Key Stage 3

Mathematics

Key Facts

Level 6

Level 6

Number and AlgebraWeek 1 • Trial and improvement based on algebra• Expressing amounts as a percentage• Equivalence between Fractions, Decimals and Percentages.• Ratio

Solve the equationx³ + x = 20

Using trial and improvement discover the value of x to the nearest tenth.

NB – You will not get the exact solutionWe are looking for the nearest tenth.

Guess Check Too Big/Too Small/Correct

Solve the equationx³ + x = 20

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

Solve the equationx³ + x = 20

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

Solve the equationx³ + x = 20

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 + 2.5 =18.125 Too Small

2.6

Now Try:Solve the equation

x³ + x = 8Using 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

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

Amounts as a %• Now try these:

• 36g out of 180g

• 12 children out of 96

• £15 out of £60

A percentage is a fraction out of 100

Now try to make your own triangles using the following please:

• 3/10

• 12.5%

• 0.28

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 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

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?