STEMEngine AI — Engineering Active Thinking
Community Lessons/3rd Grade Math
3rd Grade Math Lesson

The Fact Factory: Unlocking Multiplication & Division Superpowers with 2s, 5s, 10s, 0s, and 1s

Shared by A STEM Educator

3rd GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.3.OA.B.5, CCSS.MATH.CONTENT.3.OA.B.6, CCSS.MATH.CONTENT.3.OA.C.750 min
Learning Objective

Students will apply relational mental strategies (doubling, half-of-10s, place-value shift, Identity Property, Zero Property) to solve and explain multiplication and division facts for 2s, 5s, 10s, 0s, and 1s, and connect each multiplication equation to its inverse division fact family.

Lesson Overview

Students move through a Building Thinking Classrooms sequence at vertical non-permanent surfaces, discovering relational mental strategies — doubling, place-value shifts, half-of-10s, fact families, and the Zero and Identity Properties — by solving progressively complex thin-sliced tasks in random groups of 3.

Materials

  • Vertical whiteboards or large chart paper taped to walls
  • Dry-erase markers (1 per group — this is intentional for BTC flow)
  • Erasers or socks
  • Random grouping cards (playing cards, popsicle sticks, or a randomizer app)
  • Sticky notes for gallery walk
  • Printed or projected 'Fact Factory Mission Cards' (task prompts)
  • Printed Consolidation Note Sheets (Scaffolded Model)
  • Optional: tablets or projected screen for the interactive Desmos 10-to-5 Transformer tool

Scaffolded Task Progression

1Task 1
Fact Factory — Slice 1: The Doubling Engine (2s)

The Doubling Engine doubles every number that enters it.

1. Solve: Show your thinking using the equation
2. Solve: Show it as a double.
3. Now run it backward: and
4. Big Question: Why are all answers to even numbers? Write one sentence on your board.
2Task 2
Fact Factory — Slice 2: The Place-Value Shifter (10s) → Half-of-Ten Turbine (5s)

The Place-Value Shifter sends digits one place to the left.

Step A — Power up the 10s:
Solve and
Write: 'When I multiply by , the digit moves to the ___ place, so ___ tens = ___'

Step B — Cut it in half:
The Half-of-Ten Turbine splits every answer exactly in half to make .
Use your answer to find .
Use your answer to find .

Step C: Write the relationship as an equation: of ___

Unlock the full lesson

See all 6 scaffolded tasks, the full answer key, warm-up, exit slip, and a print-ready version — free to start.

Create a free account

Already have an account? Sign in

Make it your own

Like this lesson but want to tweak it?

Make an editable copy and adjust the tasks, warm-up, and answer key to fit your class — no need to start from scratch.

Generate a new lesson