Maths

Checking and securing understanding of solving with simple algebraic fractions

Simplifying algebraic fractions

Operations with algebraic fractions

Solving equations with algebraic fractions

Checking and securing understanding of changing the subject with simple algebraic fractions

Changing the subject with multiple algebraic fractions

Changing the subject where the variable appears in multiple terms

Problem solving with advanced algebraic fractions

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In the prior unit, pupils explored various ways to manipulate and solve various equations and formulae. In this unit, pupils apply these skills to algebraic fractions in order to change the subject and manipulate the algebraic fraction.

In this unit, pupils apply skills in manupulating and solving various equations and formulae to algebraic fractions in order to change the subject and manipulate them.

Algebraic fractions

Checking and securing understanding of trigonometric ratios

Drawing the sine and cosine graphs

Drawing the tangent graph

Interpreting the trigonometric graphs

The area of any triangle

Calculating the area of any triangle when the height is not known

The sine rule

The cosine rule

Using the sine and cosine rules

Considering the appropriate trigonometric rule

Problem solving with non right-angled trigonometry

In the prior unit, pupils explored the trigonometric ratios for right-angled triangles in a variety of situations. In this unit, pupils explore what can be done when we have a triangle that is not right-angled.

In this unit, pupils explore how to apply knowledge in trigonometry to non right-angled triangles.

Non right-angled trigonometry

Checking and securing understanding of nets of solids

Checking and securing understanding of volume of prisms

Checking and securing understanding of surface area of cuboids

Checking and securing understanding of surface area of other prisms

Checking and securing understanding of volume of a cylinder

Checking and securing understanding of surface area of a cylinder

The surface area of a pyramid

The volume of a pyramid

The surface area of a sphere

The volume of a sphere

The surface area of a cone

The volume of a cone

Surface area of composite solids

Volume of composite solids

Volume of a frustum of a cone

Surface area of a frustum of a cone

Forming equations involving complex shape calculations

Advanced problem solving with further surface area and volume

In this unit, pupils have increased their knowledge of volume which is used in the compound measures unit as the formula for density involves volume. 

In the prior unit, pupils built upon their learning of the area of different shapes. In this unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

In this unit, pupils will further develop their understanding of shapes by considering the surface area and volume of pyramids, spheres and cones.

2D and 3D shape: surface area and volume (pyramids, spheres and cones)

Checking and securing displaying outcomes

Checking and securing exhaustive events

Probabilities involving algebra

Frequency trees

Checking and securing calculating probabilities from tables

Checking and securing calculating probabilities from diagrams

Experimental probability

Experimental vs theoretical probability

Set notation

Conditional probability in a two-way table

Conditional probability in a Venn diagram

Conditional probability in a tree diagram

Algebra in tree and Venn diagrams

Constructing three event Venn diagrams

Probabilities in three event Venn diagrams

Comparing multiple representations to calculate conditional probabilities

Combinations

Advanced problem solving with conditional probability

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend this understanding to calculating conditional probabilities using all of the representations encountered in the prior unit.

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend it to calculate conditional probabilities.

Conditional probability

Checking and further securing understanding of direct proportion in context

Compound measures for speed

Compound measures for density

Compound measures for pressure

Converting between metric speed measures

Converting between metric and imperial speed measures

Converting between other compound measures

Combining speeds

Combining densities

Advanced problem solving with compound measures

In this unit, pupils will be exploring the multiplicative relationship between different compound measures. Ratio will be one of the ways in which this is explored and the skills from the prior unit will aid understanding. There are also links to the volume units as volume is required for the density formula.

In this unit, pupils explore the multiplicative relationship between different compound meaures and units such as speed, rates of pay, density and pressure.

