# Mathematics: Key Stage 3

### Year 7

#### Autumn 1: Place Value, Addition and Subtraction

 Unit 1 - Place Value (1) Read and write whole numbers in figures and words Multiply, and divide, any whole number by 10, 100, 1000, or 10 000 Round whole numbers to the nearest 1000, 100 or 10 Unit 2 & 3 – Addition and subtraction (2) Use mental strategies Add and subtract using formal algorithms Calculate and work with perimeters   Model solve word problems Unit 4 – Addition and subtraction of decimals (2) Understand decimal notation and place value Read and write decimals in figures and words Convert between decimals and fractions where the denominator is a factor of 10 or 100 Use the number line to display decimals and round decimals to the nearest whole number, to 1 or 2 decimal places Use correctly the symbols <, >, etc. and the associated language to order a set of decimals Multiply and divide decimals by 10, 100, 1000, or 10 000 Solve word problems involving the addition and subtraction of money in decimal notation Use  written methods in column format for addition and subtraction of decimals Extend existing mental calculation to include decimals Calculate the perimeter of rectangles, squares and rectilinear figures

#### Autumn 2: Multiplication and Division

 Unit 5, 6, 7 & 8 multiplication and division (5) Use multiplication facts to solve mental calculations Use the terms ‘product’, ‘multiple’ and ‘LCM’ Understand and use the column method to multiply integers and decimals Divide whole numbers and decimals by whole numbers Use the terms ‘quotient’, ‘remainder’, ‘factor’, ‘HCF’ Represent multiplication word problems using bar models Find the area of a rectangle and triangle Solve problems involving length, perimeter and area Estimate answers in calculations and check that results are reasonable Measure time, calculate with time and solve time word problems Find the mean average, interpreting average as “total amount ÷ number of items" and solve word problems involving average

#### Spring 1: 2D Shapes

 Unit 9 – Working with units (1) Record and order measurements using decimal notation Estimate and/or measure: length in kilometres (km) /metres (m)/ centimetres (cm)/ millimetres (mm) mass in kilograms (kg) /grams (g) volume of liquid in litres (l) / millilitres (ml) Unit 10 – Angles (1) Draw and measure  acute and obtuse angles reliably to the nearest degree Estimate the size of any given angle Recognise acute, right, obtuse and reflex angles Know and use the fact that the angles round a point total 360o, that angles on a straight line total 180o, and that vertically opposite angles are equal Unit 11 & 12 – Triangles and quadrilaterals (2) Classify triangles and quadrilaterals according to their properties Use a ruler and protractor to construct triangles and quadrilaterals from given data Know and use the fact that the sum of interior angles of a triangle is 180o know and use the fact that the interior angles of a quadrilateral sum to 360o Solve problems involving coordinates in the first quadrant Unit 13 Symmetry and tessellation (1) Identify lines of symmetry in any shape Identify the order of rotational symmetry in any shape Create shapes given details of their symmetries Investigate and create tessellations

#### Spring 2: Fractions

 Unit 14 – Understand and use fraction (2) Represent fractions using area diagrams, bar models and number lines Recognise and name equivalent fractions Convert fractions to decimals Convert terminating decimals to fractions in their simplest form Convert between mixed numbers and improper fractions Compare and order numbers Convert simple fractions and decimals to percentages Express one quantity as a fraction of another Unit 15 – Fractions of amounts (1) Find a fraction of a set of objects or quantity Find the whole given a fraction Unit 16 – Multiplying and dividing decimals (2) Multiply a whole number or fraction by a whole number or fraction Multiply a mixed number and a whole number Divide a whole number or proper fraction by a whole number or proper fraction

#### Summer 1: Algebra

 Unit 17 – Order of operations (2) Carry out calculations involving all four operations Understand and use brackets Use simple index notation Unit 18 – Introduction to algebra (2) Recognise and continue sequences Represent an unknown number using a letter Write and understand simple algebraic expressions Substitute numerical values into formulae and expressions Collect like terms and simplify expressions Multiply out brackets, identify and take out common factors to factorise Recognise that different-looking expressions may be identical and prove simple algebraic identities Unit 19 – Algebraic generalisation project (1)

#### Summer 2: Percentages and Handling Data

 Unit 20 – Percentages (2) Understand percentage as a fractional operator with denominator of 100 Express a part of a whole as a percentage Convert between fractions, decimals and percentages Find fractions and percentages of given quantities Find the whole given a part and the percentage Increasing and decreasing by a percentage Unit 21 – Handling data (2) Understand the difference between types of data Construct and interpret Tables (including tally and two way) Bar charts (including comparative and composite) Pictograms Line graphs Read and interpret pie charts Draw pie charts from raw data Explore misleading graphical representations

