Year 09 Higher Maths
Curriculum:
Click to Expand Autumn Content:
Number
Algebra
Prior Knowledge:
Prior Knowledge:
- Multiply numbers in a similar format to questions later in the lesson.
- Estimate the value of a square root.
- Multiply prime factors together.
- Work out simple powers.
- Work out roots.
- Convert a decimal to a fraction.
- Multiply by powers of 10 when the number is written as an ordinary number and not an index.
- Review different ways to divide by 10.
- Review the meaning of the dot in the notation for recurring decimals.
- Identify the missing multiple which practices the skills of searching for a perfect square factor.
- Recognise that squaring and taking the square root and cubing and taking the cube root are inverse operations.
- Simplify algebraic terms, including index notation.
- Solve a simple equation expressed in words.
- Substitute values into a one-step formula.
- Find the next term of a given arithmetic sequence.
- Substitute values in a simple linear expression.
- Find the next term of given sequences.
- Identify arithmetic and geometric sequences.
- Recalling a square root.
- Finding the factor pairs of small integers.
Teaching Content:
Teaching Content:
- Work out the total number of ways of performing a series of tasks.
- Estimate an answer.
- Use place value to answer questions.
- Write a number of the product of its prime factors.
- Find the HCF and LCM of two numbers.
- Use powers and roots in calculations.
- Multiply and divide using index laws.
- Work out a power raised to a power.
- Use negative indices.
- Use fractional indices.
- Write a number in standard form.
- Calculate with numbers in standard form.
- Understand the difference between rational and irrational numbers.
- Simplify a surd.
- Rationalise a denominator.
- Use the rules of indices to simplify algebraic expressions.
- Expand brackets.
- Factorise algebraic expressions.
- Solve equations involving brackets and numerical fractions.
- Use equations to solve problems.
- Substitute numbers into formulae.
- Rearrange formulae.
- Distinguish between expressions, equations, formulae and identities.
- Find a general formula for the nth term of an arithmetic sequence.
- Determine whether a particular number is a term of a given arithmetic sequence.
- Solve problems using geometric sequences.
- Work out terms in Fibonacci-like sequences.
- Find the nth term of a quadratic sequence.
- Expand the product of two brackets.
- Use the difference of two squares.
- Factorise quadratics of the form x2 + bx + c
Keywords:
Keywords:
Inclusive, Prime factor decomposition, index form, Prefixes, standard form, scientific notation, ordinary numbers, Surd, rationalise the denominator
Identity, equation, expand, consecutive integers, Expression, equation, identity, formula, variables, subject, Arithmetic sequence, common difference, Geometric sequence, constant multiplier, predict, quadratic sequence
Click to Expand Spring Content:
Interpreting and Representing data
Fractions, Ratio and Percentages
Angles and Trigonometry
Prior Knowledge:
Prior Knowledge:
Prior Knowledge:
- Work out mode, median and range from a list of numbers.
- Identify trends by noticing whether sequences of numbers increase, decrease or oscillate.
- Recognise when a line has a positive, negative or zero gradient.
- Plot points on a coordinate grid, and identify points that do not lie on a straight line.
- Understand and be able to define the meaning of correlation.
- Read values from graphs.
- Find the range of a list of numbers.
- Find the midpoint of two numbers.
- Use subtraction to find missing values.
- Draw a bar chart.
- Draw a pie chart.
- Identify unit fractions, improper fractions and mixed numbers.
- Multiply a whole number by a fraction.
- Know the priority of operations.
- Multiply a fraction by its reciprocal for a product of 1.
- Simplify ratios.
- Write ratios in the form n : 1.
- Write one number as a proportion of the total.
- Identify equivalent ratios.
- Find a percentage of a given amount.
- Work out percentage multipliers.
- Convert between fractions, decimals and percentages.
- Solve simple equations.
- Recognise special types of triangle and quadrilateral.
- Recall basic angle facts.
- Name polygons and understand the meaning of ‘regular polygon’.
- Substitute numbers into an expression.
- Find missing angles in triangles, quadrilaterals and at a point.
- Find missing angles on a straight line.
- Calculate the sum of interior angles of a polygon.
- Recall square numbers and square roots.
- Find the area of a square.
- Find square roots.
- Recognise perfect squares.
- Use Pythagoras' theorem to find the length of the hypotenuse.
- Convert fractions to decimals.
