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3rd Grade Math Lesson

The Mosaic Code: Cracking Patterns on the Multiplication Grid

Shared by A STEM Educator

3rd GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.3.OA.B.5, CCSS.MATH.CONTENT.3.OA.D.9, CCSS.MATH.CONTENT.3.OA.C.750 min
Learning Objective

Students will identify and explain arithmetic patterns on a multiplication table (even/odd products, perfect square diagonal, row relationships) and connect those patterns to the Commutative and Distributive Properties.

Lesson Overview

Students act as 'Mosaic Restorers' uncovering hidden arithmetic patterns on a 10×10 multiplication chart — exploring even/odd parity rules, grid symmetry from the Commutative Property, and row-addition relationships from the Distributive Property — building from shading simple products to predicting and restoring missing tiles on a 'broken' chart.

Materials

  • Vertical whiteboards or large chart paper (one per group)
  • Dry-erase markers (one per group — passed between members)
  • Printed 10×10 multiplication chart reference (one per group, for Tasks 3–5)
  • Colored markers or highlighters (2 colors per group)
  • Exit slip half-sheets (printed)
  • Random grouping cards

Scaffolded Task Progression

1Task 1
Slice 1 — Parity Sleuths

Here is a section of the mosaic grid (rows –, columns –).

On your whiteboard, draw this grid and fill in ALL products.

Then: shade every even product one color and every odd product a different color.

What pattern do you see? Write a rule: _'A product is odd only when...'_
×12345
1
2
3
4
5
2Task 2
Slice 2 — Prove It With Groups

Your team says: *'Even × Anything = Even.'*

But WHY? A skeptical restorer on another team says: *'That's just a coincidence for small numbers.'*

On your whiteboard, draw a group model (circles with dots inside) to prove that must be even — without just saying 'because is even.'

Then use the same reasoning to explain why must be odd.

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