Numbers

4

Multiply and divide by 10, 100, 1000, 10000, etc.

Round numbers to the nearest whole number or to one or two decimal places.

Reduce a number to its prime factors.

Estimate square roots and cube roots using trial and improvement.

Use index notation (e.g. 3 x 3 x 3 x 3 = 3⁴ )

Add, subtract, multiply and divide fractions, (cancelling common factors before multiplying or dividing.)

Solve problems involving percentage changes.

Use proportion to solve problems – split a quantity in a given ratio.

Calculations

4

Understand the effects of multiplying and dividing by numbers between 0 and 1.

Make and explain estimates and approximations of calculations.

Add and subtract whole numbers and decimals of any size using pencil and paper.

Multiply and divide by decimals using pencil and paper.

Use a calculator to perform complex calculations (see “Know Your Calculator”)

Check results using appropriate methods (e.g. estimation or working backwards)

Algebra

4

Understand the difference between expressions, formulae, functions and equations.

Use index notation in algebra (e.g.  a x a x a = a³  etc.)

Rewrite algebraic expressions using brackets (e.g. 6x + 3 = 3(2x + 1)

Solve simple equations (e.g. 3x + 2 = 14  or  4(x – 5) = 20  or  2x – 1 = x + 4 ) .

Use trial and improvement to find approximate solutions to equations such as x³ + x = 20.

Use formulae - substitute numbers into expressions and formulae;

Work out a formula for a simple real-life situation

Generate terms of a sequence using a rule.

Generate sequences from diagrams and write an expression for the nth term of a sequence;

Work out coordinates and plot graphs of given a relationship like y = 3x + 2  or  3x – 2y = 4

For a graph of y = mx + c find the gradient and the y-intercept.

Construct functions and graphs from real-life problems (e.g. converting between °C and °F) .

Interpret graphs from real situations, including distance–time graphs.

Solving problems

4

Decide when to do a calculation mentally, using a written method or using a calculator

Explain how to do a calculation in writing.

Spot and explain patterns in numbers and shapes.

Solve real-life problems involving money, measurements and time using simple calculations.

Solve problems using skills from several different topics.

Know when to use diagrams, tables or graphs to solve a problem.

Use trial and improvement to solve problems.

Give answers to problems using a sensible number of decimal places or significant figures.

Shape, space and measures

4

Find the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons.

Explain how to find the interior and exterior angles of regular polygons.

Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and polygons.

Understand congruence.

Know the definition of a circle and the names of its parts;

Draw polygons (e.g. an octagon) by dividing circles into equal parts (8 parts each of 45° for an octagon)

Use 2-D representations of 3-D objects – i.e. nets and drawings on isometric paper (triangular dotty paper).

Draw 2-D projections, including plans and elevations, of 3-D shapes.

Find planes of symmetry in 3-D shapes.

Transform 2-D shapes by translations, rotations and reflections

Enlarge 2-D shapes, given a centre of enlargement and a whole-number scale factor.

Calculate the scale factor of an enlargement using the ratio of the lengths of two corresponding lines.

Remember that enlargements do not change angles in a shape, only the lengths.

Remember that translations, rotations and reflections do not change lengths or angles.

Use and interpret maps and scale drawings.

Use a ruler and compasses to construct a triangle using information about its sides and angles.

Find the locus of a point that moves according to a simple rule.

Use units of measurement for length (mm, cm, m, km), area (cm², m²), mass (g, kg), and capacity (ml, l).

Convert one metric unit to another (e.g. grams to kilograms).

Convert between area measures (mm² to cm², cm² to m², and vice versa).

Convert between volume measures (mm³  to cm³, cm³ to m³, and vice versa).          

Know and use the formulae for the circumference and area of a circle.

Calculate the surface area and volume of prisms.

Handling data

4

Remember the difference between primary and secondary sources of data.

Design a survey or experiment to answer a question or solve a problem.

Design data collection sheets.

Construct tables for large discrete and continuous sets of data, choosing suitable class intervals.

Gather data from tables and lists.

Find the mean, median, mode and range for a set of data and discuss what they tell us about the data.

Draw line graphs

Draw scatter graphs and use them to look for correlation.

Interpret graphs and diagrams and make conclusions from them.

Compare two or more sets of data using the mean, median, mode and range.

Identify all the mutually exclusive outcomes of an experiment.

Know and use the fact that the sum of probabilities of all mutually exclusive outcomes is 1.

Estimate probabilities from experimental data.

Compare experimental and theoretical probabilities and discuss.