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Higher GCSE Scheme of Work

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Complete Curriculum

Long Term Plan

Prerequisite Knowledge statements are copied from Mathematics programmes of study: key stages 1 and 2 published by the Department for Education. Success Criteria statements are copied from the 2015 syllabus for GCSE subject content and assessment objectives published by the Department for Education.

Contents

Year 9

Fractions and Decimals .....

Averages .....Page 7

Area & Perimeter .....Page 9

Ratio & Proportion .....Page 12

Linear Graphs .....Page 14

Representing Data .....Page 16

Angles .....Page 19

Algebraic Expressions .....Page 22

Collecting Data .....Page 25

Transformations .....Page 27

Solving Equations .....Page 30

Scatter Graphs .....Page 33

Constructions .....Page 35

Pythagoras' Theorem .....Page 37

Year 10

Percentages .....Page 39

Probability .....Page 42

Compound Measures .....Page 45

Accuracy .....Page 47

Similarity .....Page 50

Inequalities .....Page 52

Sequences .....Page 54

Indices & Standard Form .....Page 56

Right-Angled Trigonometry .....Page 59

Volume and Surface Area .....Page 62

Formulae and Kinematics .....Page 65

Graphical Functions .....Page 67

Non-RIght-Angled Trigonometry .....Page 70

Proportion & Variation .....Page 72

Circle Theorems .....Page 74

Year 11

Solving Quadratics .....Page 76

Vectors .....Page 79

Trigonometrical Graphs .....Page 81

Algebraic Fractions .....Page 83

Functions .....Page 85

Proof .....Page 88

3

Topic: Fractions & Decimals Duration: 6 hours Prerequisite Knowledge

express one quantity as a fraction of another,

where the fraction is less than 1 or greater than 1

interpret fractions as operators

estimate answers; check calculations using

approximation and estimation, including

answers obtained using technology

order positive and negative decimals

Keywords

Fraction Numerator

Denominator Simplify

Equivalent Mixed number

Top heavy Decimal

Product Reciprocal

Success Criteria

apply the four operations, including formal

written methods, simple fractions (proper and

improper)

express one quantity as a fraction of another,

where the fraction is less than 1 or greater than 1

apply the four operations, including formal

written methods, to mixed numbers both positive

and negative;

calculate exactly with fractions

Key Concepts

All rational numbers are written using exact proper or improper

fractions.

When adding or subtracting fractions the denominators need to

be equal.

Dividing fractions is equivalent to multiplying by a reciprocal.

When calculating with decimal numbers encourage students to

estimate the solution as means to check their working.

Students may need to recap multiplying and diving by powers of

ten when calculating the product of decimal numbers.

Use equivalent fractions when performing long division.

Simplifying the fractions help to break down the calculation.

Common Misconceptions

A fraction with a smaller denominator has a lesser value.

Fractions such as 3

5 can incorrectly assumed to have a decimal

equivalence of 3.5.

Students incorrectly consider multiplications to always increase a

number and divisions to decrease.

Students fail to spot incorrect calculations due to not estimating

solutions.

Recurring Decimal Terminating Decimal

4

Differentiated Learning Objectives Teaching

Resources

Independent

Learning

Additional Resources & Videos

All students should be able to calculate the product of any two

integers.

Most students should be able to calculate the product of two

integers given a real life context.

Some students should be able to calculate the product of two

decimals.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Interactive Excel File

Qwizdom PowerPoint Quiz

All students should be able to divide a three digit number by a

one digit number.

Most students should be able to a divide three digit number by a

two digit number through simplifying a fraction.

Some students should be able to derive a quotient from a real life

problem and solve through simplifying the faction.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to add and subtract fractions where

one denominator is a factor or multiple of another using a

fraction wall.

Most students should be able to add and subtract fractions

where one denominator is a factor or multiple of another using

equivalences.

Some students should be able to add and subtract fractions

where neither number is a factor or multiple of the other.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Tarsia Activity


All students should be able to calculate the product of two

ordinary fractions by cross simplifying.

Most students should be able to calculate the product of a top

heavy and ordinary fraction by cross simplifying.

Some students should be able to calculate the product of two

mixed numbers.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


5

All students should be able to divide one ordinary fraction by

another using its reciprocal.

Most students should be able to divide a fraction by a mixed

number using its reciprocal.

Some students should be able to solve problems involving the

product of two ordinary fractions or mixed numbers.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Tarsia Activity


All students should be able to convert a decimal that recursin the tenths column to a simplified fraction.

Most students should be able to convert a decimal that recurs inthe tenths or hundredths column to a simplified fraction.

Some students should be able to convert any recurringdecimal to a fraction in its simplified form.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Treasure Hunt YouTube Demonstration YouTube Proof 0.999 = 1

YouTube Introduction

6

https://www.youtube.com/watch?v=PU_ip3PZ05Y

http://youtu.be/no4DU0H3YEY

http://youtu.be/Ah8aZT5jHes

Topic: Averages Duration: 5 hours Prerequisite Knowledge

Interpret and present discrete and continuousdata using appropriate graphical methods, including bar charts and time graphs.

Solve comparison, sum and difference problemsusing information presented in bar charts, pictograms, tables and other graphs.

Keywords

Data Average Mean Median Mode Range Central Tendency Stem & Leaf Frequency Class width Stem & Leaf Spread

Success Criteria

interpret, analyse and compare the distributionsof data sets from univariate empirical distributions through:

o appropriate graphical representationinvolving discrete, continuous and grouped data

o appropriate measures of central tendency(median, mean, mode and modal class) and spread

Construct and interpret stem and leaf diagrams apply statistics to describe a population

Key Concepts

It helps to teach students to associate the sound of median andmode to middle and most.

The range is not an average but a measure of spread. Illustrate the concept of the mean average as shown below.

A frequency table is used when the sample size increases beyondsimple calculations being possible from a list.

The median average of a class width is used as the mid-pint whencalculating the mean from grouped data.


Students tend to confuse the median, mode and mean averages. The range is often incorrectly thought of as a type of average. Students often find it difficult to calculate the median average from

data presented in a frequency table. When sorting continuous data into a grouped data table students

often struggle to fully understand the inequality notation.

7

Differentiated Learning Objectives Teaching Resources Independent Learning Additional Resources &

Videos

All students should be able to calculate the range from a set ofdata.

Most students should be able to compare the consistency of twoor more data sets using the range.

Some students should be able to compare two more data setsusing an average and range.

Lesson Plan Smart Notebook Activ Inspire

Flipchart Microsoft

PowerPoint

DifferentiatedWorksheet


All students should be able to plot a Stem and Leaf Diagram Most students should be able to plot and interpret the median,

mode and range from a Stem and Leaf Diagram Some students should be able to compare data sets using from a

back-to-back stem and leaf diagram.


Flipchart Microsoft

PowerPoint


All students should be able to calculate the mean from afrequency table.

