Decompose Numbers Using Number Bonds

Number Bonds

Can you picture spending several classroom periods on the number 5?  Specifically, breaking it down into parts, and putting it back together again?  Sounds like a lot of time, right?  But, spending this amount of classroom time to decompose numbers using number bonds,  allows students to gain a deeper, more flexible understanding of numbers.  You might be wondering what those periods would actually look like, how you’d keep your students engaged and learning for that amount of time.  In this blog, we will explore exactly that.

What are Number Bonds  

Simply put, number bonds are the different ways we can break apart numbers. Number bonds are all about the relationship between numbers and quantities. The relationships of parts to a whole. Building the foundation for all mathematical operations. Building mental images of number relationships. While it sounds like a simple concept, it can be difficult for students to learn.  So, it is important to dedicate time for them to learn the concept.

How to decompose numbers using number bonds

Use of color and representation helps to connect ideas.

Why Number Bonds

As Suzanne Chapin and Art Johnson mention in their book Math Matters book, “Research indicates that students instructed using a part-whole approach do significantly better with number concepts, problem solving, and place value than those students whose instruction focuses just on counting by ones. “

John Van De Walle emphasizes this critical skill in his book Teaching Student Centered Mathematics,  “The ability to think of a number in terms of parts is a major milestone in the development of number sense.  Of the 4 different types of relationships that children can and should develop with numbers (Spatial, One and Two More, One and Two Less, Anchors or Benchmarks of 5 and 10, Part-part-whole), part-whole ideas are easily the most important. “

By allowing students time to decompose numbers using number bonds, we are helping to build the 21st century skill of flexible thinking.  Students are building a deeper understanding of numbers, math concepts, math skills, while developing mental capacities.  This is a foundational skill that will continue to be built upon as they progress through grade levels.

How to Decompose Numbers Using Number Bonds in Your Classroom

Using the CPA approach (Concrete, Pictorial and Abstract) students connect dice, cards, cubes or random objects, while tapping into multiple parts of the brain- visually, analytically.  Once ideas are at an abstract level, playing number bond games such as the ones by Greg Tang develops fluency.  Children are building confidence when they figure out the sum of the parts or the parts of a whole. The benefit to the teacher is a feeling of excitement among students and a desire for bigger challenges and even more practice- like anything we are good at, right?!

Demonstrating the CPA approach.

Students demonstrate number bonds by using manipulatives first.

I have also found that white boards  fromThe Marker Board People are an excellent tool for the classroom. My good friend and colleague, renowned Singapore methods leader, Dr. Yeap Ban Har, demonstrates the concept of number models in a classroom setting using white boards in this model lesson .

Decompose numbers using number bonds

White boards are a great way to see student thinking and how to decompose using number bonds.

Have Fun While Building Little Math Whizzes!

We are reminded In Chapter 2c of the NCTM book, Develop Essential Understanding of Number & Numeration (Pre-K-Grade 2), about the importance of part-whole relationships and how it carries over into students’ understanding and development of different algorithms for computations.  When students decompose the whole based on the numbers in the given problem and are able to connect it to the standard algorithm,  we have developed students with number sense.

Decompose numbers using number bonds

First stage in renaming process.

By looking at different ways to decompose numbers using number bonds, we not only tap into the visual part of the brain, but we also build fluency and a foundation from which to build.   It’s easy. It’s fun. And t’s cheap. And it’s one of the best uses of classroom time. Start with drawing a single digit number on the board and ask students how many ways they can break it apart.  Ask if they notice any patterns.  PLAY with numbers. PLAY more with numbers.  And make it fun.

Decompose numbers using number bonds

Attaching meaning to a number bond.

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