### Year 8

#### Autumn 1: Working with Numbers

 Unit 1 – Primes and factorising (2 weeks) Find the factors and multiples of a number Find the prime factors of a number Determine HCF and LCM by prime factorisation Find squares, square roots, cubes and cube roots using prime factorisation Use indices to record repeated multiplication Y7 U5, U16 Unit 2– Add and subtract fraction (3) Use equivalent fractions Add and subtract fractions with like and unlike denominators Add and subtract fractions mixed numbers and improper fractions Convert between improper fractions and mixed numbers  Add and subtract fractions mixed numbers and improper fractions Y7 U13, U14, U15

#### Autumn 2: Number and Algebra

 Unit 3– Positive and negative numbers (2) Represent and order positive and negative integers on a number line (using the symbols >, ³, <, and £) Show addition and subtraction on a number line Apply the four basic operations on positive and negative integers Calculate with rational and decimal numbers (including negative numbers) Y7 U16 Unit 4 – Sequences, expressions and equations (3) Recognise and represent number patterns (including finding an algebraic expression for the th term) Distinguish between terms and coefficients in algebraic expressions Distinguish between like and unlike terms in algebraic expressions Simplify expressions, collect like terms and expand and factorise linear expressions Substitute numerical values into formulae and expressions Solve linear equations in one unknown Solve simple fractional equations that can be reduced to linear equations Formulate a linear equation in one unknown to solve problems Y7 U16, U17 Y8 U3

#### Spring 1: 2D Geometry

 Unit 5 – Triangles, quadrilaterals and angles in parallel lines (3) Construct a triangle from given information (sides/angles) Classify special quadrilaterals on the basis of their properties: define a parallelogram, rhombus and trapezium Construct a quadrilaterals from given information (sides/angles) Identify the different types of angles formed by parallel lines and a transversal such as corresponding angles, alternate angles and interior angles Use the various properties of angles to find unknown angles Find unknown angles in geometrical figures involving square, rectangle, parallelogram, rhombus, trapezium and triangle Y7 U9, U10, U11 Unit 6 – Length and area: parallelograms and trapezia (2) Convert between cm2 and m2 Find the area and perimeter of a figure made up of some of the following shapes: square, rectangle, triangle Find the areas of parallelograms and trapezia Find the areas and perimeters of composite plane figures Solve word problems involving area and perimeter Y7 U4, U7, U8, U10, U11

#### Spring 2: Proportional Reasoning

 Unit 7 – Percentage change (2) Use percentages greater than 100% Express one quantity as a percentage of another Compare two quantities by percentage Increase or decrease a quantity by a given percentage Understand how to compare quantities using percentages Reverse percentages: find the original quantity given a part of it and its percentage Reverse percentages: find the original quantity when we know its final value after the percentage increase or decrease Solve problems involving percentages and reverse percentages Y7 U19 Unit 8 – Ratio and rate (3) Interpret  and , where ,  and  are whole numbers Compare two or more quantities by ratio Understand the relationship between ratios and fractions Write equivalent ratios, and find the missing term in a pair of equivalent ratios Express ratios involving rational numbers in their simplest form Divide a quantity in a given ratio Find the whole/ one part when a whole is divided into parts in a given ratio Solve word problems involving ratio Use the relationship between distance, time and speed Write speed in different units such as km/h, m/min, m/s and cm/s Convert from one unit of speed to another (e.g. km/h to m/s) Solve word problems involving speed, uniform speed and average speed Y7 U13, U14, U15

#### Summer 1: 2D and 3D Geometry

 Unit 9 – Rounding (1) Round off a number to a required number of decimal places Round off a number to a required number of significant figures Estimate the answer to a given problem Identify rounding and truncation errors Y7 U1, U4 Unit 10 – Circumference and area of a circle (2) Use formulae to calculate the area and circumference of a circle Find the area and perimeter of semicircle (half circle) quarter circle Solve word problems involving area and perimeter Unit 11 – 3D shapes and nets (1) Recognise nets of 3D shapes Build and name 3D shapes Draw plans and elevations of a given solid Identify a solid from its plans and elevations Unit 12 – Surface area and volume (2) Find the volumes of cubes and cuboids Find the volumes of prisms and cylinders Find the volumes of composite solids Explore the surface area of cubes, cuboids, cylinders other prisms and  composite solids Convert between cm3 and m3 Y7 U6, U8 Y8 U6

#### Summer 2: Handling data

 Unit 13 –statistics (2) Find the mean, median more and range from raw datasets Use the mean/median/mode to compare data sets Use an average plus the range to compare datasets Find the mode, median and mean from tables and graphical representations (not grouped) Explore methods of data collection including surveys, questionnaires and the use of secondary data Appreciate the difference between discrete and continuous data Classify and tabulate data Conduct statistical investigations using collected data Draw, analyse and interpret graphs including those met in year 7 Y7 U20

