Symmetric Problem Situations:
Area/Array and Combinations

Explore the summary category of Symmetric problem situations, including grade level content for students in grades 4-8.

• Problem Situation Guide

• Mathematizing Story Map (Asymmetric x/÷ situations)

• Symmetric Multiplication/Division Problem Situations (Powerpoint slides)

• Symmetric Multiplication/Division Problem Situations (Google slides)

Symmetric problem situations are the kinds of problems students learn when they explore measurement and when they use arrays to organize their multiplication.

Rows & columns.

Length and width.

Choice #1 and choice #2.

The product of a symmetric problem will be a different unit than the two factors that created it.

Cells (in an array)

Area

Outcome (sample space)

Students may be challenged by the Symmetric problem situation because there are generally few clues in the problem situation to hint at a solution strategy. Students have to rely on the inverse relationship of multiplication and division to build an equation to solve. Help students by asking them to generalize their strategies while working with whole numbers.

The Mathematizing Story Map helps students visually map the relationship in the problem situation on the grid. Then they rely on reasoning strategies that they developed while doing whole number operations.