# Year 10 Foundation Maths

##### Curriculum:

*Halve a number.**Use a function machine.**Understand that parallel lines will never meet.**Understand that in a linear equation, the coefficient of x is the gradient.**Understand that parallel lines have the same gradient.**Interpret scales.**Understand and use the relationship between distance, average speed and time.**Interpret a distance–time graph.*

*List the four types of transformations.**Use the words ‘left’ and ‘right’.**Define the word perpendicular.**Know the number of degrees in fractions of a turn**Find scale factor from object to image and from image to object.**Recognising the properties of enlargements.**Understand key information for describing transformations.*

*Multiply and divide whole numbers.**Know and use metric conversions.**Convert units of weight, length, capacity and time.**Use index notation.**Write ratios using correct notation.**Interpret ratios.**Understand and use place value to order decimals.**Understand and use y = mx + c.**Relate common sense to real life problems.*

- Find the midpoint of a line segment.
- Recognise, name and plot straight-line graphs parallel to the axes.
- Recognise, name and plot the graphs of y = x and y = –x.
- Generate and plot coordinates from a rule.
- Plot straight-line graphs from tables of values.
- Draw graphs to represent relationships.
- Find the gradient of a line.
- Identify and interpret the gradient from an equation.
- Understand that parallel lines have the same gradient.
- Understand what m and c represent in y = mx + c.
- Find the equations of straight-line graphs.
- Sketch graphs given the values of m and c.
- Draw and interpret graphs from real data.
- Use distance–time graphs to solve problems.
- Draw distance–time graphs.
- Interpret rate of change on graphs.
- Draw and interpret a range of graphs.
- Understand when predictions are reliable.

- Translate a shape on a coordinate grid.
- Use a column vector to describe a translation.
- Draw a reflection of a shape in a mirror line.
- Draw reflections on a coordinate grid.
- Describe reflections on a coordinate grid.
- Rotate a shape on a coordinate grid.
- Describe a rotation.
- Enlarge a shape by a scale factor.
- Enlarge a shape using a centre of enlargement.
- Identify the scale factor of an enlargement.
- Find the centre of enlargement.
- Describe an enlargement.
- Transform shapes using more than one transformation.
- Describe combined transformations of shapes on a grid.

- Use ratio notation.
- Write a ratio in its simplest form.
- Solve problems using ratios.
- Solve simple problems using ratios.
- Use ratios to convert between units.
- Write and use ratios for shapes and their enlargements.
- Divide a quantity into 2 parts in a given ratio.
- Divide a quantity into 3 parts in a given ratio.
- Solve word problems using ratios.
- Use ratios involving decimals.
- Compare ratios.
- Solve ratio and proportion problems.
- Use the unitary method to solve proportion problems.
- Solve proportion problems in words.
- Work out which product is better value for money.
- Recognise and use direct proportion on a graph.
- Understand the link between the unit ratio and the gradient.
- Recognise different types of proportion.
- Solve word problems involving direct and inverse proportion.

*Calculation of simple squares and square roots.**Understand the meaning of ≠.**Interpret a surd expression shown on the calculator display.**Simplifying fractions.*

*Write probability as a fraction, a decimal and a percentage.**List outcomes.**Simplify fractions.**Convert fractions, decimals and percentages.**Compare fractions.**Understand theoretical probability (single event).**Add and subtracting equivalent fractions.**List primes and multiples.*

*Convert percentages to decimals.**Write powers of numbers in index form.**Understand ‘rate’ as a mathematical concept.**Find speed in km/h, when given ‘distance travelled in minutes’.**Identify graphs which show direct proportion.*

- Understand Pythagoras’ theorem.
- Calculate the length of the hypotenuse in a right-angled triangle.
- Solve problems using Pythagoras’ theorem.
- Calculate the length of a line segment AB.
- Calculate the length of a shorter side in a right-angled triangle.
- Understand and recall the sine ratio in right-angled triangles.
- Use the sine ratio to calculate the length of a side in a right-angled triangle.
- Use the sine ratio to calculate an angle in a right-angled triangle.
- Use the sine ratio to solve problems.
- Understand and recall the cosine ratio in right-angled triangles.
- Use the cosine ratio to calculate the length of a side in a right-angled triangle.
- Use the cosine ratio to calculate an angle in a right-angled triangle.
- Use the cosine ratio to solve problems.
- Understand and recall the tangent ratio in right-angled triangles.
- Use the tangent ratio to calculate the length of a side in a right-angled triangle.
- Use the tangent ratio to calculate an angle in a right-angled triangle.
- Solve problems using an angle of elevation or depression.
- Understand and recall trigonometric ratios in right-angled triangles.
- Use trigonometric ratios to solve problems.
- Know the exact values of the sine, cosine and tangent of some angles.

