This is the course page for your Level 3 maths number workshop. You can follow the links below to access the resources you need for this session.
Please have your ILP to hand as you work through these activities. Your trainer will explain which of the activities below you need to do after the session.

### Session PowerPoint

L3 Number online presentation Mar18 v2

### R1 – Rounding, approximating and accuracy

Instructions
After the session, look at the questions below for more practice in approximating fractions and ratios:
1. In a local by-election 57 328 people turned out to vote, of which 7 241 voted for the Liberal party.

• Approximately, what fractions of voters voted for the Liberals?  Give your answer in its simplest form.
• Of the other voters, 27 971 voted Labour and 21 106 voted Conservative.  Approximately, what was the ratio of Labour to Conservative voters? Give your answer in its simplest form.

2. TV viewing figures for a particular evening showed that 11.8 million people watched BBC1, 2.6 million watched BBC2, 8.3 million watched ITV, and 12.6 million watched other channels.

• Approximately, what was the ratio of ITV viewers to BBC1 viewers?  Give your answer in its simplest form.
• Approximately, what fraction of all viewers watched either BBC1 or BBC2?  Give your answer in its simplest form.

### R2 Proportional reasoning

Instructions
Look at the problems below which have numbers missing. Now:

• Decide which situations are direct proportions and which are not.
• Think of your own numbers to fill the spaces.
• Solve the problems that are created.

### R3 – Percentage increase and decrease

Instructions
1. Place set A (money cards) in the form of a square on the table, so that values increase clockwise from top left, as follows:
£100            £120
£200             £150
2. Using set B (pairs of percentage cards),  place a set between each pair of money cards to show correct percentage increase or decrease.
3. Add card sets C and D to the arrangement.
4. Place card set E in position.

### R4 – Percentage increase and decrease – interest

Instructions
During the break watch one or more of the videos below and be prepared to share your reflections.

### R5 – Compound increase and decrease

Instructions
After the session, try the question below:
In 2007, the population of Scotland was 5.1 million and the population of Wales was 3.0 million,
The population in Scotland is shrinking at a rate of 0.2% per year, while the population of Wales is growing at a rate of 3.7% per year.
If the populations continue to change at these rates, in what year will the population of Wales be larger than that of Scotland?
You can also download Compound interest / access this website below for more practice after the session.

### R6 – Laws of indices

Instructions
Part A:
Suggest a possible value for each of the question marks in the following examples:

1.   23 x 24 = 2?
2.   37 ÷ 32 = 3?
3. 5? x 5? = 512
4.   2? ÷ 2? = 2?

Part B:
Re-write each of the following calculations in powers of 2.  Use the rules of indices to work out any that you do not know:

1. 16 ÷ 8 = 2
2. 16 x ½ = 8
3. 8 x ¼ = 2
4. √2 x √2 = 2
5. 8 x 4 = 32
6. 16 ÷ ¼ = 64
7. 8 ÷ 8 = 1
8. 3√2 x 3√2 x 3√2  = 2

You can access the Laws of Indices ANSWERS after you have tried the questions above.
The Indices fact sheet and this website are for your reference after the session.

### R7 – Understanding and using standard form

Instructions
Look at the images below and estimate the size of the each object:

Can you match any of these measurements to the images?
2m, 0.0000002m, 400 000 000m, 0.02m, 0.0008m, 20 000 000m, 800 000 000 000 000 000 000m, 400m, 8 000m, 0.00000000000008m
What about the remaining images – can you estimate their size/ length/ distance in m?
After the session, print off Measurements and standard form cards (2 more sets of cards) and match them to the above objects/ measurements.
Now try the problems below:
John downloads a music track for five minutes to a file in MP3 format for his own use.   What size (in Megabytes) will the MP3 file need to be?
If his MP3 player has a memory of 5 Gigabytes, calculate an estimate of the maximum number of album tracks he can store on his portable MP3 player.  Show, by estimation, how to check your answer without using a calculator.
During downloading music is sampled 44 100 times each second. The size of each of these samples is 16 bits. Before it is stored in MP3 format the file is compressed to make it smaller using a ratio of 12:1.

• 8 bits are equal to 1 byte
• 1 Megabyte (MB) is equal to 1 048 576 bytes
• 1 Gigabyte (GB) is equal to 1 073 741824 bytes
• 1 Gigabyte (GB) is equal to 1 024 Megabytes (MB)

2. Standard form problems
a. The mass of a hydrogen atom is 1.7 x 10-24 g.  One litre of air contains 2.5 x 1022 atoms of hydrogen.
What is the mass of hydrogen in one litre of air?
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b(i). The population of Portugal in 1986 was 1.025 x 107.
The number of working people in Portugal in 1986 was 4.48 x 106.
Calculate the percentage of people in Portugal who were working.
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b(ii). In 1986, 9.98 x 105 people in Portugal were farm workers.
How many working people in Portugal were not farm workers?