Part-part-whole reasoning represents a quantity within 100 as a whole composed of two parts, allowing a situation to be modeled with a bar model or related addition and subtraction equations, with the unknown in any position (a + b = □, a + □ = c, or □ + b = c). The learner identifies whether the unknown is the whole or a part and uses the inverse relationship between operations, rather than treating subtraction only as taking away; larger numbers, multiple-part compositions, and generalized algebraic treatment are outside this scope.
A part-part-whole problem has:
First, find out whether the missing number is a part or the whole.
Example:
A library has 27 books. 12 books are picture books. The rest are storybooks. How many storybooks are there?
The whole is 27 books. One part is 12 picture books. The other part is unknown.
You can show this with a bar model:
Write the addition equation:
The unknown is a part, so use subtraction to find it. Subtraction is the inverse, or opposite, of addition:
So, storybooks are in the library.
Check your answer with addition:
The parts, 12 and 15, make the whole, 27.
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