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Fraction Classroom · 2.0.0 · Teacher answers & responses

Area Product Lab

Select rows and columns, count their overlap, and connect fractional side lengths to square units.

Explore, draw, and explain

Use the online model or draw a diagram. Label the whole and show your reasoning.

M1. Set 3 rows with 2 selected and 4 columns with 3 selected. What fraction of the unit square is in both selections?

Answer: 1/2

Look for:

  • The square has 3 × 4 = 12 equal cells. The overlap covers 2 × 3 = 6 cells: 6/12 = 1/2.

Teacher response: If students are counting the union of the shaded rows and columns instead of the overlap. The complete rectangle represents one square unit. Only the double-shaded intersection represents the product; a selected row or column alone represents one factor.

M2. Set 4 rows with 3 selected and 2 columns with 1 selected. What is 3/4 of 1/2?

Answer: 3/8

Look for:

  • The overlap is three of eight equal cells. Taking three quarters of one half gives less than one half.

Teacher response: If students are assuming multiplication must make a number larger. The complete rectangle represents one square unit. Only the double-shaded intersection represents the product; a selected row or column alone represents one factor.

M3. Set 2 rows with 1 selected and 2 columns with 1 selected. The whole square has side length 1 meter. What is the overlap area in square meters?

Answer: 1/4

Look for:

  • The overlap has side lengths 1/2 m and 1/2 m. Its area is 1/4 square meter, not the sum of its side lengths.

Teacher response: If students are adding side lengths to calculate area. The complete rectangle represents one square unit. Only the double-shaded intersection represents the product; a selected row or column alone represents one factor.

Teaching notes