Module 1

### Number

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

- What are the four operations?

- What are multiples and factors

- What are indices and roots?

- What is a prime number?

- What is the relationship between place value columns?

- How to apply the place value table to identify the value of any digit.

- Understanding the additive and multiplicative number properties such as commutativity.

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

- Order positive and negative integers, decimals and fractions.

- Apply the four operations to integers, decimals, simple fractions and mixed numbers both positive and negative.

- To solve problems involving roots and indices.

- To prime factorise and giving the solution in index form.

- Understand decimal notation and place values and identify the values of the digits in a decimal.

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

- Read, write and interpret mathematical statements involving addition, subtraction and equals signs.

- Represent and use number bonds and related subtraction facts.

- Add and subtract one-digit and two-digit numbers to including zero.

- Solving one-step problems that involve addition and subtraction.

- Using concrete objects and pictorial representations and missing number problems.

### Expressions

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

- What is an expression?

- What is an equation?

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

- Write an expression.

- Use and interpret algebraic notation.

- Substitute numerical values into formulae and expressions, including scientific formulae.

- Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors.

- Simplify and manipulate algebraic expressions.

- Use index notation and laws in algebra.

- Expand and factorise with single brackets.

- Expand and factorise with double brackets.

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

- Using simple formulae.

- Use and interpret algebraic notation.

- Simplify and manipulate algebraic expressions.

- Collecting like terms.

- Adding and subtracting negative numbers.

- Order positive and negative integers.

### Equations & Inequalities

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

- The difference between an equation and an identity.

- To solve an equation is to find the only value (or values) of the

unknown that make the mathematical sentence correct.

- For every unknown an equation is needed.

- Knowledge of <,>, ≤ & ≥ notation.

- Numbers which are less or greater than but not equal to are represented on a number line with an unshaded circle.

- Shaded circles are used when an inequality can be equal to a number.

- Inequations have a set of solutions whereas equations have distinct

solutions.

- Inequations can be solved using the balance method.

- When dividing or multiplying both sides of an inequality by a negative number the sign is reversed.

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

- Solve linear equations in one unknown algebraically.

- Solve linear equations with unknowns on both sides of the equation.

- Solve linear inequalities with one variable.

- Represent the solution of linear inequalities on a number line.

- List sets of numbers for an inequality

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

- Using simple formulae.

- Use and interpret algebraic notation.

- Simplify and manipulate algebraic expressions.

- Collecting like terms.

- Adding and subtracting negative numbers.

- Order positive and negative integers.

### 2D Shapes

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

- What are the properties of different quadrilaterals?

- What are the properties of different triangles?

- What is the formula for the area of a triangle?

- What is the formula for the area of a rectangle/square/parallelogram?

- What is the formula for the area of a trapezium?

- How do work out the area of a compound shape?

- What are the units of measurement for length and area?

- How mm in a cm? How many cm in a m? How many m in a km?

- How mm2 in a cm2? How many cm2 in a m2? How many m2 in a km2?

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

- Indicate given values on a scale, including decimal value;

- Know that measurements using real numbers depend upon the choice of unit;

- Convert between units of measure within one system, including time;

- Convert metric units to metric units;

- Make sensible estimates of a range of measures in everyday settings;

- Measure shapes to find perimeters and areas using a range of scales;

- Find the perimeter of rectangles and triangles;

- Find the perimeter of parallelograms and trapezia;

- Find the perimeter of compound shapes;

- Recall and use the formulae for the area of a triangle and rectangle;

- Find the area of a rectangle and triangle;

- Find the area of a trapezium and recall the formula;

- Find the area of a parallelogram;

- Calculate areas and perimeters of compound shapes made from triangles and rectangles;

- Convert between metric area measures.

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

- Use geometric language appropriately;

- Use letters to identify points, lines and angles;

- Use two-letter notation for a line and three-letter notation for an angle;

- Identify a line perpendicular to a given line;

- Mark perpendicular lines on a diagram and use their properties;

- Identify parallel lines;

- Mark parallel lines on a diagram and use their properties;

- Recall the properties and definitions of special types of quadrilaterals, including symmetry properties;

- List the properties of each special type of quadrilateral, or identify (name) a given shape;

- Draw sketches of shapes;

- Name all quadrilaterals that have a specific property;

- Identify quadrilaterals from everyday usage;

- Distinguish between scalene, equilateral, isosceles and right-angled triangles;

Module 2

### Circles

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

- What are the different parts of a circle?