Most students should be able to calculate the mean from afrequency table to compare distributions.

Some students should be able to calculate the mean from a barchart or line graph.


Flipchart Microsoft

PowerPoint



All students should be able to calculate the mean average fromgrouped data.

Most students should be able to compare frequency tablesthrough the use of the mean average.

Some students should be able to calculate the mean fromnumerical data in a bar chart


Flipchart Microsoft

PowerPoint


Interactive Excel File I.T. Activity Raw Data

Treasure Hunt

8

Topic: Area & Perimeter Duration: 9 hours Prerequisite Knowledge

know and apply formulae to calculate the area

of rectangles

calculate the perimeters of 2D shapes,

including composite shapes;

compare and order lengths, mass, volume /

capacity and record the results using >, < and =

measure, compare, add and subtract: lengths

(m/cm/mm); mass(kg/g); volume/capacity

(l/ml)

identify and apply circle definitions and

properties, including: centre, radius, chord,

diameter, circumference, tangent, arc, sector

and segment

Keywords

Area Compound Shape

Triangle Parallelogram

Perpendicular Trapezium

Circle Diameter

Radius Metric

Arc Sector

Success Criteria

know and apply formulae to calculate: area of

triangles, parallelograms and trapezia;

know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes;

calculate arc lengths, angles and areas of

sectors of circles

Key Concepts

Demonstrate a triangle as being half a rectangle so students know

to use the perpendicular height in their calculation. Demonstrate

a parallelogram as having an equal area to a rectangle.

To calculate the area of composite rectilinear shapes have

students break them up in different ways.

A sector is a fraction of 360° of the entire circle.


Students often confuse area and perimeter.

When calculating the area of a triangle or parallelogram students

tend to use the slanted height rather than the correct

perpendicular height.

Arc length and area of a sector are often rounded incorrectly.

Encourage students to evaluate as a multiple of pi and calculate

the decimal at the end.

9

Differentiated Learning Objectives Teaching Resources Independent

Learning


All students should be able to determine the area of a

compound rectilinear shape by counting.

Most students should be able to determine the area of a

compound rectilinear shape by calculating.

Some students should be able to determine possible perimeters

when given the area of a compound rectilinear shape.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to calculate the area of a right-

angled triangle as half of a rectangle.

Most students should be able to derive the formula for the area

of a triangle and use it.

Some students should be able to calculate the area of a

compound shape involving rectangles and triangles.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


Interactive Geogebra File

All students should be able to calculate the area of a

parallelogram using the formula 𝐴 = 𝑏ℎ

Most students should be able to calculate the area of a

parallelogram and trapezium using the formulae 𝐴 = 𝑏ℎ & 𝐴 =

(𝑎+𝑏

2) ℎ

Some students should be able to calculate the area of

compound shapes involving parallelograms and trapeziums.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


Parallelograms


Trapezia


All students should be able to derive and use the formulae for the

circumference of a circle 𝑐 = 𝜋𝐷

Most students should be able to derive and use the formulae for

the circumference of a circle 𝑐 = 𝜋𝐷 and 𝑐 = 2𝜋𝑟

Some students should be able to calculate the radius and

diameter of a circle when given its circumference.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint



All students should be able to calculate the circumference of a

circle.

Most students should be able to calculate the perimeter or

circumference of circular shapes.

Some students should be able to calculate the radius or

diameter when given the circumference.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



10

http://ggbtu.be/m153215





All students should be able to derive the formula for the area of a

circle.

Most students should be able to derive and apply the formula for

the area of a circle.

Some students should be able to calculate the area of a semi-

circle.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint



All students should be able to calculate the area of a circle and

semi-circle.

Most students should be able to calculate the area of

compound shapes involving circles.

Some students should be able to calculate the radius or

diameter when given the area of a circle.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Treasure Hunt



All students should be able to calculate the arc length of a major

and minor sector.

Most students should be able to calculate the perimeter around

a sector.

Some students should be able to calculate the perimeter of

compound shapes involving sectors.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to calculate the area of a major and

minor sector.

Most students should be able to calculate the area of

compound shapes involving sectors.

Some students should be able to calculate the angle or radius of

a sector when given the area.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


11





Topic: Ratio and Proportion Duration: 3 hours Prerequisite Knowledge

solve problems involving the relative sizes of two quantitieswhere missing values can be found by using integermultiplication and division facts

solve problems involving the calculation of percentages solve problems involving unequal sharing and grouping

using knowledge of fractions and multiples

Keywords Ratio Proportion Unitary method Simplify Inverse Proportion Direct proportion Formula Notation Equivalent Scale

Success Criteria use ratio notation, including reduction to simplest form express a multiplicative relationship between two quantities

as a ratio understand and use proportion as equality of ratios relate ratios to fractions express the division of a quantity into two parts as a ratio apply ratio to real contexts and problems (such as those

involving conversion, comparison, scaling, mixing,concentrations)

understand and use proportion as equality of ratios

Key Concepts It is important for students to visualise equivalent and ratios by categorising

objects and breaking them down into smaller groups. It is important to apply equivalent ratios when solving problems involving

proportion. Including the use of the unitary method. To share amount given a ratio it is necessary to find the value of a single

share. When two or more measurements increase at a linear rate they are in direct

proportion. Inverse proportion is when one increases at the same rate theother decreases.

Common Misconceptions Ratios amounts are often confused with fractions involving the same digits.

For instance 2 : 3 is confused with 2 3 or 1 : 2 = 1 2. When solving problems involving proportion students tend to struggle with

forming a ratio. For instance, 3 apples cost 45p would form the ratio apples :cost.

When writing ratios into the form 1 : n students incorrectly assume that n hasto be an integer or greater than 1.

12

Differentiated Learning Objectives Teaching Resources Independent Learning


All students should be able to simplify a ratio using commonfactors.

Most students should be able to fully simplify a ratio using thehighest common factor.

Some students should be able to calculate equivalent ratiosinvolving multiple different units.

Lesson Plan Smart Notebook ActivInspire

Flipchart Microsoft

PowerPoint

Differentiated Worksheet

YouTube Demonstration

All students should be able to calculate the highest commonfactor between two equivalent ratios.

Most students should be able to calculate proportionateamounts using equivalent ratios.

Some students should be able to solve problems involvingequivalent ratios in context.


Flipchart Microsoft

PowerPoint



All students should be able to share to a ratio where the totalshares are a factor of the amount.

Most students should be able to share to a ratio by calculatingthe value of a single share.

Some students should be able derive and simplify a ratioinvolving three terms and share to any amount.