- Calculate simple probabilities from equally likely events.
- Understand mutually exclusive and exhaustive outcomes.
- Use two-way tables to record the outcomes from two events.
- Work out probabilities from sample space diagrams.
- Find and interpret probabilities based on experimental data.
- Make predictions from experimental data.
- Use Venn diagrams to work out probabilities.
- Understand the language of sets and Venn diagrams.
- Use frequency trees and tree diagrams.
- Work out probabilities using tree diagrams.
- Understand independent events.
- Understand when events are not independent.
- Solve probability problems involving events that are not independent.

- Calculate a percentage profit or loss.
- Express a given number as a percentage of another in more complex situations.
- Find the original amount given the final amount after a percentage increase or decrease.
- Find an amount after repeated percentage changes.
- Solve growth and decay problems.
- Solve problems involving compound measures.
- Convert between metric speed measures.
- Calculate average speed, distance and time.
- Use formulae to calculate speed and acceleration.
- Use ratio and proportion in measures and conversions.
- Use inverse proportion.

*Recall names of common 2D shapes.**Identify names of 2D shapes from faces of 3D solids.**Understand of the meaning of ‘congruence’.**Knowledge of scale factors of enlargement.**Work out scale factor of an enlargement.**Identify parallel and perpendicular lines.**Convert distances from map scale to real life distance and vice versa.**Working out the complement to 180 or 360 (addition and subtraction).*

*Be able to work out the area of a shape using algebraic terms.**Be able to square terms.**Define the origin and x-axis on a graph.**Calculating the square root of a number will result in both a positive and a negative answer.**Work out factor pairs of negative numbers.*

- Recognise 3D shapes and their properties.
- Describe 3D shapes using the correct mathematical words.
- Understand the 2D shapes that make up 3D objects.
- Identify and sketch planes of symmetry of 3D shapes.
- Understand and draw plans and elevations of 3D shapes.
- Sketch 3D shapes based on their plans and elevations.
- Make accurate drawings of triangles using a ruler, protractor and compasses.
- Identify congruent triangles.
- Draw diagrams to scale.
- Correctly interpret scales in real-life contexts.
- Use scales on maps and diagrams to work out lengths and distances.
- Know when to use exact measurements and estimations on scale drawings and maps.
- Draw lengths and distances correctly on given scale drawings.
- Accurately draw angles and 2D shapes using a ruler, protractor and compasses.
- Construct a polygon inside a circle.
- Recognise nets and make accurate drawings of nets of common 3D objects.
- Draw accurately using rulers and compasses.
- Bisect angles and lines using rulers and compasses.
- Draw loci for the path of points that follow a given rule.
- Identify regions bounded by loci to solve practical problems.
- Find and use three-figure bearings.
- Use angles at parallel lines to work out bearings.
- Solve problems involving bearings and scale diagrams.

- Multiply double brackets.
- Recognise quadratic expressions.
- Square single brackets.
- Plot graphs of quadratic functions.
- Recognise a quadratic function.
- Use quadratic graphs to solve problems.
- Solve quadratic equations, such as ax
^{2}+ bx + c = 0, using a graph. - Solve quadratic equations, such as ax
^{2}+ bx + c = k, using a graph. - Factorise quadratic expressions.
- Solve quadratic functions algebraically.

##### Subject Overview:

In Year 10 our Foundation students will continue to work through the contents of the Edexcel International GCSE (IGCSE). We aim to cover as much of the curriculum as possible so that all the Foundation students will have learned enough material to access a Grade 5 at the end of Year 10 for their IGCSE Foundation Early Entry Exam.

Students who gain grade 5 in their Early Entry Exam, which is the highest possible grade for the Foundation tier, will get the chance to be moved into GCSE Higher classes in Year 11. This gives them the opportunity to improve their GCSE grade at the end of Year 11.

This approach to Early Entry and using it as a 'springboard' into Year 11 has proven very successful over the years.

##### Assessments:

In Year 10 there are end of unit assessments. In the summer students will be given the opportunity to sit the Early Entry Foundation IGCSE Maths exam.