Year 3 Exam > Year 3 Notes > Year 3 Mathematics > Fact families - addition and subtraction bonds to 20
Fact families - addition and subtraction bonds to 20 | Year 3 Mathematics PDF Download
Fact Families and Number Sentences
- Fact families are created using three numbers. For example, the numbers 18, 3, and 15 form a fact family. Here, 18 is the whole, 15 represents the red counters, and 3 represents the yellow counters.
- When arranged in a number sentence, they create the addition 15 + 3 = 18. In this case, the whole comes at the end because the sentence is an addition.
- The two parts, 15 and 3, can be swapped, and the number sentence remains correct: 3 + 15 = 18.
- What about subtraction using the same numbers?
- The subtraction is 18 - 15 = 3. In subtraction, you cannot swap the numbers, so 15 - 18 = 3 does not make sense.
- Each fact family has 8 number sentences, all containing the same numbers.
Part whole models
A part-whole model is useful for solving basic calculations visually. It represents number sentences and aids in determining missing numbers within a fact family.
- Consider another fact family where there are 8 red counters and 7 yellow counters, resulting in the numbers 8, 7, and 15.
- Using a part-whole model effectively represents this fact family. Here, the parts are 8 and 7, and the whole number is 15.
- By covering any one of the three parts shown in the part-whole model, you can determine the missing part using the remaining numbers. In this case, the missing number is 15 because the sum of the two parts is 8 + 7 = 15.
- This method also applies when covering a different part. For instance, with the whole number known as 15 and one of the parts known as 7, the missing part can be found by subtracting: 15 - 7 = 8.
- Another effective way to represent this fact family is through a bar model. In this model, the whole number 15 is shown, with the two parts 8 and 7 fitting appropriately under the whole.
Solved Example
Example: Have a look at this part whole model.
The model shows that the numbers 20, 12 and 8 are part of a fact family.
The number 20 is made of two parts, 12 and 8.
The diagram can help you work out possible number sentences in the fact family.
12 + 8 = 20
8 + 12 = 20
20 - 8 = 12
20 - 12 = 8
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