## Introduction

Numbers by Heart focuses on the following for the numbers 1–10:

- Perceptual subitizing
- Comparing quantities
- Correspondence and cardinality

The final deck in the set introduces addition within 5.

## Deck Visualizations

### Deck 1

This deck focuses on perceptual subitizing for the numbers 1–5. Students are shown one representation at the top of the card and then click the matching or corresponding representation at the bottom of the card. Representations used include dot arrangements, hands, and connecting cubes.

### Deck 2

This deck focuses on comparing the sizes of up to 10 persistent images of objects. Each card shows two different representations with the prompt “Which is more?” or “Which is less?” Students click the representation that is either more or less. Representations used include dot arrangements, hands, connecting cubes, and 10-frames.

### Deck 3

This deck introduces the concept of flashing representations and focuses on the numbers 1–6. This is the natural progression toward the subitization of numbers. When the card loads on the screen, the representation appears for 2 seconds. After disappearing, a “refresh” button appears that students can click to see the image again. The representation reappears for 2 seconds and then the button goes away. Students can only click the button once. Representations used include dot arrangements, hands, connecting cubes, and 5-frames.

### Deck 4

This deck focuses on learning the numerals for the numbers 1–10. Students see a persistent image at the top of the card and click the numeral at the bottom of the card. Representations used include dot arrangements, hands, connecting cubes, and 10-frames.

### Deck 5

This deck builds on Deck 3 by focusing on the numbers 1–10. This is the natural progression toward the subitization of numbers. When the card loads on the screen, the representation appears for 2 seconds. After disappearing, a “refresh” button appears that students can click to see the image again. The representation reappears for 2 seconds and then the button goes away. Students can only click the button once. Representations used include dot arrangements, hands, connecting cubes, and 10-frames.

### Deck 6

This deck has two separate types of cards: sums to 5 and missing addends to make 10. This deck formally introduces addition within 5 by explicitly introducing the addition symbol. Representations used include dot arrangements, hands, connecting cubes, 5-frames, and 10-frames.