The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Checking and securing understanding of the distributive law

Maths

Pupils use their understanding of place value and fluency with decimals from this unit in order to extend this understanding to fractions.  In the future unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required.

The prior unit on factors, multiples, squares and cubes helped pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used here to explore multiplying and dividing with decimals.

Arithmetic procedures with integers and decimals

The __________ says that multiplying a sum is the same as multiplying each addend and summing the result.

Match each law with an example of the law.

Without using a calculator, use the distributive law to work out: $$1.3\times7.2 + 1.3\times2.8$$ = {{ }}

Without using a calculator, use the distributive law to work out:  $$50\times99$$ = {{ }}

Work out the missing number:  $$22 \times 0.3 + 22 \times $$ {{ }} $$= 22$$

Work out the missing number:  $$4.8 \times 0.6 + 4.8 \times 1.2 − 4.8 \times$$ {{ }} $$= 4.8$$

An operation is __________ if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.

Select all the examples of the associative law.

Use the commutative law you can rewrite 10 + 4 as {{ }}.

Match each calculation to an equivalent commutative calculation.

He is correct as both answers do equal 1.

He is incorrect as the commutative law would also give 4 ÷ 3 ÷ 12 which isn't 1 

He is correct as he has repositioned all the numbers.

Andeep says, "Division is commutative because 12 ÷ 4 ÷ 3 = 1 and is the same as 12 ÷ 3 ÷ 4 = 1." Select the correct statement.

The sum of the first 10 integers is {{ }}. (Do not use a calculator.)

This lesson will be removed by end of Summer Term 2025.

Checking and securing understanding of the distributive law

Lesson outcome

This lesson will be removed by end of Summer Term 2025.