Explain why the product stays the same when one factor is doubled and the other is halved
Lesson details
Learning outcome
I can explain why the product stays the same when one factor is doubled and the other is halved.
Key learning points
- When one factor is doubled and the other is halved, the product remains the same.
- Arrays can be rearranged to represent the product staying the same when one factor is doubled and the other halved.
- Doubling one factor and halving the other maintains equivalence.
Keywords
Equivalent - Equivalent means having the same value.
Factor - A factor is a number which exactly divides another whole number.
Product - The product is the result of two or more numbers multiplied together.
Common misconception
Pupils may double or halve both factors, instead of doubling one and halving the other.
Spend time exploring arrays and the area models (from Cycle B of the lesson). Model these misconceptions, showing why they are incorrect (e.g. show how 4 x 8 cannot be equivalent to 8 x 16).
Teacher tip
To ensure that pupils understand this, spend time exploring this concept using numbers facts that they are familiar with (e.g. numbers within the times tables that they already know). Use arrays and area models to show equivalence, getting pupils to manipulate these.
Licence
except where otherwise stated. See Oak's terms & conditions (Collection 2).Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What multiplication fact is represented by the array?
Q2.What is 7 × 6 =
Q3.What is double 27?
Q4.What is half of 70?
Q5.What is the missing number in this equation? 6 × = 72
Q6.What is the missing number in this equation? 11 × = 220
Assessment exit quiz
6 Questions
Q1.What is the missing factor in the equation in this diagram?
Q2.What is the missing number in this equation? 8 × 10 = × 20
Q3.What is the missing number in this equation? 6 × 13 = 26 ×
Q4. Which expressions are equal to 34 × 24?
Q5.Use scaling to help you find the product: 5 × 46 =
Q6.Use scaling to help you find the product: 50 × 36 =
To help you plan your 6 maths lesson on: Explain why the product stays the same when one factor is doubled and the other is halved, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 6 maths lesson on: Explain why the product stays the same when one factor is doubled and the other is halved, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 2 maths lessons from the Using equivalence to calculate unit, dive into the full primary maths curriculum, or learn more about lesson planning.