Explain how making a factor 10 times the size affects the product | Maths

Starter quiz

Which of the numbers in the following equation is the product? 3 × 6 = 18
- '18' ✓
Match the times table expressions with the correct product.
- 5 × 3
  
  ⇔
  
  15 ✓
- 4 × 3
  
  ⇔
  
  12 ✓
- 3 × 3
  
  ⇔
  
  9 ✓
- 2 × 3
  
  ⇔
  
  6 ✓
Which of these times table facts is being shown by the array?
- 5 × 5 = 25
- 4 × 5 = 20 ✓
- 3 × 5 = 15
- 4 × 3 = 12
Match the expressions showing commutativity.
- 5 × 4
  
  ⇔
  
  4 × 5 ✓
- 4 × 7
  
  ⇔
  
  7 × 4 ✓
- 8 × 2
  
  ⇔
  
  2 × 8 ✓
- 7 × 3
  
  ⇔
  
  3 × 7 ✓
Tick the expressions that this array is showing.
- 5 × 4
- 3 × 5
- 5 x 3
- 4 × 3 ✓
- 3 × 4 ✓
True or false? To multiply a whole number by 10, place a zero after the final digit of that number.
- True ✓
- False

Exit quiz

True or false? If one factor is made 10 times the size the product will be 10 times the size.
- True ✓
- False
Match the equations to the related multiplications with a factor 10 times the size.
- 5 × 9 = 45
  
  ⇔
  
  5 × 90 = 450 ✓
- 4 × 5 = 20
  
  ⇔
  
  40 × 5 = 200 ✓
- 3 × 5 = 15
  
  ⇔
  
  3 × 50 = 150 ✓
- 4 × 3 = 12
  
  ⇔
  
  4 × 30 = 120 ✓
Match the expressions with the same value.
- 7 × 50
  
  ⇔
  
  5 × 70 ✓
- 3 × 90
  
  ⇔
  
  9 × 30 ✓
- 12 × 50
  
  ⇔
  
  5 × 120 ✓
- 70 × 3
  
  ⇔
  
  30 × 7 ✓
5 × 50 = ______
- '250' ✓
60 × 9 = ______
- '540' ✓
In the art cupboard, plastic pots hold 40 paintbrushes each. There are 8 pots. How many paintbrushes are there in total? ______ paintbrushes.
- '320' ✓

Worksheet

Presentation

Video

Lesson Details

Key learning points

If one factor is made ten times the size, the product will be ten times the size.
One factor has been multiplied by 10 so the product is multiplied by 10
When multiplying two numbers, if either factor is made 10 times the size, the product will be 10 times the size.
6 multiplied by 30 is equal to 60 multiplied by 3 or 6 tens multiplied by 3

Common misconception

Place value counters don't have proportionality in the same way that Base 10 does which can make the concepts here more abstract.

Smaller multiplications can be used with Base 10 to model scaling to start off with. Try 2 × 1 or 3 × 1 scaling up to become 2 × 10 or 3 × 10 with Base 10 and then put this modelling side-by-side with place value counters to make the links.

Keywords

Factor - A factor is a number which exactly divides another whole number.
Product - A product is the result of two or more numbers multiplied together.