## What are Number Bonds and Their Importance in Math Education?

### Definition and Concept of Number Bonds

Number bonds help students understand and break down numbers effectively. They show how numbers combine and separate. For example, in the number bond 4 + 6 = 10, 4 and 6 are the pairs of numbers that add up to 10. These fundamental math concepts help children quickly understand and visualize the relationships between numbers, improving their mental math skills and laying a strong foundation for more advanced mathematical operations.

### Benefits of Teaching Number Bonds

#### Building a Strong Foundation in Math

Number bonds are essential for building a strong math foundation. They help students see and understand how numbers connect, making addition and subtraction easier to learn. Mastering number bonds improves mental math skills and problem-solving abilities, preparing them for more advanced math concepts.

#### How Number Bonds Help Develop Number Sense

Number bonds help children understand and break down numbers, showing how they combine and split into parts. This concept is crucial for developing number sense, enabling children to perform mental calculations with confidence and laying a strong foundation for addition and subtraction.

## How to Teach Number Bonds effectively?

### Strategies for Introducing Number Bonds

One of the most effective strategies to introducing students to number bonds is the Concrete, Pictorial, Abstract (CPA) Approach. This method helps students build meaningful connections and think mathematically instead of rote memorization.

#### Concrete step

Students start with physical objects like counters, blocks, and shapes to explore and understand math concepts. They use math manipulatives, which can include items like base ten blocks and ten frames to represent real-world objects.

For example, by splitting four counters into two groups, children explore the different ways four can be made as illustrated below. With guided practice, students discover different groups to split numbers into smaller parts.

#### Pictorial step

In this step, students draw pictorial models or use tools like number bonds to visualize problems. Building upon the Concrete step, number bonds simply reflect the two circles of counters that they already create.

#### Abstract step

With the concrete and pictorial steps mastered, students advance to using simple arithmetic expressions, developing fluency in math facts. For example, 4 + 2 = 6

### Utilizing Number Bonds in Singapore Math Approach

Number bonds are a key strategy in the Singapore Math approach. They visually show how numbers can be split into parts and combined to form a whole, reinforcing the ‘part-part-whole’ concept. This method helps students develop strong number sense and mental math skills, making it easier to understand addition, subtraction, and more complex math concepts.

## Exploring Number Bonds to 10 and Beyond

### Understanding Bonds to 10 and Its Relevance

Here at Singapore Math Classes and Camps, we pride ourselves on helping learners understand, reorganize, and combine different concepts. Starting at the youngest ages, we pair our number bonds into “best friends”. Each number pair (best friend) that makes 10 is a best friend. For instance, 1 and 9 are best friends and so on.

The number bonds to 10 are:

- 1 + 9
- 2 + 8
- 3 + 7
- 4 + 6
- 5 + 5
- 6 + 4
- 7 + 3
- 8 + 2
- 9 + 1

### Progressing to Number Bonds to 20

Following the mastery based approach is clear. By building upon the foundation of previously learned concepts, the number bonds to 10 pattern is clear to students. Simply add 10 to one side of the number bond pattern to progress to Number Bonds to 20. 1 + 9 = 10 → 1 + (10 + 9) = 20

The number bonds to 20 are:

- 1 + 19
- 2 + 18
- 3 + 17
- 4 + 16
- 5 + 15
- 6 + 14
- 7 + 13
- 8 + 12
- 9 + 11
- 10 + 10
- 11 + 9
- 12 + 8
- 13 + 7
- 14 + 6
- 15 + 5
- 16 + 4
- 17 + 3
- 18 + 2
- 19 + 1

### Using Number Bonds to Teach Addition and Subtraction

Number bonds are extremely helpful when learning basic arithmetic addition and subtraction. For example, we can break the number 20 into two parts. The first part is 2, and the second part is 18. By understanding simple equations like 2 + 8 = 10, students can easily solve problems like 20 = 2 + 18. This method simplifies addition and builds a strong foundation in arithmetic.