- What is the formula for the area of a circle?

- What is the formulae for the circumference of a circle?

- What is pi? What is a useful approximation of pi?

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

- Recall the definition of a circle;

- Identify, name and draw parts of a circle including tangent, chord and segment;

- Recall and use formulae for the circumference of a circle and the area enclosed by a circle circumference of a circle = 2πr = πd, area of a circle = πr2;

- Find circumferences and areas enclosed by circles;

- Use π ≈ 3.142 or use the π button on a calculator;

- Give an answer to a question involving the circumference or area of a circle in terms of π;

- Find radius or diameter, given area or perimeter of a circles;

- Find the perimeters and areas of semicircles and quarter-circles;

- Calculate perimeters and areas of composite shapes made from circles and parts of circles;

- Calculate arc lengths, angles and areas of sectors of circles;

- Round answers to a given degree of accuracy.

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

- Know and apply formulae to calculate rectangles.

- Know and apply formulae to calculate composite shapes.

- Know and apply formulae to calculate area of triangles.

- Know and apply formulae to calculate parallelograms.

- Know and apply formulae to calculate trapeziums.

### 3D Shapes

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

- What are the properties of cubes and cuboids?

- What are the properties of prisms?

- How are prisms and cylinders different?

- How do you calulate the volume of any prism?

- What is the difference between surface area and volume?

- How mm3 in a cm3? How many cm3 in a m3? How many m3 in a km3?

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

- Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone;

- Sketch nets of cuboids and prisms;

- Recall and use the formula for the volume of a cuboid;

- Find the volume of a prism, including a triangular prism, cube and cuboid;

- Calculate volumes of right prisms and shapes made from cubes and cuboids;

- Find the surface area of a cylinder;

- Find the volume of a cylinder;

- Find the surface area and volume of spheres, pyramids, cones and composite solids;

- Estimate volumes etc by rounding measurements to 1 significant figure;

- Convert between metric volume measures;

- Convert between metric measures of volume and capacity e.g. 1ml = 1cm3;

- Estimate surface areas by rounding measurements to 1 significant figure;

- Find the surface area of a prism;

- Find surface area using rectangles and triangles.

- Round answers to a given degree of accuracy.

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

- Draw 2-D shapes.

- Recognising 3-D shapes in different orientations and describing them.

- Recognise angles as a property of shape or a description of a turn.

- Comparing and classifying geometric shapes including quadrilaterals

and triangles based on their properties and sizes.

- Identifying acute and obtuse angles.

- Identifying lines of symmetry in 2-D shapes presented in different

orientations.

### FDP

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

- The four operations of number.

- What common factors are

- Basic understanding of fractions as being ‘parts of a whole’.

- Define percentage as ‘number of parts per hundred’.

- Number complements to 10 and multiplication tables.

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

- Convert between frations and decimals.

- Convert between deimals and percentages.

- Convert between percentages and fractions.

- Recognise recurring decimals and convert fractions into recurring decimals.

- Compare and order fractions, decimals and integers, using inequality signs.

- Express a given number as a percentage of another

- Order fractions, decimals and percentages using lists and inequalities

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

- Students should be able to use the four operations of number.

- Students should be able to find common factors.

- Students have a basic understanding of fractions as being ‘parts of a whole’.

- Students should be able to define percentage as ‘number of parts per hundred’.

### Fractions

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

- What is the numerator?

- What is the denominator?

- What is the vinculum?

- Can identify an improper fraction.

- Define the word ‘reciprocal’.

- The four operations of number.

- Basic understanding of fractions as being ‘parts of a whole’.

- Define factors of a number.

- Define multiples of a number.

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

- Use diagrams to find equivalent fractions or compare fractions.

- Write fractions to describe shaded parts of diagrams.

- Express a given number as a fraction of another, using very simple numbers and where the fraction is both < 1 and > 1.

- Write a fraction in its simplest form and find equivalent fractions.

- Order fractions, by using a common denominator.

- Compare fractions, use inequality signs, compare unit fractions.

- Convert between mixed numbers and improper fractions.

- Add and subtract fractions.

- Add fractions and write the answer as a mixed number.

- Multiply and divide an integer by a fraction.

- Multiply and divide a fraction by an integer, including finding fractions of quantities or measurements, and apply this by finding the size of each category from a pie chart using fractions.

