# KS3 Curriculum Overview: Maths

## Year 7

### Autumn Term 1

#### Project

‘How to make a profit running a shop in centre MK’

Sustainability – Students will consider sustainability with their packaging. They will also look at how they can support the Milton Keynes economy.
Milton Keynes – considering what is like to run a business in Milton Keynes

##### Knowledge & Skills
• Understand profit and loss.
• Percentages and fractions.
• Area, scale drawing and surface area.
• Line graphs
• Problem solving, research, planning and organisation, collecting, using and distilling data
• Presentation

### Autumn Term 2

#### Algebra

• Introduction to algebraic notation
• Sequences
• Solving simple equations
• Coordinates and graphs

STEM – Use of algebra in many different STEM areas
– Highlight use of graphs

##### Knowledge & Skills
###### Introduction to algebraic notation
• Use and interpret algebraic notation
• Collect like terms
• Multiplying a single term over a bracket
###### Sequences
• Generate terms of a sequence
• Find term-to-term and position-to-term rule
• Use the nth term
###### Solving simple equations
• Use algebraic methods to solve linear equations in one variable
###### Coordinates and graphs
• Work with coordinates in all four quadrants
• Sketch graphs of linear functions of one variable (ranging from y = 1 to y = 3x – 4)

Listening, making links and applying knowledge, resilience and learning from mistakes (algebra is something that students may not get immediately so they will need to build up resilience to overcome issues)

##### Assessment
• Knowledge test (low stakes assessment throughout term)

### Spring Term 1

#### Properties of number; Calculations using 4 operations; Measures and Scale Factors; Area and Perimeter; Averages

STEM

##### Knowledge & Skills
###### Properties of number
• Use the concepts and vocabulary of prime numbers, factors, multiples
• Calculate highest common factor and lowest common multiple
• Use conventional notation for the priority of operations (BIDMAS)
• Use integer powers and associated real roots (squares and cubes)
###### Calculations using 4 operations
• Use four operations, including formal written methods
• Recognise relationships between inverse operations
###### Measures and Scale Factors
• Change freely between related standards units (time, length)
• Use scale factors, scale diagrams and maps
###### Area and Perimeter
• Derive and apply formulae to calculate and solve problems including: perimeter, area of triangles, parallelograms, trapeziums
• Calculate and solve problems involving: perimeters of 2D shapes, area of circles and composite shapes
###### Averages
• Calculate appropriate measures of central tendency (mean, mode, median) and spread (range)

Problem solving, questioning, thinking and reasoning, making links and applying knowledge

##### Assessment
• Knowledge test (low stakes assessment throughout term)

### Spring Term 2

#### Directed Numbers; Percentages; Calculations involving fractions

STEM

##### Knowledge & Skills
###### Directed Numbers
• Understand and use place value for decimals, measures and integers of any size
• Order positive and negative integers
• Use four operations with both positive and negative integers
###### Percentages
• Define percentage as ‘number of parts per hundred’
• Interpret percentages as operators
• Solve problems involving percentage changes, including: percentage increase and decrease
###### Calculations with fractions
• Calculate fractions of amounts
• Convert between improper fractions and mixed numbers
• Use the four operations with proper and improper fractions and mixed numbers

Potential project: The face of a country in fractions

Problem solving, research, planning and organisation, making links and applying knowledge, questioning, communication

##### Assessment
• Knowledge test (low stakes assessment throughout term)

### Summer Term 1

STEM

##### Knowledge & Skills
###### Introduction to probability
• 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
• Understand that the probabilities of all possible outcomes sum to 1
###### Use of Ratio Notation
• Use ratio notation, including reduction to simplest form
• Divide a given quantity into two parts in a given ratio

Potential project: Designing the world around me

Creating, imagining and innovating, communication, questioning, problem solving, research, planning and organisation

##### Assessment
• Knowledge test (low stakes assessment throughout term)

### Summer Term 2

#### Transformations; Properties of shape; Angles; Charts and graphs

STEM

##### Knowledge & Skills
###### Transformations
• Identify properties of and describe the results of translations, rotations and reflections applied to given figures
###### Properties of shape
• Draw and measure line segments and angles in geometric figures
• Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons
• Derive and illustrate properties of triangles, quadrilaterals and other plane figures (e.g. equal lengths and angles) using appropriate language
###### Angles
• Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
• Derive and use the sum of angles in a triangle
• Understand the relationship between parallel lines and alternate and corresponding angles
###### Charts and Graphs
• Construct and interpret appropriate tables, charts and diagrams, including frequency tables, bar charts and pictograms for categorical data and vertical line (or bar) charts for ungrouped and grouped numerical data

Potential project: Planning and making mathematical games and crafts

Collecting, using and distilling data, problem solving, research, planning and organisation, communication, listening

