Problem solving using knowledge of the composition of powers of 10 | Maths

Starter quiz

Look at the bar model and complete the sentence. Each part has a value of ___

10

100

200

250 ✓

500
Look at the bar model and complete the sentence. Each part has a value of ___

1,000

2,000

2,500 ✓

5,000
Complete the sentence. ______ is one-tenth of 1,000

'100' ✓
Look at the bar model. Which equations can be formed from the bar model?

1,000 × 4 = ?

1,000 ÷ 4 = ? ✓

? × 4 = 1,000 ✓

? ÷ 4 = 1,000
Laura thinks of a number. She says, “One-tenth of my number is 200”. What number is Laura thinking of?

20

200

2,000 ✓

20,000

200,000
A and B represent different numbers on the number line. What is the difference between the two numbers?

'400' ✓

Exit quiz

Complete the sentence. If 250 is one-quarter of 1,000 then ______ must be one-quarter of 1,000 thousands.

'250,000' ✓
If 2,000 is a fifth of 10,000 and 20,000 is a fifth of 100,000 then ______ is one-fifth of 1,000,000

'200,000' ✓
A detached house sells for £1,000,000 and a terrace house sells for one-fifth times this amount. How much does the terrace house sell for? The terrace house sells for £______

'200,000' ✓
A detached house sells for £1,000,000 and a terrace house sells for one-fifth times this amount. How much more does the detached house sell for? The detached house is £______ more.

'800,000' ✓
A detached house sells for £1,000,000 This is one-tenth of what a castle sells for. How much does the castle sell for? The castle sells for £______

'10,000,000' ✓
A detached house sells for £1,000,000 This is one-tenth of what a castle sells for. How much more expensive is the castle? The castle is £______ more.

'9,000,000' ✓

Worksheet

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Lesson Details

Key learning points

An understanding of the composition of the powers of 10 supports us when we solve problems.
If we know one-quarter of 1,000 is 250, we know one-quarter of 1,000 thousands (1,000,000) is 250 thousands (250,000)
Just as with smaller numbers, word problems can be represented visually as a bar model.
A bar model supports us to form an equation to then solve.

Common misconception

Children may misinterpret a word problem especially where they are insecure on the key words such as 'difference' or 'how much more'.

Teacher should model own thoughts when problem solving and encourage children to represent the word problems in a bar model. Construct bar models alongside a retelling of the problem so children can see where the mathematics is found.

Keywords

Million - One million is composed of 1,000 thousands. One million is written as a one followed by six zeros.