# Multiplication by Heart

## Introduction

Multiplication by Heart focuses on multiplication facts through 12 × 12. Representations used include dot arrangements, area models, and prime factor circles.

## Deck Visualizations

### Deck 1

Deck 1 uses dot representations and includes all multiplication facts from 1 × 1 through 5 × 5.

### Deck 2

Deck 2 uses rectangular arrays and includes all multiplication facts from 1 × 1 through 10 × 10.

### Deck 3

Deck 3 uses prime factor circles and includes 37 assorted facts. See below for the complete list. Prime Factor Circles, from the board game Prime Climb from Math for Love, are also available as virtual manipulatives on Polypad.

### Deck 4

Deck 4 also uses rectangular arrays and includes all multiplication facts for 11 and 12.

## Facts in Each Deck

### Deck 1

1 × 1, 1 × 2, 1 × 3, 1 × 4, 1 × 5

2 × 1, 2 × 2, 2 × 3, 2 × 4, 2 × 5

3 × 1, 3 × 2, 3 × 3, 3 × 4, 3 × 5

4 × 1, 4 × 2, 4 × 3, 4 × 4, 4 × 5

5 × 1, 5 × 2, 5 × 3, 5 × 4, 5 × 5

### Deck 2

1 × 1, 1 × 2, 1 × 3, 1 × 4, 1 × 5, 1 × 6, 1 × 7, 1 × 8, 1 × 9, 1 × 10

2 × 1, 2 × 2, 2 × 3, 2 × 4, 2 × 5, 2 × 6, 2 × 7, 2 × 8, 2 × 9, 2 × 10

3 × 1, 3 × 2, 3 × 3, 3 × 4, 3 × 5, 3 × 6, 3 × 7, 3 × 8, 3 × 9, 3 × 10

4 × 1, 4 × 2, 4 × 3, 4 × 4, 4 × 5, 4 × 6, 4 × 7, 4 × 8, 4 × 9, 4 × 10

5 × 1, 5 × 2, 5 × 3, 5 × 4, 5 × 5, 5 × 6, 5 × 7, 5 × 8, 5 × 9, 5 × 10

6 × 1, 6 × 2, 6 × 3, 6 × 4, 6 × 5, 6 × 6, 6 × 7, 6 × 8, 6 × 9, 6 × 10

7 × 1, 7 × 2, 7 × 3, 7 × 4, 7 × 5, 7 × 6, 7 × 7, 7 × 8, 7 × 9, 7 × 10

8 × 1, 8 × 2, 8 × 3, 8 × 4, 8 × 5, 8 × 6, 8 × 7, 8 × 8, 8 × 9, 8 × 10

9 × 1, 9 × 2, 9 × 3, 9 × 4, 9 × 5, 9 × 6, 9 × 7, 9 × 8, 9 × 9, 9 × 10

10 × 1, 10 × 2, 10 × 3, 10 × 4, 10 × 5, 10 × 6, 10 × 7, 10 × 8, 10 × 9, 10 × 10

### Deck 3

2 × 2, 2 × 3, 2 × 4, 2 × 5, 2 × 7

3 × 3, 3 × 4, 3 × 5, 3 × 6, 3 × 7, 3 × 9

4 × 4, 4 × 5, 4 × 6, 4 × 7, 4 × 8

5 × 5, 5 × 6, 5 × 7, 5 × 8, 5 × 9, 5 × 10

6 × 6, 6 × 7, 6 × 8, 6 × 9, 6 × 10

7 × 7, 7 × 8, 7 × 9, 7 × 10

8 × 8, 8 × 9, 8 × 10

9 × 9, 9 × 10

10 × 10

### Deck 4

1 × 11, 2 × 11, 3 × 11, 4 × 11, 5 × 11, 6 × 11, 7 × 11, 8 × 11, 9 × 11, 10 × 11, 11 × 11

11 × 1, 11 × 2, 11 × 3, 11 × 4, 11 × 5, 11 × 6, 11 × 7, 11 × 8, 11 × 9, 11 × 10

1 × 12, 2 × 12, 3 × 12, 4 × 12, 5 × 12, 6 × 12, 7 × 12, 8 × 12, 9 × 12, 10 × 12, 11 × 12, 12 × 12

12 × 1, 12 × 2, 12 × 3, 12 × 4, 12 × 5, 12 × 6, 12 × 7, 12 × 8, 12 × 9, 12 × 10

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