Flipchart Microsoft

PowerPoint






13

https://www.youtube.com/watch?v=a6Ma7ptR8zo

https://www.youtube.com/watch?v=X0Upa5au92o

https://www.youtube.com/watch?v=I0vnicONb2I

Topic: Linear Graphs Duration: 5 hours Prerequisite Knowledge

Interpret simple expressions as functions with

inputs and outputs;

Work with coordinates in all four quadrants

Keywords

Function Linear

Axes Graph

Gradient Intercept

Plot Scale

Continuous Table of Results

Parallel Perpendicular

Success Criteria

Plot graphs of equations that correspond to

straight-line graphs in the coordinate plane;

Find the equation of the line through two given

points, or through one point with a given

gradient

Identify and interpret gradients and intercepts of

linear functions graphically and algebraically

use the form y = mx + c to identify parallel and

perpendicular lines;

Key Concepts

Gradient is a measure of rate of vertical change divided by

horizontal change.

Graphs like

this have a

negative

gradient

Graphs like this

have a

positive

gradient

Parallel lines have an equal gradient. Perpendicular lines have a

negative reciprocal gradient.

Graphical solutions to an equation are not always exact due to

inaccuracies when plotting.


Students often confuse linear graphs to have the same notation

as statistical graphs.

The gradient can be calculated from any two points along the

graph. Not necessarily from the origin.

A linear function is always a straight-line graph.

Perpendicular gradients are often confused with parallel ones.

14


Learning


All students should be able to plot linear functions in the form

y = x + c.

All students should be able to plot linear functions in the form

y = mx + c.

All students should be able to plot and solve graphically equations

in the form y = mx + c.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to plot a straight-line graph in the form

ax+by=c using two points on the axes.

Most students should be able to plot a positive or negative graph

in the form ax ± by=c using two points on the axes.

Some students should be able to plot graphs in the form of ±ax

±by = ±c where the variables are not integers.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to calculate a positive gradient of a

linear function using the graph.

Most students should be able to calculate a gradient of a line

segment between two coordinate pairs.

Some students should be able to calculate the gradient of a

function in a real life context.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to derive the equation of a positive

straight line graph in the form y = mx + c

Most students should be able to derive the equation of a straight

line graph in the form y = mx + c

Some students should be able to derive the equation of a straight

line graph using two pairs of coordinates.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet Interactive Geogebra File

All students should recognise parallel lines when comparing their

gradients.

Most students should be able to calculate the gradients of two

perpendicular lines.

Some students should be able to derive the equation of a

perpendicular line when given a coordinate it passes through.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to calculate the gradient of

perpendicular lines.

Most students should be able to calculate the equation of a

perpendicular line.

Some students should be able to calculate the equation of lines in

the form ax + by + c = 0.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



15



https://www.youtube.com/watch?v=PlYcQsep9mM




Topic: Representing Data Duration:7 hours Prerequisite Knowledge

interpret and construct:

o frequency tables

o bar charts

o pictograms

for categorical data.

Construct and interpret stem and leaf diagrams

Apply statistics to describe a population

Keywords

Statistical Diagram Histogram

Frequency Density Frequency

Class Width Cumulative Frequency

Box Plot Interquartile Range

Upper Quartile Lower Quartile

Trend Time Series

Spread Skew

Success Criteria

infer properties of populations or distributions

from a sample, whilst knowing the limitations of

sampling

interpret and construct tables and line graphs for

time series data and know their appropriate use

construct and interpret diagrams for grouped

discrete data and continuous data, i.e.

histograms with equal and unequal class

intervals and cumulative frequency graphs, and

know their appropriate use

Key Concepts

Students need to spend time interpreting the diagrams as well as

creating them.

When using pie charts to compare distributions the frequency of

corresponding sectors is dependent on the total sample size.

Frequency diagrams are used to represent discrete data whereas

histograms are used for continuous data.

Histograms with unequal class widths represent data with an

unequal spread. Frequency is found using the area of a bar

rather than its height.

Cumulative frequency is the running total of the frequency.

The interquartile range (IQR) shows the boundaries of where the

most representative data is located.


Histograms are often confused with frequency diagrams.

Students tend to be more competent with constructing the

various representations than using them to analyse and make

summative comments about distributions.

16

17

Differentiated Learning Objectives Teaching Resources Independent Learning Additional Resources & Videos

All students should be able to plot and interpret basic facts from

a Pie Chart where the sample size is a factor of 360.

Most students should be able to plot and compare facts about a

pie chart.

Some students should be able to plot and compare facts about

a pie chart and appreciate the limitations of using pie charts to

represent data.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

I.C.T. Lesson


All students should be able to recognize the limitations of

representing data using pie charts.

Most students should be able to calculate frequencies from a pie

chart when given the sample size.

Some students should be able to compare data distributions by

comparing frequencies found from pie charts.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


Plenary Activity

All students should be able to recognize and describe a trend

over time from a time series.

Most students should be able to plot a time series and trend line

to describe upwards, downwards or level trends.

Some students should be able to recognize and describe

seasonal variations from a time series.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to plot a cumulative frequency graph

from a grouped data table.

Most students should be able to plot and interpret the median

and IQR from a cumulative frequency graph.

Some students should be able to plot and interpret a cumulative

frequency to compare multiple data sets.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Cumulative

Frequency

Differentiated

Worksheet Box

Plots


Autograph V3.3 Heights Autograph V3.3 Babies Autograph V3.3 Plenary

All students should be able to plot and interpret a Frequency

Diagram and Polygon for data presented in a frequency table.

Most students should be able to plot and interpret a Frequency

Diagram and Polygon for data presented in a grouped

frequency table.

Some students should be able to compare distributions using

Frequency Polygons.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

https://www.youtube.com/watch?v=a7HzTIaHfQ0

18

All students should understand the need for histograms with

unequal class width and calculate the frequency density.

Most students should understanding the need for and be able to

plot histograms with unequal class widths.

Some students should be able to compare data sets by plotting

and interpreting histograms with unequal class widths.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to calculate the total frequency from

a histogram with unequal class widths.

Most students should be able to calculate an estimate of

frequency within a given range for a histogram with unequal

class widths.

Some students should be able to estimate the mean average

from a histogram with unequal class widths.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


Autograph V3.3 Commuters Autograph V3.3 Age Autograph V3.3 Plenary

All students should be able to calculate the median from a Box

and Whisker Diagram to comment on a distribution.

Most students should be able to calculate the median and IQR

from a Box and Whisker Diagram to comment on a distribution.

Some students should be able to compare multiple distributions

using the Median and IQG from a Box and Whisker diagram.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

I.C.T Lesson

Data Sheet Autograph V3.3 Heights Autograph V3.3 Dot Plot Autograph V3.3 Subjects Autograph V3.3 Plenary


http://youtu.be/W3ju_Mvwd6I

Topic: Angles Duration: 6 hours

Prerequisite Knowledge

know angles are measured in degrees: estimate and

compare acute, obtuse and reflex angles

draw given angles, and measure them in degrees (°)

identify:

o angles at a point and one whole turn (total 360°)

o angles at a point on a straight line and 1/2 a turn

(total 180°)

o other multiples of 90°

apply the properties of angles at a point, angles at a

point on a straight line, vertically opposite angles;

Keywords

Angle Degree

Obtuse Reflex

Right angle Acute

Polygon Parallel

Straight line About a point

Triangle Perpendicular

Corresponding Interior

Alternate Polygon

Exterior Σ (sum)

Success Criteria

understand and use alternate and corresponding

angles on parallel lines;

derive and use the sum of angles in a triangle (e.g. to

deduce use the angle sum in any polygon, and to

derive properties of regular polygons)

measure line segments and angles in geometric

figures, including interpreting maps and scale drawings

and use of bearings

Key Concepts

Rather than being told (or given) angle properties students

should have the opportunity to discover and make sense

of them practically.

