Use Number Bonds and Friendly Numbers

Mental math means working with numbers in your head, sometimes with a quick sketch or note to keep track. A helpful starting point is knowing how numbers can be split and recombined. In this lesson, you will use number bonds and friendly numbers to make calculations easier without changing their value.

Break numbers into useful parts

A number bond shows how a number can be made from parts. For example, 10 can be split into 7 and 3, so 7 + 3 = 10. The same relationship helps with subtraction: if 10 – 7 = 3, then 10 – 3 = 7. Knowing these related facts helps you solve new problems faster.

Connect ones, tens, and hundreds

You can split two-digit numbers into tens and ones. The number 46 is 40 + 6. The number 32 is 30 + 2. If you combine the tens first, 40 + 30 = 70; then combine the ones, 6 + 2 = 8. So 46 + 32 = 78. This is called partitioning: breaking a number into place-value parts.

Try making bonds to 10 and 100. If you know 8 needs 2 to make 10, you can use that fact when adding or subtracting around a ten. If you know 64 needs 36 to make 100, you can use it to check a sum such as 64 + 36.

Use friendly numbers

A friendly number is a nearby number that is easy to calculate with, such as 10, 20, 50, or 100. For 39 + 24, you might move 1 from 24 to 39: 39 becomes 40, and 24 becomes 23. The total stays the same, and 40 + 23 = 63. You can also think 39 + 24 as 40 + 24 – 1 = 63.

When splitting and moving parts, keep the total balanced. If you add one to one part, subtract one from the other part when the sum must stay the same. Picture two piles of counters: shifting one counter between piles does not change how many counters there are altogether.

Choose a strategy that makes sense

Explain the parts

There may be more than one useful way to break apart a number. For 58 + 17, you can add 10 to get 68, then add 7 to get 75. Or split 17 into 2 and 15: 58 + 2 = 60, then 60 + 15 = 75. Choose the path that is easiest for you and say what you changed.

Number bonds are not only for addition. To solve 52 – 8, notice that subtracting 2 from 52 reaches the friendly number 50. Subtract 2 first and then 6: 52 – 2 = 50, and 50 – 6 = 44. Breaking the 8 into 2 and 6 makes the step across the ten easier.

As you practise, you will remember more number relationships. If you are unsure, draw a quick part-part-whole sketch or use counters, then explain how the parts fit together.

Key takeaways

• Number bonds show how a number can be split into parts.
• Place value helps you combine tens and ones separately.
• Friendly numbers such as 10 or 100 can make mental steps easier.
• Keep totals equal when you shift or split parts.

Practice

Solve 58 + 26 using a friendly number or by splitting tens and ones. Explain your steps. Sample answer: Move 2 from 26 to 58 to make 60, leaving 24. Then 60 + 24 = 84. Another clear strategy is 50 + 20 + 8 + 6 = 84.