KS3 Mathematics

Module 1 - The Grammar of Written Calculations

Key Concept

Form

Related Concept(s)

Representations and systems

ATLs

Communication: Interpet and use effectively modes of non-verbal communication.
Collaboration: Listen actively to others perspectives and ideas

Core declarative knowledge: What should students know?

What is a number?
What is the difference between measuring and counting?
Why is using place value helpful?
What is base 10?
What is the relationship between place value columns?
Describe what happens when you multiply by 10, 100 or 1000?
How does rounding help with estimating?
When might mental methods be more efficient than written methods?
What is multiplication?
What is division?
Is division commutative?
How are multiplication and division linked?
What happens if a number does not divide exactly?
What is commutativity, associativity & disributivity?
How do arrays and area models help you understand commutativity of multiplication?
How do arrays and area models help you understand associativity and distributivity?

Core procedural knowledge: What should students be able to do?

Recognise concrete representations and place value models of integers and decimals
Understand decimal notation and place values and identify the values of the digits in a decimal
Convert between decimal and fraction where the denominator is a factor of 10 or 100
Use correctly the symbols <, > and the associated language
Multiply, and divide, any integer or decimal by 10, 100, 1000, or 10,000
Mentally add and subtract sets of numbers including decimals
Use the commutativity and associativity of addition
Understand and use the formal written algorithms for addition and subtraction including decimals
Use commutativity, associativity and distributivity to solve calculations efficiently
Use column method to multiply integers
Use a formal algorithm for division
Multiply and divide whole numbers and decimals
Find factors and multiples.
Recognise and define: prime, square and cube numbers
Use the definitions of factors and multiples to find common factors and common multiples
Express an integer as a product of its factors

Links to prior learning (to be made explicit and tested)

Primary KS1 & KS2 Maths

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/335158/PRIMARY_national_curriculum_-_Mathematics_220714.pdf

Use the number line to display decimals and round decimals to the nearest whole number, to 1 or 2 dp Round whole numbers to the nearest 1000, 100 or 10 Mark the approximate position of a number on a number line Read and write decimals with up to 6 digits in figures and words Use approximation to estimate the answers to calculations Relate decimal arithmetic to integer arithmetic

Link to assessment (criterion A and ‘x’)

A and C

Module 2 - Negatives & Introduction to Algebra

Key Concept

Form

Related Concept(s)

Quantity and representations

ATLs

Communication: Understand and use mathematical notation
Collaboration: Give and receive meaningful feedback

Core declarative knowledge: What should students know?

Does the order of addition and subtraction matter?
Why might BIDMAS be misleading?
Does it make a difference if you multiply or divide first? Where else have we met this idea?
Why might you want to divide first? Why might you want to multiply first?
For worded problems, should we apply operations in the same order that they appear?
How are indices linked to multiplication? Can you think of any similar relationships?
What does equal priority mean?
How can the language of temperature help me work out calculations?
How can multiplying negative numbers help me in dividing negative numbers?
What links can I make between addition and multiplication of negative numbers?
How does multiplying and dividing by negatives affect the concept of multiplication as scaling?
If I am adding a negative number, does my number want to get more/less positive/negative?
If I am subtracting a negative number, does my number want to get more/less positive/negative?
Why do we need to use letters?
What can letters in maths represent?
What is the difference between the equal sign and the identity sign?
How can we use substitution to check answers?
What is the difference between 3x^2 and (3x)^2 ?
Is ab the same or different to ba? What about a/b and b/a? a+b and b+a? a-b or b-a?

Core procedural knowledge: What should students be able to do?

Define each element of BIDMAS
Understand the priority of operations, including equal priority
Form and identify equivalent calculations based on distributivity, commutativity and the order of operations
Interpret negative numbers in a variety of contexts
Compare and order positive and negative numbers
Use positive and negative numbers to express change and difference
Calculate using all four operations with positive and negative values
Use number lines to model calculations with negative numbers
Explore scaling with negative multipliers
Form and manipulate expressions involving negative numbers
Use number lines to model calculations with negative numbers
Develop understanding of algebraic notation
Collect like terms to simplify expressions and understand that this is a result of the distributive property
Substitute numerical values into expressions and evaluate
Expand and factorise single brackets
Develop understanding of the equality and inequality signs
Form equations or inequalities from abstract and real life contexts
Use different contexts, including sequences, to construct expressions, equations and inequalities

