Questions: Composing and Decomposing Two-Digit Numbers
5 questions to test your understanding
Score: 0 / 5
Question 1 Multiple Choice
Which of the following correctly shows 63 broken into tens and ones?
A60 tens and 3 ones
B6 tens and 3 ones
C6 tens and 30 ones
D63 tens and 0 ones
The digit 6 in 63 is in the tens place, meaning 6 tens (which equals 60). The digit 3 is in the ones place, meaning 3 ones. So 63 = 6 tens + 3 ones = 60 + 3. Option A confuses the digit with the number of tens — the digit 6 means 6 tens, not 60 tens.
Question 2 Multiple Choice
A student wants to add 32 + 25 by thinking about tens and ones separately. What should she do first?
ACount up from 32 to 57 one number at a time
BDecompose: 32 = 30 + 2 and 25 = 20 + 5, then add tens together and ones together
CGuess an answer close to 50
DMemorize that 32 + 25 = 57
Decomposing both numbers lets you add in parts: 30 + 20 = 50 (tens), and 2 + 5 = 7 (ones), so the total is 57. This is the power of decomposition — it turns one complicated addition into two easy ones. Counting one at a time works but is slow and error-prone.
Question 3 True / False
The number 40 + 7 is the same as the number 47.
TTrue
FFalse
Answer: True
40 + 7 = 47. This is exactly what decomposing means — breaking the number into its tens and ones parts. 40 is 4 tens, and 7 is 7 ones. Putting them together gives 47. The number hasn't changed; we just wrote it in a different form.
Question 4 True / False
Decomposing a number into tens and ones changes its value.
TTrue
FFalse
Answer: False
Decomposing only changes the form — how the number is written or thought about — not its value. 47 and '4 tens + 7 ones' and '40 + 7' all represent exactly the same amount. This flexibility of representation is the point: you can switch between forms to make calculation easier without changing what the number means.
Question 5 Short Answer
How does breaking apart 24 and 13 into tens and ones make it easier to add them together?
Think about your answer, then reveal below.
Model answer: You break 24 into 20 + 4 and 13 into 10 + 3. Then add the tens: 20 + 10 = 30. Add the ones: 4 + 3 = 7. Put them together: 37. Instead of one harder problem, you solve two easy ones.
This is the core payoff of place-value decomposition. Students who understand why it works can apply the strategy flexibly; students who only memorize a procedure may get lost when the numbers change slightly.