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Checking understanding of similarity

Checking understanding of congruence

Similarity in shapes

Congruence in shapes

Congruent, similar or neither

Rotational symmetry

Congruent triangles (SSS)

Congruent triangles (SAS)

Congruent triangles (ASA and AAS)

Congruent triangles (RHS)

Applying the criteria for congruence

Demonstrating Pythagoras' theorem

Further demonstrating of Pythagoras' theorem

Length of the hypotenuse

Length of a shorter side

Determining which side

Pythagoras' theorem in context

Problem solving with similarity and Pythagoras' theorem

In this unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In the future unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In the prior unit, pupils explored the effects of different transformations and whether the transformed shape was congruent or similar to the original shape. This is built on in this unit where pupils formalise the criteria for determining congruence in triangles and study rotational symmetry.

This unit explores the concepts of congruence and similarity, and ways to prove or disprove similarity between shapes. We then explore further properties of triangles with Pythagoras' Theorem.

Geometrical properties: similarity and Pythagoras' theorem

Equally likely outcomes

Non-equally likely outcomes

The scale of likelihoods

Experiments to determine how likely an outcome is

Using lists to display outcomes for two events

Using two-way tables to display outcomes for two events

Using an outcome tree to display outcomes for two events

Using a Venn diagram to display outcomes for two events

Comparing representations of outcomes for two events

Using lists to display outcomes for more than two events

Using an outcome tree to display outcomes for more than two events

Using a Venn diagram to display outcomes for more than two events

Comparing representations of outcomes for more than two events

Problem solving with possible outcomes

In this unit, pupils learn techniques for systematically listing all of the possible outcomes for both one event and two events. In the future unit, pupils use lists of outcomes to find theoretical probabilities

In this unit, pupils find all the factors of a number systematically and they understand that systematic listing is helpful in organising their work. The idea of being systematic is built on in this unit as pupils work to identify all possible outcomes

This unit introduces and explores the concept of liklihood as a relative measure, and demonstrates multiple ways to represent likelihood such as Venn diagrams, tree diagrams and two-way tables.

Probability: possible outcomes

Checking listing possible outcomes

The probability scale

Calculating theoretical probabilities from lists (one event)

Calculating theoretical probabilities from a table (one event)

Calculating theoretical probabilities from probability tree diagrams (one event)

Calculating theoretical probabilities from Venn diagrams (one event)

Comparing multiple representations to calculate theoretical probabilities

Summing probabilities

Calculating theoretical probabilities from two-way tables (two events)

Calculating theoretical probabilities from Venn diagrams (two events)

Calculating theoretical probabilities from probability trees (two events)

Comparing multiple representations to calculate theoretical probabilities for combined events

Problem solving with theoretical probability

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

In the prior unit, pupils learnt techniques for systematically listing all of the possible outcomes for both one event and two events. In this unit, pupils use lists of outcomes to find theoretical probabilities. 

In this unit we build upon the concept of likelihood to work more mathematically with more measurable probability using fraction and decimal representations to both interpret and calculate. We revisit and develop ways to represent and compare probabilities.

Probability: theoretical probabilities

Checking understanding of arithmetic sequences

Securing understanding of arithmetic sequences

Features of geometric sequences

Recognising geometric sequences

Representing geometric sequences graphically

Features of special number sequences

Recognising special number sequences

Graphing special number sequences using technology

Extrapolating a sequence

Problem solving with non-linear relationships

In this unit, pupils considered geometric sequences and how they might be represented graphically. In this future unit, pupils study the graphical representation to link features of the graph to its equation.

In the sequences unit, pupils learnt how to graphically represent an arithmetic sequence. In this unit, pupils now consider geometric sequences and how these can be represented graphically.

In this unit we explore geometric and special number sequences like the Fibonacci sequence. We develop strategies to recognise types of sequence and continue them.

Non-linear relationships

Checking and securing understanding of the distributive law with algebraic terms

Checking and securing solving linear equations

The product of two binomials

Difference of two squares

More complex binomial products

Additive relationships

Multiplicative relationships between terms

Changing the subject with simple formula

Changing the subject with more complex formula

Changing the subject to suit the context

Evaluating expressions with and without changing the subject

Problem solving with expressions and formulae

In this unit, pupils use the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

In the prior unit, pupils learnt how to rearrange an equation to find a specific value that satisfied the equation. In expressions and formulae, pupils use their understanding of rearrangement to change the subject of a formula.

This unit develops pupil understanding of formulae and how to rearrange them. Pupils will learn how to recognise and manipulate binomials and learn to recognise the difference of two squares.

Expressions and formulae

Checking and securing understanding of similar triangles

Checking and securing understanding of Pythagoras' theorem

The unit circle

Scaling the right-angled triangle from the unit circle

Sine and cosine ratios

Tangent ratio

Using the sine ratio

Using the cosine ratio

Using the tangent ratio

Choosing the right trigonometric ratio

Choosing an appropriate method for finding lengths of a triangle

Problem solving with trigonometry

In this unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In the future unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In the prior unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.

Trigonometry

Checking and securing understanding of multiples of 10

Checking and further securing understanding of the commutative law

Multiples of 10 involving negative exponents

Writing large numbers in standard form

Writing small numbers in standard form

Ordering numbers in standard form

Problem solving with standard form

The conditions for standard form mean that pupils have explored how different powers of 10 can be written. In this unit, this understanding is generalised and the index laws formalised. 

In the prior unit, pupils learnt how to factorise multiples of 10 in order to simplify calculations. This understanding is built on in this unit as values are converted to meet the conditions for standard form. 

In this unit pupils learn to recognise, interpret and write in standard form. Pupils then extend this knowledge so that they can order numbers written in standard form.

Standard form

Checking and securing understanding of non-linear sequences

Extending thinking about sequences

Exploring the shapes of graphs using technology

Equations and their graphs

Efficiently drawing linear graphs

Reading from graphs

Modelling with graphs

Graphically solving two linear graphs that intersect

Problem solving with graphical representations

In this unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In the future unit, other types of graphs are introduced and their key features identified.

In the prior unit, pupils considered geometric sequences and how they might be represented graphically. In this unit, pupils study the graphical representation to link features of the graph to its equation.

In this unit pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.

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