Links to prior learning (to be made explicit and tested)

Primary
KS1 & KS2 Maths

Recognise the difference between the four operations.
Recognise the relationship between the inverse operations
Being able to represent numbers as a position on a numberline
Knowing the placement of negative numbers
Being able to order negative numbers
0>-1

Link to assessment (criterion A and ‘x’)

A and D

Module 3 - Classifying 2D Shapes

Key Concept

Form

Related Concept(s)

Measurement

ATLs

Affective: Demonstrate persistence and perseverance
Communication: Take effective notes from online lessons

Core declarative knowledge: What should students know?

How would you describe what an angle is?
What do they measure?
What is a degree?
How do you use protractors/angle measurers correctly?
What is a point of intersection?
How could you define a line of symmetry?
What are the possible orders of rotational symmetry for a triangle?
What is the difference between scalene, isosceles and equilateral triangles?
What is the difference the radius and the diameter of a circule?
How do you use a compass correctly?

Core procedural knowledge: What should students be able to do?

Draw and measure acute and obtuse angles to the nearest degree
Estimate the size of a given angle
Know and use the angle facts:
angles at a point, angles at a point on a straight line, vertically opposite angles
Define parallel and perpendicular lines
Use angle facts around corresponding, alternate and cointerior angles to find missing angles
Find unknown angles.
Form algebraic expressions and solve equations related to unknown angles
Define and identify the order of rotational symmetry
Identify and count the lines of symmetry
Describing the properties of scalene, isosceles and equilateral triangles
Know that the interior angles in a triangle sum to 180°
Solve problems involving unknown angles in triangles
Comparing the symmetry, side length, number of parallel sides and angles in quadrilaterals
Naming the basic features of circles.
Constructing triangles using a pair of compasses and ruler given the length of the sides.
Constructing triangles with the same interior angles using a protractor.
Constructing triangles given two sides and an angle

Links to prior learning (to be made explicit and tested)

KS1 & KS2 Maths
Relate the word angle to the distance between two intersecting straight lines
Be able to define acute, obtuse, right angle, straight line in terms of degrees
Be able to recognise a triangle
Be able to recognise different types of triangle
Be able to recognise a circle

From Y7:
Be able to solve equations (From M2)
Be able to form expressions (From M2)
Be able to represent an unknown angle with a letter (From M2)

Link to assessment (criterion A and ‘x’)

A, B and C

Module 4 - The Cartesian Plane

Key Concept

Relationships

Related Concept(s)

Generalisation and measurement

ATLs

Affective: Demonstrate persistence and perseverance
Communication: Take effective notes from online lessons

Core declarative knowledge: What should students know?

Does the order of the numbers matter?
If you know the mid-point, can you find the line segment?
What shapes can be described as rectilinear?
What lengths are multiplied to find the area?
What is the difference between area and perimeter?
What is a vector?
How does moving the point of rotation effect the image?
What is a rotation?
Does an enlargement always make a shape bigger?
Describe the effect of a scale factor of enlargement.

Core procedural knowledge: What should students be able to do?

Reading and writing coordinates of points in all four quadrants. Including non-integer coordinates
Finding the mid-point of a line segment or two points
Using the midpoint and a point on the line to find the coordinates of another point on the line
Recognise and plot horizontal and vertical lines on a coordinate axis
Understanding equations of horizontal and vertical lines
Calculating the perimeter of polygons
Finding the area of rectilinear shapes
Finding the area of other 2-D shapes including triangles, and special quadrilaterals
Find the area & perimeter of compound shapes (inc finding missing sides)
Translate shapes and describe translations using column vectors
Rotate shapes about a point by multiples of 90 degrees, clockwise or anti-clockwise
Describe rotations accurately
Reflecting shapes by horizontal, vertical and diagonal lines
Enlarge a shape by a positive and/or unit fraction scale factor

Links to prior learning (to be made explicit and tested)

KS1 & KS2 Maths:

Be able to define the words horizontal and vertical
Recognise a cartesian plane
Be able to define perimeter and area, recognising the difference

From Y7:
Definition of translation (From Negatives M2)

Link to assessment (criterion A and ‘x’)

A and C

Module 5 - Fractions

Key Concept

Logic

Related Concept(s)

Quantity and simplification

ATLs

Communication: Organise and depict information logically
Affective: Practice focus and concentration to avoid distractions – Independent work

Core declarative knowledge: What should students know?

