KS3 Mathematics

Module 1 - Place Value & Axiom, Arrays & Decimal Calculations

Statement of Inquiry

Different systems and forms of representation develop as civilizations evolve and humans interact.

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?
Can you use a numberline to represent 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?
What techniques can you use to multiply and divide decimals?
How does lining up your decimal numbers help with calculating/problem solving?

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

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

Module 2 - Factors & Multiples, Order of Operations & Negative Numbers

Statement of Inquiry

Being able to represent different forms of quantities has helped humans explore and describe our planet.

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?
For worded problems, should we apply operations in the same order that they appear?
How are indices linked to multiplication?
What does equal priority mean?
How can multiplying negative numbers help me in dividing 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?
What is the difference between 3x^2 and (3x)^2?
Is ab the same or different to ba?
Is a/b the same as 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
Develop understanding of algebraic notation
Collect like terms to simplify expressions
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 number line

Knowing the placement of negative numbers Being able to order negative numbers 0>-1

Link to assessment (criterion A and ‘x’)

A, B and C

Module 3 - Introduction to Algebra & Angles

Statement of Inquiry

Generalising relationships between measurements can help explore the formation of human and natural landscapes.

Core declarative knowledge: What should students know?

What can letters in maths represent?
What is the difference between the equal sign and the identity sign?
What is the difference between 3x^2 and (3x)^2?
Is ab the same or different to ba?
Is a/b the same as b/a?
a+b and b+a?
a-b or b-a?

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?

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

Develop understanding of algebraic notation
Collect like terms to simplify expressions
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.

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

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

Link to assessment (criterion A and ‘x’)

A and D

Module 4 - Classifying 2D Shapes, Constructions & Coordinates

Statement of Inquiry

Artistry and creativity are enhanced through an understanding of how measurement helps to define forms.

Core declarative knowledge: What should students know?

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 circle?
How do you use a compass correctly?

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 circle?
How do you use a compass correctly?

Does the order of the numbers matter?
If you know the mid-point, can you find the line segment?

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

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

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

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

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

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

Link to assessment (criterion A and ‘x’)

A

Module 5 - Coordinates, Area & Perimeter, Transformations, Prime Factorisation

Statement of Inquiry

Using logic to simplify and manipulate quantities can help us explore human connections within families, communities and cultures.

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 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?

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

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)

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

Be able to recognise a triangle
Be able to recognise different types of triangle
Be able to recognise a circle

From Y7:

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

Link to assessment (criterion A and ‘x’)

D

Module 6 - Prime Factorisation, Fractions & Fraction Operations

Statement of Inquiry

Using a logical process to simplify quantities and establish equivalence can help analyse competition and cooperation.

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 an 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?
What is a bar model?
What is simplifying?

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

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
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, B and C

Module 1 - Sequences, Forming and Solving Equations & Inequalities

Statement of Inquiry

Producing equivalent forms through simplification can help to clarify, solve and create puzzles and tricks.

Core declarative knowledge: What should students know?

What is a sequence?
What does it mean to generalise?
What is the nth term?

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?
What happens when you multiply/divide both sides of an inequality by a negative number?
Can you prove why the above happens?

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 on 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

Module 2 - Linear Graphs, Accuracy & Estimation

Statement of Inquiry

Representing patterns of change as relationships can help determine the impact of human decision-making on the environment.

Core declarative knowledge: What should students know?

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 coefficient of x becomes negative?
What happens as the y-intercept changes?
How do you know if two lines are parallel?

How do you round to decimal places?
How do you round to significant figures?
What is the difference between rounding to d.p and rounding to s.f?
How can we use estimation to help solve a problem?
How do we estimate an answer to a question?

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

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

Identify whether to round up or down.

Round to decimal places and significant figures.

Use estimation to solve problems.

Make links between fact family questions and using estmation to help.

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

KS1 & KS2:

Round to the nearest whole number, 10, 100, 1000 etc…

Year 7 – place value, tenths, hundredths.. etc..

Link to assessment (criterion A and ‘x’)

A, B and C

Module 3 - Ratio, Real Life Graphs & Proportion

Statement of Inquiry

Using a logical process to simplify quantities and establish equivalence can help analyse competition and cooperation.

