Maths

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

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

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

Algebraic manipulation

In the future 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 the prior unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in this unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.

Simultaneous equations: 2 variables

The ratio unit will cover comparing fractions, percentages and ratios and being able to move fluently between them. This unit ensures pupils have had the opportunity to work with finding the percentage of an amount and the opportunity to calculate interest.

In the prior unit, pupils developed the skills to calculate a given percentage of an amount. In this unit, these skills are extended to performing simple and compound interest calculations.

In this unit pupils will learn how to perform simple and compound interest calculations using percentages.

Percentages

In this unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

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

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Arithmetic procedures: index laws

In the prior unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

In this unit pupils will learn how to add, subtract, multiply and divide numbers written in standard form.

Standard form calculations

In the prior unit, pupils explored the concept of square root, including calculating this on their calculators. In this unit, pupils work with surds and the notion that a surd is both an operation and the result of that operation.

In this unit pupils will learn how to recognise surds, handle them in calculations and rationalise fractions with surds as denominators.

Surds

In this unit, pupils are given the opportunity to assess how valid a sample may be and what the averages might tell us. In the future unit, pupils extend their knowledge of averages to stem and leaf diagrams as well as comparing two data sets.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils are given the opportunity to consider where the data came from and how it was collected and can therefore start to evaluate how good a representation the sample is of the whole population.

In this unit pupils will learn how to sample, and explore accuracy and limitations with various sampling strategies and data collection techniques.

Sampling

In the prior unit, pupils explored different graphs and charts as a way of presenting data visually. Pupils were introduced to scatter graphs and learnt how to construct them. In this unit, this understanding is extended to using a line of best fit to allow interpolation.

In this unit pupils will learn how to interpret and extract data from scatter graphs and time series graphs.

Graphical representations of data: scatter graphs and time series

In this unit, pupils began to compare two different sets of data. In the future unit, pupils will consider cumulative frequency graphs and histograms and compare the data from these diagrams to other graphical representations.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils extend this learning to comparing two different data sets and comparing these measures of central tendency.

In this unit pupils will compare two different data sets and compare different measures of central tendancy when interpreting the data. Pupils will learn to interrogate frequency tables and stem and leaf diagrams both with and without technology.

Comparisons of numerical summaries of data

In the prior unit, pupils learnt how to round to a given number of decimal places or significant figures and explored the effect of using rounded numbers for calculations. In this unit, pupils will investigate the bounds and perform calculations to determine a best/worst case scenario.

This unit explores the impact of upper and lower bounds on additive and multiplicative calculations.

Rounding, estimation and bounds

In the compound measures 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 this unit will aid understanding.

The ratio unit will cover comparing fractions, percentages and ratios and being able to move fluently between them. The percentages unit ensured pupils had the opportunity to work with finding the percentage of an amount and the opportunity to calculate interest.

In this unit pupils will learn how to combine ratios, interpret algebraic ratios, and investigate quantity changes and their effect on ratios.

Ratio

The work on gradient in this unit is expanded further in the future 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 the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

In this unit pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

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

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

In this unit graphical representations of non-linear graphs are introduced and explored, and their key features identified.

Non-linear graphs

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

In the prior unit, pupils derived the formula for the circumference and area of a circle. In this unit, this knowledge is combined with knowledge of fractions to find the arc length and area of a sector.

In this unit, knowledge of circles and polygons is drawn upon to find the arc length and area of a circle sector and areas of complex compound shapes.

2D and 3D shape: compound shapes

In this unit, pupils applied their understanding of angles to solve increasingly complex problems. In the future unit, pupils will use their mathematical reasoning to derive and use various circle theorems. 

In the prior unit, pupils learnt how to identify corresponding, alternate and co-interior angles. In this unit, pupils use their knowledge of these angles to reason through and solve more complicated problems.

In this unit pupils use their knowledge of corresponding, alternate and co-interior angles to reason through and solve more complicated problems.

Angles

In this unit, pupils enhanced their understanding of enlargement. In this future unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape. 

In the prior unit, pupils learnt about the different types of transformations. In this unit, pupils' knowledge is extended as negative scale factors are considered as are multiple transformations.

In this unit pupils apply their knowledge of transformations to explore negative enlargement factors and the application of multiple transformations.

Further transformations

In the prior unit, pupils enhanced their understanding of enlargement. In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

Similarity

In the prior unit, pupils applied their understanding of angles to solve increasingly complex problems. In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

Circle theorems

In the prior unit, pupils considered different views of a 3-D shape in order to understand how to calculate the surface area and volume. In this unit, pupils will be considering a 3-D shape from different viewpoints in order to draw the side and front elevations as well as the plan.

In this unit, pupils will be considering a 3-D shape from different viewpoints in order to draw the side and front elevations as well as the plan view.

Plans and elevations

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

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

In this unit, pupils are introduced to a variety of situations where trigonometric ratios are required, such as 3-D problems and problems of elevation or depression.

Right-angled trigonometry

In the angles unit, pupils reasoned through more complex problems involving angles. In the bearings unit, pupils apply their knowledge of angles in order to calculate bearings and solve angle problems within the context of bearings.

In this unit, pupils apply their knowledge of angles in order to calculate bearings and solve angle problems within the context of bearings.

Maths

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