What is a prime number?
What is the Lowest Common Multiple? (LCM)
What is the Highest Common Factor? (HCF)
What does it mean to prime factorise a number?
What is a numerator? What is a denominator?
What is a improper fraction?
What is a proper fraction?
What is the relationship between the division of fractions and the multiplication of them?
How do we add fractions with unlike denominators?
What does equivalent mean?

Core procedural knowledge: What should students be able to do?

Be able to ‘build’ numbers by considering products.
Use index notation
Find factors and multiples, square numbers, cube numbers, prime number, triangular numbers
Write a number as a product of primes
Find the common factor and common multiple using the prime factorisation
Find the highest common factor and lowest common multiple using the prime factorisation
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 (including like and unlike fractions)
Find a fraction of a set of objects or quantity
Find the whole given a fractional part
Multiply and divide fractions by a whole number or fraction
Add and subtract fractions with like denominators
Add and subtract fractions with unlike denominators
Add and subtract fractions mixed numbers and improper fractions
Convert between improper fractions and mixed numbers

Links to prior learning (to be made explicit and tested)

KS1 & KS2 Maths:
Relationship between fractions, decimals and percentages
Algorithms for manipulation of fractions.

From Y7:
Find factors (From M1)
Find HCF/LCM (From M1)

Link to assessment (criterion A and ‘x’)

A and D

Module 6 - Ratio & Proportion

Key Concept

Logic

Related Concept(s)

Equivalence, quantity and simplification

ATLs

Organisation: Use appropriate strategies for organising complex information
Communication: Make effective notes for studying i.e. Revision notes

Core declarative knowledge: What should students know?

What is a ratio?
Why do we use ratios to share?
What does a part of a ratio look like?
What is a percentage?
Why do we say percent?
What is a bar model?
What is simplifying?
How do decimals and percentages relate to each other?
How can you use a decimal to calculate a percentage of amount?
What does a percentage over 100 mean?

Core procedural knowledge: What should students be able to do?

Compare two or more quantities in a ratio.
Use bar models to represent percentage and ratio
Simplifying ratios.
Understand percentages as a ratio of two quantities where one quantity is standardised to 100.
Interpret a percentage as a fraction and decimal.
Find a percentage of an amount with and without a calculator.
Increase and decrease a quantity by a given percentage.
Compare two quantities using percentages.
Find a quantity given a percentage of it.
Solve ratio and proportion problems in a variety of contexts.
Understand percentages as a fractional operator with a denominator of 100.
Understand and interpret percentages over 100.

Links to prior learning (to be made explicit and tested)

Primary
KS1 & KS2 Maths

Be able to recognise ratio notation
Be able to define percent
Be able to construct bar models for ratio

From Year 7:
Convert FDP (M5)

Link to assessment (criterion A and ‘x’)

A, B and C

Module 1 - Equivalence through Fractions and Percentages

Key Concept

Logic

Related Concept(s)

Equivalence and quantity

ATLs

Thinking: Use visible thinking strategies and techniques
Communication: Organise and depict information logically

Core declarative knowledge: What should students know?

What is a prime number/multiple/factor?
What is the Lowest Common Multiple? (LCM)
What is the Highest Common Factor? (HCF)
What does it mean to prime factorise a number?
What does it mean to simplify?
What is an equivalent fraction?
What is a numerator? What is a denominator?
What is a improper fraction?
What is a proper fraction?
What is the relationship between the division of fractions and the multiplication of them?
How do we add fractions with unlike denominators?
What is a proportion?
What is the relationship between percent and 100?

Core procedural knowledge: What should students be able to do?

Be able to ‘build’ numbers by considering products.
Use index notation
Find factors and multiples, square numbers, cube numbers, prime number, triangular numbers
Write a number as a product of primes
Find the common factor and common multiple using the prime factorisation
Find the highest common factor and lowest common multiple using the prime factorisation
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 (including like and unlike fractions)
Find a fraction of a set of objects or quantity
Find the whole given a fractional part
Multiply and divide fractions by a whole number or fraction
Add and subtract fractions with like denominators
Add and subtract fractions with unlike denominators
Add and subtract fractions mixed numbers and improper fractions
Convert between improper fractions and mixed numbers

Links to prior learning (to be made explicit and tested)

Unit 5.1 of Y7 (2019/20) moved due to school closures.