Compound measures

Checking and securing understanding of reading from context-based graphs

Checking and securing understanding of drawing distance-time graphs

Distance-time graphs

Speed-time graphs

Non-linear distance-time graphs

Interpreting and drawing real-life graphs

Interpreting and drawing more real-life graphs

Calculating the rate of change

Estimating the gradient of a curve

Improving the estimate of the gradient of a curve

Finding the equation of a radius of a circle

Finding the equation of the tangent to a circle

Calculating journeys from linear speed-time graphs

Estimating journeys from non-linear graphs

Efficiently estimating journeys from non-linear graphs

Advanced problem solving with real-life graphs

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.

Real-life graphs

Checking and securing understanding of direct proportion graphs

Checking and securing understanding of inverse proportion graphs

Abstract direct proportion

Finding the constant of proportionality for direct proportion

Finding the constant of proportionality for directly proportional relationships

Abstract inverse proportion

Finding the constant of proportionality for inverse proportion

Proportion modelled algebraically

Problem solving with direct and inverse proportion

In the linear graphs unit, pupils learnt to recognise and interpret graphs that illustrate direct and inverse proportion. In this unit, pupils learn how to represent these relationships algebraically.

In this unit, pupils learn how to represent direct and inverse proportion algebraically as an extension of work done in the linear graphs unit.

Direct and inverse proportion

Checking and securing understanding of functions

Defining function notation

Finding the inverse of a function

Writing composite functions

Solving equations involving functions

Solving equations involving composite functions

General algebraic forms for specific number properties

Making conjectures about patterns and relationships

Proving or disproving a statement

Writing a generalised statement about specific number properties

Writing a proof

Logical arguments

Multiple approaches to logical arguments

Problem solving with functions and proof

In this future unit, pupils continue to explore composite functions, thereby building on their work from this unit. Pupils need to understand function notation from this unit as this is used in iteration.

In this unit pupils will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.

Functions and proof

Checking and securing understanding of special number sequences

Fibonacci and alternating sequences

Checking and securing rules for generating arithmetic sequences

Identifying values in an arithmetic sequence

Reasoning about values in an arithmetic sequence

Conditions in arithmetic sequences

Arithmetic sequences and their graphs

Introducing quadratic sequences

Quadratic sequences

Checking and securing understanding of geometric sequences

Sequence notation

Advanced problem solving with further sequences

In the prior unit, pupils considered other types of graphs. In this unit, pupils consider different types of sequences such as Fibonacci and oscillating. Their knowledge is consolidated by linking all prior learning together.

In this unit, pupils consider different types of sequences such as Fibonacci and oscillating sequences. They then consolidate their knowledge of different types of sequences by solving contextual problems.

Further sequences

Checking and securing understanding of compound interest calculations

Building on composite functions

Evaluating iterative formulas

Approximating solutions to equations

Signs of a solution

Problem solving with iteration

In this unit, pupils continue to explore composite functions, thereby building on their work from the prior unit. Pupils need to understand function notation from the prior unit as this is used in iteration.

In this unit, pupils continue to explore composite functions and develop understanding of iteration, building on their work on functions and proof.

Iteration

Constructing a cumulative frequency graph

Interpreting a cumulative frequency graph

Constructing box plots

Comparing box plots

Interquartile range

Histograms with equal bar width

Histograms with unequal bar width

Moving between tables and histograms

Summary statistics from histograms

Constructing histograms and box plots using technology

Problem solving with cumulative frequency and histograms

In the prior unit, pupils compared two different sets of data. In this unit, pupils consider cumulative frequency graphs and histograms and compare these with other known graphical representations.

In this unit, pupils consider cumulative frequency graphs and histograms, and compare these with other known graphical representations.

Graphical representations of data: cumulative frequency and histograms

Checking and securing understanding of simultaneous equations

Non-solutions to simultaneous linear equations

Inequalities on number lines

Solving simple linear inequalities

Solving more complicated linear inequalities

Linear inequalities in context

A single solution set

Solution set notation

Solving a linear inequality graphically

Solving a set of linear inequalities graphically

Relating graphical solutions to algebraic solutions for inequalities

Solving quadratic inequalities in one variable graphically

Solving quadratic inequalities algebraically

Advanced problem solving with linear inequalities

In this unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.

Maths

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