3rd Grade Math Lesson

The Array Chopper: Splitting Big Facts into Small, Known Facts

Shared by A STEM Educator

3rd GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.3.OA.B.5, CCSS.MATH.CONTENT.3.OA.C.750 min

Learning Objective

Students will apply the Distributive Property (decomposing a factor into known addends) and the Associative Property (doubling strategies) to derive multiplication facts for 3s, 4s, 6s, and 8s from known facts, and will identify and repair decomposition errors in broken array equations.

Lesson Overview

Students use vertical whiteboards in random groups to discover that every tricky multiplication fact (3s, 4s, 6s, 8s) can be derived from facts they already know (2s, 5s, 10s) by splitting — or 'chopping' — arrays using the Distributive and Associative Properties. The progression moves from concrete doubling strategies to symbolic decomposition and reverse-engineering broken equations.

Materials

Vertical whiteboards (VNPS) or large chart paper per group
Dry-erase markers (1 per group, passed between members)
Erasers or socks
Random group generator (cards, sticks, or app)
Printed or projected Array Chopper Desmos tool
Consolidation note sheets (Scaffolded Model, 1 per student)
Exit slip cards

Scaffolded Task Progression

1Task 1

Slice 1 — Double-Double for 4s

The factory needs

4 \times 6

power cells. Your team only has the

2

s table memorized.

Step A: What is

2 \times 6

?
Step B: Double your answer from Step A.
Step C: Write the full equation:

4 \times 6 = 2 \times (2 \times 6) = 2 \times

___

=

___

Draw the array on your whiteboard: show the

4 \times 6

grid, then draw a horizontal line splitting it into two

2 \times 6

halves.

2Task 2

Slice 2 — Build-On-From-2s for 3s

The factory needs

3 \times 7

power cells. You know

2 \times 7

by heart.

Step A: What is

2 \times 7

?
Step B: You need ONE more group of

7

. Add it on.
Step C: Write:

3 \times 7 = (2 \times 7) + (1 \times 7) =

___ + ___

=

___

On your whiteboard, draw the

3 \times 7

array. Draw a dotted line after row

2

. Label the top chunk and the bottom chunk.

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