1. Key Stage 3 Mathematics Key Facts Level 6

2. Level 6 Number and Algebra Week 1
Trial and improvement based on algebra
Expressing amounts as a percentage
Equivalence between Fractions, Decimals and Percentages.
Ratio

3. Solve the equation x³ + x = 20
Using trial and improvement discover the value of x to the nearest tenth.
NB – You will not get the exact solution
We are looking for the nearest tenth.
Guess
Check
Too Big/Too Small/Correct

4. Solve the equation x³ + x = 20 3 3³ + 3 = 30 Guess Check
Using trial and improvement and give your answer to the nearest tenth
Guess
Check
Too Big/Too Small/Correct 3
3³ + 3 = 30
Too Big

5. Solve the equation x³ + x = 20 3 3³ + 3 = 30 2 2³ + 2 = 10 Guess Check
Using trial and improvement and give your answer to the nearest tenth
Guess
Check
Too Big/Too Small/Correct 3
3³ + 3 = 30
Too Big 2
2³ + 2 = 10
Too Small

6. Solve the equation x³ + x = 20 3 3³ + 3 = 30 2 2³ + 2 = 10 2.5
Using trial and improvement and give your answer to the nearest tenth
Guess
Check
Too Big/Too Small/Correct 3
3³ + 3 = 30
Too Big 2
2³ + 2 = 10
Too Small
2.5
2.5³ =18.125
2.6

7. Now Try: Solve the equation x³ + x = 8
Using trial and improvement and give your answer to the nearest tenth
Remember you will not get the exact answer.
Guess
Check
Too Big/Too Small/Correct

8. Fat in a mars bar 28g out of 35g. What percentage is this?
Amounts as a %
Fat in a mars bar 28g out of 35g. What percentage is this?
Write as a fraction
=28/35
Convert to a percentage (top ÷ bottom x 100)
28 ÷ 35 x 100 = 80%
top ÷ bottom converts a fraction to a decimal
Multiply by 100 to make a decimal into a percentage

9. Amounts as a %
Now try these:
36g out of 180g
12 children out of 96
£15 out of £60

10. A percentage is a fraction out of 100

13. Now try to make your own triangles using the following please:
3/10
12.5%
0.28

14. The ratio of boys to girls in a class is 3:2
Altogether there are 30 students in the class.
How many boys are there?

15. The ratio of boys to girls in a class is 3:2
Altogether there are 30 students in the class.
How many boys are there?
The ratio 3:2 represents 5 parts (add 3 + 2)
Divide 30 students by the 5 parts (divide)
30 ÷ 5 = 6
Multiply the relevant part of the ratio by the answer (multiply)
3 × 6 = 18 boys

16. Now try these: The ratio of boys to girls in a year group is 4:3
Altogether there are 210 students in the year group.
How many boys are there?
The ratio of flour, sugar and butter in a recipe is 1:3:5
Altogether there are 360g of ingredients used.
How much sugar was used?