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

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

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)

KS1 & KS2:

Be able to recognise ratio notation
Be able to define percent
Be able to construct bar models for ratio
Understand the terms horizontal and vertical

Year 7 – Equation of vertical and horizontal lines

Link to assessment (criterion A and ‘x’)

A and D

Module 4 - Proportion & Univariate Data

Core declarative knowledge: What should students know?

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 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?

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

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

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

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

KS1 & KS2:

Mean, Median, Mode and Range

Link to assessment (criterion A and ‘x’)

A

Module 5 - Bivariate Data & Circles and Compound Shapes

Statement of Inquiry

Being able to represent relationships effectively can help justify characteristics and trends uncovered in communities.

Core declarative knowledge: What should students know?

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?

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 be 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?

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

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

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

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

KS1 & KS2:

2D Shapes
Drawing a graph

Link to assessment (criterion A and ‘x’)

A, B, C and D

Module 6 - Volume, Surface Area & Bearings

Statement of Inquiry

Generalizing the relationship between measurements can influence decisions that impact the environment.

Core declarative knowledge: What should students know?

What are the characteristics of 3D shapes?
What is volume?
What is surface area?
What is a cross section?
How do you convert bewtween different units of measure?
How do you convert between different units of area & volume?

How do you use a protractor?
Do you know the bearing from A to B will be different from B to A?

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

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

Name angles use the associated language with bearings. Find the bearing of one location to the other. After finding the bearing of A to B, what is the relationship of that bearing to the bearing of B to A.

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

KS1 & KS2:

3D shape names

Year 7:

2D shapes and their characteristics
Area and perimeter

Module 1 - Probability & Sample Spaces, Solving Simultaneous Equations Algebraically

Statement of Inquiry

Producing equivalent forms through simplification can help to clarify, solve and create puzzles.

Core declarative knowledge: What should students know?

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?
What is a sample space?
Calculate probabilities from a sample space.
What does solving simultaneous equations mean?
When you solve simultaneous equations, what do the solutions mean? What are they?

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

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)

KS1 & KS2:

Basic probability

Year 8:

Two way tables and data

Link to assessment (criterion A and ‘x’)

A, B and C

Module 2 - Solving Simultaneous Equations Algebraically & Graphically and Angles in Polygons

Statement of Inquiry

Generalisations about complex systems, such as, climate or social and economic organisations, become more logical when consideration is given to the ordered spontaneity nature of nonlinearity.

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?

How can we manipulate equations to solve simultaneous equations algebraically?
In what situations will there be 2 roots? 3 roots?
What do the roots of the equations mean?
Can you sketch a linear graph? What about a quadratic graph?

What is a polygon?
What is a regular polygon?
What are the characteristics of regular polygons?
How do you calculate the interior angles of a polygon?
How do you calculate the exterior angles of a polygon?
How do you find the sum of the angles in a regular polygon both interior and exterior?

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)
Use algebraic manipulation to solve simultaneous equations to find the root/roots Use knowledge of angles in a triangle and angles in a quadrilateral to find the angles (interior and exterior) of any polygon.

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

KS1 & KS2:

Adding and subtracting with negative numbers.

Year 7:

Solving equations, making the variable the subject

Year 8:

Manipulating equations
Students learnt last year how to plot straight line graphs and the characteristics of intersecting lines.

Link to assessment (criterion A and ‘x’)

A

Module 3 - Polygons, Bearings & Constructions

Statement of Inquiry

Generalizing the relationship between measurements can influence decisions that impact the environment.

Core declarative knowledge: What should students know?

What is a polygon?
What is a regular polygon?
What are the characteristics of regular polygons?
How do you calculate the interior angles of a polygon?
How do you calculate the exterior angles of a polygon?
How do you find the sum of the angles in a regular polygon both interior and exterior?

Can you bisect a line?
Can you bisect an angle?
How do you use a protractor?
Do you know the bearing from A to B will be different from B to A?

Can you construct a circle with a given radius?
How do you construct a SSS SAS ASA triangle?
How do you construct an equilateral triangle?
How do you construct different quadrilaterals?