KS1 & KS2 Maths:
Relationship between fractions, decimals and percentages
Algorithms for manipulation of fractions.

From Y7:
Find factors (From M1)
Find HCF/LCM (From M1)

Link to assessment (criterion A and ‘x’)

A and C

Module 2 - Forming and Solving Equations and Inequalities

Key Concept

Form

Related Concept(s)

Simplification and equivalence

ATLs

Thinking: Apply existing knowledge to generate new ideas, products or processes
Affective: Demonstrate persistence and perserverance

Core declarative knowledge: What should students know?

What is a sequence?
What does it mean to generalise?
What is the nth term and how can I use it to solve problems?
What is the difference berween an equation, expression and inequality?
Does an equation always have a solution?
What does the word inverse mean?
Why do I need to perform the same operations to both sides of my equation?
How do I decide what order to perform the inverse operations in?
What do inequalities represent?
How do inequalities relate to equations?
Are the same methods for solving inequalities the same as equations?

Core procedural knowledge: What should students be able to do?

Identify and generate terms of a sequences
Finding a given term in a linear sequence
Developing a rule for finding a term in a linear sequence
Generalising the position to term rule for a linear sequence (nth term)
Form and solve equations including those with unknowns both sides and those involving algebraic fractions
Represent, form and solve inequalities
Use number lines and inequality symbols to represent and describe sets of numbers.
Use substitution to determine whether values satisfy given inequalities.
Solve linear inequalities with the unknown on one side.
Form inequalities in geometrical contexts
Use bar models to manipulate linear inequalities between two variables.
Compare manipulating linear equations and linear inequalities.

Links to prior learning (to be made explicit and tested)

From KS1 & 2:

Recognise the inequalities symbols, but will refer to them as crocodiles eating the larger number.

From Y7 M2:

Be able to use letters to represent unknowns or variables
Be able to define generalisation in maths
Form and solve equations

Link to assessment (criterion A and ‘x’)

A and D

Module 3 - Graphs & Proportions

Key Concept

Relationships

Related Concept(s)

Change and models

ATLs

Critical Thinking: Draw reasonable conclusions and generalisations
Communication: Take effective notes from online lessons

Core declarative knowledge: What should students know?

What is an object?
What is an image?
What other translations can be described with a vector?
How does moving the point of rotation effect the image?
What happens when I move the shapes vertices?
What happens to the image if I move the reflection line?
Can a combination of transformations be described by a single transformations?
What is the effect of a scale factor on the area of a shape?
What is the effect of a scale factor on the perimeter of a shape?
How does the word linear relate to general form of y=ax+c
What happens as the coefficient of x changes?
What happens as the coefficent of x becomes negative?
What happens as the y-intercept changes?
How do you know if two lines are parallel?

Core procedural knowledge: What should students be able to do?

Translate shapes and describe translations using column vectors
Rotate shapes about a point by multiples of 90 degrees, clockwise or anti-clockwise
Describe rotations accurately
Reflecting shapes by horizontal, vertical and diagonal lines
Describing rotations by giving the vertical or horizontal equation of the line
Apply a combination of transformations to a shape
Describe the single transformation made by applying a combination of transformation
Enlarge a shape by a positive and/or unit fraction scale factor
Identify the equations of horizontal and vertical lines (from year 7)
Plot coordinates from a rule to generate a straight line
Recognise y = ax & equations of the form y= ax + c
Identify key features of a linear graph including the y-intercept and the gradient
Make links between the graphical and the algebraic representation of a linear graph
Recognise different algebraic representations of a linear graph
Identify parallel lines from algebraic representations

Links to prior learning (to be made explicit and tested)

Unit 4.3 of Year 7, transformations, moved due to school closures.

Link to assessment (criterion A and ‘x’)

A, B and C

Module 4 - Proportional Reasoning

Key Concept

Logic

Related Concept(s)

Equivalence, quantity and simplification

ATLs

Critical Thinking: Draw reasonable conclusions and generalisations
Communication: Take effective notes from online lessons

Core declarative knowledge: What should students know?

