# Mathematics

“When He established the heavens, I was there; When He inscribed a circle on the face of the deep, I was there when he established the heavens, when he laid out the horizon on the surface of the ocean, I was there when he established the heavens, when he drew the horizon on the oceans. When he prepared the heavens, I *was* there: when he set a compass upon the face of the depth.”

Proverbs 8:27

#### Overview

#### KS3 Curriculum

In Key Stage 3 (KS3), pupils will be introduced to multiple new mathematical concepts and ideas, whilst also revisiting and extending upon some of the mathematics they have learnt previously. The core aims are to:

- Develop fluency with each concept
- Be able to apply mathematical reasoning to explain/justify
- Use what they have learnt to solve problems of varying difficulty.

Pupils will be challenged to think mathematically and will be expected to try their best each lesson. Everyone can do Maths!

#### Year 7

##### Sequences

Linear and non-linear sequences

Interpret/draw sequences graphically

Recognise arithmetic, geometric, and other types of sequences

Understand and use Algebraic Notation

Use functions machines numerically and algebraically

Use letters/symbols to define unknown values

##### Substitute into expressions

Equality and Equivalence

Understand equality, and fact families (numerically and algebraically)

Form and solve one-step equations, using inverse operations

Simplify expressions, by collecting like terms

##### Place Value

Recognise and use numbers up to one billion, in words, figures, and with diagrams and number lines

Compare, order and round integers and decimals

Find the range and median of sets of numbers

Investigate numbers in standard index form

##### Fractions, Decimals and Percentages

Represent fractions, decimals and percentages using diagrams and number lines

Convert fluently between fractions, decimals and percentages

Convert between improper fractions and mixed numbers

##### Applications of Addition and Subtraction

Develop mental and written methods for addition and subtraction of integers and decimals

Solve problems involving perimeter, financial mathematics, time

Construct and interpret frequency trees, bar charts and line graphs

##### Applications of Multiplication and Division

Develop mental and written method for multiplication and division of integers and decimals

Understand factors, multiples, highest common factor (HCF) and lowest common multiple (LCM)

Convert metric units of length, capacity and mass

Use order of operations (BIDMAS)

Solve problems involving area of rectangles, triangles, parallelograms and compound shapes

Find fraction of an amount, percentage of an amount

Find the mean of sets of numbers

##### Directed Numbers

Order directed numbers using diagrams and number lines

Add, subtract, multiply and divide directed numbers

Using a scientific calculator efficiently

Form and solve two-step equations, including with directed numbers

Adding and Subtracting Fractions

Add and subtract fractions and mixed numbers with a common denominator

Add and subtract fractions and mixed numbers with different denominators (by finding a common denominator)

Solve problems involving fractions and mixed numbers

##### Construct, Measure and use Geometric Notation

Develop labelling of vertices, sides and faces of shapes

Understand parallel and perpendicular lines, and types of triangles and quadrilaterals

Measure and draw angles using a protractor, and construct triangles

##### Geometric Reasoning

Use angle facts on a line, around a point, in a triangle, in a quadrilateral, and vertically opposite

Solve problems involving angles in triangles and quadrilaterals

##### Sets and Probability

Identify and represent sets

Draw and interpret Venn diagrams

Understand and use the rules of probability

##### Prime Numbers and Proof

Recognise prime numbers, square numbers and triangular numbers

Write a number as a product of its prime factors

Create and test/disprove mathematical conjectures

##### Developing Number Sense

Develop mental strategies to simplify problems

Use estimation

Use known numbers and algebraic facts to derive other facts

#### Year 8

##### Sequences

Generate sequences from a position-to-term rule

Find the nth term of a linear (arithmetic) sequence

Find the nth term for other sequences and patterns

##### Expand and Factorise Expressions

Multiply to expand single brackets

Expand two sets of single brackets, and simplify the expression by collecting like terms

Expand double brackets

Factorise expressions by taking out the highest common factor

##### Ratio

Express, simplify and compare ratios

Express ratios in the form 1:n and/or n:1, and solve problems

Divide a quantity into a ratio, and solve more complex problems

Recognise and use pi (π) as the ratio between the circumference and diameter of a circle

##### Equations and Inequalities

Form and solve two-step equations, and three-step equations involving brackets

Form and solve equations involving unknowns on both sides

Represent inequalities on number lines, and form inequalities from number lines

Solve linear inequalities and find sets of integers which satisfy an inequality

##### Indices

Evaluate expressions involving squares, cubes and roots (mentally and using a scientific calculator)

Add, subtract, multiply and divide numbers in index form

Use the laws of indices to multiply and divide numbers written in index form

##### Multiplicative Change

Solve problems involving direct proportion, including recipes

Explore similar shapes, and scale factors / scale drawings

Draw and interpret scale drawings, and interpret maps using scale and ratios

##### Multiplying and Dividing Fractions

Multiply and divide an integer by a fraction

Multiply and divide fractions

Multiply and divide mixed numbers

##### Percentages

Calculate percentages of amounts (mentally and using a scientific calculator)

Calculate percentage increase and decrease (mentally and using a scientific calculator)

