# Year 09 Foundation Maths

##### Curriculum:

*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.*

- 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.

*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.*

- 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.

*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.*

- 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 m
^{2}. - 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.

##### 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.

##### 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.