- Understand and use unit fractions as multiplicative inverses.

- Multiply fractions: simplify calculations by cancelling first.

- Divide a fraction by a whole number.

- Divide fractions by fractions.

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

- Recognise, find and name a half as one of two equal parts of an

object, shape or quantity.

- Recognise, find and name a quarter as one of four equal parts of

an object, shape or quantity.

- Interpret fractions as operators.

- Ordering positive and negative decimals.

Module 3

### Percentages

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

- The four operations of number.

- Define percentage as ‘number of parts per hundred’.

- Percentage is a fraction out of 100.

- Factors of a number.

- Multiples of a number.

- How to draw bar models.

- Use the place value table to illustrate the equivalence between

fractions, decimals and percentages.

- To calculate a percentage of an amount without a calculator i.e to calculate 10% of any number by dividing by 10.

- To calculate a percentage of an amount with a calculator.

- Convert percentages to decimals.

- Understanding 100% as the original amount. E.g 10% decrease represents 10% less than 100% = 0.9.

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

- Express a given number as a percentage of another number.

- Find a percentage of a quantity without a calculator: 50%, 25% and multiples of 10% and 5%.

- Find a percentage of a quantity or measurement.

- Calculate amount of increase/decrease.

- Use percentages to solve problems, including comparisons of two quantities using percentages.

- Calculate percentages over 100%.

- Use percentages in real-life situations, including percentages greater than 100%.

- Calculate price after VAT (not price before VAT).

- Calculate simple interest.

- Income tax calculations.

- Use decimals to find quantities.

- Find a percentage of a quantity, including using a multiplier.

- Use a multiplier to increase or decrease by a percentage in any scenario where percentages are used.

- Understand the multiplicative nature of percentages as operators.

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

- Multiply and divide by powers of ten.

- Understand that per cent relates to ‘number of parts per hundred’.

- Write one number as a fraction of another.

- Calculate equivalent fractions.

### Ratio

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

- How to draw bar models.

- How to simplify fractions.

- How to find factors, common factors and highest common factor of numbers.

- How to use scale factors.

- How to use standard units of mass, length, time, money and other measures.

- It is important to apply equivalent ratios when solving problems

involving proportion including the use of the unitary method.

- To share amount given a ratio it is necessary to find the value of a single share.

- Use ratio notation, including reduction to simplest form.

- Express a multiplicative relationship between two quantities as a

ratio.

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

- Understand and express the division of a quantity into a of number parts as a ratio.

- Write ratios in their simplest form.

- Write/interpret a ratio to describe a situation.

- Share a quantity in a given ratio including three-part ratios.

- Solve a ratio problem in context.

- Use a ratio to find one quantity when the other is known.

- Use a ratio to convert between measures and currencies.

- Compare ratios.

- Write ratios in form 1 : m or m : 1.

- Write a ratio as a fraction.

- Write a ratio as a linear function.

- Write lengths, areas and volumes of two shapes as ratios in simplest form.

- Express a multiplicative relationship between two quantities as a ratio or a fraction.

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

- Problems involving the relative sizes of two quantities where

missing values can be found by using integer multiplication and

division facts.

- Problems involving the calculation of percentages.

- Problems involving unequal sharing and grouping using

knowledge of fractions and multiples.

### Proportion

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

- Define and state the difference between direct and inverse proportion.

- Understand direct proportion as: as x increase, y increases.

- Understand inverse proportion as: as x increases, y decreases.

- The constant of proportionality, k, is used to define the rate at which two or more measures change.

- Recognising the graphical representations of direct and indirect proportion is vital to understanding the relationship between two

measurements.

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

- Calulcate direct proportion.

- Calculate inverse proportion.

- Solve word problems involving direct and inverse proportion.

- Convert between currencies.

- Solve proportion problems using the unitary method.

- Recognise when values are in direct proportion by reference to the graph form;

- Understand inverse proportion: as x increases, y decreases.

- Recognise when values are in direct proportion by reference to the graph form.

- Understand direct proportion relationship y = kx.

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

- Solve problems involving the relative sizes of two quantities

where missing values can be found by using integer.

- Multiplication and division facts.

- Solve problems involving the calculation of percentages.

- Solve problems involving unequal sharing and grouping using

knowledge of fractions and multiples.

### Coordinates

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

- Identify which is the x and y ordinate.