Use the Geogebra files to demonstrate the angle

properties.

Geometric problems can often be solved using various

angle properties. Encourage students to look for and

apply alternative properties.

Demonstrate how a polygon is made up from interior

triangles when calculating their angles.

Bearings always go clockwise from North and have three

digits. North lines are parallel.


Students often forget the definition of properties associated

to angles in parallel lines.

Exterior angles in a polygon have to travel in the same

direction for the sum to be 360°.

19


Learning

Additional Resources &

Videos All students should be able to calculate the remaining angle in a

scalene and right angled triangle when given the two.

Most students should be able to use the properties of triangles to

calculate angles in isosceles and equilateral triangles.

Some students should be able to calculate angles in compound

shapes involving multiple types of triangles.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Treasure Hunt


All students should understand that a quadrilateral is made up to

two triangles and therefore has a sum of 360 degrees.

Most students should be able to calculate an unknown angle

with a quadrilateral.

Some students should be able to prove there are 360° within a

quadrilateral by considering the sum of its external angles.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to recognise alternate and

corresponding angles to be equal and interior angles to have a

sum of 180 degrees.

Most students should be able to calculate unknown angles in

parallel lines using the alternate, interior or corresponding

property.

Some students should be able to calculate unknown angles in

parallel lines using a combination of alternate, corresponding

and interior angles.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint


All students should be able to calculate an unknown angle in

parallel lines using either alternate, corresponding or interior

angle properties.

Most students should be able to calculate an unknown angle in

parallel lines using a combination of alternate, corresponding

and interior angle properties.

Some students should be able to set up and solve an equation

involving the properties of angles in parallel lines.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



• Interactive Geogebra Files

20


https://www.youtube.com/watch?v=tSWvC5_xdfA



https://www.youtube.com/watch?v=tSWvC5_xdfA


All students should be able to measure the bearing from one

point to another.

Most students should be able to create a sketch map and

accurate construction to scale using bearings.

Some students should be able to prove a ‘back bearing’ using

the properties of angles in parallel lines.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to construct a regular polygon using

a pair of compasses and a straight edge.

Most students should be able to discover the sum of the exterior

angles around a polygon.

Some students should be able to discover the sum of interior and

exterior angles around a polygon

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Geogebra File

Microsoft Excel

Spreadsheet

All students should be able to calculate an exterior angle for a

regular polygon.

Most students should be able to calculate an interior and exterior

angle for a regular polygon.

Some students should be able to calculate the number of sides in

a polygon when given an exterior or interior angle.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Polygons

Treasure Hunt

PowerPoint Quiz


21

http://youtu.be/z-6O7J8qAFI

http://www.youtube.com/watch?v=eWXMbFQAeaI



Topic: Algebraic Expressions Duration:8 Hours Prerequisite Knowledge

• use simple formulae• generate and describe linear number sequences• express missing number problems algebraically• find pairs of numbers that satisfy an equation with two unknowns

Keywords • Algebra • Unknown• Expression • Substitute• Expand • Factorise• Product • Sum• Simplify • Like Terms• Binomial • Quadratic• Coefficient • Index Notation

Success Criteria • use and interpret algebraic notation, including:

o 𝑎𝑏 in place of 𝑎 + 𝑏o 3𝑦 in place of 3×𝑦o 𝑎2 in place of 𝑎×𝑎, 𝑎3 in place of 𝑎×𝑎×𝑎, 𝑎2𝑏 in place of

𝑎×𝑎×𝑏o

�b

in place of 𝑎 ÷ 𝑏

o coefficients written as fractions rather than decimalso brackets

• simplify and manipulate algebraic expressions by:o collecting like termso multiplying a single term over a bracketo taking out common factorso expanding products of two or more binomialso factorising quadratic expressions of the form 𝑥2 + 𝑏𝑥 + 𝑐,

including the difference of two squareso simplifying expressions involving sums, products and powers,

including the laws of indices

Key Concepts • Students need to appreciate that writing with algebra applies the

rules of arithmetic to unknown numbers which are represented as letters.

• It is important to define the difference between an expression,equation and formula.

• The multiplication symbol is omitted when using algebraic notation toavoid confusion between 𝑥 and ×. Quotients are written as using simplified fractions.

• Linear (𝑥), quadratic (𝑥2) and cube terms (𝑥3)cannot be collectedtogether.

• Understanding quadratics in the general form (𝑥2 + 𝑏𝑥 + 𝑐) helps tofactorise and expand expressions.

Common Misconceptions • Students often forget 𝑎𝑏 = 𝑏𝑎 = 𝑎 ×𝑏 and 𝑏 + 𝑎 = 𝑎 + 𝑎 = 𝑎 + 𝑏 when

collecting like terms. • When multiplying out brackets students incorrect forget to multiply the

second term especially with negative products. E.g., 2 𝑥 + 5 = 2𝑥 + 5 and −2 𝑥 − 5 = −2𝑥 + 5.

• When factorising expressions a common misconception is to not fullyfactorise. E.g., 18𝑥 + 24𝑦 = 9𝑥 + 12𝑦

• When expanding the product of two or more brackets students oftenincorrectly collect the like terms associated to the linear unknown.

• Students often struggle to factorise quadratics when 'a' is not one.Encourage them to expand their solution to double check correctfactorisation.

o factorising quadratic expressions of the form ax2 + bx + c.

22

Differentiated Learning Objectives Teaching Resources

Independent Learning


• All students should be able to simplify like terms involving one • Lesson Plan • • Interactive Excel Fileunknown. • Smart


• Most students should be able to simplify like terms involving Notebook • Tarsia Activitymultiple unknowns and constants. • Activ Inspire

• Some students should be able to simplify like terms using addition Flipchartand subtractions involving multiple unknowns and constants. • Microsoft

PowerPoint

• All students should be able to simplify the product and quotient • Lesson Plan •of an unknown and number. • Smart


• Most students should be able to simplify a product and quotient Notebookinvolving powers. • Activ Inspire

• Some students should be able to calculate the area of a Flipchartrectangle with algebraic lengths. • Microsoft

PowerPoint

• All students should be able to substitute a known value into an • Lesson Plan • • Interactive Excel Filealgebraic expression in the form 𝑎𝑥 + 𝑏 • Smart


• Most students should be able to substitute a known value into analgebraic expression in the form 5

X + 𝑏

• Some students should be able to substitute a known value into

Notebook• Activ Inspire

Flipchart

an algebraic expression in the form a +b-

• MicrosoftPowerPoint

• All students should be able to expand a pair of brackets with a • Lesson Plan • • Interactive Excel Fileconstant on the outside. • Smart


• Most students should be able to expand two pairs of brackets Notebook • Tarsia Activityand simplify the result. • Activ Inspire

• Some students should be able to expand two pairs of brackets Flipchartone with a negative on the outside. • Microsoft

PowerPoint

23

• Most students should be able to fully factorise an algebraicexpression in the form ax2+bx where a and b are both constants.

