Apply commutative and associative laws to simplify multiplications
I can apply the commutative and associative laws to simplify multiplications of three or more numbers.
- Year 5
Apply commutative and associative laws to simplify multiplications
I can apply the commutative and associative laws to simplify multiplications of three or more numbers.
Lesson details
Key learning points
- Rearranging or grouping the factors in a multiplication can make it easier to solve.
Keywords
Efficient - Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.
Commutative - The commutative law states that you can write the values of a calculation in a different order without changing the solution; the result is the same. It applies to addition and multiplication.
Associative - 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 to addition and multiplication.
Common misconception
Pupils continue to work only from left to right in calculations, therefore making calculations more time-consuming.
Support pupils to find pairs of factors that are easy to multiply with. For example, finding factors that make a power of ten often make calculations easier as they can multiply by 10, 100 or 1000 for example at the end.
Equipment
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What is the product of 7 and 9?
Q2.What does the number 6 represent in the image below? 3 × 2 × 6
Q3.What is the missing number in the expression? 4 × × 2 Use the image to help.
Q4.Look at the equation. Which two numbers would you multiply together first? 2 × (7 × 4)
Q5.Which equations could you use to work out the total number of cubes?
Q6.Match the expressions that are equal.
