QCA Unit |
Mathematics at KS 3, Unit : Percentages. | |||

Year Group |
Year 8 | Number in class |
30 | |

Time for lesson |
1 hour | No. of computers |
15 (minimum). | |

**Aims/Learning Outcomes: **Learners will be able to calculate percentage decreases and increases.

**All:**. Will know how to calculate the percentage of a quantity.

**Some: **Will be able to make objective judgements as to the usefulness of different types of percentage calculation in specific calculations.

**Keywords: ** add, divide, percentage, subtract, sum.

**Resources:**interactive whiteboard, pre-prepared presentation and questions on calculating percentages and numbers as percentages of other numbers (see below).

**Differentiation: **By learning outcome, and differentiated tasks activities. Group work at different levels where the tasks are simplified/extended in terms of content and/or language for specific groups. Those in this class who are in lower ability Maths groups to be aided by teaching support staff as available.

Mental Maths Start Up.

Go through some equivalent percentages and decimal and common fractions, i.e.

0.125 = 1 or 12.5 %

8

0.33 = 1 or 33 %

3

Find some percentages of numbers i.e. 10%, 15% 25%, 40%, 85% etc.

Introduction.

At present, energy bills in the UK are set to increase by approximately 6 or 8 per cent. There has been a lot of discussion about what this actually means to individual households. What information do we need in order to calculate how much difference that kind of percentage rise would make, and what kinds of calculations would need to be done?

On the interactive whiteboard, look at an example.

A household has annual bills of £832 for gas and £528 for electricity. If it is due to pay an 8% increase in the following year, how can the difference be calculated?

Find the total for the year, i.e. £832 + £528 = £1360.

1360 = 13.6 x 8 = 108.8

100

The household will see its combined gas and electricity bills rise by £108.8 in the following year, if it uses the same amount of energy.

Therefore the new bill would be £1468.8.

The same household could save 12 per cent of its annual energy bill by installing solar power panels. How much would it save?

1360 = 13.6 x 12 = 163.2

100

The household will see its combined gas and electricity bills reduced by £163.2 in the following year. If it uses the same amount of energy, its new bill would be £1305.6.

If cavity wall insulation could save another £75.3 of the new year bill, i.e. £1305.6, what percentage would that be?

To find one number a s a percentage of another,

£163.2 divided by £1305.6 = 0.125.

0.125 x 100 = 12.5.

So, cavity wall insulation would save 12.5%.

Main Task.

In their ability groups, the class will attempt some similar problems, i.e. percentages of numbers, and finding one number as a percentage of another.

1. A household has annual bills of £765 for gas and £1028 for electricity. If it is due to pay an 8% increase in the following year, by how much will its combined energy bill rise?

2. A household has annual bills of £1237 for gas and £928 for electricity. If it is due to pay an 6% increase in the following year, by how much will its combined energy bill rise?

3. A household has annual bills of £427 for gas and £612 for electricity. If it is due to pay an 8% increase in the following year, by how much will its combined energy bill rise?

Go through the answers as a class and address any misconceptions or problems.

1. A household has annual bills of £765 for gas and £1028 for electricity. If it is due to pay an 8% increase in the following year, by how much will its combined energy bill rise?

£765 + £1028 = 1793

1793 = 17.93 x 8 = £143.44

100

2. A household has annual bills of £1237 for gas and £928 for electricity. If it is due to pay an 6% increase in the following year, by how much will its combined energy bill rise?

£1237 + £928 = £2165.

2165 = 21.65 x 6 = £129.9

100

3. A household has annual bills of £427 for gas and £612 for electricity. If it is due to pay an 8% increase in the following year, by how much will its combined energy bill rise?

£427 + £612 = £1039.

1039 = 10.39 x 8 = £83.12.

100

Explain that the calculations learned today may also be done by pencil and paper methods. For example, if you get 40 marks out of 60 in a test, you can calculate you percentage marks as follows,

40 x 100%

60

= 40 x 100%

60 1

= 200%

3

= 66 2%

3

= 67% (round to the nearest ten per cent.

Relevant NC Level Descriptors.

For assessment purposes, successful completion of this lesson will enable pupils to achieve the following aspects of the National Curriculum Level Descriptors in Mathematics.

**Level 4. ****In solving number problems, pupils use a range of mental methods of computation with the four operations, including mental recall of multiplication facts up to 10 x 10 and quick derivation of corresponding division facts. They use efficient written methods of addition and subtraction and of short multiplication and division. They recognise approximate proportions of a whole and use simple fractions and percentages to describe these. Pupils recognise and describe number patterns, and relationships. **These requirements will be met by learning how to calculate the percentage of a quantity, and one number as a percentage of another. This includes the use of various skills, including the recognition of known number facts.

**Level 5. ****They calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate. Pupils understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any three-digit number by any two-digit number. **These requirements will be met by learning how to calculate the percentage of a quantity, or one number as a percentage of another, by both calculator and non-calculator methods. This includes the use of various skills, including the recognition of known number facts.

**Level 6. ****Pupils order and approximate decimals when solving numerical problems and equations, using trial-and-improvement methods. Pupils evaluate one number as a fraction or percentage of another. They understand and use the equivalences between fractions, decimals and percentages, and calculate using ratios in appropriate situations. **These requirements will be met by learning how to calculate the percentage of a quantity, or one number as a percentage of another, by integrating their knowledge of common fractions, decimal fractions, and percentages. They will also use the four operations to make the necessary calculations, in both calculator and non- calculator form.

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