• Some students should be able to fully factorise an algebraicexpression the form ax2y + bxy2 where a and b are bothconstants.


Flipchart• Microsoft

PowerPoint

• All students should be able to expand and simplify two bracketsin the form (x+a)(x+b).

• Most students should be able to expand and simplify twobrackets in the form (x±a)(x±b).

• Some students should be able to expand and simplify twobrackets in the form (ax±c)(bx±d).

• Lesson Plan• Smart



PowerPoint

• DifferentiatedWorksheet

• Interactive Excel File

• All students should be able to factorise quadratics in the formax2+bx+c where a = 1 and both factors are positive.

• Most students should be able to factorise quadratics in the formax2+bx+c where a = 1 and either or both factors are negative.

• Some students should be able to factorise quadratics using thedifference of two squares.




PowerPoint


• Tarsia Activity


•

•

•




PowerPoint


• Interactive Excel FileAll students should be able to factorise a quadratic where the coefficient of x2 is a prime number and the constant is a positive integer.Most students should be able to factorise a quadratic where the coefficient of x2 is a prime number and the constant is a positive or negative integer.Some students should be able to factorise a quadratic where the coefficient of x2 is a non prime number and the constant is a positive or negative integer.

• All students should be able to fully factorise an algebraicexpression in the form ax+b where a and b are both constants.




24

Topic: Collecting Data Duration: 4 hours Prerequisite Knowledge

Interpret and construct statistical diagrams for discrete and

continuous data and know their appropriate use.

interpret, analyse and compare the distributions of data sets from

univariate empirical distributions through:

o appropriate graphical representation involving discrete,

continuous and grouped data

o appropriate measures of central tendency (median,

mean, mode and modal class) and spread

Keywords

Sample Handling Data Cycle

Survey Questionnaire

Discrete Continuous

Quantitative Qualitative

Two-way table Bias

Stratified Strata

Proportion Stratum

Success Criteria

Infer properties of populations or distributions from a sample, whilst

knowing the limitations of sampling.

apply statistics to describe a population

Interpret, analyse and compare the distributions of data sets from

univariate empirical distributions through appropriate graphical

representation involving discrete, continuous and grouped data.

Key Concepts

Students need to understand the benefits of using two-way tables as a

means to exhaustively cover each outcome for multiple events and

use them to calculate probabilities.

When designing questionnaires students need to consider time periods,

multiple check boxes which do not overlap and the need to collect a

wide ranging sample to reduce bias.

It is important to recognise the different statistical techniques that are

used to analyse and represent qualitative, quantitative, discrete and

continuous data.

Stratified sampling takes an equal proportion of the data from each

category quota sampling takes an equal number of samples.


Students often have difficulty designing two-way tables.

When designing questionnaires common errors include:

o No time period

o Overlapping responses

o Lack of ‘none’ or ‘other’ option.

o Check boxes with unequal widths.

o Double negative questions.

Students often try to represent continuous data using methods that are

only applicable for discrete sets.

25


Resources

Independent

Learning


All students should be able to complete a two-way table by

calculating missing values.

Most students should be able to design and interpret a two-way

table.

Some students should be able to use two-way tables to record

results in a probability experiment.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to understand the difference

between qualitative and quantitative data.

Most students should be able to design a data collection table

for discrete qualitative data, discrete quantitative data and

continuous quantitative data.

Some students should be able to apply the most appropriate

statistical tools to analyse different types of data.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to understand the difference

between a closed and open question when designing a

questionnaire.

Most students should be able to identify bias and choose suitable

response boxes when designing a questionnaire.

Some students should be able to identify bias and choose

suitable response boxes when designing a questionnaire

considering the various sample methods.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to find out what proportion of the

population is in each stratum.

Most students should be able to calculate the number of people

to be sampled in a stratum.

Some students should be able to calculate the total stratified

sample size given the number of people sampled in a stratum.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


26

Topic: Transformations Duration:6 hours Prerequisite Knowledge

use conventional terms and notations: points, lines, vertices, edges,

planes, parallel lines, perpendicular lines, right angles, polygons,

regular polygons and polygons with reflection and/or rotation

symmetries;

identify an order of rotational and reflective symmetry for two

dimensional shapes

use the standard conventions for labelling and referring to the sides

and angles of triangles; draw diagrams from written description

Recognise linear functions in the form y = ± a and x = ± a

Keywords

Object Image

Perpendicular Parallel

Transformation Rotation

Clockwise Anticlockwise

Centre Direction

Translation Vector

Reflection Mirror line

Enlargement Scale Factor

Similar Congruent

Success Criteria

identify, describe and construct congruent and similar shapes,

including on coordinate axes, by considering rotation, reflection,

translation and enlargement (including fractional and negative

scale factors)

Key Concepts

An object is transformed to create an image.

Rotation, Translation and Reflections involve congruent objects and

images whereas enlargement leads to the object being similar to the

image.

Translation vectors are used to describe movements along Cartesian

axes.

When reflecting objects the image is always the same distance from

the line of reflection as the object.

Rotations and enlargements are constructed from a centre.

A negative scale factor transforms the object through the centre.


Translation vectors can incorrectly be written using the name notation

as coordinate pairs.

Translations, Rotations, Enlargement and Reflections all come under

the umbrella term of transformation. Students often confuse the term

translation for transformation.

Students often have more difficulty describing single transformations

rather than performing them.

Enlargements can involve making a shape smaller as well as bigger.

Fractional scale factors between 0 and 1, not negative, decrease the

size.

27


Learning


All students should be able to reflect an object on a Cartesian

grid using a vertical or horizontal linear function as the mirror line.

Most students should be able to reflect an object on a Cartesian

grid using a mirror line in the form y = mx + c.

Some students should be able to perform and describe a

reflection on a Cartesian grid.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to translate an object in the first

quadrant using a translation vector.

Most students should be able to translate an object on Cartesian

axes using a translation vector.

Some students should be able to perform and describe a

translation on Cartesian axes using a translation vector.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to rotate an object 180 degrees

about a centre on a Cartesian grid.

Most students should be able to rotate an object about a centre

in any direction on a Cartesian grid.

