Take a part. See the product.

SparkClass

Shade an overlap, then resize an amount. Two ways to make multiplication visible.

CCSS 5.NF.B.4a–b · 5.NF.B.5
Area Model · Unit Square
8 / 15 cells overlap
Area model of two thirds times four fifths A unit square with 3 columns and 5 rows. Two thirds of the width and four fifths of the height overlap in exactly 8 of 15 cells.
01

The overlap is exactly 8 of 15 cells. So 2/3 × 4/5 = 8/15.

Two shadings, one overlap
First Factor · Width2/32 of 3 columns
×
Second Factor · Height4/54 of 5 rows
=
Overlap · ac / bd8/158 of 15 cells

Teacher notes · two meanings of product

Use the controls to slow down the meaning of multiplication before asking students to use an algorithm.

1

Area: name the whole and the parts

Start at step 0. Ask: “How many columns and rows partition the unit square?” Replay the steps: first shade a/b of the width, then take c/d of the height. The two translucent shadings overlap in exactly a × c of the b × d equal cells.

2

Keep the raw count visible

The overlap readout keeps ac/bd visible even when the product can be simplified. For example, 2/4 × 3/6 gives 6/24, which is also 1/4. Ask students to explain why both fractions name the same area.

3

Scaling: compare before calculating

Try 8 × 3/4, 8 × 1, and 8 × 5/4 in order. Before revealing each result, ask whether the new amount will be smaller, equal, or greater. Both bars always use the same unit scale; neither bar is resized independently to fit.

4

Interrupt the “multiplication makes bigger” idea

Require a factor-to-1 comparison before any arithmetic. A positive amount multiplied by a factor less than 1 gets smaller; multiplied by 1 it stays equal; multiplied by a factor greater than 1 it gets greater.

CCSS alignment: 5.NF.B.4a–b — interpret a fraction product as part of a partition and connect products to rectangular area. 5.NF.B.5 — interpret multiplication as scaling, compare the size of a product with the size of one factor, and explain the effects of factors less than, equal to, or greater than 1.