# KS3 Mathematics

The LAB Maths department’s guiding principle for curriculum intent is as follows:

• To provide the highest quality education in mathematics that prepares all students for future learning or employment.
• To ensure that all students receive a knowledge rich education in mathematics rooted in conceptual understanding, reasoning, communication and language and problem solving.
• For all students to recognise the interconnectedness of mathematics and to have an appreciation for both its utility and its beauty.
• The maths curriculum builds iteratively in order for students to build an extensive knowledge base at Key Stage 3 in preparation for Key Stage 4. All students will experience the main pillars of mathematics: number, geometry, algebra, ratio and proportion, probability and statistics.
Module 1 - Place Value & Axiom, Arrays & Decimal Calculations

#### Statement of inquiry

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

• 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

Criterion A

#### 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 number line 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 & distributivity?
• 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
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.

• 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

Criterion A, B and C

#### 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.
Module 3 - Introduction to Algebra & Angles

#### Statement of inquiry

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

• 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

Criterion A and D

#### 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 co interior angles to find missing angles Find unknown angles. Form algebraic expressions and solve equations related to unknown angles
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.

• 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

Criterion A

#### 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
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.

• 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)

Criterion D

#### 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
•
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.

• 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)

Criterion A, B and C

#### 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
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.

• 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

Criterion A

#### 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 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?
• 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 this 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.
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.

• KS1 & KS2:

• Round to the nearest whole number, 10, 100, 1000 etc…
• Year 7 – place value, tenths, hundredths.. etc..

Criterion A, B and C

#### 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 estimation to help
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.

• 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

Criterion A and D

#### 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
Module 4 - Proportion & Univariate Data

#### Statement of inquiry

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

• KS1 & KS2:
• Mean, Median, Mode and Range

Criterion A

#### 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
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.

• KS1 & KS2:

• 2D Shapes
• Drawing a graph

Criterion A, B, C and D

#### 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
•
Module 6 - Volume, Surface Area & Bearings

#### Statement of inquiry

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

• KS1 & KS2:

• 3D shape names

• Year 7:

• 2D shapes and their characteristics
• Area and perimeter

Criterion A

#### 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 between 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.
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.

• KS1 & KS2:
• Basic probability
• Year 8:
• Two way tables and data

Criterion A, B and C

#### 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.
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.

• 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.

Criterion A

#### 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.
Module 3 - Polygons, Bearings & Constructions

#### 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.

• KS1 & KS2:
• Names of different polygons
• Year 8:
• Circles and compound shapes
• Volume and S.A

Criterion A and D

#### 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.
Module 4 - Pythagoras, Volume & Surface Area

#### Statement of inquiry

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

• KS1 & KS2:
• Volume of a cuboid.
• Year 7:
• Area of 2D shapes
• Year 8:
• Circles and compound shapes
• Volume and S.A

Criterion A and D

#### 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
Module 5 - Enlargement, Similarity, Surds & Trigonometry

#### Statement of inquiry

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

• KS1 & KS2:
• Names of 2D shapes.
• Multiplication & division.
• Year 7:
• Name and characteristics of 2D shapes.
• Year 8:
• Ratio, proportion and roots.

Criterion A, B and C

#### 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 characteristics of similar shapes?  How do you prove two or more shapes are similar?  How can you calculate a missing length on a similar shape?
• What is a surd?  How can you simplify 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 enlargement 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 regurgitate 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 denominator 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 dimensions. 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.

#### Statement of inquiry

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

• KS1 & KS2:
• Axes and graphs.
• Year 7:
• Expanding and factorising.
• Year 8:
• Plotting linear graphs and identifying points of intersection.

Criterion A, B and C

#### Core declarative knowledge: What should students know?

• 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.