Mathematics

Statement of inquiry

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

Links to prior learning

• Primary: KS1 & KS2 Maths
• Use the number line to display decimals and round decimals to the nearest whole number, to 1 or 2 dp Round whole numbers to the nearest 1000, 100 or 10
• Mark the approximate position of a number on a number line
• Read and write decimals with up to 6 digits in figures and words
• Use approximation to estimate the answers to calculations
• Relate decimal arithmetic to integer arithmetic

Link to assessment

Criterion A

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

Statement of inquiry

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

Links to prior learning

• Primary KS1 & KS2 Maths
• Recognise the difference between the four operations.
• Recognise the relationship between the inverse operations
• Being able to represent numbers as a position on a number line
• Knowing the placement of negative numbers Being able to order negative numbers 0>-1

Link to assessment

Criterion A, 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.

Statement of inquiry

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

Links to prior learning

• KS1 & KS2 Maths
• Relate the word angle to the distance between two intersecting straight lines
  Be able to define acute, obtuse, right angle, straight line in terms of degrees

Link to assessment

Criterion A and 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

Statement of inquiry

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

Links to prior learning

• KS1 & KS2 Maths:
  • Relate the word angle to the distance between two intersecting straight lines
  • Be able to define acute, obtuse, right angle, straight line in terms of degrees
  • Be able to recognise a triangle
  • Be able to recognise different types of triangle
  • Be able to recognise a circle
• KS1 & KS2 Maths:
  • Be able to define the words horizontal and vertical
  • Recognise a cartesian plane
  • Be able to define perimeter and area, recognising the difference

Link to assessment

Criterion A

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

Statement of inquiry

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

Links to prior learning

• KS1 & KS2 Maths:
  • Be able to define the words horizontal and vertical
  • Recognise a cartesian plane
  • Be able to define perimeter and area, recognising the difference
  • Be able to recognise a triangle
  • Be able to recognise different types of triangle
  • Be able to recognise a circle
• From Y7:
  • Find factors (From M1)
  • Find HCF/LCM (From M1)

Link to assessment

Criterion 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

Statement of inquiry

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

Links to prior learning

• 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, 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

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.

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.

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

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.

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.

Link to prior learning

• 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.

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 calculate 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 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 fractions and decimals.
  
• Convert between decimals 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

Link to prior learning

• 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.

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 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.

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.

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?

• Calculate 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.

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.

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.

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.

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.

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.

Link to prior learning

• 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.

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

• What quantitative and qualitative data is.
  
• What continuous 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.

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.