SGSE

Year 09 Foundation Maths

Curriculum:

Click to Expand Autumn Content:

Number

Algebra

Prior Knowledge:

Understand the meaning of the words ‘less than’.
Find a fraction of a number.
Recall square numbers.
Understand the meaning of ‘total’.
Understand the commutative property of multiplication.
Identify place value.
Round to the nearest 100, 10 and whole number.
Understand the meaning of the words ‘prime’, ‘factor’, ‘multiple’ and ‘product’.
Find the area of a square and identify square numbers.
Use simple powers of 10.
List the factors of numbers; identify which factors are prime.

Simplify simple expressions.
Multiply and divide simple terms.
Recognise equivalent expressions.
Calculate with negative numbers and terms.
Multiply negative and positive terms.
Find HCFs of number pairs.
Translate words into algebraic terms.

Teaching Content:

Use priority of operations with positive and negative numbers.
Simplify calculations by cancelling.
Use inverse operations.
Round to a given number of decimal places.
Multiply and divide decimal numbers.
Write decimal numbers of millions.
Round to a given number of significant figures.
Estimate answers to calculations.
Use one calculation to find the answer to another.
Recognise 2-digit prime numbers.
Find factors and multiples of numbers.
Find common factors and common multiples of two numbers.
Find the HCF and LCM of two numbers by listing.
Find square roots and cube roots.
Recognise powers of 2, 3, 4 and 5.
Understand surd notation on a calculator.
Use index notation for powers of 10.
Use index notation in calculations.
Use the laws of indices.
Write a number as the product of its prime factors.
Use prime factor decomposition and Venn diagrams to find the HCF and LCM.

Use correct algebraic notation.
Write and simplify expressions.
Use the index laws.
Multiply and divide expressions.
Substitute numbers into expressions.
Recognise the difference between a formula and an expression.
Substitute numbers into a simple formula.
Expand brackets.
Simplify expressions with brackets.
Substitute numbers into expressions with brackets and powers.
Recognise factors of algebraic terms.
Factorise algebraic expressions.
Use the identity symbol ≡ and the not equals symbol ≠
Write expressions and simple formulae to solve problems.
Use maths and science formulae.

Keywords:

Function, inverse, square root, cube root, Highest Common Factor (HCF), Lowest Common Multiple (LCM), Surd, Base, index, power, product, indices, prefix, Prime factor decomposition

Term, like terms, letters, variable, vary, Formula(e), Common factor, Highest Common Factor (HCF)

Click to Expand Spring Content:

Graphs, Tables and Charts

Fractions and Percentages

Equations, Inequalities and Sequences

Prior Knowledge:

Addition of numbers.
Counting tally symbols and drawing tally charts.
Interpret a frequency table, including calculating the total population.
Convert between 12 and 24 hour clock times.
Calculate with time.
Understand use of fractions.
Determine what features are missing from a graph.
Interpret bar charts.
Write decimal numbers of millions.
Plot a line graph.
Place numbers in order of size.
Express a part of a circle as a fraction or percentage of the whole.
Know the number of degrees in a circle.
Draw a circle.
Draw a given angle.
Understand depreciation of value as things age, as well as an understanding of exceptions (e.g. classic cars)
Plot coordinates in the first quadrant.
Recall definitions of positive, negative and no correlation.
Read values from a graph.

Identify equivalence in fractions.
Identify the denominator of a fraction.
Identify the numerator of a fraction.
Find the LCM.
Write fractions in their simplest form.
Convert between units of length.
Add and subtract fractions.
Convert between mixed numbers and improper fractions.
Find a fraction of a quantity.
Know that 1000 g = 1 kg.
Know the commutative rule a x b = b x a.
Write 1 million pounds as a figure.
Divide larger numbers by smaller numbers.
Convert between mixed numbers and improper fractions.
Multiply a whole number or a fraction by a fraction.
Identify the (place) value of a digit in a decimal number.
Convert between common fractions and decimals.
Write one value as a fraction of another.
Write common fractions and decimals as percentages.
Find percentages of quantities.
Convert a fraction to a decimal.
Convert a percentage to a fraction.
Calculate with percentages.
Convert a percentage to a decimal.

Understand the meaning of the term ‘inverse operation’.
Find the output of a function machine when given the input.
Use all four operations to solve simple, single one-step equations.
Work out the outputs of a function machine.
Simplify expressions.
Expand a single bracket, involving positive and negative numbers.
Solve two-step equations.
Identify numbers that satisfy an inequality.
Use the inequality signs between numbers.
List integer values that satisfy an inequality.
Identify the inverse of all four operations.
Substitute into and evaluate expressions.
Find the missing numbers in simple arithmetic sequences.
Write down missing terms in sequences.
Find the term-to-term rule.
Substitute into a simple expression.
Solve simple equations.

Teaching Content:

Designing tables and data collection sheets.
Reading data from tables.
Use data from tables.
Design and use two-way tables.
Draw and interpret comparative and composite bar charts.
Interpret and compare data shown in bar charts, line graphs and histograms.
Plot and interpret time series graphs.
Use trends to predict what might happen in the future.
Construct and interpret stem and leaf and back-to-back stem and leaf diagrams.
Draw and interpret pie charts.
Plot and interpret scatter graphs.
Determine whether or not there is a relationship between sets of data.
Draw a line of best fit on a scatter graph.
Use the line of best fit to predict values.