##### Assessment
• Knowledge test (low stakes assessment throughout term)

## Year 8

### Autumn Term 1

#### Algebra

• Algebra notation (brackets)
• Sequences
• Coordinates and Linear graphs
• Properties of number

STEM – use of graphs in many STEM related careers

##### Knowledge & Skills
###### Algebra Notation
• Recap on Year 7 knowledge
• Go over simplifying expressions and substitution
• Multiply a single term over a bracket
• Taking out common factors
###### Sequences
• Recap on Year 7 knowledge
• Recognise arithmetic sequences and find the nth term
###### Linear Graphs
• Recap on Year 7 knowledge of coordinates
• Recognise, sketch and produce graphs of linear functions of one variable
• Use linear graphs to estimate values of y for given values of x
• Reduce a given linear equation in two variables to the standard form y=mx+c
###### Properties of Number
• Recap on Year 7 knowledge
• Further examples on Highest common factor and lowest common multiple
• Recap knowledge of cubes, primes, roots and square numbers

Resilience, questioning, problem solving, making links and applying knowledge

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Autumn Term 2

#### Rounding and estimation; Measures and Scale factors; Area and Perimeter; Directed numbers

STEM – encourage use of rounding and estimation in shopping

##### Knowledge & Skills
###### Rounding and estimation
• Round numbers and measures to an appropriate degree of accuracy (for example, to a number of decimal places or significant figures)
• Use approximation through rounding to estimate answers (basic examples)
###### Measures and Converting units
• Multiplication and division by powers of 10
• Change freely between related standards units (time, length, area, volume)
• Use scale factors, scale diagrams and maps
###### Area and Perimeter (circles focus)
• Recap on Year 7 knowledge
• Calculate and solve problems involving perimeters of 2D shapes (including circles), area of circles and composite shapes
###### Directed Numbers
• Recap on Year 7 knowledge

Thinking and reasoning, making links and applying knowledge

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Spring Term 1

#### Solving equations; Calculations involving fractions; Probability

Milton Keynes – Milton Keynes link process of ratios and percentages to real situations found in MK

##### Knowledge & Skills
###### Equations and Inequalities
• Recap on Year 7 knowledge
• Use algebraic methods to solve linear equations in one variable
• Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
###### Fractions
• Recap on Year 7 knowledge
• Work interchangeably between terminating decimals and their corresponding fractions
• Interpret fractions as operators
###### Probability
• Recap on Year 7 knowledge
• Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities

Questioning, listening communication, thinking and reasoning

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Spring Term 2

#### Ratio Notation; Transformations; Percentages

Sustainability – Sustainability when producing items

##### Knowledge & Skills
###### Use of ratio
• Recap on Year 7 knowledge
• Use ratio notation
• Solve problems involving ratio notation
• Divide a given quantity into two parts
###### Transformations
• Recap on Year 7 knowledge and extend with further reflections, rotations and translations
###### Percentages and percentage change
• Recap on Year 7 knowledge
• Solve problems involving percentage changes, including: percentage increase and decrease.
• Interpret percentages as operators

Creating, imagining and innovating, problem solving, making links and applying knowledge, questioning

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Summer Term 1

#### Properties of shape; Angles; Volume and Surface area

Character – a lot of discussion in groups and classes on opinions. Students to uphold ethos of character when expressing their opinions

##### Knowledge & Skills
###### Properties of shape
• Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons
• Derive and illustrate properties of triangles, quadrilaterals and other plane figures (e.g. equal lengths and angles) using appropriate language
###### Angles and parallel lines
• Recap on Year 7 knowledge
• Understand and use the relationship between parallel lines and alternate and corresponding angles
###### Volume and surface area
• Recap on area knowledge from year 7
• Derive and apply formulae to calculate and solve problems involving volume of cuboids (including cubes) and other prisms
• Calculate the surface area of cubes and cuboids
• Use the properties of faces, surfaces, edges and vertices of cubes, cuboids and prisms to solve problems in 3D

Collecting, using and distilling data, planning and organisation, communication, listening, questioning

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Summer Term 2

#### Charts and graphs; Averages; Scatter graphs

STEM – Use of algebra and equations in software production

##### Knowledge & Skills
###### Charts and graphs
• Recap on Year 7 knowledge
• Include pie charts
###### Averages and tables
• Recap on Year 7 knowledge
• Use of tables to represent measures of central tendency (mean, mode, median) and spread (range)
###### Scatter graphs
• Describe simple mathematical relationships between two variable in observational and experimental contexts and illustrate using scatter graphs

