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Checking and securing understanding of solving with simple algebraic fractions

Checking and securing understanding of changing the subject with simple 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 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

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

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

Combining speeds

Combining densities

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

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

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 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

Checking and securing understanding of geometric sequences

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 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

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.

Inequalities

Checking and securing understanding of translations

Column vectors

Parallel vectors

Addition with vectors

Subtraction with vectors

Multiplication with vectors

Fluency in arithmetic procedures with vectors

Problem solving with vectors

In the prior unit, pupils described a translation using column vector notation. Pupils' understanding of vectors is further developed in this unit, with pupils exploring column vector notation and arithmetic procedures.

In this unit, pupil understanding of vectors is deepened with pupils exploring column vector notation and arithmetic procedures.

Vectors

Checking and securing understanding of constructing the perpendicular bisector of a line segment

Checking and securing understanding of constructing a perpendicular to a given line through a point

Checking and securing understanding of bisecting an angle

Constructing angles of  90° and 45°

Constructing a triangle given three side lengths using compasses

Constructing a triangle given two side lengths and the angle between them using a compass

Constructing a triangle given two angles and the side length between them

Constructing a right-angled triangle given the length of the hypotenuse and one other side length

Constructing a triangle given two side lengths and an angle not between them

Constructing loci

Applying constructions to loci problems

Solving loci problems in context

Problem solving with loci and constructions

The constructions covered in the prior unit are built on in this unit. In this unit, pupils construct triangles and construct diagrams following specific restrictions.

In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.

Loci and construction

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