### Year 9

#### Autumn 1: Graphs and Proportion

 Unit 1 Coordinates (1 week) Plot coordinates in all four quadrants Find the midpoint of a line segment joining two points Find an endpoint of a line segment, given the midpoint and one endpoint Solve problems using coordinate grids Y8 U3 Unit 2Linear graphs (2 weeks) Identify the equations of horizontal and vertical lines Plot coordinates from a rule to generate a straight line Identify key features of a linear graph Make links between the graphical and the algebraic representation Identify parallel lines from algebraic equations Y7 U18 Y8 U4 Unit 3Proportion (2 weeks) Recognise when two quantities are directly or inversely proportional to each other Recognise the graphical representation of a proportional relationship Solve proportion problems Interpret and use conversion graphs and other graphs of proportional relationships Y8 U8 Unit 4Scales and standard form (1) Use standard form to express very large and small numbers Convert between standard form and ordinary numbers Order large and small numbers KS4 content:  Use standard form to solve simple problems Use scales to solve distance and area problems in context Y7 U4

#### Autumn 2: Algebra

 Unit 5Linear and non-linear sequences (1 week) Recognise that linear and quadratic expressions can be used to represent sequences of different types Recognise arithmetic and geometric sequences and appreciate other sequences that may arise Solve problems involving linear and non-linear sequences in a variety of contexts Y7 U18 Y8 U4 Unit 6  Expanding and factorising (2 weeks) Multiply a term over a single bracket Expand products of two or more binomials Factorise expressions into a single bracket KS4 Content: Factorise quadratic expressions where the coefficient of  is equal to one Y7 U18 Y8 U4 Unit 7 Changing the subject of a formula (2 weeks) Write expressions, equations and formulae to represent relationships Use substitution to find the value of one variable given other values Make links between solving linear equations and rearranging formulae Apply “changing the subject” to equations of straight lines Manipulate familiar formulae such as formulae for area and perimeter Y7 U18 Y8 U4

#### Spring 1: 2D Geometry

 Unit 8Constructions (1 week) Use the standard ruler and compass constructions for: perpendicular bisector of a line segment constructing a perpendicular to a given line from/at a given point bisecting a given angle Understand and use the perpendicular distance from a point to a line as the shortest distance to the line Y7 U10Y7 U11Y7 U12 Y8 U5 Unit 9Congruence(1 week) Know the criteria for congruence of triangles Apply properties of plane figures, and the criteria for congruence, using appropriate language Y7 U11Y7 U12 Y8 U5 Unit 10Pythagoras’ theorem (2 weeks) Derive Pythagoras’ theorem Use Pythagoras’ theorem to find missing sides in right-angled triangles Solve associated problems in other shapes where right-angled triangles exist Deduce whether a triangle is right-angled by considering its sides Y8U1 Unit 11Angles in polygons (1 week) Derive the proof of the sum of the angles in a triangle Find the formula for sum of the angles of any polygon Understand and use the sum of the exterior angles of a polygon Solve problems involving the angles/number of sides in a regular polygon Y7 U10Y7 U11Y7 U12 Y8 U5

Spring 2: Equations and Inequalities

 Unit 12Linear equations and inequalities (3 weeks) Form and solve linear equations and inequalities in one unknown, including those where the unknown appears on both sides Rearrange and solve linear equations and inequalities given in any form, including those involving fractions and brackets Y7 U18Y8 U4 Y9 U2 Unit 13Graphical solutions (2 weeks) Use linear and quadratic graphs to estimate values of  for given values of   Use linear graphs to find approximate solutions of simultaneous linear equations KS4 content: Solve simultaneous equations algebraically Find approximate solutions to contextual problems from given graphs of a variety of functions including: Piecewise linear (e.g. real-life linear graphs) Exponential Reciprocal Y9 U1Y9 U2

#### Summer 1: Handling Data and Probability

 Unit 14Probability (3 weeks) Understand and use the probability scale from 0 to 1 Understand and use the language associated with probability Understand the relationship between relative frequency and theoretical probability Understand that different trials of an experiment may produce different outcomes Systematically list outcomes using a variety of representations Use Venn diagrams and understand the meaning of union and intersection KS4 content: Frequency tree diagrams Y7 U4Y7 U14Y7 U15Y7 U16Y7 U20 Unit 15 Working with data (1 week) Appreciate the difference between discrete and continuous data Understand why the exact mean cannot be found from grouped data Find an estimate of the mean from grouped data and continuous data Describe, interpret and compare distributions, involving appropriate measures of central tendency and spread Y8 U13 Unit 16Scatter graphs (1 week) Plot scatter graphs Describe the type of correlation observed Interpret correlation in context Y9 U1Y9 U2

#### Summer 2: Geometry

 Unit 17Similarity and enlargement (1 week) Enlarge shapes from a given centre, with and without coordinate grids Understand that the corresponding angles of similar shapes are equal Solve problems involving similar triangles Y8 U8Y9 U9 Unit 18Transformations (2 weeks) Translate a shape by a given vector Reflect a shape in a line, including on coordinate axes Rotate a shape about a centre, including on coordinate axes Identify the type of transformation carried out by comparing an object and image Y8 U3 Y9 U1Y9 U2 Unit 19Trigonometry (2 weeks) Develop an understanding of the trigonometric ratios Solve problems using trigonometric ratios in right-angled triangles Y9 U10Y9 U17