Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction.

Interpret percentage as the operator ‘so many hundredths of’; express one given number as a percentage of another.

Reduce a ratio to its simplest form, including a ratio expressed in different units; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.

Recall known facts, including fraction to decimal conversions.

Round positive numbers to any given power of 10 and decimals to the nearest whole number, 1 or 2 decimal places.

Core:

Use efficient methods to add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing.

Recognise when fractions or percentages are needed to compare proportions; solve problems involving percentage changes.

Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.

Understand the effects of multiplying and dividing by numbers between 0 and 1; use the laws of arithmetic and inverse operations.

Understand the order of precedence and effect of powers.

Use known facts to derive unknown facts; extend mental methods of calculation, working with decimals, fractions, percentages, factors, powers and roots; solve word problems mentally.

Make and justify estimates and approximations of calculations.

Check results using appropriate methods.

Extension:

Understand and use proportionality and calculate the result of any proportional change using only multiplicative methods; understand the implications of enlargement for area and volume.

Recognise and use reciprocals.

Estimate calculations by rounding numbers to one significant figure and multiplying or dividing mentally.

## Objectives:

Support:divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.Core:add, subtract, multiply and divide fractions,interpreting division as a multiplicative inverse; cancel common factors before multiplying or dividing.Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole;compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.Understand the effects of multiplying and dividing by numbers between 0 and 1;use the laws of arithmetic and inverse operations.Make and justify estimates and approximations of calculations.Extension:Understand and use proportionality and calculate the result of any proportional change using only multiplicative methods;understand the implications of enlargement for area and volume.## Key Vocabulary:

## Suggested Lesson Outcomes:

SUPPORT TARGET

CORE## Framework:

## Teaching & Learning Resources:

Fractions Resources

Percentages Resources

Number Facts Resources

Written Methods Resources

Mental Methods Resources

Estimating Resources

Ratio Resources

Proportion Resources