Explain how making a factor 100 times the size affects the product | Maths

Starter quiz

Which of the numbers in the following equation are factors? 4 × 12 = 48
- 4 ✓
- 12 ✓
- 18
Match the times table expressions with the correct product.
- 5 × 7
  
  ⇔
  
  35 ✓
- 9 × 3
  
  ⇔
  
  27 ✓
- 8 × 3
  
  ⇔
  
  24 ✓
- 2 × 6
  
  ⇔
  
  12 ✓
Which of these times table facts is being shown by the array?
- 4 × 4 = 16
- 7 × 4 = 28 ✓
- 3 × 7 = 21
- 4 × 3 = 12
Match the expressions showing commutativity.
- 6 × 4
  
  ⇔
  
  4 × 6 ✓
- 9 × 7
  
  ⇔
  
  7 × 9 ✓
- 8 × 6
  
  ⇔
  
  6 × 8 ✓
- 2 × 3
  
  ⇔
  
  3 × 2 ✓
Tick the expressions that this array is showing.
- 5 × 6
- 3 × 8 ✓
- 2 × 5
- 7 × 3
- 8 × 3 ✓
True or false? To multiply a whole number by 100, place two zeros after the final digit of that number.
- True ✓
- False

Exit quiz

True or false? If one factor is made 100 times the size the product will be 100 times the size.
- True ✓
- False
Match the equations to the related multiplications with a factor 100 times the size.
- 6 × 9 = 54
  
  ⇔
  
  6 × 900 = 5,400 ✓
- 4 × 7 = 28
  
  ⇔
  
  400 × 7 = 2,800 ✓
- 8 × 5 = 40
  
  ⇔
  
  8 × 500 = 4,000 ✓
- 7 × 3 = 21
  
  ⇔
  
  7 × 300 = 2,100 ✓
Match the expressions with the same value.
- 9 × 300
  
  ⇔
  
  900 × 3 ✓
- 4 × 600
  
  ⇔
  
  400 × 6 ✓
- 12 × 700
  
  ⇔
  
  7 × 1,200 ✓
- 800 × 4
  
  ⇔
  
  400 × 8 ✓
5 × 600 = ______
- '3,000' ✓
800 × 7 = ______
- '5,600' ✓
4 classes each raise £700 for charity. How much have they raised altogether? £______
- '2,800' ✓

Worksheet

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Lesson Details

Key learning points

If one factor is made one hundred times the size, the product will be one hundred times the size.
One factor has been multiplied by 100 so the product is multiplied by 100
When multiplying two numbers, if either factor is made 100 times the size, the product will be 100 times the size.
6 multiplied by 300 is equal to 600 multiplied by 3 or 6 hundreds 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 × 100 or 3 × 100 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.