Ben has 5 red blocks and some blue blocks. He has 11 blocks in all. In the part-part-whole model, which number is the WHOLE?
A5
BThe unknown number of blue blocks
C11
DAll of the numbers together
The whole is always the total — the complete group before it is split into parts. 11 is the whole because it represents all the blocks combined. 5 and the unknown number of blue blocks are the two parts. Knowing the whole (11) and one part (5) lets you find the missing part by subtracting: 11 − 5 = 6.
Question 2 Multiple Choice
A student sees the problem 8 − 3 = ? and says, 'This is subtraction, so I cannot use my part-part-whole model — that model is only for addition.' Is she correct?
AYes — the part-part-whole model only works for addition
BNo — the model works for both addition and subtraction because they share the same three-number relationship
CYes — subtraction always needs a different diagram
DNo — but only because the numbers in this problem are small
Addition and subtraction are the SAME part-part-whole relationship viewed from different directions. The numbers 3, 5, and 8 are connected: 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3. Addition finds the whole when you know both parts; subtraction finds a missing part when you know the whole and one part. The model applies to both operations — it is the relationship that matters, not the operation symbol.
Question 3 True / False
If you know the whole and one part in a part-part-whole relationship, you can always find the missing part.
TTrue
FFalse
Answer: True
Yes — the whole equals the sum of its parts, so if you know the whole and one part, subtracting gives the other part. For example: whole = 9, one part = 4, missing part = 9 − 4 = 5. This is exactly what subtraction does in the part-part-whole model.
Question 4 True / False
The part-part-whole model is mainly useful for addition problems.
TTrue
FFalse
Answer: False
This is the key misconception to avoid. The part-part-whole model applies equally to addition and subtraction. Addition uses the model to find the whole from two known parts (part + part = whole). Subtraction uses the same model to find a missing part when the whole and one part are known (whole − part = missing part). They are not separate operations — they are two ways of navigating the same three-number relationship.
Question 5 Short Answer
You have 7 apples. Some are red and some are green. You know 4 are red. Explain how the part-part-whole model helps you find how many are green.
Think about your answer, then reveal below.
Model answer: In the part-part-whole model, 7 is the whole, 4 (red apples) is one part, and the unknown green apples are the other part. Because the parts must add up to the whole, you subtract: 7 − 4 = 3 green apples.
The model makes the structure of the problem visible: whole = part + part. When the whole and one part are known, the missing part is found by subtraction. This is not a different kind of problem from addition — it is the same relationship, just asking for a different piece of information.