Checking and securing understanding of multiples of 10 | Maths

Starter quiz

When a number is multiplied by itself multiple times, it can be written more simply in __________ form.
- exponential ✓
- fractional
- irregular
- regular
Fill in the missing exponent of $8\times8\times8\times8\times8 = 8^\square$
- $2$
- $3$
- $4$
- $5$ ✓
- $8$
Match each missing exponent with the correct statement.
- $7$
  
  ⇔
  
  $8\times8\times8\times8\times8\times8\times8 = 8^\square$ ✓
- $8$
  
  ⇔
  
  $4\times4\times4\times4\times4\times4\times4\times4= 4^\square$ ✓
- $5$
  
  ⇔
  
  $5\times5\times5\times5\times5= 5^\square$ ✓
- $2$
  
  ⇔
  
  $100 = 10^\square$ ✓
- $4$
  
  ⇔
  
  $10000 = 10^\square$ ✓
- $1$
  
  ⇔
  
  $10 = 10^\square$ ✓
Which of the following equate to 240?
- 24 × 10 ✓
- 8 × 3 × 10 ✓
- 3 × 4 × 2 × 10 ✓
- 3 × 4 × 20 × 10
- 6 × 2 × 20 ✓
Match each number written in exponent form with its value.
- $10^4$
  
  ⇔
  
  $10 000$ ✓
- $10^2$
  
  ⇔
  
  $100$ ✓
- ${1} \over {10^2}$
  
  ⇔
  
  $0.01$ ✓
- $10^0$
  
  ⇔
  
  $1$ ✓
- $10^6$
  
  ⇔
  
  $1 000 000$ ✓
- ${1} \over {10^3}$
  
  ⇔
  
  $0.001$ ✓
Without a calculator, work out 3.4 × 1.5.
- '5.1' ✓

Exit quiz

Using the Gattegno chart or otherwise, work out which of the following calculations equate to 24.
- 3 × 8 ✓
- 30 × 0.8 ✓
- 4 × 6 ✓
- 0.4 × 60 ✓
- 4 × 60
Using the Gattegno chart or otherwise, match each calculation to its correct answer.
- 2 × 3 = 0.2 × 30 = 0.3 × 20
  
  ⇔
  
  6 ✓
- 4 × 2 = 0.4 × 20 = 0.2 × 40
  
  ⇔
  
  8 ✓
- 0.7 × 20 = 0.2 × 70 = 7 × 2
  
  ⇔
  
  14 ✓
- 0.3 × 30 = 3 × 3 = 0.03 × 300
  
  ⇔
  
  9 ✓
Using the associative law to partition 4000 and 2000 into powers of 10, find the calculations that are equivalent to 4000 × 2000.
- $4 \times 2 \times 1000 \times 1000$ ✓
- $8\times 10^6$ ✓
- $4\times2\times 100\times 100$
- $4\times2\times 10000\times 1000$
- $4\times10000\times2\times1000$
Which of the following calculations are equivalent to $5000\times5000$ ?
- $5\times1000\times5\times1000$ ✓
- $25\times 10^6$ ✓
- $2.5\times 10^7$ ✓
- $2.5\times 10^6$
- $25\times 10^7$
Which of the following calculations are equivalent to $6.5\times2.4$ ?
- $65\times24\times\frac{1}{100}$ ✓
- $\frac{6.5\times2.4}{100}$
- $65\times24\times\frac{1}{10^2}$ ✓
- $\frac{65\times24}{100}$ ✓
- $\frac{6.5\times2.4}{10^2}$
Which of the following calculations are equivalent to $4.5\times0.03$ ?
- $\frac{45\times3}{10^2}$
- $\frac{45\times3}{1000}$ ✓
- $\frac{45\times3}{10000}$
- $\frac{45\times3}{10^3}$ ✓
- $\frac{135}{10^3}$ ✓

Worksheet

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Lesson Details

Key learning points

Factorising multiples of 10 can scale the calculation to easier values.
It is important to consider place value so answers are scaled back correctly when multiplying.
Equivalent fractions can be used to simplify division.

Common misconception

There are many ways to multiply decimals or large numbers. With decimals, some pupils choose to multiply decimals using the column method and incorrectly use a decimal point when calculating answers.

When multiplying decimals, converting the calculation using integers and powers of 10 makes the calculation easier to work with.

Keywords

Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.