Factors are whole numbers which exactly divide another whole number.

The commutative law states that you can write the values of a calculation in a different order without changing the calculation; the result is the same. It applies for addition and multiplication.

The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.

Use properties of numbers and the commutative and associative laws to simplify calculations

Maths

Explain how to identify common factors between two or more numbers

Explain how to identify a common multiple of two or more numbers

Use knowledge of properties of number to solve problems

Explain how to use the factor pairs of 100 to solve calculations efficiently

 In this unit pupils will explain how to identify a multiple or common multiple to solve problems in a range of contexts. In the future unit pupils will explain why the product stays the same when one factor is doubled and the other is halved and use knowledge of equivalence when scaling factors to solve problems.

In the prior unit pupils understood and used the concept of factorisation, explaining what a factor is and how to use arrays and multiplication/division facts to find them. They identified prime numbers, square numbers and composite numbers. In this unit pupils will explain how to identify common factors and multiples and use this with knowledge commutative and associative laws to solve problems.

In this unit pupils will explain how to identify common factors and multiples and use this knowledge of properties of number along with knowledge of the commutative and associative laws to solve problems in a range of contexts.

Use common factors and multiples to solve calculations efficiently

Which factors would be best to associate together to calculate efficiently?     4 × 5 × 7 = ___

Tick the three factor equations that would be equal to this two factor equation. 15 × 20 = ___ × ___ × ___

Tick the numbers that could be multiplied by a one digit number and would be equal to a multiple of 10.

Match the 4 factor equations that are equal to the two factor equations.

Find the product of this equation. 32 × 15 = {{ }}

You must start multiplying with the first factor in an equation.

You can reorder the factors in an equation and the product will remain the same.

You can reorder the factors in an equation but the product will change.

You do not need to multiply these factors.

If a pair of brackets are placed around two factors such as in 2 × (4 × 7) = , this means:

Match the equation to the factor pairs that would be best used to help solve the calculations.

Find the product of this equation. 50 × 54 = {{ }}

Use properties of numbers and the commutative and associative laws to simplify calculations

Lesson outcome