Fractions, Decimals and Percentages: Everyday Maths That Scores
GCSE MATHS RESIT · EDEXCEL FOUNDATION · 2 OF 7
Fractions, decimals and percentages
Three ways of writing the same amount, and the quickest routes to the marks they carry.
Paper 1 · Paper 2 · Paper 3
Lesduur is: 60 minIntroductie
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GCSE MATHS RESIT · EDEXCEL FOUNDATION · 2 OF 7
Fractions, decimals and percentages
Three ways of writing the same amount, and the quickest routes to the marks they carry.
Paper 1 · Paper 2 · Paper 3
Lesson 2 of 7, about 60 minutes. Timings: do now 5 min, equivalence and sorting 12 min, percentages of amounts 12 min, multipliers 10 min, fractions of amounts 8 min, exam question and exit 13 min.
Percentages appear on all three papers, usually in a money context. That makes this one of the best-value hours in the course.
Device-free fallback for the whole lesson: every activity works on mini whiteboards or paper; the notes on each slide say how. Image credit: Helena Lopes / Unsplash
DO NOW · 4 MINUTES
Four from last lesson
Which is bigger, 0.6 or 0.58?
0.6 (6 tenths beats 5 tenths)
Work out −2 − 5
−7
Work out 4 + 6 × 2
16 (multiply first)
Work out 32 × 5 without a calculator
160
Students answer on paper or whiteboards as they arrive. Click four times to reveal the answers one by one.
If lesson 1's exit poll picked out one skill as the weakest, spend an extra minute on that card.
32 × 5: a quick route is 32 × 10 = 320, then halve it to 160.
Device-free: write the four questions on the board before the lesson starts.
THE BIG IDEA
Same amount, three ways to write it
3 of 4 equal parts shaded
1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
3/4 = 0.75 = 75%
1/10 = 0.1 = 10%
1/5 = 0.2 = 20%
1/100 = 0.01 = 1%
Learn the six on the right and most conversions are one step away.
The bar is drawn to scale: four equal parts, three shaded.
Per cent means "out of 100". A decimal is just a fraction with 10, 100 or 1000 on the bottom. So 0.75 = 75 hundredths = 75%.
Ask: "How would you turn 2/5 into a percentage?" (Double top and bottom to get 4/10, then 40/100 = 40%.)
Device-free: students copy the six equivalents into the back of their book. They will use them all course.
Match each to its decimal. One fits nowhere.
= 0.25
= 0.5
= 0.75
75%
2/8
0.4
1/2
6/8
25%
5/10
3/4
50%
1/4
Answers: 0.25 takes 1/4, 2/8 and 25%. 0.5 takes 1/2, 5/10 and 50%. 0.75 takes 3/4, 6/8 and 75%.
0.4 belongs nowhere. It is the classic slip: reading 1/4 as "1 point 4" or "0.4". A quarter is 25 hundredths, not 4 tenths.
2/8 and 6/8 test simplifying: divide top and bottom by 2.
Device-free: draw the three columns on the board and call out the items in random order; students write the column letter.
PERCENTAGE OF AN AMOUNT · NO CALCULATOR
35% of £60, built from 10%
£60 = 100%
£6
£6
£6
£6
£6
£6
£6
£6
£6
£6
each box is 10%
10%
£60 ÷ 10 = £6
5%
half of £6 = £3
35% = 10 + 10 + 10 + 5
£6 + £6 + £6 + £3 = £21
Other building blocks: 50% is half, 25% is a quarter, 1% is ÷ 100. Any percentage can be built from these.
The bar is to scale: £60 split into ten boxes of £6. Three and a half boxes are shaded, which is 35%.
Three clicks: 10%, then 5%, then the total £21.
Common slip: working out 35% as £60 ÷ 35. Ask: "Is the answer going to be more or less than half of £60?" (Less: 35% is under 50%, so under £30.)
Device-free: draw the ten-box bar on the board and shade it together.
Work out 15% of £80
£12
£15
£8
£1.20
Answer: £12. 10% = £8, 5% = £4, so 15% = £12.
Wrong answers tell you the slip: £15 = mixing up the percentage and the answer. £8 = stopped at 10%. £1.20 = divided by 100 twice or slipped a place value.
Device-free: mini whiteboards, show on a count of three.
MULTIPLIERS · PAPERS 2 AND 3
One multiplication does the whole job
100%
+20%
Increase by 20% → 120% → × 1.2
70%
−30%
Decrease by 30% → 70% → × 0.7
A £45 jacket
20% more: £54. 30% off: £31.50 (money has two decimal places).
Find the multiplier by changing the new percentage into a decimal: 120% → 1.2, 70% → 0.7, 105% → 1.05.
The bars are to scale: 100% is 400 units wide, +20% adds 80 and 70% is 280.