What is a ratio?
Why do we use ratios to share?
What does a part of a ratio look like?
What is a coordinate?
What is a gradient?
What does parallel mean?
What is the Y-intercept?
What does it mean to be proportional?
What does it mean to be inversely proportional?
What do the graphical representations of proportion look like?

Core procedural knowledge: What should students be able to do?

Understand the concept of ratio and use ratio language and notation
Connect ratio with understanding of fractions
Compare two or more quantities in a ratio
Recognise and construct equivalent ratios
Express ratios involving rational numbers in their simplest form
Construct tables of values and use graphs as a representation for a given ratio
Compare ratios by finding a common total value
Explore ratios in different contexts including speed and other rates of change
Contrast ratio relationships involving discrete and continuous measures
Use speed and other rates of change to draw and interpret graphical representations
Explore density and concentration as other contexts for proportional relationships
Explore contexts involving proportional relationships
Represent proportional relationships using tables and graphs
Represent proportional relationships algebraically
Recognise graphs of proportional relationships
Solve proportion problems
Define inverse proportional relationships
Represent inverse proportion relationships algebraically

Links to prior learning (to be made explicit and tested)

Unit 6.3 of Year 7, Ratio, moved due to school closures.

Primary
KS1 & KS2 Maths

Be able to recognise ratio notation
Be able to define percent
Be able to construct bar models for ratio

Link to assessment (criterion A and ‘x’)

A and C

Module 5 - Statistics (Types of Dates, Averages and Interpretations)

Key Concept

Relationships

Related Concept(s)

Representation and justification

ATLs

Thinking: Apply skills and knowledge in unfamiliar situations
Communication: Interpet and use effectively modes of non-verbal communication.

Core declarative knowledge: What should students know?

What happens to the original mean when one of the numbers is removed?
When will the mean go up? When will it go down? Why?
How could you compare the two data sets?
When is the mean better to use?
When is the median better to use?
When is the mode better to use?
What is continuous data?
What is discrete data?
What is the difference between univariate data and bivariate data?
What is an outlier?
Why do we use scatter diagrams?
What does the line of best fit allow us to do?
What does interpolation mean?
What does extrapolation mean?

Core procedural knowledge: What should students be able to do?

Find the mean, median mode and range from raw datasets
Use the mean, median and 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
Construct scatter graphs
Recognise clusters and outliers
Analyse the shape, strength and direction to make conjectures for possible bivariate relationships
Plot a line of best fit
Use a line of best fit to interpolate and extrapolate inferences

Links to prior learning (to be made explicit and tested)

KS1 & 2 Maths:

Definitions of the averages
Simple discrete data sets

Link to assessment (criterion A and ‘x’)

A and D

Module 6 - Circles, 3D Shapes (Surface Area and Volume)

Key Concept

Relationships

Related Concept(s)

Generalisation and measurement

ATLs

Critical Thinking: Interpret Data
Critical Thinking: Evaluate evidence and arguments

Core declarative knowledge: What should students know?

What are the definitions of the circumference, radius, diameter, a chord, a sector and a segment?
Is the circumference proportional to the diameter?
What is pi?
What is an irrational number?
What approximation can used for pi?
How many decimal places of pi do you need to calculate the circumference of earth at the equator to accuracy of a hydrogen atom?
When did you convert between the units?

Core procedural knowledge: What should students be able to do?

Explore relationship between circumference and diameter/radius
Use the formula for circumference
Explore relationship between area and radius
Use the formula for area of a circle
Find the area and circumference of a semi-circle and other sectors
Find the area and perimeter of composite shapes involving sectors of circles
Name prisms, nets of prisms and using language associated with 3-D shapes
Finding the volume and surface area of cuboids
Finding the volume and surface area of other prisms including cylinders
Finding the volume and surface area of composite solids
Solving equations and rearranging formulae related to volumes
Convert between different units of area and volume

Links to prior learning (to be made explicit and tested)

From KS1 & 2:

Parts of a circle.
Area and perimter of 2D shapes

From Y7 M3:

Classification of 2D and 3D shapes

Link to assessment (criterion A and ‘x’)

A, B and C

Module 1 - Graphs & Proportion

Key Concept

Relationships

Related Concept(s)

Change and models

ATLs

Critical Thinking: Draw reasonable conclusions and generalisations
Communication: Interpet and use effectively modes of non-verbal communication.