- Identify the hypotenuse.
- Use the angle sum of a triangle to work out missing angles.
- Identify the opposite and adjacent sides of a given angle in right-angled triangles.
- Use the trigonometric ratios to find lengths in right-angled triangles.
Teaching Content:
Teaching Content:
Teaching Content:
- Construct and use back-to-back stem and leaf diagrams.
- Construct and use frequency polygons and pie charts.
- Plot and interpret time series graphs.
- Use trends to predict what might happen in the future.
- Plot and interpret scatter graphs.
- Determine whether or not there is a linear relationship between two variables.
- Draw a line of best fit on a scatter graph.
- Use the line of best fit to predict values.
- Decide which average is best for a set of data.
- Estimate the mean and range from a grouped frequency table.
- Find the modal class and the group containing the median.
- Construct and use two-way tables.
- Choose appropriate diagrams to display data.
- Recognise misleading graphs.
- Add, subtract, multiply and divide fractions and mixed numbers.
- Find the reciprocal of an integer, decimal or fraction.
- Write ratios in the form 1 : n or n : 1.
- Compare ratios.
- Find quantities using ratios.
- Solve problems involving ratios.
- Convert between currencies and measures.
- Recognise and use direct proportion.
- Solve problems involving ratios and proportion.
- Work out percentage increases and decreases.
- Solve real-life problems involving percentages.
- Work out percentage increases and decreases.
- Solve real-life problems involving percentages.
- Derive and use the sum of angles in a triangle and in a quadrilateral.
- Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- Calculate the sum of the interior angles of a polygon.
- Use the interior angles of polygons to solve problems.
- Know the sum of the exterior angles of a polygon.
- Use the angles of polygons to solve problems.
- Calculate the length of the hypotenuse in a right-angled triangle.
- Solve problems using Pythagoras’ theorem.
- Calculate the length of a shorter side in a right-angled triangle.
- Solve problems using Pythagoras’ theorem.
- Use trigonometric ratios to find lengths in a right-angled triangle.
- Use trigonometric ratios to solve problems.
- Use trigonometric ratios to calculate an angle in a right-angled triangle.
- Find angles of elevation and angles of depression.
- Use trigonometric ratios to solve problems.
- Know the exact values of the sine, cosine and tangent of some angles.
Keywords:
Keywords:
Keywords:
Back-to-back stem and leaf diagram, frequency polygon, time series, bivariate data, scatter graph, line of best fit, interpolation, extrapolation, outliers, modal class
Reciprocal, unit ratios, direct proportion, Value Added Tax (VAT), depreciates, simple interest, income
Interior angle, exterior angle, hypotenuse, opposite, adjacent, sine, cosine, tangent, angle of elevation, angle of depression, inverse trigonometric functions
Click to Expand Summer Content:
Graphs
Area and Volume
Transformations and Constructions
Prior Knowledge:
Prior Knowledge:
Prior Knowledge:
- Identify positive and negative gradients and intercepts from graphs.
- Rearrange equations.
- Identify lines with the same gradient or y-intercept from their equations.
- Write the equation of a line from a graph.
- Find speed from given distance and time.
- Find the area of triangles and rectangles.
- Write the equation of a line from a sketch graph.
- Plot a graph using values given in a table.
- Identify parallel and perpendicular lines
- Know properties of gradients of parallel lines.
- Identify the gradient and intercept from an equation in the form y = mx + c.
- Identify quadratic expressions.
- Write the equation of a line from a graph.
- Know the shape of linear and quadratic graphs.
- Match the shape of a container to the graph of depth of water against time.
- Recognising units of length (perimeter) and area.
- Work out the area and perimeter of rectangles, triangles and parallelograms.
- Recall the formulae for the area of quadrilaterals and triangles. Identify the possible integer values of x from an inequality.
- Round numbers to a specified degree of accuracy.
- Work out percentages of quantities.
- Calculate the volume and surface area of a cuboid.
- Calculate the volume of a shape made from cuboids.
- Understand ‘radius’ and ‘diameter’.
- Solve and rearrange simple equations.
- Work out fractions of a circle given the angle of a sector.
- Simplify equations.
- Find the area and circumference of a circle in terms of π.
- Sketch a net of a cylinder.
- Solve simple equations.
- Find the volume of a cube.
- Find the side length of a cube given its volume.