Problem solving, questioning, resilience, risk taking

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

## Year 9

### Autumn Term 1

#### Algebraic notation; Sequences (nth term); Graphs (linear and quadratic); Ratio and Proportion

STEM – Use of algebra throughout many different programing areas

##### Knowledge & Skills
###### Algebraic Notation
• Recap on Year 8 knowledge
• Taking out common factors
• Multiplying a single term over a bracket
• Expanding products of two or more binomials
###### Sequences
• Recap on Year 8 knowledge
• Recognise geometric sequences and appreciate other sequences that arise
• Recap on Year 8 knowledge
• Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
• Recognise, sketch and produce graphs of linear and quadratic functions of one variable
• Interpret mathematical relationships both algebraically and graphically
• Use and interpret y=mx+c, calculate and interpret gradients and intercepts of graphs
###### Ratio and Proportion
• Build upon Year 8 knowledge
• Solve problems involving direct and inverse proportion, including graphical representations
• Algebraic representations to only be used with highest ability

Problem solving, communication, creating, imagining and innovating, making links and applying knowledge

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Autumn Term 2

#### Compound units and Measures; Properties of Number; Rounding; Estimation and bounds; Averages and charts; Directed Numbers

STEM – Estimation and bounds link to real life scenarios through engineering

##### Knowledge & Skills
###### Compound Units and Measures
• Use of real life graphs to interpret compound units
• Use compound units such as speed, unit pricing and density to solve problems
###### Properties of number
• Recap on Year 8 knowledge
• Use of Venn diagrams for HCF and LCM
• Potential introduction of surds
###### Rounding, Estimation and Bounds
• Recap on Year 8 knowledge
• Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation
###### Averages and charts
• Build upon Year 8 knowledge
• Compare distributions using averages
###### Directed Numbers
• Recap on year 8 knowledge using 4 operations with directed numbers
• Solve problems with directed numbers

Thinking and reasoning, making links and applying knowledge

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Spring Term 1

#### Standard Form; Percentages; Fractions; Probability

STEM – Use of percentages in real life

##### Knowledge & Skills
###### Standard form
• Recap on year 8 knowledge of powers and roots
• Interpret and compare numbers in standard form, when n is a positive or negative integer or zero
###### Percentage problems including interest
• Recap on Year 8 knowledge
• Solve problems involving percentage change including original value problems and simple interest in financial mathematics
###### Fractions
• Recap on Year 8 knowledge
• More calculations with mixed numbers
###### Probability including diagrams
• Recap on Year 8 probability
###### Venn diagrams
• Enumerate sets and unions/intersections of sets systematically using tables, grids and Venn diagrams (with-hold use of set notation)
###### Tree diagrams
• Use tree diagrams to calculate probability

Questioning, listening communication, thinking and reasoning, problem solving

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Spring Term 2

#### Area and Perimeter; Volume and Surface Area; Plans and elevations; Loci and constructions

Milton Keynes – plans and elevations use real life examples of MK planning
Sustainability – volume and surface area considerations of packaging and other things and how to be sustainable

##### Knowledge & Skills
###### Area, volume and surface area
• Recap on year 8 knowledge
• Derive and apply formulae to calculate and solve problems including volume of prisms (including cylinders)
• Calculate surface area of prisms
• Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D
###### Plans and Elevations
• Construct views of 3D shapes including front, plan and side views
• Use of isometric paper
###### Loci and constructions
• 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
• Construct triangles

Creating, imagining and innovating, problem solving, making links and applying knowledge, questioning

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Summer Term 1

#### Angles; Pythagoras (and trigonometry); Similar Shapes; Transformations

STEM – Drawings and scales – how similar shapes are used – link to careers

##### Knowledge & Skills
###### Angles
• Recap on year 8 knowledge
• 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
###### Pythagoras
• Use Pythagoras’ Theorem to solve problems involving right angled triangles
###### Similar shapes
• Use the standard conventions of labelling the sides and angles of triangle ABC and know and use the criteria for congruence of triangles
• Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides
###### Transformations including enlargement
• Recap on Year 8 knowledge
• Identify and construct congruent triangles and construct similar shapes by enlargement with and without coordinate grids

Creating, imagining and innovating, problem solving, making links and applying knowledge, questioning

##### Assessment
• Knowledge test (low stakes assessments throughout the term)

### Summer Term 2

#### Equations and Inequalities; Changing the subject; Charts and graphs (including scatter graphs)

Sustainability – charts and graphs linked to several different environmental factors
Milton Keynes – charts and graphs linked to the growth of Milton Keynes

##### Knowledge & Skills
###### Equations and Inequalities
• Recap on year 8 knowledge
• Build upon solving equations, including solving inequalities
• Potential to find solutions of simultaneous equations
###### Changing the subject
• Understand and use mathematical formulae; rearrange formulae to change the subject
###### Charts and graphs
• Recap on year 8 knowledge include histograms
###### Scatter graphs
• Describe simple mathematical relationships between two variable in observational and experimental contexts and illustrate using scatter graphs

Collecting, using and distilling data, planning and organisation, communication, listening, questioning

##### Assessment
• Knowledge test (low stakes assessments throughout the term)