

We add the tens first (2+3=5) and then add the ones (7+8=15) to get 20, because the tens are more important than the ones.

Answer

We treat the whole numbers as single units and add 27+38 directly to get 65, so separating tens and ones is unnecessary.

Answer

We add the ones (7+8=15), write the 5 in the ones place, and ignore the extra ten because it is already included in the tens column.

Question 3

You need to add 46 + 27. One strategy is to add the tens first (40 + 20 = 60), then add the ones (6 + 7 = 13), and finally combine the results to get 73. Which statement best explains why this strategy works?

Accepted Answer

It separates each number into its tens and ones, adds each place value separately, and then combines the sums, which follows the place‑value system.

Answer

It subtracts 46 from 27 and then adds 100 to correct the negative result.

Answer

It adds the numbers as whole numbers without separating tens and ones, relying only on the commutative property of addition.

Answer

It rounds each number to the nearest ten before adding, which makes the calculation easier.

Try three questions

When adding 34 + 27, a student adds the tens (30 + 20) to get 50 and the ones (4 + 7) to get 11, then combines 50 and 11 to write 61. Which explanation best describes why this addition strategy works?

You need to add 46 + 27. One strategy is to add the tens first (40 + 20 = 60), then add the ones (6 + 7 = 13), and finally combine the results to get 73. Which statement best explains why this strategy works?

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