- Calculate the area of a triangle.
- Use Pythagoras' theorem to work out the length of the hypotenuse.
- Draw 3D shapes on an isometric grid.
- Recognise dimensions of a cuboid.
- Draw simple straight lines on a coordinate grid.
- Know whether the image is congruent to the original following a reflection or a rotation.
- Enlarge shapes on a coordinate grid in one quadrant.
- Describe translations.
- Convert metric measures and apply to scales.
- Accurate drawing of right-angled triangle.
- Accurate drawings of triangles given SSS and ASA.
- Know the meaning of the terms perpendicular, bisect, arc.
- Draw angles with a protractor.
Teaching Content:
Teaching Content:
Teaching Content:
- Find the gradient and y-intercept from a linear equation.
- Rearrange an equation into the form y = mx + c.
- Compare two graphs from their equations.
- Plot graphs with equations ax + by = c.
- Sketch graphs using the gradient and intercepts.
- Find the equation of a line, given its gradient and one point on the line.
- Find the gradient of a line through two points.
- Draw and interpret distance–time graphs.
- Calculate average speed from a distance–time graph.
- Understand velocity–time graphs.
- Find acceleration and distance from velocity–time graphs.
- Draw and interpret real-life linear graphs.
- Recognise direct proportion.
- Draw and use a line of best fit.
- Find the coordinates of the midpoint of a line segment.
- Find the gradient and length of a line segment.
- Find the equations of lines parallel or perpendicular to a given line.
- Draw quadratic graphs.
- Solve quadratic equations using graphs.
- Identify the line of symmetry of a quadratic graph.
- Interpret quadratic graphs relating to real-life situations.
- Draw graphs of cubic functions.
- Solve cubic equations using graphs.
- Draw graphs of reciprocal functions.
- Recognise a graph from its shape.
- Interpret linear and non-linear real-life graphs.
- Draw the graph of a circle.
- Find the perimeter and area of compound shapes.
- Recall and use the formula for the area of a trapezium.
- Convert between metric units of area.
- Calculate the maximum and minimum possible values of a measurement.
- Convert between metric units of volume.
- Calculate volumes and surface areas of prisms.
- Calculate the area and circumference of a circle.
- Calculate area and circumference in terms of π.
- Calculate the perimeter and area of semicircles and quarter circles.
- Calculate arc lengths, angles and areas of sectors of circles.
- Calculate volume and surface area of a cylinder and a sphere.
- Solve problems involving volumes and surface areas.
- Calculate volume and surface area of pyramids and cones.
- Draw plans and elevations of 3D solids.
- Reflect a 2D shape in a mirror line.
- Rotate a 2D shape about a centre of rotation.
- Describe reflections and rotations.
- Enlarge shapes by fractional and negative scale factors about a centre of enlargement.
- Translate a shape using a vector.
- Carry out and describe combinations of transformations.
- Draw and use scales on maps and scale drawings.
- Solve problems involving bearings.
- Construct triangles using a ruler and compasses.
- Construct the perpendicular bisector of a line.
- Construct the shortest distance from a point to a line using a ruler and compasses.
- Bisect an angle using a ruler and compasses.
- Construct angles using a ruler and compasses.
- Construct shapes made from triangles using a ruler and compasses.
- Draw a locus.
Keywords:
Keywords:
Keywords:
Linear equations, distance-time graph, steady speed, constant rate, velocity-time graph, deceleration, direct proportion, line segment, midpoint, perpendicular, quadratic equation, parabola, minimum point, maximum point, trajectory, cubic function, asymptotes
Isosceles trapezium, surface area, prism, volume, capacity, circumference, arc
Plan, front elevation, side elevation, object, image, centre of rotation, scale factor, negative scale factor, column vector, resultant vector, construct, perpendicular bisector, angle bisector, locus, equidistant
Subject Overview:
Our Higher students follow the Edexcel GCSE Higher course which covers the following areas:
Number, Algebra, Ratio, Proportion and Rates of Change, Geometry and Measures, Probability and Statistics
The qualification consists of three equally-weighted written examination papers.
Paper 1 is a non-calculator assessment. Calculators are required for paper 2 and paper 3.
Each paper is 1 hour and 30 minutes long and is worth 80 marks.
Assessments:
In Year 9 students are assessed at the end of each unit. There are also End of Term assessments and an End of Year assessment.
