Key Stage 3 Mathematics Key Facts Level 6

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

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

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

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

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 + 2.5 =18.125 2.6

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

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

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?