Percentages Learning objective We are learning to: • solve problems involving the calculation of percentages (e.g. of measures, such as 15% of 360) and the use of percentages for comparison (e.g. to find a percentage of a price).
What pupils already know • Pupils are secure with recognising the per cent symbol (%) and understand that per cent means ‘number of parts per hundred’. • They can write percentages as a fraction with the denominator one hundred, and as a decimal.
Key vocabulary percentage, discount, reduce, increase
Teaching notes • Explain that there are different ways of finding a percentage of an amount. Example: What is 40% of £50? Method 1: Convert the percentage to a fraction and find the fraction of the amount. 40% = 1 5
40 100
=
2 5
of £50 = £50 ÷ 5 = £10
Therefore,
2 5
= £10 × 2 = £20
Method 2: Find 10% first by dividing by 10, and then use this to work out the total percentage. 10% of £50 = £5 Therefore 40% = £5 × 4 = £20
For pupils – Steps to success: 1. Method 1: convert the percentage to a fraction and find the fraction of the amount. 2. Method 2: find 10% first by dividing by 10, and then use this to work out the total percentage.
Independent activity Refer pupils to the Year 6 Mental Arithmetic Pupil Book, pages 36–37.
32
Percentages Use and apply
Here are the two TVs with their prices before any discount:
Task A: TV sales investigation TV STARS are offering a further discount of 20% on the last Bank Holiday in August. The TVs were already reduced by 30%, so the company claims to be offering a total of 50%. Prove that this is an incorrect claim.
£1
£6
00
10
0
Task B: Explain how you know Claire did a survey of 55 people to see how many were right-handed. Claire says:
The results show that exactly 10% of the people in the survey are right-handed. Explain why Claire cannot be correct. Task C: Sale tags A game for two players You need: a paper clip, a pencil, Spinner D*, a set of different coloured counters each, the price tag images below • Take turns to spin Spinner D. Then find the sale price tag that is equivalent to the fraction shown on the spinner. Cover the sale price tag with a counter. • If the sale price tag has already been covered, then you miss a go. • After five rounds, the player who has more sale tags covered wins!
Spinner D
33 100
1 10 2 5
40% OFF
30% OFF
75% OFF
33% OFF
50% OFF
10% OFF
60% OFF
25% OFF
1 4
6 10
Sale price tags
20% OFF
1 2
3 10
1 5
3 4
* See the Resources page for a full-sized photocopiable version © 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
33
Ratio and proportion Learning objective We are learning to: • solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.
What pupils already know • Pupils are secure with multiplication facts up to 12 × 12
Key vocabulary ratio, proportion, part, direct proportion
Teaching notes • Explain that there is a difference between ‘ratio’ and ‘proportion’. Example 1: What is the ratio of grey to white tiles? What is the proportion of grey tiles?
For every 2 grey tiles there are 6 white tiles. The ratio can be written as 2 : 6 but simplified to 1 : 3. For example, you could have, 1 grey tile and 3 white tiles, 2 grey tiles and 6 white tiles, or 3 grey tiles and 9 white tiles. The proportion of grey is 2 out of 8, which is equivalent to 14 . • Explain that two quantities are in direct proportion when they decrease or increase in the same ratio. Example 2: If 150 g of flour is needed to bake 12 cupcakes, how much flour is needed to bake 36 cupcakes? Establish that 36 cupcakes is 3 times more than 12 cupcakes, so three times the amount of flour is needed. 150 g × 3 = 450 g
For pupils – Steps to success: 1. Ratio: compare part to part. 2. Proportion: find the fraction of the whole amount. 3. Direct proportion: increase or decrease in the same ratio.
Independent activity Refer pupils to the Year 6 Mental Arithmetic Pupil Book, pages 38–39. 34
Ratio and proportion Use and apply Task A: 3D shape building Aaliyah and Mustafah are making 3D shapes using blue and red cubes. Aaliyah has 18 cubes and Mustafah has 30 cubes. They both have red and blue cubes and use the same ratio of blue to red cubes as one another. Investigate the ratios they could use and how many of each colour cube they need. Task B: Explain how you know Izzy is having four friends over for tea and she wants to make 12 pancakes.