Compare fractions.
Add and subtract fractions.
Use fractions to solve problems.
Find a fraction of a quantity or measurement.
Use fractions to solve problems.
Multiply whole numbers, fractions and mixed numbers.
Simplify calculations by cancelling.
Divide a whole number by a fraction.
Divide a fraction by a whole number or a fraction.
Convert fractions to decimals and vice versa.
Use decimals to find quantities.
Write one number as a fraction of another.
Convert percentages to fractions and vice versa.
Write one number as a percentage of another.
Convert percentages to decimals and vice versa.
Find a percentage of a quantity.
Use percentages to solve problems.
Calculate simple interest.
Calculate percentage increases and decreases.
Use percentages in real-life situations.
Calculate VAT (value added tax).

Understand and use inverse equations.
Rearrange simple linear equations.
Solve simple linear equations.
Solve two-step equations.
Solve linear equations with brackets.
Solve equations with unknowns on both sides.
Use correct notation to show inclusive and exclusive inequalities.
Solve simple linear inequalities.
Write down whole numbers which satisfy an inequality.
Represent inequalities on a number line.
Solve two-sided inequalities.
Substitute values into formulae and solve equations.
Change the subject of a formula.
Know the difference between an expression, an equation, a formula and an identity.
Recognise and extend sequences.
Use the nth term to generate terms of a sequence.
Find the nth term of an arithmetic sequence.

Keywords:

Grouped frequency table, inequality, discrete data, continuous data, data collection sheet, distance chart, two-way table, comparative bar chart, composite bar chart, histogram, line graph, trend, time series, stem and leaf diagram, pie chart, scatter graph, correlation, variables, outlier, line of best fit, interpolation, extrapolation

Denominator, unit fraction, numerator, reciprocal, simple interest, depreciates

Equation, solve, balancing method, brackets, integer, inequality, mass, perimeter, formula, substitution, equation, subject, sequence, terms, term-to-term rule, general term

Click to Expand Summer Content:

Angles

Averages and Range

Perimeter, Area and Volume

Prior Knowledge:

Identify lines of symmetry and rotational symmetry in 2D shapes.
Draw angles.
Know that the angles in a quadrilateral sum to 360°.
Identify parallel and perpendicular lines.
Identify acute and obtuse angles.
Identify different types of triangles.
Know that the angles in a triangle sum to 180°.
Recall the number of sides of different polygons.
Know the properties of special triangles and quadrilaterals.
Recall the number of interior angles in different polygons.
Identify exterior and interior angles.
Using angle facts to find missing angles.

Understand that sharing equally involves dividing a total.
Identify the mode.
Identify the mode, median and range.
Identify an incorrect value.
Draw a stem and leaf diagram.
Understand inequality notation.
Find the mode, median and mean.
Calculate the value halfway between pairs of numbers.
Calculate the mean.
Read data from a frequency table.
Understand the use of random numbers in a real-life situation.

Understand the meaning of ‘perpendicular’.
Work out the perimeter and area of triangles and rectangles.
Multiplying and dividing by powers of 10, converting between millimetres, centimetres and metres.
Know that 1 km = 1000 m
Multiply and divide by powers of 10.
Convert between metric measures of area.
Describe shapes using correct vocabulary, including face, edge and vertex.
Sketch the net of a cuboid.
Work out the area of rectangles, triangles and trapezia.
Identify cross sections of prisms.
Decide whether a 3D solid is a prism.
Multiply and divide by large powers of 10.
Know that 1 litre = 1000 ml.
Work out the volume and surface area of a prism.

Teaching Content:

Solve geometric problems using side and angle properties of quadrilaterals.
Identify congruent shapes.
Understand and use the angle properties of parallel lines.
Find missing angles using corresponding and alternate angles.
Solve angle problems in triangles.
Understand angle proofs about triangles.
Calculate the interior and exterior angles of regular polygons.
Calculate the interior and exterior angles of polygons.
Explain why some polygons fit together and some others do not
Solve angle problems using equations.

Calculate the mean from a list and from a frequency table.
Compare sets of data using the mean and range.
Find the mode, median and range from a stem and leaf diagram.
Identify outliers.
Estimate the range from a grouped frequency table.
Recognise the advantages and disadvantages of each type of average.
Find the modal class.
Find the median from a frequency table.
Estimate the mean of grouped data.
Understand the need for sampling.
Understand how to avoid bias.

Calculate the perimeter and area of rectangles, parallelograms and triangles.
Estimate lengths, areas and costs.
Calculate a missing length, given the area.
Calculate the area and perimeter of trapezia.
Find the height of a trapezium given its area.
Convert between area measures.
Calculate the perimeter and area of shapes made from triangles and rectangles.
Calculate areas in hectares, and convert between ha and m².
Calculate the surface area of a cuboid.
Calculate the surface area of a prism.
Calculate the volume of a cuboid.
Calculate the volume of a prism.
Solve problems involving surface area and volume.
Convert between measures of volume.

Keywords:

Congruent, similar, diagonal, bisect, parallel lines, alternate angles, corresponding angles, co-interior angles, exterior angle, interior angle, polygon, regular polygon, irregular polygon

Estimate, sample, population, bias, random sample

Perimeter, area, perpendicular height, trapezium, isosceles trapezium, compound shape, surface area, volume, capacity

Subject Overview:

Our Foundation students follow the Edexcel International GCSE (IGCSE) Foundation course which covers the following areas:

Numbers and the number system, Equations, Formulae and Identities, Sequences, Functions and Graphs, Geometry and Trigonometry, Vectors and Transformation Geometry, Statistics and Probability

The qualification consists of two equally-weighted written examination papers. Students can achieve up to a grade 5.

Calculators are required for both papers.

Each paper is 2 hours long and is worth 100 marks.