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

Use knowledge of angles in a triangle and angles in a quadrilateral to find the angles (interior and exterior) of any polygon.

Name angles use the associated language with bearings. Find the bearing of one location to the other. After finding the bearing of A to B, what is the relationship of that bearing to the bearing of B to A.

Use different techniques to construct polygons and circles.

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

KS1 & KS2:

Names of different polygons

Year 8:

Circles and compound shapes
Volume and S.A

Link to assessment (criterion A and ‘x’)

A and D

Module 4 - Pythagoras, Volume & Surface Area

Statement of Inquiry

Generalising relationships between measurements can help develop principles, processes and solutions.

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 between 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?

How do I calculate volume of a prism?
How do I find the area of a cross section?
What is a cross section?
How do you calculate the surface area of a prism?
How is surface area different to volume?
How can the nets of shapes help us calculate surface area?
What are the correct units for the answer?
Can you work backwards to find the area of the cross section or a missing length?

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

Find the length of the hypotenuse. Find the length of one of the shorter sides. Prove whether a triangle is right angle triangle. Applying knowledge to real life problems around missing sides of right angle triangles.

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)

KS1 & KS2:

Volume of a cuboid.

Year 7:

Area of 2D shapes

Year 8:

Circles and compound shapes
Volume and S.A

Link to assessment (criterion A and ‘x’)

A and D

Module 5 - Enlargement, Similarity, Surds & Trigonometry

Key Statement

Producing equivalent forms through simplification can help to clarify, solve and create puzzles.

Core declarative knowledge: What should students know?

What is a scale factor?
Why does a shape sometimes get smaller when we enlarge it?
What happens to the shape when we use a negative scale factor to enlarge it?
What are the charateristics of similar shapes?
How do you prove two or more shapes are similar?
How can you calculate a missing length on a imilar shape?

What is a surd?
How can you simiplify a surd?
Can you add subtract multiply and divide surds?

What are the trigonometric ratios?
How can we use the trigonometric ratios to calculate missing lengths and missing angles?

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

Describe a single englargement with the scale factor and centre of enlargement. Enlarge a shape by a fractional scale factor. Enlarge a shape by a negative scale factor. Understand and be able to regergitate the characteristics of similar shapes. Finding missing lengths and angles.

Define a surd and non-examples. Understand how to simplify surds and add & subtract surds. Understand how to multiply and divide surds. Understand how to expand brackets with surds. Understand how to rationalise the demoniator of a fraction involving surds.

Be able to label the sides of a triangle: Hypotenuse, Adjacent and Opposite. Use the trigonometric ratios to calculate missing lengths and missing angles. Use the trigonometric ratios to calculate accurate values for the angles 30° and 60°. Use the trigonometric ratios to calculate angles of elevation and depression. Apply knowledge to trigonometry in 3 dimentions. Understand and recognise the trigonometric graphs and be able to sketch them. Understand and be able to use the sine and cosine rule. Know and understand how to use the formula for area of a triangle involving sine.

Students apply knowledge of pythagoras and trigonometry to their problem solving.

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

KS1 & KS2:

Names of 2D shapes.
Multiplication & division.

Year 7:

Name and characteristics of 2D shapes.

Year 8:

Ratio, proportion and roots.

Link to assessment (criterion A and ‘x’)

A, B and C

Module 6 - Quadratics

Statement of Inquiry

Modeling the relationship between quantities can highlight what it means to be human.

Core declarative knowledge: What should students know?

What is a quadratic?
What characteristics does it have?
How do you solve a quadratic equation?
What methods are there available to us to solve a quadratic?
What is the quadratic formula?
Can you sketch a quadratic?
Can you factorise a quadratic?
Do you know and understand how to use the complete the square method?
Can you solve a quadratic equation using iteration?
What are the roots of a quadratic equation? What do they mean?
Can you the turning point and the line of symmetry?

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

Know and understand the different methods for solving a quadratic equations. Understand and recognise when a method is more efficient than the others. Be able to accurately sketch a quadratic graph. Understand and recognise maximum, minimum and turning points.

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

KS1 & KS2:

Axes and graphs.

Year 7:

Expanding and factorising.

Year 8:

Plotting linear graphs and identifying points of intersection.