Number Bond: An Essential Strategy of Singapore Math
Number bonds show how numbers are split or combined. An essential strategy of Singapore maths, number bonds reflect the ‘part-part-whole’ relationship of numbers.
By Gbenga Ayanfe
WHAT IS A NUMBER BOND?
Number bonds let students split numbers in useful ways. They show how numbers join together, and how they break down into component parts. When used in year 1, number bonds forge the number sense needed for early primary students to move to addition and subtraction. As students progress, number bonds become an essential mental problem solving strategy.
HOW DO NUMBER BONDS WORK?
Number bonds are represented by circles connected by lines. The ‘whole’ is written in the first circle, while the ‘parts’ are in the adjoining circles.
HOW TO TEACH NUMBER BONDS?
Children are usually introduced to number bonds through the concrete, pictorial, and abstract approach. Here’s just one way to introduce and teach number bonds.
1. THE CONCRETE STEP
Children start out by counting familiar real-world objects that they can interact with. They then use counters to represent the real-world objects. From here, they progress to grouping counters into two groups.
By putting five counters into two groups, children learn the different ways that five can be made. For example, 3 and 2 as illustrated below. With further exploration, children work out other ways to break numbers into two groups.
2. THE PICTORIAL STEP
Now that they understand the concept with hands-on objects and experience, children progress to writing number bonds in workbooks or on whiteboards. Early number bond explorations might simply reflect the two groups of counters that they created during the concrete step, along with other combinations.
3. THE ABSTRACT STEP
With the concrete and pictorial steps done and dusted, children progress to representing abstract problems using mathematical notation (for example, 3 + 2 = 5).
TAKING THE CONCEPT A STEP FURTHER
Number bonds also develop problem solving strategies such as ‘making ten’ with ten frames, multilink or unifix cubes.
By mastering number bonds early on, pupils build the foundations needed for subsequent learning and are better equipped to develop mental strategies and mathematical fluency. By building a strong number sense, pupils can decide what action to take when trying to solve problems in their head.
This example shows how a pupil would develop their number sense, or mathematical fluency, by using number bonds to perform a mental calculation.
Ten is the most important number in our decimal (base ten) number system, so it is vital that our children learn to recognize it in any disguise. When the student knows the bonds for ten automatically, we move on to 20, then 100, then any number we desire.
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Don’t “Drill.” Play Games!
Here are a few number bond games to enjoy with your children:
- Throw two dice and tell how many more you would need to make 10. (On the rare throws of 11 or 12, the answer is a negative number.)
- Throw 3 dice and tell how many more it takes to make 20.
- One player names any number 0-100, and the other tells how many more it takes to make 100.
- You could also play the last game with math cards[take out the jokers and face cards, leaving just ace (1) through 10], turning up one for the tens place and one for the ones, to make a two digit number.
- 10’s Concentration — Turn all the math cards face down on the table. On her turn, each player turns up two cards. If they add up to 10, she gets to keep them and try again. If one of the cards is a 10, she gets to keep it and turn up another card. Whoever takes the most cards, wins.
- Use Number Bond App! –Check My Number Bond App!