Core declarative knowledge: What should students know?

What is a coordinate?
What is a gradient?
What does parallel mean?
What is the Y-intercept?
What does it mean to be proportional?
What does it mean to be inversely proportional?
What do the graphical representations of proportion look like?
What is standard form?
What is the purpose of standard form?
How do you know if a number is very large or small when written in standard form?

Core procedural knowledge: What should students be able to do?

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
Identify the equations of horizontal and vertical lines
Plot a straight line from a rule by generating coordinates
Find the gradient and y-intercept of a line (inc negative and fractional gradients)
Find the equation of a line
Identify parallel lines
Recognise when two quantities are directly proportional to each other
Solve direct proportion problems using the unitary method
Recognise when two quantities are inversely proportional to each other
Use standard form to express very large and small numbers
Convert between standard form and ordinary numbers
Order large and small numbers that are in standard form
Use standard form to solve addition and subtraction problems

Links to prior learning (to be made explicit and tested)

From Y7:

Introduction to Algebra

From Y8 M2:

Sequences 2.4
Linear Equations 2.6

Link to assessment (criterion A and ‘x’)

A and C

Module 2 - Algebra (Manipulating Variables)

Key Concept

Logic

Related Concept(s)

Generalisation

ATLs

Communication: Understand and use mathematical notation
Thinking: Make informed choices about effective and efficient methods

Core declarative knowledge: What should students know?

Why do we round numbers?
What effect does rounding have in subsequent calculations?
What does it mean to generalise? (In the context of a sequence)
What is an expression?
What is an equation?
What is a formula?
What is a binomal or a polynomial?
What is the best method for expanding double/triple brackets

Core procedural knowledge: What should students be able to do?

Round numbers to powers of 10
Round numbers to a required number of decimal places
Round numbers to a required number of significant figures
Find the nth term of a linear sequence
Recognise linear and quadratic expressions
Recognise arithmetic and geometric sequences
Generate and describe linear and non-linear sequences
Multiply a term over a single bracket
Expand products of two binomials
Factorise expressions into a single bracket
Expand products of three binomials
Define what an expression, equation and formula are
Manipulate familiar formulae such as known formulae for area and perimeter
Make a specific term the subject of the formula

Links to prior learning (to be made explicit and tested)

From Y8:

Algebraic expressions 2.5
Index notation 1.2

Link to assessment (criterion A and ‘x’)

A and D

Module 3 - Circles, 3D Shapes (Surface Area & Volume)

Key Concept

Relationships

Related Concept(s)

Generalisation and measurement

ATLs

Thinking: Apply skills and knowledge in unfamilar situations
Communication: Take effective notes from online lessons

Core declarative knowledge: What should students know?

What are the definitions of the circumference, radius, diameter, a chord, a sector and a segment?
Is the circumference proportional to the diameter?
What is pi?
What is an irrational number?
What approximation can used for pi?
How many decimal places of pi do you need to calculate the circumference of earth at the equator to accuracy of a hydrogen atom?
When did you convert between the units?
How do you use a compass correctly?
How do you use a protactor/angle measurer correctly?

Core procedural knowledge: What should students be able to do?

Explore relationship between circumference and diameter/radius
Use the formula for circumference
Explore relationship between area and radius
Use the formula for area of a circle
Find the area and circumference of a semi-circle and other sectors
Find the area and perimeter of composite shapes involving sectors of circles
Name prisms, nets of prisms and using language associated with 3-D shapes
Finding the volume and surface area of cuboids
Finding the volume and surface area of other prisms including cylinders
Finding the volume and surface area of composite solids
Solving equations and rearranging formulae related to volumes
Convert between different units of area and volume
Constructing triangles using a pair of compasses and ruler given the length of the sides.
Constructing triangles with the same interior angles using a protractor.
Constructing triangles given two sides and an angle

Links to prior learning (to be made explicit and tested)

Unit 5.2 of Year 8 (2019/20) moved due to school closure.

Constructions unit 3.1 & 3.2 (Skipped from Y8 due to time)

Link to assessment (criterion A and ‘x’)

A, B and C

Module 4 - Mensuration

Key Concept

Relationships

Related Concept(s)

Generalisation and measurement

ATLs

Thinking: Apply skills and knowledge in unfamilar situations
Communication: Take effective notes from online lessons

Core declarative knowledge: What should students know?