- Know how to draw a coordinate grid (cartesian plane)

- State coordinate points on a grid.

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

- Use axes and coordinates to specify points in all four quadrants in 2D.

- Identify points with given coordinates and coordinates of a given point in all four quadrants.

- Find the coordinates of points identified by geometrical information in 2D (all four quadrants).

- Find the coordinates of the midpoint of a line segment.

- Draw, label and scale axes.

- Complete the shape after being given some information about a shape on coordinate axes.

Module 4

### Sequences

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

- Generate terms of a sequence from either a term-to-term or a

position-to-term rule.

- Recognise and use sequences of triangular, square and cube

numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric

progressions.

- Deduce expressions to calculate the nth term of linear and quadratic sequences.

- Quadratic sequences have a constant second difference.

- Linear sequences have a constant first difference.

- Geometric sequences share common multiplying factor rather than

common difference.

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

- Recognise sequences of odd and even numbers, and other sequences including Fibonacci sequences.

- Use function machines to find terms of a sequence.

- Write the term-to-term definition of a sequence in words.

- Find a specific term in the sequence using position-to-term or term-to-term rules.

- Generate arithmetic sequences of numbers, triangular number, square and cube integers and sequences derived from diagrams.

- Recognise such sequences from diagrams and draw the next term in a pattern sequence.

- Find the next term in a sequence, including negative values.

- Find the nth term for a pattern sequence.

- Find the nth term of a linear sequence.

- Find the nth term of an arithmetic sequence.

- Use the nth term of an arithmetic sequence to generate terms.

- Use the nth term of an arithmetic sequence to decide if a given number is a term in the sequence, or find the first term over a certain number.

- Use the nth term of an arithmetic sequence to find the first term greater/less than a certain number.

- Continue a geometric progression and find the term-to-term rule, including negatives, fraction and decimal terms.

- Continue a quadratic sequence and use the nth term to generate terms.

- Distinguish between arithmetic and geometric sequences.

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

- Using symbols and letters to represent

variables and unknowns in mathematical situations.

- Using simple formulae.

- Generate and describe linear number sequences.

- Express missing number problems algebraically.

### Straight Line Graphs

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

- Interpret simple expressions as functions with inputs and outputs.

- How to work with coordinates in all four quadrants.

- Plot graphs of equations that correspond to straight-line graphs in

the coordinate plane.

- How to use the form y = mx + c to identify parallel lines.

- Find the equation of the line through two given points, or through

one point with a given gradient.

- How to identify and interpret gradients and intercepts of linear functions

graphically and algebraically.

- Gradient is a measure of rate of vertical change divided by

horizontal change.

- Parallel lines have the same gradient.

- The intercept always has the x value equal zero.

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

- Use function machines to find coordinates (i.e. given the input x, find the output y).

- Plot and draw graphs of y = a, x = a, y = x and y = –x.

- Recognise straight-line graphs parallel to the axes.

- Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane.

- Plot and draw graphs of straight lines of the form y = mx + c using a table of values.

- Sketch a graph of a linear function, using the gradient and y-intercept.

- Identify and interpret gradient from an equation y = mx + c.

- Identify parallel lines from their equations.

- Plot and draw graphs of straight lines in the form ax + by = c.

- Find the equation of a straight line from a graph.

- Find the equation of the line through one point with a given gradient.

- Find approximate solutions to a linear equation from a graph.

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

- Describe positions on a 2-D grid as coordinates in the first quadrant.

- Describe positions on the full coordinate grid (all four quadrants).

- Recognise and describe linear number sequences, including those

involving fractions and decimals, and find the term-to-term rule.

- Generating and describing linear number sequences.

### Quadratics

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

- Square negative numbers.

- Substitute into formulae.

- Plot points on a coordinate grid.

- Expand single brackets and collect ‘like’ terms.

- Draw a coordinate plane.

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

- Define a ‘quadratic’ expression.

- Multiply together two algebraic expressions with brackets.

- Square a linear expression, e.g. (x + 1)2.

- Factorise quadratic expressions of the form x2 + bx + c.

- Factorise a quadratic expression x2 – a2 using the difference of two squares.

- Solve quadratic equations by factorising.

- Find the roots of a quadratic function algebraically.

- Generate points and plot graphs of simple quadratic functions, then more general quadratic functions.

- Identify the line of symmetry of a quadratic graph.

