Autumn 1

Revise and Improve

•  Four operations
• Order of operations
• Negative numbers
• Fractions
• Algebra
   

Number - Fractions 2

Multiply and divide proper and improper fractions and mixed numbers both positive and negative.

• Fraction x Integer
• Fraction x Fraction
• Fraction ÷ Integer
• Integer ÷ Fraction
• Fraction ÷ Fraction
• All of the above proper, improper, mixed, positive and negative.
   

Find a fraction of an amount.

Find the whole amount, given a fraction of the amount.

Find a fractional increase and decrease.

Autumn 2

Number – Percentages

• Define percentage as ‘number of parts per hundred’
• Interpret diagrams as percentages and vice versa
• Interpret percentages as a fraction or as a decimal
• Express one quantity as a percentage of another
• Compare two quantities using percentages, and work with percentages greater than 100%
• Interpret percentages as operators, with and without a calculator.

Solve problems involving percentage change, including:

• Percentage increase, decrease and original value problems and simple interest in financial mathematics.

Spring 1

Algebra 2

Substitute numerical values into formulae and expressions, including scientific formulae.

• Include all prior learning specifically fractions, decimals and negatives

Simplify and manipulate algebraic expressions to maintain equivalence by:

• multiplying a single term over a bracket
• taking out common factors
• expanding products of two or more binomials.
• simplifying expressions involving sums, products and powers, including the laws of indices .

Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

• Include equations with brackets
• Include fractional equations

Understand and use the concepts and vocabulary of inequalities.

• Represent the solution set to an inequality on a number line and vice versa
• Find the integer solutions of an inequality.
• Solve linear inequalities in one variable.

Rearrange formulae to change the subject, where the subject appears once.

Spring 2

Geometry – Circles and Area

Convert between cm2 and m2

Derive and apply formulae to calculate and solve problems involving area of circles, composite shapes and trapeziums.

Calculate and solve problems involving perimeters of 2-D shapes (including circles).

Include examples using algebra, fractions, decimals, etc.

Summer 1

Ratio and Proportion and Rates of Change

Change freely between related standard units [for example time, length, area, volume/capacity, mass]

Use ratio notation, including reduction to simplest form.

Divide a given quantity into two or more parts.

Given information about one part, find the whole or other part(s).

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction.

Use compound units such as speed, unit pricing and density to solve problems.

Solve problems involving direct and inverse proportion, including graphical and algebraic representations.

Examples may include:

• Recipe problems
• Best buy problems
• Exchange rates

Draw and interpret pie charts.

Summer 2

Statistics

Construct and analyse stem and leaf diagrams, including back to back.

For non-grouped data given in the form of a table, find the mean, median, mode and range.

Geometry – 3D Shapes

Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D.

Convert between cm3 and m3

Know and use the fact that 1 litre =

1000cm3

Derive and apply formulae to calculate and solve problems involving volume and surface area of cuboids (including cubes) and other prisms (including cylinders).

Construct and interpret plans and elevations of 3-D shapes.