What are the properties of a right angled triangle?
What is the hypotenuse?
How can you identify the hypotenuse or the longest side of any triangle from its angles?
What is the Pythagoras Theorem?
What is the difference berween an equation, expression and inequality?
Does an equation always have a solution?
What does the word inverse mean?
Why do I need to perform the same operations to both sides of my equation?
How do I decide what order to perform the inverse operations in?
What do inequalities represent?
How do inequalities relate to equations?
Are the same methods for solving inequalities the same as equations?

Core procedural knowledge: What should students be able to do?

Identify the sides of a right angled triangle in relation to Pythagoras.
Identify the hypotenuse of a right angled triangle
Recognise the formula for the Pythagoras Theorem
Use the formula to find the length of the hypotenuse.
Use the formula to find the length of one of the shorter sides of a right angled triangle
Form and solve equations including those with unknowns both sides and those involving algebraic fractions
Represent, form and solve inequalities
Use number lines and inequality symbols to represent and describe sets of numbers.
Use substitution to determine whether values satisfy given inequalities.
Solve linear inequalities with the unknown on one side.
Form inequalities in geometrical contexts
Use bar models to manipulate linear inequalities between two variables.
Compare manipulating linear equations and linear inequalities.

Links to prior learning (to be made explicit and tested)

From Y7:

Classifying 2D Shapes 3.2

From Y8:

Linear equations 2.6

Link to assessment (criterion A and ‘x’)

A and C

Module 5 - Equations, Inequality & Probability

Key Concept

Form

Related Concept(s)

Simplification and equivalence

ATLs

Critical Thinking: Recognise unstated assumptions and bias
Information Literacy: Present information in a variety of formats

Core declarative knowledge: What should students know?

Why is using a graph to find a solution sometimes an estimate?
What does using the graph to find a solution physically represent?
What are the characteristics of a linear, exponential and reciprocal graph?

What is probability?
What does it mean to be random?
What is the likelihood of winning the lottery?
What does the probabilities of all possible outcomes sum to?
What does 0 and 1 represent in probability?
Is anything certain?
What regions do the intersection and union represent on a venn diagram?
What does mutually exclusive mean?
What is the difference between experimental and theoretical probability?

Core procedural knowledge: What should students be able to do?

Use linear and quadratic graphs to estimate values of y or x for given values of x or y
Find approximate solutions of simultaneous linear equations
Find approximate solutions to contextual problems from given graphs of a variety of functions
Use linear, exponential and reciprocal graphs to find solutions (including in context)

Record, describe and analyse the frequency of outcomes of simple probability
experiments
Define and use key language terms such as randomness, fairness, equally and unequally likely outcomes
Use the 0-1 probability scale
Understand that the probabilities of all possible outcomes sum to 1
Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Links to prior learning (to be made explicit and tested)

From Y9:

Linear graphs 1.2

Probability prior learning relates to Key Stage 1/2

Link to assessment (criterion A and ‘x’)

A and D

Module 6 - Handling Data

Key Concept

Relationships

Related Concept(s)

Models and quantity

ATLs

Critical Thinking: Interpret Data
Critical Thinking: Evaluate evidence and arguments

Core declarative knowledge: What should students know?

What happens to the original mean when one of the numbers is removed?
When will the mean go up? When will it go down? Why?
How could you compare the two data sets?
When is the mean better to use?
When is the median better to use?
When is the mode better to use?
What is continuous data?
What is discrete data?
What is the difference between univariate data and bivariate data?
What is an outlier?
Why do we use scatter diagrams?
What does the line of best fit allow us to do?
What does interpolation mean?
What does extrapolation mean?

Core procedural knowledge: What should students be able to do?

Find the mean, median mode and range from raw datasets
Use the mean, median and 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
Construct scatter graphs
Recognise clusters and outliers
Analyse the shape, strength and direction to make conjectures for possible bivariate relationships
Plot a line of best fit
Use a line of best fit to interpolate and extrapolate inferences

Links to prior learning (to be made explicit and tested)

Unit 6.1 & 6.2 of Year 8 2019/20 moved due to school closures.

KS1 & 2 Maths:

Definitions of the averages
Simple discrete data sets

Link to assessment (criterion A and ‘x’)

A, B and C