A student adding 48 + 35 thinks: '48 needs 2 more to reach 50, so I'll take 2 from 35, leaving 33, and compute 50 + 33 = 83.' What strategy is she using?
AThe standard regrouping algorithm
BCounting on from the larger number
CMaking tens by decomposing an addend
DUsing a hundred chart
The student is using the making tens strategy. She splits 35 into 2 + 33, uses the 2 to bring 48 up to the friendly number 50, then completes the addition as 50 + 33. This works because addition is associative: reorganizing how the parts are grouped doesn't change the total. The strategy is especially powerful because multiples of ten are easy to add to any number.
Question 2 Multiple Choice
Which pair of numbers is BEST suited for the 'counting on' strategy?
A37 + 48
B50 + 30
C64 + 7
D28 + 35
Counting on works best when one addend is small. For 64 + 7, you start at 64 and count up just 7 steps: 65, 66, 67, 68, 69, 70, 71. For large addends like 37 + 48, counting on 48 steps is slow and error-prone — decomposing or the standard algorithm is better. For 50 + 30, mental math (add the tens) is instant. Fluency means choosing the right strategy for the numbers at hand.
Question 3 True / False
When using the making tens strategy on 47 + 36, taking 3 from 36 to make 50 + 33 gives the correct total of 83.
TTrue
FFalse
Answer: True
Taking 3 from 36 brings 47 up to 50, leaving 33 from the 36. Then 50 + 33 = 83. This works because of the associative property: (47 + 3) + 33 = 50 + 33 = 83. No quantity was added or removed — only the grouping changed. The total 47 + 36 = 83 is preserved.
Question 4 True / False
Fluency in addition within 100 means a student can quickly and accurately execute the standard regrouping algorithm for any problem.
TTrue
FFalse
Answer: False
Fluency means flexible, efficient computation — choosing the best strategy for a given pair of numbers. A student who only knows the standard algorithm is not truly fluent. For 50 + 30, mental math is far faster; for 99 + 1, counting on is instant. Fluency includes knowing when NOT to use the standard algorithm. The goal is owning number relationships well enough to navigate adaptively across multiple strategies.
Question 5 Short Answer
Why is the making tens strategy mathematically valid? What property of arithmetic allows you to reorganize addends without changing the total?
Think about your answer, then reveal below.
Model answer: Because addition is associative: you can regroup and reorder addends in any way and the total stays the same. Taking part of one addend and giving it to the other reorganizes the pieces without adding or removing any quantity. The total depends only on what is being combined, not on how it is grouped.
The making tens strategy is not a trick — it is a consequence of the associative property. (a + b) = ((a − x) + (b + x)) for any x, because the two changes cancel out. Students who understand this recognize they are not 'cheating' or changing the problem; they are using arithmetic's structure to create friendlier numbers. This understanding separates strategy comprehension from rote procedure.