MathsNumber, algebra and geometry: connected foundations30 min★★ difficulty

Chapter 2: Fractions, decimals and percentages

Fractions, decimals and percentages are three notations for the same quantities.

Part of your national curriculum

Number: Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'

Lesson overview

What you'll learn in this lesson

Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'

Key learning points

• Equivalent forms
• Percentage of an amount
• Choose an efficient form

This lesson at a glance

30 minutes
14 parts to scroll through
3 quick checks
Marked quiz at the end
Gentle pace: short sittings with pauses

Words to know

interchangeablyterminatingdecimalscorrespondingfractions

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%

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Part 1 of 14

Watch first

Chapter 2: Fractions, decimals and percentages

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Equivalent forms

A short piece of teaching, then a check to make sure it has landed.

Explore the idea

Part 3 of 14

Learn

Equivalent forms

Divide numerator by denominator to make a decimal. Multiply a decimal by 100 to make a percentage. Thus 3/8 = 0.375 = 37.5%.

Explore the idea

Part 4 of 14

Learn

Percentage of an amount

Find 15% of £80 by using 10% (£8) plus 5% (£4), giving £12. A multiplier gives the same result: 0.15 × 80.

Quick check

Part 5 of 14

Quick check

Write 3/8 as a percentage.

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now

Quick check

Part 7 of 14

Quick check

What is 15% of £80?

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Choose an efficient form

A short piece of teaching, then a check to make sure it has landed.

Explore the idea

Part 9 of 14

Learn

Choose an efficient form

Fractions preserve exact values, decimals suit calculation and percentages make relative comparisons easy. Switch form without changing the value.

Quick check

Part 10 of 14

Quick check

Which fraction equals 0.45?

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Fractions preserve exact values, ____ suit calculation and percentages make relative comparisons easy.

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Chapter 2: Fractions, decimals and percentages

3 questions, marked with the reasoning shown. No timer.

1. Write 3/8 as a percentage.
2. What is 15% of £80?
3. Which fraction equals 0.45?

Lesson round-up

Part 14 of 14

Lesson round-up

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Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

Work out the total cost of the trip if 50 pupils go.
Show why the price per pupil falls when more pupils go, using numbers.
At £20 each, how many pupils must go before the trip makes money? Show your working.

Working out
Working out
Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
Writing
Copy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working out
Write your own real-life problem that uses today's method, then solve it.
1 problem + solution

Write your answer, notes or working here

Saved as you type.

Photos of paper work, diagrams or working outHow many minutes did the written work take?

Part 1 of 14 · Watch & discover

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Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'