This understanding involves interpreting a situation as a sequence of related whole-number quantities, selecting and combining addition, subtraction, multiplication, and division to represent the relationships, and preserving the meaning of units and any remainder. A solver can model the structure with an equation, expression, table, or bar model, determine the order of operations from the context rather than applying calculations mechanically, and check whether the result is reasonable. The scope is whole-number contexts, not operations involving fractions, decimals, negative numbers, or generalized algebraic variables.
A multi-step word problem describes several quantities that are connected. Solve it by identifying what happens first, choosing an operation for each step, and keeping track of the units.
Example:
A school buys boxes of pencils. Each box contains pencils. The school gives pencils to teachers. The remaining pencils are shared equally among classes. How many pencils does each class receive?
1. Find the total number of pencils.
There are groups of pencils, so multiply:
The school has pencils to begin with.
2. Find how many pencils remain.
The school gives away pencils, so subtract:
There are pencils left.
3. Share the remaining pencils equally.
Divide the remaining pencils among classes:
Each class receives pencils.
A matching expression is
Check:
If each of classes receives pencils, then
which matches the number of pencils remaining. The answer is reasonable because shared among equal groups is about in each group.
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