Some students should be able to perform and describe rotations

using a centre on a Cartesian grid.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to enlarge an object to a positive

integer scale factor and centre on Cartesian axes.

Most students should be able to enlarge an object to a positive

scale factor and centre on Cartesian axes.

Some students should be able to describe and perform an

enlargement using a positive scale factor on Cartesian axes.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to enlarge an object by a negative

integer scale factor and centre.

Most students should be able to enlarge an object by a negative

scale factor and centre.

Some students should be able to perform and describe

enlargements using a negative scale factor.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


28


https://www.youtube.com/watch?v=MDPTLBPv-tw


https://www.youtube.com/watch?v=ZiCwy60Rpv8


https://www.youtube.com/watch?v=-cw1X0eKJ3M


https://www.youtube.com/watch?v=ZiCwy60Rpv8


All students should be able to fully describe a single

transformation using a rotation or translation.

Most students should be able to fully describe a single

transformation as a reflection, rotation or translation.

Some students should be able to fully describe a single

transformation as an enlargement, reflection, rotation or

translation.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Interactive Autograph V3.3

File


29

Topic: Equations Duration: 7 hoursPrerequisite Knowledge

use simple formulae

generate and describe linear number sequences

express missing number problems algebraically

find pairs of numbers that satisfy an equation with two

unknowns

use and interpret algebraic notation

simplify and manipulate algebraic expressions by:

o collecting like terms

o multiplying a single term over a bracket

Keywords

Algebra Equation

Brackets Expression

Solve Solution

Equals (=) Symbol

Unknown Variable

verify Elimination Method

Simultaneous Equation Linear Equation

Coefficient Substitution

Lowest Common Multiple

Success Criteria

solve linear equations in one unknown algebraically

(including those with the unknown on both sides of the

equation)

solve two simultaneous equations in two variables

algebraically;

find approximate solutions to simultaneous equations in two

variables using a graph;

Translate simple situations or procedures into algebraic

expressions or formulae; derive an equation (or two

simultaneous equations), solve the equation(s) and interpret

the solution.

Key Concepts

To solve an equation is to find the only value (or values) of the

unknown that make the mathematical sentence correct.

For every unknown an equation is needed.

Students need to have a secure understanding of adding and

subtracting with negatives when eliminating an unknown.

Coefficients need to be equal in magnitude to eliminate an

unknown.


Students can forget to apply the same operation to both sides

of the equation therefore leaving it unbalanced.

Students often struggle knowing when to add or subtract the

equations to eliminate the unknown. Review addition with

negatives to address this.

Equations need to be aligned so that unknowns can be easily

added or subtracted. If equations are not aligned students

may add or subtract with non like variables.

Students often try to eliminate variables with their coefficients

being equal

30


Learning


Videos All students should be able to solve a two-step linear equation

where the unknown appears on one side.

Most students should be able to solve a linear equation involving

a fraction where the unknown appears on one side.

Some students should be able to derive and solve a two-step

linear equation where the unknown appears on one side.

Lesson Plan

Smart Notebook

Activ Inspire Flipchart

Microsoft PowerPoint

Differentiated

Worksheet


All students should be able to solve equations with the unknown

on both sides

Most students should be able to solve equations with the

unknown on both sides involving brackets.

Some students should be able to solve equations with the

unknown on both sides involving fractions and brackets.

Lesson Plan

Smart Notebook



Differentiated

Worksheet



All students should be able to solve a quadratic equation in the

form x2+ab=c using trial and improvement.

Most students should be able to solve a quadratic and cubic

equation using trial and improvement.

Some students should be able to solve any none linear equation

using trial and improvements as well as derive the equation using

known facts.

Lesson Plan

Smart Notebook



Differentiated

Worksheet


All students should be able to solve equations involving fractions

using the balance method.

Most students should be able to solve equations involving

addition and subtraction of fractions.

Some students should be able to recognise equations that will

lead to quadratics.

Lesson Plan

Smart Notebook



Differentiated

Worksheet


All students should be able to plot a linear function.

Most students should be able to solve a pair of simultaneous

equations with integer solutions graphically.

Some students should be able to generate and solve a pair of

simultaneous equations graphically.

Lesson Plan

Smart Notebook



Differentiated

Worksheet

Treasure Hunt

Tarsia Activity

31

http://youtu.be/ndFZVF9ATRU

https://www.youtube.com/watch?v=kRlA283Deg8

All students should be able to solve a pair of equations

simultaneously using the method of elimination given equal

coefficients of one unknown.

Most students should be able to solve a pair of equations

simultaneously using the method of elimination where one

coefficient is a factor of the other.

Some students should be able to derive and solve a pair of

equations simultaneously using the method of elimination where

one coefficient is a factor of the other.

Lesson Plan

Smart Notebook



Differentiated

Worksheet


All students should be able to solve a pair of simultaneous

equations with different coefficients using the elimination method

Most students should be able to derive and solve a pair of

simultaneous equations by equating two unknowns.

Some students should be able to equate two unknowns from a

diagram and solve using the method of elimination.

Lesson Plan

Smart Notebook



Differentiated

Worksheet



32

http://www.youtube.com/watch?v=aTuodqC4Rjk

Duration: 4 hours Topic: Scatter GraphsPrerequisite Knowledge

• solve comparison, sum and difference problems usinginformation presented in a line graph

• Interpret and present discrete and continuous data usingappropriate graphical methods, including bar charts and timegraphs.

• work with coordinates in all four quadrants

Keywords • Scatter Graph • Line of best Fit• Scale • Axes• Axis • Correlation• Positive Correlation • Negative Correlation• No Correlation • Strong• Week • Association• Causal Relationship • Linear Relationship

Success Criteria • apply statistics to describe a population• use and interpret scatter graphs of bivariate data; recognise

correlation and know that it does not indicate causation;• draw estimated lines of best fit; make predictions; interpolate and

extrapolate apparent trends whilst knowing the dangers of sodoing

Key Concepts • Scatter graphs need to be drawn on graph paper or using I.C.T to

ensure accuracy and help identify the line of best fit.• Two measurements are ‘associated’ if the points lie approximately

along a straight line. This shows a linear relationship. However, anassociation between two variables can exist in a non-linearrelationship.

• Correlation is used to describe the strength of a linear relationshipbetween two variables. If no correlation exists (the points do notappear to follow a trend of direction) the two variables areconsidered to have no linear relationship.

Common Misconceptions • Students often have difficulty choosing a suitable scale to use for

each axis. Encourage the use of graph paper to ensure the graph isappropriately scaled.

• When drawing the line of best fit by eye it should represent thedirectional trend of the data. It does not have to intersect the origin ortravel through every point.

• Correlation does not always imply a causal relationship since otherfactors could contribute.

33

Differentiated Learning Objectives Teaching Resources Independent Learning


All students should be able to plot a scatter graph when thescales are provided.

Most students should be able to choose their own scales to plot ascatter graph.

