Maths

Checking and securing understanding of simplifying

Checking and securing understanding of substitution

Further algebraic terminology

Checking and securing understanding of expanding a single bracket

Checking and securing understanding of factorising

Checking and securing understanding of forming linear equations

Checking and securing understanding of solving and interpreting linear equations

Checking and securing understanding of changing the subject

Checking and securing understanding of the product of two binomials

Factorising a quadratic expression

Factorising using the difference of two squares

Solving quadratic equations by factorising

Problem solving with algebraic manipulation

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

Checking and securing understanding of interpreting graphs

Forming simultaneous equations

Combining equations

Solving simultaneous equations by elimination from a context

Solving algebraic simultaneous equations by elimination

Solving more complex simultaneous equations by elimination

Solving simultaneous linear equations by substitution

Solving simultaneous linear equations graphically

Solving simultaneous equations via any method

Problem solving with simultaneous equations

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

Checking and securing understanding of finding a percentage

Checking and securing understanding of percentage increase

Checking and securing understanding of percentage decrease

Percentage profit and loss

Simple and compound interest

Simple interest calculations

Simple interest calculations with technology

Compound interest calculations

Compound interest calculations with technology

Problem solving with percentages

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

Checking and securing understanding of converting between fractions and decimals

Checking and securing understanding of calculating with fractions and decimals

Checking and securing understanding of prime factorisation

Checking and securing understanding of LCM and HCF

Checking and securing understanding of roots and integer indices

Checking and securing understanding of calculations involving negative numbers

The laws of indices - multiplication

The laws of indices - division

The laws of indices - raising a power to a power

The laws of indices - negative and zero exponents

Problem solving with the laws of indices

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

Checking and securing understanding of writing large numbers in standard form

Checking and securing understanding of writing small numbers in standard form

Adding numbers in standard form

Subtracting numbers in standard form

Multiplying numbers in standard form

Dividing numbers in standard form

Problem solving with standard form calculations

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

Accuracy of final answers

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

Checking understanding of statistical problems

The Statistical Enquiry Cycle

Types of data

Sampling methods

Sampling limitations

Data collection

Biased questioning

Problem solving with sampling

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

Checking understanding of scatter graphs

Checking understanding of correlation

Estimating from scatter graphs

Interpolation versus extrapolation

Outliers in scatter graphs

Constructing time series graphs

Interpreting time series graphs

Problem solving with scatter graphs and time series

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

Checking understanding of summary statistics from a list

Checking understanding of summary statistics from a frequency table

Calculating summary statistics from a grouped frequency table

Calculating the mean from a grouped frequency table

Constructing stem and leaf diagrams

Calculating summary statistics from stem and leaf diagrams

Checking understanding of measures of central tendency

Comparing data sets in context

Checking understanding of bar charts and pictograms

Checking understanding composite and bar-line charts

Statistical summaries using technology

Checking understanding of pie charts

Comparing various representations of data sets

Problem solving with comparisons of numerical data

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

Checking and securing understanding of rounding and truncating

Checking and securing understanding of estimating through rounding

Problem solving with rounding, estimation and bounds

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

Checking and securing understanding of simplifying and unitising ratios

Checking and securing understanding of equivalent ratios

Checking and securing understanding of sharing in a ratio

Checking and securing understanding of converting between ratios, percentages and fractions

Checking and securing understanding of real world ratios

Combining ratios

Changing ratios

Problem solving with ratios

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

Checking and securing understanding of drawing linear graphs

Checking and securing understanding of drawing vertical and horizontal graphs

Checking and securing understanding of finding the equation of the line from the graph

Checking and securing understanding of finding the equation of the line from coordinates

Parallel linear graphs

Checking and understanding graphs showing direct proportion

Graphs showing inverse proportion

Problem solving with linear graphs

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

Checking and securing understanding of drawing quadratic graphs

Key features of a quadratic graph

Drawing cubic graphs

Drawing reciprocal graphs

Problem solving with non-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

Checking and securing understanding of converting between metric and imperial measures

Checking and securing understanding of scales and conversion

Checking and securing understanding of perimeter for standard shapes

Checking and securing understanding of perimeter for compound shapes

Checking and securing understanding of area for standard shapes

Checking and securing understanding of area for compound shapes

Perimeter and area in a contextual setting

Checking and securing understanding of circles

Calculating arc length

Area of a sector

Area of compound shapes

Problem solving with 2D shapes

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

Checking and securing understanding of angle notation and drawing/measuring angles

Checking and securing understanding of basic angle facts

Checking and securing understanding of advanced angle facts

Checking and securing understanding on chains of reasoning with angle facts

Checking and securing understanding of properties of shapes

Checking and securing understanding of polygons

Checking and securing understanding of interior angles

Checking and securing understanding of exterior angles

Forming equations with angles

Problem solving with angles

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

Checking and securing understanding of congruence and similarity

Checking and securing understanding of rotation

Checking and securing understanding of translation

Checking and securing understanding of reflection

Checking and securing understanding of enlargement with positive integer scale factors

Checking and securing understanding of enlargement with positive fractional scale factors

Multiple transformations

Identifying multiple transformations

Problem solving with further transformations

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.

Maths

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