Why bother? Two steps (find 20%, then add it on) means two chances to slip. The multiplier is one button press on Papers 2 and 3, and it is also how compound interest and depreciation work later.
Two clicks: £54, then £31.50. Point out the calculator shows 31.5 and the money answer needs 31.50.
Common slip: using × 0.3 for "30% off". That gives the discount, not the sale price.
Device-free: students write the multiplier for 10% off, 25% more and 3% more (0.9, 1.25, 1.03).
Fill in the multipliers
1. Increase by 20%: multiply by 1.2.
2. Decrease by 15%: multiply by 0.85.
3. Increase by 5%: multiply by 1.05.
4. Decrease by 40%: multiply by 0.6.
Answers: 1.2, 0.85, 1.05, 0.6.
Distractors match the common slips: 0.2 (the change, not the new amount), 1.15 (adding instead of taking away), 0.5 (reading 5% as 0.5), 1.4 (adding instead of taking away).
The 5% one catches many students: 105% is 1.05, not 1.5.
Device-free: write the four lines on the board and fill them in together.
FRACTION OF AN AMOUNT
Divide by the bottom, times by the top
£40
£8
£8
£8
£8
£8
3 of the 5 parts
3/5 of £40
£40 ÷ 5 = £8
£8 × 3 = £24
The bottom number says how many equal parts. The top number says how many of them you want.
The bar is to scale: five equal parts of £8, three shaded.
Two clicks: the working, then the formula line.
Ask: "What would 4/5 of £40 be?" (£32.) "And 5/5?" (£40, the whole lot: a good sense check.)
Device-free: draw the five-part bar on the board.
Work out 2/3 of 54
Answer: 36. 54 ÷ 3 = 18, then 18 × 2 = 36.
Common slips: 27 (halving instead of thirds), 18 (stopping after dividing), 81 (dividing by 2 and multiplying by 3: top and bottom swapped).
Device-free: whiteboards.
EXAM-STYLE · PAPER 2 · CALCULATOR
A phone normally costs £340.
In a sale, the price is reduced by 15%.
Jade has £300. Does she have enough money to buy the phone in the sale?
(3 marks)
4
minute
00
second
4 minutes on the timer. Students write full working on paper, then answer on the next slide.
Mark scheme style: M1 for 340 × 0.85, or for 15% = 51 (340 × 0.15). M1 for 340 − 51. A1 for £289 with the conclusion "Yes, she has enough" (or "Yes, £11 left").
The conclusion matters: a correct £289 with no "yes" can lose the final mark. "Does she have enough?" needs an answer in words.
Device-free: same question on paper; the teacher keeps time. Image credit: Artem Beliaikin / Unsplash
Can Jade afford the phone in the sale?
Yes, it costs £289
No, it costs £325
Yes, it costs £51
No, it costs £391
Answer: Yes, the sale price is £340 × 0.85 = £289, leaving her £11.
The wrong answers are real slips: £325 = took away £15 instead of 15%. £51 = found the discount and stopped. £391 = added 15% instead of taking it off.
Ask the class to say which slip each wrong answer comes from. Spotting the slip is half of not making it.
Put these in order, smallest first
Order: 2/3 (0.666…), 0.69, 0.7, 72%, 3/4 (0.75).
The trick is to change everything into the same form first, usually decimals. The next slide shows the conversions.
Common slips: putting 0.7 before 0.69 because "69 is bigger than 7"; treating 2/3 as 0.23.
Device-free: write the five on cards and have five students stand in order at the front.
MAKE THEM MATCH, THEN COMPARE
Change everything into a decimal
2/3
0.666…
0.69
0.69
0.7
0.70 (zero added)
72%
0.72
3/4
0.75
Now line up the decimal points and compare column by column, like lesson 1.
Give every number the same number of decimal places by adding zeros.
Five clicks reveal the decimals one by one.
2/3 on a non-calculator paper: 2 ÷ 3 = 0.666… (short division, or remember a third is 0.333…). On Papers 2 and 3, just divide on the calculator.
Device-free: same table on the board, filled in as students call out.
Which felt most solid today?
Converting between the three
Percentage of an amount
Multipliers
Fraction of an amount
Exit poll. The least-voted skill goes into next lesson's do now.
Device-free: students write their answer on a sticky note as they leave.
BEFORE NEXT LESSON · 10 MINUTES
Three to try at home
1
Work out 30% of £70 without a calculator.
2
Increase £80 by 15%. Use a multiplier.
3
Work out 3/8 of 64.
Show the working, not just the answer. Corbettmaths 5-a-day (Foundation) has more of these every day, free: corbettmaths.com/5-a-day/gcse
Answers: 1) £21 (10% = £7, × 3). 2) £92 (80 × 1.15). 3) 24 (64 ÷ 8 = 8, × 3).
Next lesson: ratio and proportion. It uses the same "find one part first" idea as the fraction bar today.
