A student wants to add 38 + 14. She thinks: '38 needs 2 more to reach 40, so I'll split 14 into 2 + 12: now 38 + 2 = 40, then 40 + 12 = 52.' What strategy is she using?
ACounting on — she is counting up from 38 one step at a time
BMaking tens — she bridges to the nearest multiple of 10 by splitting one addend
CBreaking apart — she separated both numbers into tens and ones place values
DRounding up — she rounded 38 to the nearest ten
Making tens (bridging to ten) works by identifying how far one number is from the nearest multiple of 10, then splitting the other number to fill that gap. Once you reach a round number like 40, the remaining addition is simple. This is different from rounding, which approximates; making tens is exact. It is also different from breaking apart, which decomposes both numbers fully by place value.
Question 2 Multiple Choice
A student says mental math is harder than written addition because you might 'lose track of numbers in your head.' What does this misunderstand?
ANothing — mental math is always harder and less reliable than written column addition
BMental math strategies are designed to simplify the problem first — making tens, for instance, turns a hard problem into two easy ones, reducing what you need to hold in mind
CMental math is only appropriate for adding single-digit numbers
DWritten addition is error-free, so the student is correct to prefer it
Mental math strategies do not ask you to hold a hard problem in your head — they transform the problem into a simpler one before you compute. Making tens replaces one difficult step with two trivial steps: add to reach a round number, then add the rest. The purpose of the strategy is to reduce cognitive load, not increase it.
Question 3 True / False
The 'making tens' strategy works by splitting one addend to create a round multiple of ten, which makes the remaining addition easier.
TTrue
FFalse
Answer: True
Correct — the strategy exploits the base-10 structure of our number system. Multiples of ten are easy to add to anything because you simply increase the tens digit. By bridging to a multiple of ten first, you reduce the second step to adding to a number that ends in zero, which is straightforward.
Question 4 True / False
When using the 'breaking apart' strategy, you should split both addends by place value before adding.
TTrue
FFalse
Answer: False
You can split just one number and leave the other intact. For example, to add 47 + 25, you might think '47 + 20 = 67, then 67 + 5 = 72' — only decomposing 25. Breaking apart both numbers is valid but not required. The strategy is flexible: decompose as much or as little as makes the calculation easier.
Question 5 Short Answer
Why is 'making tens' considered especially powerful as a mental math strategy? Explain what it does and why it simplifies the calculation.
Think about your answer, then reveal below.
Model answer: Making tens works by identifying how far one addend is from the nearest multiple of ten, then splitting the other addend to bridge that gap. For example, 28 + 15: 28 is 2 away from 30, so split 15 into 2 + 13 — add 2 to get 30, then add 13 to get 43. It is powerful because multiples of ten are the easiest numbers to add to in a base-10 system: adding 13 to 30 only requires changing the tens digit. The strategy converts one harder problem into two trivial ones.
Making tens works because addition is associative and commutative — you can split and rearrange the addends any way you like without changing the sum. Every time you make a ten, you are choosing a decomposition that puts a round number in the computation, which reduces the mental effort required to complete the problem.