Number

Students will:

Understand and use the structures that underpin the four operations strategies, using laws and conventions of arithmetic efficiently.
Understand the value of digits in decimals, measure, and integers.
Understand properties of number, through integer exponents and roots and use the unique prime factorisation of a number.

Algebra

Students will:

Understand and use the conventions and vocabulary of algebra, including forming and interpreting algebraic expressions and equations.
Simplify algebraic expressions by collecting like terms and manipulate expressions, maintaining equivalence.
Understand the features of a sequence and investigate the link between these, co-ordinates, and graphs.

Number

Students will:

Work interchangeably with terminating decimals and their corresponding fractions.
Know, understand, and use fluently a range of calculation strategies for addition, subtraction, multiplication, and division of fractions.

Number

Students will:

Understand the multiplicative relationships between fractions and ratios.
Understand that fractions and ratio are examples of multiplicative relationships and apply this to a range of contexts.
Use percentages in a variety of contexts and solve problems.

Geometry, Shape, and Measure

Students will:

Understand the concepts of perimeter and area and use them in a range of problem-solving situations.
Become familiar with angle notation and rules and use these to find missing angles in 2D shapes.

Probability and Statistics

Students will:

Understand and calculate accurately central tendencies and spread.
Construct accurately statistical representations.
Interpret statistical measures and representations.
Become familiar with a probability scale and sample spaces. Start to determine probabilities of events.
Explore, describe, and analyse the frequency of outcomes in a range of situations.

Number

Students will:

Understand integer exponents and roots and use the unique prime factorisation of a number with Venn Diagrams, to determine The Highest Common Factors and Lowest Common Multiples.
Round numbers to a required number of decimal places or significant figures.
Use significant figures and other measures to estimate calculations by rounding.
Understand that percentages are an example of a multiplicative relationship and apply this understanding to a range of contexts.
Understand proportionality.

Algebra

Students will:

Understand index notation in the context of algebra.
Understand what is meant by finding a solution to a linear equation with one unknown.
Solve linear equations with:

• Single unknowns on one side where obtaining the solution requires one step.
• Single unknowns where the solution requires two steps.

Understand how to expand brackets.
Solve a linear equation with a single unknown involving brackets efficiently. Understand how to graph linear functions.

Geometry, Shape, and Measure

Students will:

Understand the laws of geometry when working with parallel lines and use these to solve problems in a variety of contexts.
Use the laws of geometry when working with polygons and use these to solve problems in a variety of contexts.
Understand the concepts of both line and rotational symmetry.
Understand what is meant by the term ‘tessellate’ and investigate this within the context of 2D shapes.

Geometry, Shape, and Measure

Students will:

Understand what is meant by the term ‘transforming’ a shape.
Understand and use:

• Translations.
• Rotations.
• Reflections.
• Enlargements.

Investigate the art of 2D representation of 3D solids through:

• Isometric drawing
• Plans
• Elevations.

Geometry, Shape, and Measure

Students will:

Understand the concepts of perimeter and area and use them in a range of problem-solving situations.
Understand circumference and area when problem-solving with circles.
Understand the concept of surface area and use this with cubes and cuboids.
Understand the concept of volume and use this with prisms.
Understand bearings, how to calculate them and where they are used in the real world.
Understand how to use a protractor and a pair of compasses when performing constructions.

Probability and Statistics

Students will:

Understand how to calculate probabilities of independent events.
Systematically record outcomes to find theoretical probabilities.
Understand sampling methods.
Understand how to collect and present data in a frequency table.
Understand questionnaire design and use one to carry out a small survey.
Understand how to interpret charts and tables including Stem and Leaf and Scatter diagrams.

Number and Algebra

Students will:

Explore number problems and reasoning.
Estimate answers using place value.
Use index laws, powers, and roots in calculations.
Calculate with numbers in standard form.
Understand the difference between rational and irrational numbers.
Simplify surds and rationalise denominators
Use the rules of indices to simplify algebraic expressions. Factorise algebraic expressions.
Solve equations involving brackets and numerical fractions.

Algebra and Data

Students will:

Understand how to substitute numbers into formulae and build on methods to rearrange formulae.
Distinguish between expressions, equations, formulae, and identities.
Understand how to find the general rule as an nth term for a particular sequence and determine whether a particular number is a term in each sequence.
Understand how to solve problems using geometrical and Fibonacci sequences.
Understand how to expand the product of two brackets and use the difference of two squares.
Factorise quadratics written in the form ax^2 +bx +c
Understand how to interpret and present data.
Understand how to construct a range of diagrams and plot relevant graphs for a given set of data.

Number and Shape

Students will:

Understand and be fluent in the four operations with fractions.
Use ratio in different contexts to solve problems.
Understand the difference between ratio and proportion and solve problems involving them.
Solve real life problems using percentages.
Derive and use rules in geometry to solve problems.
Solve problems using Pythagoras’ Theorem. Use trigonometric ratios to solve problems.

Algebra and Shape

Students will:

Understand that top athletes and sports teams use graphs to track progress, to show the improvement they have made.
Understand that linear graphs are written in the form y=mx+c and be able to rearrange, compare and plot equations in this format.
Find equations of lines given gradients and intercepts.
Understand how to draw and interpret distance-time graphs.
Understand velocity-time graphs and their link to acceleration.
Draw and interpret real life linear graphs and make the link between direct proportion and y=mx+c
Understand how to plot non-linear graphs from real life context.
Plot quadratic, cubic and reciprocal graphs, understanding roots and turning points. Solve problems involving circles.
Solve area and volume problems with:

• Prisms.
• Cones.
• Pyramids.
• Cylinders.

Shape and Algebra

Students will:

Solve volume problems with frustums.
Understand bounds and how they can affect a calculation.
Understand the four aspects of transformations and the affect they have upon a shape.
Understand how to use constructions with angle and shape.
Understand why we use bearings and be able to calculate them from a given point.
Understand how to solve simultaneous equations by elimination and substitution.

Algebra and Probability 

Students will:

Solve quadratic equations by completing the square and the quadratic formula.
Solve simultaneous equations graphically and understand how inequalities can be used to define a region.
Solve inequalities.
Understand how to use Venn diagrams and space diagrams with probability.
Use tree diagrams to calculate probabilities for independent and conditional events.

Number and Shape

Students will:

Understand how to solve multiplicative reasoning problems in a range of contexts.
Understand similarity and congruence in 2D and 3D solids.
Understand how to use trigonometry in non-right-angled problems.

Algebra and Data

Students will:

Understand different sampling methods.
Understand how to create cumulative frequency tables and draw their respective curves.
Understand box plots and histograms.
Solve more complex equations and understand iteration.
Sketch quadratics and Cubics.

Shape and Algebra

Students will:

Understand the rules associated with circle theorems and use them to solve geometry problems.
Study more complex algebraic concepts, including fractions and proof.
Understand vector notation and use it to solve vector problems.

Number

Students will:

Draw direct and inverse proportion graphs.
Understand how to find the area under a curve.
Understand the concepts to transform graphs.

Revision and Exam Preparation

Students will:

Prepare for their summer exams following individual bespoke learning programs.