Calculate percentage change (mentally and using a scientific calculator)

##### Standard Index Form

Write a number in standard index form (positive and negative indices)

Convert a number from standard index form back into an ‘ordinary’ number (positive and negative indices)

Add and subtract numbers in standard form (mentally and using a scientific calculator)

##### Number Sense

Round numbers to a given number of decimal places / significant figures

Use estimation

Use inequality notation to show an error interval for a rounded number

##### Working in the Cartesian Plane

Plot and read coordinates in all four quadrants, and solve problems to find missing coordinates

Recognise and draw equations of horizontal and vertical lines, including the x and y axes

Recognise and draw equations of y=x and y=-x

Plot graphs of functions in the form y=mx+c

Find/interpret the gradient of a line, and find/interpret the y-intercept of a line

Find the midpoint of two points, graphically and algebraically

##### Representing Data

Draw and interpret scatter graphs of bivariate data

Identify outliers, draw a line of best fit, and make predictions

Understand types of correlation

Draw and complete two-way tables

List outcomes for single and combined events systematically

##### Tables and Probability

Construct sample space diagrams for more than one event

Find probabilities from a sample space diagram

##### Angles

Revisit angle rules and use in complex diagrams

Find angles in parallel lines, using alternate, corresponding and co-interior angle rules

##### Area

Find area of composite shapes

Solve problems involving area, including money, fractions and algebra

##### Plans and Elevations

Visualise and draw plan view, front and side elevations of a 3D shape

Sketch a 3D shape from its plan view, front and side elevations

##### The Data Handling Cycle

Interpret statistical diagrams, including vertical line graphs, time series, pie charts & bar charts (dual and composite)

Construct and interpret pie charts

##### Measures of Location

Revisit mean, median, mode & range

Solve problems involving the reverse mean

##### Constructions

Use a ruler and pair of compasses to construct the bisector of a given angle

Use a ruler and pair of compasses to construct angles of 90o and 45o

#### Year 9

Straight Line Graphs

Plot and interpret graphs in the form y=mx+c

Find the equation of a straight line from a graph, from the gradient & y-intercept, and from two coordinates

Find solutions to linear simultaneous equations graphically

##### Ratio and Proportion

Direction and inverse proportion problems and graphs, including drawing and interpreting conversion graphs

Currency conversions, working with recipes and scale

Divide a quantity into a ratio, and solve more complex problems – extending from Year 8

Solve problems by combining ratios

##### Area

Revisit area of rectangles, parallelograms, triangles, and compound shapes

Find the area of a trapezium, and solve problems

Find the area of a circle, and solve problems

##### 3D Shapes

3D shapes, including finding the number of faces, edges and vertices, and drawing nets

Find the surface area of prisms, including cubes, cuboids, triangular prisms, cylinders.

Draw and interpret plans and elevations of 3D shapes, and sketch a shape from its plan and elevations

##### Algebraic Thinking

Form and solve equations in a variety of contexts

Change the subject of formulae

Expand double and triple brackets

Factorise and solve simple quadratic equations

##### Volume

Find the volume of prisms, including cubes, cuboids, triangular prisms, cylinders

##### Compound Measures

Solve problems involving speed, distance, time

Solve problems involving density, mass, volume

Solve problems involving pressure, force, area

##### Standard Index Form

Revisit writing numbers in standard form, and converting back into regular form

Multiply and divide numbers in standard form

##### Percentages

Revisit percentage change with and without a calculator, including simple interest

Solve problems involving compound interest and depreciation

Reverse percentage problems

Repeated percentage change problems

##### YEAR 9 MONEY WEEK

Work with contexts around bills, wages, tax, interest, bank statements

Value for money

##### Angle Rules

Revisit angle rules on a straight line, in a triangle, around a point, in a quadrilateral

Revisit angle rules on parallel lines

Introduce bearings – drawing, measuring, reading, calculating

Solve algebraic problems involving angles

##### Congruency and Enlargement

Understand congruency and similarity – differences between them

Enlarge shapes by a positive integer scale factor, and by a positive fractional scale factor

Describe enlargements fully

##### Pythagoras’ Theorem

Introduction to Pythagoras’ Theorem with right-angled triangles – language of hypotenuse

Use Pythagoras’ Theorem to find missing lengths in right-angled triangles

Use Pythagoras’ Theorem to solve problems

Investigate trigonometric ratios (introduction to trigonometry) in right-angled triangles

##### Transformations

Identify and draw lines of symmetry; Identify the order of rotational symmetry of shapes

Drawing and describing reflections

Drawing and describing translations, including introducing column vectors

Drawing and describing rotations

Combining multiple transformations

##### Statistics

Find mode and range from lists and frequency tables, for both discrete and continuous data

Calculate the mean from lists and frequency tables, for both discrete and continuous data

##### Graphs

Recognise, sketch & produce graphs of quadratic functions

Recognise reciprocal and reciprocal graphs

##### Testing Conjectures

Investigate mathematical conjectures, including true/false problems, always/sometimes/never problems

##### Constructions

Construct, using pairs of compasses, an angle bisector

Construct, using pairs of compasses, a perpendicular bisector of a line