Some students should be able to determine whether twomeasurements correlate by plotting a scatter graph and line ofbest fit.

• Lesson Plan• Smart Notebook• Activ Inspire


PowerPoint


•

All students should be able to determine whether two measurescorrelation using a scatter graph.

Most students should be able to plot a line of best fit from ascatter graph and use that to determine the strength and type ofcorrelation between two measures.

Some students should be able to use a line of bit fit and theirunderstanding of correlation to estimate one measure when theother is provided.



PowerPoint


• I.T. Activity

All students should be able to recognise when one variablecauses a change in another.

Most students should be able to understand the limitations ofscatter graphs in identifying causal relationships.

Some students should be able to suggest reasons for lack ofcausality between variables despite correlation being apparent.



PowerPoint


•

• Geogebra Activity

34


Topic: Constructions Duration: 4 hoursPrerequisite Knowledge

identify and construct a radius, diameter, circumference, area,

chord, tangent and arc.

measure and begin to record lengths and heights

identify acute and obtuse angles and compare and order angles

up to two right angles by size

Keywords

Construct Scale

Triangle Angle, Side, Angle

Side, Side, Side Side, Angle, Side

Bisector Bisect

Perpendicular Bisector Inscribed

Perpendicular Midpoint

Equidistant Locus (loci)

Success Criteria

use the standard conventions for labelling and referring to the sides

and angles of triangles; draw diagrams from written description

use the standard ruler and compass constructions (perpendicular

bisector of a line segment, constructing a perpendicular to a given

line from/at a given point, bisecting a given angle);

use these to construct given figures and solve loci problems;

know that the perpendicular distance from a point to a line is the

shortest distance to the line

Key Concepts

It is important for students to sketch the diagram before attempting

their construction. The sketch should be drawn freehand and contain

all the necessary information.

Bisectors are used to half an angle as well as a length of a line

segment.

Constructing a 60° angle using a pair of compasses is an essential skills

throughout this topic as it goes on to equilateral triangles and reflex

angles.


Students often have difficulty constructing smooth arcs using a pair of

compasses. Encourage them to try different techniques such as

rotating the paper rather than the compasses.

It is important to leave in construction lines as these form the working

out.

35


Videos

All students should be able to construct a triangle using a

protractor and straight edge.

Most students should be able to construct a quadrilateral and

pentagon using a protractor and straight edge.

Some students should be able to construct a regular polygon

using a protractor and straight edge.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint


All students should be able to construct an acute angle bisector.

Most students should be able to bisect an acute, obtuse, right

angle and straight line.

Some students should be able to find the equidistant point in a

polygon using angle bisectors.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to determine the locus around a

point.

Most students should be able to determine the locus about a

line.

Some students should be able to determine the locus about a

point and line.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet Handout

All students should be able to construct angle bisectors to

identify an equidistant path between two lines.

Most students should be able to perpendicular bisectors to

identify an equidistant path between two points.

Some students should be able to combine loci to identify regions

or points within a given area.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet Handout

36

Topic: Pythagoras’ Theorem Duration: 5 hours Prerequisite Knowledge

derive and apply the properties and definitions of: special

types of quadrilaterals, including square, rectangle,

parallelogram, trapezium, kite and rhombus; and triangles

and other plane figures using appropriate language

know and apply formulae to calculate:

o rectangles

o rectilinear composite shapes

o area of triangle

calculate the perimeters of 2D shapes, including composite

shapes;

use the standard conventions for labelling and referring to

the sides and angles of triangles; draw diagrams from written

description

Keywords

Right-Angled Triangle Hypotenuse

Pythagoras’ Theorem Area

Isosceles Triangle Sum

Success Criteria

know the formulae for: Pythagoras’ theorem, a2 + b2 = c2

apply angle facts, triangle congruence, similarity and

properties of quadrilaterals to conjecture and derive results

about angles and sides, including Pythagoras’ Theorem and

the fact that the base angles of an isosceles triangle are

equal, and use known results to obtain simple proofs

Key Concepts

Pythagoras’ Theorem identifies how the three sides of a right angled

triangle are connected by the areas of shapes on each edge. To fully

engage with this concept students could construct the theorem using a

3,4,5 triangle to measure the hypotenuse and calculate the area of

each square. Their hypothesis can then by tested on a 5, 12, 13 triangle.

Pythagoras’ Theorem can be applied to a wide variety of geometrical

and real world problems. Students need to practise identifying when

the theorem can be applied by recognising triangular components.


Students often believe that the areas of the shapes on the edges have

to be squares in order for a2 + b2 = c2 to apply. In fact, the formula

applies for all shapes as long as the dimensions are in proportion to the

edges of the triangle.

Confusion often lies in identifying the Hypotenuse side of a right-angled

triangle since it is not always apparent which side is longest. Encourage

students to identify the hypotenuse as opposite the right angle.

There is often difficulty when trying to calculate a shorter side of a

triangle since students tend to memorise the formula with the

hypotenuse as the subject.

37


Learning


All students should be able to identify the hypotenuse of a right

angled triangle as the longest side.

Most students should be able to calculate length of the

hypotenuse in a right angled triangle.

Some students should be able to calculate the length of the

hypotenuse in an isosceles triangle when given its base and


Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint



Proof of Pythagoras Video

All students should be able to calculate length of the hypotenuse

in a right-angled triangle.

Most students should be able to calculate length of the

hypotenuse in a right-angled triangle when given in a real life

context.

Some students should be able to calculate the distance

between two coordinate pairs.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet Interactive Geogebra File


Proof of Pythagoras Video

All students should be able to calculate either of the two short

sides in a right-angled triangle using Pythagoras’ Theorem

Most students should be able to calculate the perpendicular

height of an isosceles triangle when given its hypotenuse and

base.

Some students should be able to calculate the area of an

equilateral and isosceles triangle by calculating either its base or


Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Match-Up

Activity



ProofWorksheet

Proof Worksheet

38


https://www.youtube.com/watch?v=rb6i4LCoJVs

https://www.youtube.com/watch?v=rb6i4LCoJVs



Topic: Percentages Duration: 9 hoursPrerequisite Knowledge

Multiply and divide by powers of ten

Recognise the per cent symbol (%)

Understand that per cent relates to ‘number of parts per hundred’

Write one number as a fraction of another

Calculate equivalent fractions

Keywords

Percentage Percent

Fraction Decimal

Of Percentage increase

Percentage Decrease Amount

Compound Interest Compound depreciation

Multiplier

Success Criteria

Define percentage as ‘number of parts per hundred

Interpret fractions and percentages as operators

Interpret percentages as a fraction or a decimal

Interpret percentages changes as a fraction or a decimal

Interpret percentage changes multiplicatively

Express one quantity as a percentage of another

Compare two quantities using percentages

Work with percentages greater than 100%;

Solve problems involving percentage change

Solve problems involving percentage increase/decrease

Solve problems involving original value problems

Solve problems involving simple interest including in financial

mathematics

set up, solve and interpret the answers in growth and decay

problems, including compound interest and work with general

iterative processes.

