#### 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)

#### Link to assessment (criterion A and ‘x’)

A and C

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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