- Find approximate solutions to quadratic equations using a graph.

- Interpret graphs of quadratic functions from real-life problems.

- Identify and interpret roots, intercepts and turning points of quadratic graphs.

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

- Simplify expressions.

- Expanding products of two or more binomials.

- Factorising simple expressions including the difference of two squares.

- Simplifying expressions involving sums, products and powers,

including the laws of indices.

- Factorising quadratic expressions.

### Graphs

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

- Distance time graphs show distance away from a point.

- A speed-time graph tells us how the speed of an object changes over time.

- The steeper the gradient of the line, the greater the acceleration.

- Graphs can be used to represent a number of real life situations.

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

- Read values from straight-line graphs for real-life situations.

- Draw straight line graphs for real-life situations, including ready reckoner graphs, conversion graphs, fuel bills graphs, fixed charge and cost per unit.

- Draw distance–time graphs and velocity–time graphs.

- Work out time intervals for graph scales.

- Interpret distance–time graphs, and calculate: the speed of individual sections, total distance and total time.

- Interpret information presented in a range of linear and non-linear graphs.

- Interpret graphs with negative values on axes.

- Find the gradient of a straight line from real-life graphs.

- Interpret gradient as the rate of change in distance–time and speed–time graphs, graphs of containers filling and emptying, and unit price graphs.

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

- Reading and plotting coordinates.

- Straight line graphs.

- Calculating the gradient of a line.

Module 5

### Probability

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

- The terms outcome, event and probability are key to describing the likelihood of an event occurring.

- Outcome is the result of an experiment.

- An event is a set of outcomes of a probability experiment.

- Probability describes the likelihood of an event occurring.

- A probability can be given as fraction, decimal or percentage.

- An event which is impossible has a probability of zero.

- An event which is certain to occur has a probability of one.

- When listing all the permutations of two or more events students need a logical and exhaustive systematic method.

- When working with experimental data a probability can only be estimated as contextual factors are likely to be a factor.

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

- Distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur.

- Mark events and/or probabilities on a probability scale of 0 to 1.

- Write probabilities in words or fractions, decimals and percentages.

- Find the probability of an event happening using theoretical probability.

- Use theoretical models to include outcomes using dice, spinners, coins.

- List all outcomes for single events systematically.

- Work out probabilities from frequency tables.

- Work out probabilities from two-way tables.

- Record outcomes of probability experiments in tables.

- Add simple probabilities.

- Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1.

- Using 1 – p as the probability of an event not occurring where p is the probability of the event occurring.

- Find a missing probability from a list or table including algebraic terms.

- Find the probability of an event happening using relative frequency.

- Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities.

- List all outcomes for combined events systematically.

- Use and draw sample space diagrams.

- Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values.

- Use union and intersection notation.

- Compare experimental data and theoretical probabilities.

- Compare relative frequencies from samples of different sizes.

- Find the probability of successive events, such as several throws of a single dice.

- Use tree diagrams to calculate the probability of two independent events.

- Use tree diagrams to calculate the probability of two dependent events.

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

- Compare and order fractions, including fractions > 1.

- Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.

- Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.

### Statistics

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

- What quantitative and qualitative data is.

- What continous and discrete data is.

- The different types of averages.

- State the median, mode, mean and range from a small data set.

- Extract the averages from a stem and leaf diagram.

- Estimate the mean from a table.

- Frequency tables must not have overlapping categories.

- Diagrams must not imply bias e.g equal width bar charts.

- Pictograms need to use suitable symbols to illustrate fractional

amounts.

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

- Recognise types of data: primary secondary, quantitative and qualitative.

- Identify which primary data they need to collect and in what format, including grouped data.

- Collect data from a variety of suitable primary and secondary sources.

- Understand how sources of data may be biased.

- Explain why a sample may not be representative of a whole population.

- Understand sample and population.

- Calculate the mean, mode, median and range for discrete data.

- Can interpret and find the median, mean and range from a (discrete) frequency table.

- Can interpret and find the range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table.

- Can interpret and find the mode and range from a bar chart.

- Can interpret and find the median, mode and range from stem and leaf diagrams.

- Can interpret and find the mean from a bar chart.

- Understand that the expression ‘estimate’ will be used where appropriate, when finding the mean of grouped data using mid-interval values.

- Compare the mean, median, mode and range (as appropriate) of two distributions using bar charts, dual bar charts, pictograms and back-to-back stem and leaf.

