Key stage 3 mathematics lesson plans (national curriculum)

ENG-NC-MA-KS3-001

consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots

ENG-NC-MA-KS3-002

select and use appropriate calculation strategies to solve increasingly complex problems

ENG-NC-MA-KS3-003

use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships

ENG-NC-MA-KS3-004

substitute values in expressions, rearrange and simplify expressions, and solve equations

ENG-NC-MA-KS3-005

move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]

ENG-NC-MA-KS3-006

develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

ENG-NC-MA-KS3-007

use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics

ENG-NC-MA-KS3-008

extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

ENG-NC-MA-KS3-009

extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically

ENG-NC-MA-KS3-010

identify variables and express relations between variables algebraically and graphically

ENG-NC-MA-KS3-011

make and test conjectures about patterns and relationships; look for proofs or counter-examples

ENG-NC-MA-KS3-012

begin to reason deductively in geometry, number and algebra, including using geometrical constructions

ENG-NC-MA-KS3-013

interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

ENG-NC-MA-KS3-014

explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally

ENG-NC-MA-KS3-015

develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

ENG-NC-MA-KS3-016

develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics

ENG-NC-MA-KS3-017

begin to model situations mathematically and express the results using a range of formal mathematical representations

ENG-NC-MA-KS3-018

select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems

ENG-NC-MA-KS3-019

understand and use place value for decimals, measures and integers of any size

ENG-NC-MA-KS3-020

order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

ENG-NC-MA-KS3-021

use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

ENG-NC-MA-KS3-022

use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

ENG-NC-MA-KS3-023

use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

ENG-NC-MA-KS3-024

recognise and use relationships between operations including inverse operations

ENG-NC-MA-KS3-025

use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

ENG-NC-MA-KS3-026

interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or 0

ENG-NC-MA-KS3-027

work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and [Fraction:7/2] or 0.375 and [Fraction:3/8])

ENG-NC-MA-KS3-028

define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%

ENG-NC-MA-KS3-029

interpret fractions and percentages as operators

ENG-NC-MA-KS3-030

use standard units of mass, length, time, money and other measures, including with decimal quantities

ENG-NC-MA-KS3-031

round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

ENG-NC-MA-KS3-032

use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b

ENG-NC-MA-KS3-033

use a calculator and other technologies to calculate results accurately and then interpret them appropriately

ENG-NC-MA-KS3-034

appreciate the infinite nature of the sets of integers, real and rational numbers

ENG-NC-MA-KS3-035

use and interpret algebraic notation, including:

ENG-NC-MA-KS3-036

substitute numerical values into formulae and expressions, including scientific formulae

ENG-NC-MA-KS3-037

understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

ENG-NC-MA-KS3-038

simplify and manipulate algebraic expressions to maintain equivalence by:

ENG-NC-MA-KS3-039

understand and use standard mathematical formulae; rearrange formulae to change the subject

ENG-NC-MA-KS3-040

model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

ENG-NC-MA-KS3-041

use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)

ENG-NC-MA-KS3-042

work with coordinates in all 4 quadrants

ENG-NC-MA-KS3-043

recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane

ENG-NC-MA-KS3-044

interpret mathematical relationships both algebraically and graphically

ENG-NC-MA-KS3-045

reduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

ENG-NC-MA-KS3-046

use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

ENG-NC-MA-KS3-047

find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

ENG-NC-MA-KS3-048

generate terms of a sequence from either a term-to-term or a position-to-term rule

ENG-NC-MA-KS3-049

recognise arithmetic sequences and find the nth term

ENG-NC-MA-KS3-050

recognise geometric sequences and appreciate other sequences that arise

ENG-NC-MA-KS3-051

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

ENG-NC-MA-KS3-052

use scale factors, scale diagrams and maps

ENG-NC-MA-KS3-053

express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1

ENG-NC-MA-KS3-054

use ratio notation, including reduction to simplest form

ENG-NC-MA-KS3-055

divide a given quantity into 2 parts in a given part:part or part:whole ratio; express the division of a quantity into 2 parts as a ratio

ENG-NC-MA-KS3-056

understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction

ENG-NC-MA-KS3-057

relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

ENG-NC-MA-KS3-058

solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

ENG-NC-MA-KS3-059

solve problems involving direct and inverse proportion, including graphical and algebraic representations

ENG-NC-MA-KS3-060

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

ENG-NC-MA-KS3-061

derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

ENG-NC-MA-KS3-062

calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

ENG-NC-MA-KS3-063

draw and measure line segments and angles in geometric figures, including interpreting scale drawings

ENG-NC-MA-KS3-064

derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

ENG-NC-MA-KS3-065

describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

ENG-NC-MA-KS3-066

use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

ENG-NC-MA-KS3-067

derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

ENG-NC-MA-KS3-068

identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

ENG-NC-MA-KS3-069

identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

ENG-NC-MA-KS3-070

apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

ENG-NC-MA-KS3-071

understand and use the relationship between parallel lines and alternate and corresponding angles

ENG-NC-MA-KS3-072

derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

ENG-NC-MA-KS3-073

apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

ENG-NC-MA-KS3-074

use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

ENG-NC-MA-KS3-075

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

ENG-NC-MA-KS3-076

interpret mathematical relationships both algebraically and geometrically

ENG-NC-MA-KS3-077

record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

ENG-NC-MA-KS3-078

understand that the probabilities of all possible outcomes sum to 1

ENG-NC-MA-KS3-079

enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

ENG-NC-MA-KS3-080

generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

ENG-NC-MA-KS3-081

describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

ENG-NC-MA-KS3-082

construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

ENG-NC-MA-KS3-083

describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs