Number

Integers, powers and roots

• 9Ni.01 Understand the difference between rational and irrational numbers.
• 9Ni.02 Use positive, negative and zero indices, and the index laws for multiplication and division.
• 9Ni.03 Understand the standard form for representing large and small numbers.
• 9Ni.04 Use knowledge of square and cube roots to estimate surds.

Place value, ordering and rounding

• 9Np.01 Multiply and divide integers and decimals by 10 to the power of any positive or negative number.
• 9Np.02 Understand that when a number is rounded there are upper and lower limits for the original number.

Fractions, decimals, percentages, ratio and proportion

• 9Nf.01 Deduce whether fractions will have recurring or terminating decimal equivalents.
• 9Nf.02 Estimate, add and subtract proper and improper fractions, and mixed numbers, using the order of operations.
• 9Nf.03 Estimate, multiply and divide fractions, interpret division as a multiplicative inverse, and cancel common factors before multiplying or dividing.
• 9Nf.04 Use knowledge of the laws of arithmetic, inverse operations, equivalence and order of operations (brackets and indices) to simplify calculations containing decimals and fractions.
• 9Nf.05 Understand compound percentages.
• 9Nf.06 Estimate, multiply and divide decimals by integers and decimals.
• 9Nf.07 Understand the relationship between two quantities when they are in direct or inverse proportion.
• 9Nf.08 Use knowledge of ratios and equivalence for a range of contexts.

Algebra

Expressions, equations and formulae

• 9Ae.01 Understand that the laws of arithmetic and order of operations apply to algebraic terms and expressions (four operations and integer powers).
• 9Ae.02 Understand how to manipulate algebraic expressions including:
  • expanding the product of two algebraic expressions
  • applying the laws of indices
  • simplifying algebraic fractions.
• 9Ae.03 Understand that a situation can be represented either in words or as an algebraic expression, and move between the two representations (including squares, cubes and roots).
• 9Ae.04 Understand that a situation can be represented either in words or as a formula (including squares and cubes), and manipulate using knowledge of inverse operations to change the subject of a formula.
• 9Ae.05 Understand that a situation can be represented either in words or as an equation. Move between the two representations and solve the equation (including those with an unknown in the denominator).
• 9Ae.06 Understand that the solution of simultaneous linear equations:
  • is the pair of values that satisfy both equations
  • can be found algebraically (eliminating one variable)
  • can be found graphically (point of intersection).
• 9Ae.07 Understand that a situation can be represented either in words or as an inequality. Move between the two representations and solve linear inequalities.

Sequences, functions and graphs

• 9As.01 Generate linear and quadratic sequences from numerical patterns and from a given term-to-term rule (any indices).
• 9As.02 Understand and describe nth term rules algebraically (in the form an ± b, where a and b are positive or negative integers or fractions, and in the form nᵃ, n², n³ or n² ± a, where a is a whole number).
• 9As.03 Understand that a function is a relationship where each input has a single output. Generate outputs from a given function and identify inputs from a given output by considering inverse operations (including indices).
• 9As.04 Understand that a situation can be represented either in words or as a linear function in two variables (of the form y = mx + c or ax + by = c), and move between the two representations.
• 9As.05 Use knowledge of coordinate pairs to construct tables of values and plot the graphs of linear functions, including where y is given implicitly in terms of x (ax + by = c), and quadratic functions of the form y = x² ± a.
• 9As.06 Understand that straight-line graphs can be represented by equations. Find the equation in the form y = mx + c or where y is given implicitly in terms of x (fractional, positive and negative gradients).
• 9As.07 Read, draw and interpret graphs and use compound measures to compare graphs.

Geometry and Measure

Geometrical reasoning, shapes and measurements

• 9Gg.01 Know and use the formulae for the area and circumference of a circle.
• 9Gg.02 Know and recognise very small or very large units of length, capacity and mass.
• 9Gg.03 Estimate and calculate areas of compound 2D shapes made from rectangles, triangles and circles.
• 9Gg.04 Use knowledge of area and volume to derive the formula for the volume of prisms and cylinders. Use the formula to calculate the volume of prisms and cylinders.
• 9Gg.05 Use knowledge of area, and properties of cubes, cuboids, triangular prisms, pyramids and cylinders to calculate their surface area.
• 9Gg.06 Identify reflective symmetry in 3D shapes.
• 9Gg.07 Derive and use the formula for the sum of the interior angles of any polygon.
• 9Gg.08 Know that the sum of the exterior angles of any polygon is 360°.
• 9Gg.09 Use properties of angles, parallel and intersecting lines, triangles and quadrilaterals to calculate missing angles.
• 9Gg.10 Know and use Pythagoras’ theorem.
• 9Gg.11 Construct 60°, 45° and 30° angles and regular polygons.

Position and transformation

• 9Gp.01 Use knowledge of bearings and scaling to interpret position on maps and plans.
• 9Gp.02 Use knowledge of coordinates to find points on a line segment.
• 9Gp.03 Transform points and 2D shapes by combinations of reflections, translations and rotations.
• 9Gp.04 Identify and describe a transformation (reflections, translations, rotations and combinations of these) given an object and its image.
• 9Gp.05 Recognise and explain that after any combination of reflections, translations and rotations the image is congruent to the object.
• 9Gp.06 Enlarge 2D shapes, from a centre of enlargement (outside, on or inside the shape) with a positive integer scale factor. Identify an enlargement, centre of enlargement and scale factor.
• 9Gp.07 Analyse and describe changes in perimeter and area of squares and rectangles when side lengths are enlarged by a positive integer scale factor.

Statistics and Probability

Statistics

• 9Ss.01 Select, trial and justify data collection and sampling methods to investigate predictions for a set of related statistical questions, considering what data to collect, and the appropriateness of each type (qualitative or quantitative; categorical, discrete or continuous).
• 9Ss.02 Explain potential issues and sources of bias with data collection and sampling methods, identifying further questions to ask.
• 9Ss.03 Record, organise and represent categorical, discrete and continuous data. Choose and explain which representation to use in a given situation:
  • Venn and Carroll diagrams
  • tally charts, frequency tables and two-way tables
  • dual and compound bar charts
  • pie charts
  • line graphs, time series graphs and frequency polygons
  • scatter graphs
  • stem-and-leaf and back-to-back stem-and-leaf diagrams
  • infographics
• 9Ss.04 Use mode, median, mean and range to compare two distributions, including grouped data.
• 9Ss.05 Interpret data, identifying patterns, trends and relationships, within and between data sets, to answer statistical questions. Make informal inferences and generalisations, identifying wrong or misleading information.

Probability

• 9Sp.01 Understand that the probability of multiple mutually exclusive events can be found by summation and all mutually exclusive events have a total probability of 1.
• 9Sp.02 Identify when successive and combined events are independent and when they are not.
• 9Sp.03 Understand how to find the theoretical probabilities of combined events.
• 9Sp.04 Design and conduct chance experiments or simulations, using small and large numbers of trials. Calculate the expected frequency of occurrences and compare with observed outcomes.