- Recognise the advantages and disadvantages between measures of average.

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

- Students should be able to calculate the midpoint of two numbers.

- Students will have used inequality notation.

- Complete, read and interpret information in tables.

### Constructions

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

- The standard conventions for labelling and referring to the sides

and angles of triangles.

- Draw diagrams from written descriptions.

- Use the standard ruler and compass constructions (perpendicular

bisector of a line segment, constructing a perpendicular to a given

line from/at a given point, bisecting a given angle).

- Know that the perpendicular distance from a point to a line is the

shortest distance to the line

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

- Use straight edge and a pair of compasses to do standard constructions:

- Understand, from the experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not.

- Construct the perpendicular bisector of a given line.

- Construct the perpendicular from a point to a line.

- Construct the bisector of a given angle.

- Construct angles of 90°, 45°.

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

- Identify and construct a radius, diameter, circumference, area,

chord, tangent and arc.

- Measure and begin to record lengths and heights.

- Identify acute and obtuse angles and compare and order angles up

to two right angles by size.

Module 6

### Probability

#### 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?

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

- Distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur.

- Mark events and/or probabilities on a probability scale of 0 to 1.

- Write probabilities in words or fractions, decimals and percentages.

- Find the probability of an event happening using theoretical probability.

- Use theoretical models to include outcomes using dice, spinners, coins.

- List all outcomes for single events systematically.

- Work out probabilities from frequency tables.

- Work out probabilities from two-way tables.

- Record outcomes of probability experiments in tables.

- Add simple probabilities.

- Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1.

- Using 1 – p as the probability of an event not occurring where p is the probability of the event occurring.

- Find a missing probability from a list or table including algebraic terms.

- Find the probability of an event happening using relative frequency.

- Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities.

- List all outcomes for combined events systematically.

- Use and draw sample space diagrams.

- Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values.

- Use union and intersection notation.

- Compare experimental data and theoretical probabilities.

- Compare relative frequencies from samples of different sizes.

- Find the probability of successive events, such as several throws of a single dice.

- Use tree diagrams to calculate the probability of two independent events.

- Use tree diagrams to calculate the probability of two dependent events.

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

- Students should understand that a probability is a number between 0 and 1, and distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur.

- Students should be able to mark events and/or probabilities on a probability scale of 0 to 1.

- Students should know how to add and multiply fractions and decimals.

- Students should have experience of expressing one number as a fraction of another number.

### Statistics

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

- What are the different averages?

- When is it better to use the mean?

- When is it better to use the median?

- When is it better to use the mode?

- 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?

- What is quantitative data?

- What is qualitative data?

- 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?

- Specify the problem and plan an investigation.

- Decide what data to collect and what statistical analysis is needed.

- Consider fairness.

- Recognise types of data: primary secondary, quantitative and qualitative.

- Identify which primary data they need to collect and in what format, including grouped data.

- Collect data from a variety of suitable primary and secondary sources.

- Understand how sources of data may be biased.

- Explain why a sample may not be representative of a whole population.

- Understand sample and population.

- Use statistics found in all graphs/charts in this unit to describe a population;

- Know the appropriate uses of cumulative frequency diagrams;

- Construct and interpret cumulative frequency tables;

- Construct and interpret cumulative frequency graphs/diagrams and from the graph:

estimate frequency greater/less than a given value;

find the median and quartile values and interquartile range;

- Compare the mean and range of two distributions, or median and interquartile range, as appropriate;

- Interpret box plots to find median, quartiles, range and interquartile range and draw conclusions;

- Produce box plots from raw data and when given quartiles, median and identify any outliers;

- Know the appropriate uses of histograms;

- Construct and interpret histograms from class intervals with unequal width;

- Use and understand frequency density;

- From histograms:

complete a grouped frequency table;

understand and define frequency density;

- Estimate the mean from a histogram;

- Estimate the median from a histogram with unequal class widths or any other information from a histogram, such as the number of people in a given interval.

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

- Students should understand the different types of data: discrete/continuous.

- Students should have experience of inequality notation.

- Students should be able to multiply a fraction by a number.

- Students should understand the data handling cycle.

### Constructions

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

- How do you use a compass correctly?

- How do you use a protactor/angle measurer correctly?

- What does it mean to bisect a line/angle?

- What does equidistant mean?