Pancake recipe (makes 4 pancakes) • 120 g plain flour
She knows she needs to increase the quantity of each ingredient, so she multiplies each ingredient by 4 and gets the following quantities:
• 1 egg • 200 ml of milk
• 480 g flour • 4 eggs • 800 ml of milk Are her new quantities correct for 12 pancakes? Explain your answer. Task C: What’s that in Yuan? A game for two players
You will need: a dice, the conversion grid and the shopping items below. The ratio of pounds to Chinese Yuan is 5 : 64. • Take turns to roll the dice and match the number rolled to one of the shopping items below 1–6. • Convert the cost of the item from pounds to Yuan. Then place a counter on the Yuan conversion grid, in the correct place. • The first player to cover all the Yuan prices on their row wins. Conversion Grid Player 1
192 Yuan
256 Yuan
32 Yuan
160 Yuan
128 Yuan
285 Yuan
Player 2
160 Yuan
192 Yuan
285 Yuan
128 Yuan
32 Yuan
256 Yuan
1
2 2
3
55
44
£2
0
£2
.5 0
£2
£1
66
£7
.5
5 £1
0
0
2. 50
5
6 £
© 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
35
Progress test 3 1
Write these decimals as fractions. Simplify them if possible.
Use this pattern to answer questions 13–14.
0.5 = 0.6 = 2
12 Median =
Write the smallest fraction and then the largest fraction. 8 10
34 100
9 10
52 100
3
4 5
4
Write these decimals as fractions. Simplify them if possible.
=
.
=
%
0.65 = 0.7 = 5
41 100
6
What is 15% of £90?
7
In a sale there is 20% off a chair that usually costs £80. What is the sale price of the chair?
8
=
.
=
13 What proportion of this pattern is grey?
%
14 What is the ratio of grey to white boxes in its simplest ratio?
Write these as fractions. Simplify them if possible. 0.48 =
9
The ratio for making a drink is 1 : 5 cordial to water. Now answer questions 15–16.
0.72 =
15 If 50 ml of cordial is used, how much water is needed to complete the drink?
Change these to tenths or hundredths and write them as decimal fractions.
16 How much cordial is needed if 200 ml of water is used?
22 250 =
=
12 320
=
=
Look at these maths test scores for Alan, then answer questions 17–18.
Use the following information to answer questions 10–12. Here are the numbers of children in each of the 5 sports classes that take place every Saturday. 31
27
31
29
32
Find the mode, mean and median.
Monday 21 Tuesday 30 Wednesday 25 Thursday 32 17 What is Alan’s mean score? 18 On Friday Alan got 12 in his maths test. What is his mean score now? 19 A 400 g pear pie is made with 75% pears and 25% pastry. What is the proportion of pears in the pie, in its simplest form? 20 What is 30% of 120?
10 Mode = 11 Mean = 44
Score
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© 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
End-of-year test 1
Write the largest number and then the smallest number. 8 237 470
8 234 608
8 731 410
8 347 400
3
21 100
4
In a sale there is 20% off a table that usually costs £120. What is the sale price of the table?
5
What is the difference between −3 and −15?
6
82 =
7
What is the value of t in 7t + 30 = 51?
8
Write the prime number.
.
=
%
Use these class sizes to answer questions 14–16. 29
31
30
30
30
14 Mode =
41
15 Mean = 16 Median =
82 39
27 75
Copy this pair of fractions and write < or > between them to make this true. 4 16
8×4=
These are the numbers of children in each class in Year 1 in a school.
(35 + 10) ÷ 9 =
9
13 Multiply these:
0.8 × 4 =
8 214 560
2
=
12 172 + 42 =
10 20
17 Copy and complete these equivalent fractions. 3 20
=
6 18
=
80 12
18 (84 − 54) × (10 ÷ 2) = 19 Will 5 divide exactly into 2061? 20 What is 53p less than 97p?
Use the grid below to answer questions 10–11.
10 What proportion of this pattern is grey? 11 What is the ratio of grey to white boxes?
Score © 2015 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.
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