Key Concepts

Use the place value table to illustrate the equivalence between

fractions, decimals and percentages.

To calculate a percentage of an amount without calculator students

need to be able to calculate 10% of any number by dividing by 10.

To calculate a percentage of an amount with a calculator students

should be able to convert percentages to decimals mentally and use

the percentage function.

Equivalent ratios are useful for calculating the original amount after a

percentage change.

To calculate the multiplier for a percentage change students need to

understand 100% as the original amount. E.g., 10% decrease

represents 10% less than 100% = 0.9.

Students need to have a secure understanding of the difference

between simple and compound interest.


Students often consider percentages to limited to 100%. A key

learning point is to understand how percentages can exceed 100%.

Students sometimes confuse 70% with a magnitude of 70 rather than

0.7.

Students can confuse 65% with1

65rather than

65

100.

Compound interest is often confused with simple interest, i.e., 10%

compound interest over two years = 110% x 110% not 110% x 2.

39


Learning


All students should be able to convert between fractions,

decimals and percentages using the place value grid.

Most students should be able to convert between fractions,

decimals and percentages using equivalent fractions

Some students should be able to order and compare fractions,

decimals and percentages by choosing a common

representation.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Tarsia Activity

Excel Questions

All students should be able to write one number as a percentage

of another using equivalent fractions.

Most students should be able to write one number as a

percentage of another using written and calculator methods

Some students should be able to calculate the one number as a

percentage of another from problems given in context.

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Tarsia Activity


All students should be able to calculate a multiple of ten percent

of an amount

Most students should be able to calculate integer percentages

of an amount

Some students should be able to calculate decimal percentages

of an amount.

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All students should be able to use the percentage button on a

calculator to solve simple proportional problems.

Most students should be able to calculate a percentage of an

amount using various methods on a calculator.

Some students should be able to solve real life percentage

problems efficiently using multiple calculator methods.

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All students should be able to calculate a percentage increase

using a multiplier.

Most students should be able to calculate a percentage

increase from a problem given in a real life context.

Some students should be able to calculate percentage

increases in context to determine best value.

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40

https://www.youtube.com/watch?v=RAYEYebl6lM


All students should be able to calculate a percentage decrease

using a multiplier.

Most students should be able to calculate a percentage

decrease from a problem given in a real life context.

Some students should be able to calculate percentage

decreases in context to determine best value.

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Differentiated

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Microsoft

PowerPoint

Quiz



All students should be able to calculate 100% when given a

representative percentage change.

Most students should be able to calculate the original value after

a real life percentage change.

Some students should be able to calculate the original value

after a compound percentage change.

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All students should be able to calculate a multiplier for a

compound percentage increase.

Most students should be able to calculate a compound

percentage increase using a multiplier

Some students should be able to calculate an overall compound

percentage change using a multiplier.

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All students should be able to calculate a multiplier for a

compound percentage decrease.

Most students should be able to calculate a compound

percentage decrease using a multiplier

Some students should be able to calculate an overall compound

percentage change using a multiplier.

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Treasure Hunt


41



Topic: Probability Duration: 8 hoursPrerequisite Knowledge

compare and order fractions whose denominators are all multiples

of the same number

identify, name and write equivalent fractions of a given fraction,

represented visually, including tenths and hundredths

add and subtract fractions with the same denominator and

denominators that are multiples of the same number

Keywords

Probability Venn Diagram

Likelihood Certain

Chance Even

Sample Space Dice

Possible Impossible

Probable Random

Bias Risk

Spinner Outcome

Event Relative Frequency

Success Criteria

record describe and analyse the frequency of outcomes of

probability experiments using tables and frequency trees

apply ideas of randomness, fairness and equally likely events to

calculate expected outcomes of multiple future experiments

relate relative expected frequencies to theoretical probability,

apply the property that the probabilities of an exhaustive set of

outcomes sum to one; apply the property that the probabilities of

an exhaustive set of mutually exclusive events sum to one

understand that empirical unbiased samples tend towards

theoretical probability distributions, with increasing sample size

enumerate sets and combinations of sets systematically, using

tables, grids, Venn diagrams and tree diagrams

construct theoretical possibility spaces for single and combined

experiments with equally likely outcomes and use these to

calculate theoretical probabilities

calculate the probability of independent and dependent

combined events, including using tree diagrams and other

representations, and know the underlying assumptions

Key Concepts

When writing probabilities as a fraction using the probability scale to

show equivalences with the keywords

Discuss the effect of bias and sample size when comparing

theoretical and experimental probabilities.

Use the random function on a calculator or spreadsheet to

demonstrate simple randomisation.

When listing the outcomes of combined events ensure students use a

logical and systematic method.

Branches on a probability tree have a sum of one as they are

mutually exclusive.

Conditional probability is where the outcome of a future event is

dependent on the outcome of a previous event.


Writing probabilities as a ratio is a common misconception.

When creating Venn diagrams students often forget to place the

remaining events outside the circles.

When listing permutations of combined events students often repeat

events when they do not use a logical and systematic method.

Students often have difficulty completing Venn diagrams involving 3

intersecting circles.

42


Learning


Videos All students should be able to write the theoretical probability of

a single event as a simplified fraction.

Most students should be able to write a theoretical probability of

combined events as a simplified fraction.

Some students should be able to calculate a theoretical

probability from a two-way table.

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Probability

Treasure Hunt


All students should be able to use an experimental or theoretical

probability to calculate an expected frequency.

Most students should be able to use the sum of mutually exclusive

events to calculate an expected frequency.

Some students should be able to use an expected frequency to

calculate a sample size.

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All students should be able to understand that mutually exclusive

events have a sum of one.

Most students should be able to calculate the probability of one

event when the other is known if both

are mutually exclusive.

Some students should be able to calculate probabilities of

mutually exclusive events using tables.

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All students should be able to list in a systematic and logical

manner all the permutations of two events.

Most students should be able to list in a systematic and logical

manner all the permutations of two events in a sample space

diagram.

Some students should be able to use a Sample Space Diagram

to calculate probabilities of two or more combined events.

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All students should be able to determine a set of overlapping

events given probabilities.

Most students should be able to design an experiment to

compare theoretical and experimental probabilities.

Some students should be able to compare theoretical and

experimental probabilities and understand the concept of

relative frequency.

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Lesson Blog

43

http://www.youtube.com/watch?v=vbWqqFxZid0

http://www.mr-mathematics.com/blog/?cat=33

All students should be able to draw a Probability Tree for two

independent events.

Most students should be able to draw and use a probability tree

to calculate the probability of independent events.

Some students should be able to draw use a probability tree with

three or more branches to calculate the probability of

independent events.

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All students should be able to calculate the probability from a

Venn diagram with two intersecting circles.

Most students should be able to complete a Venn diagram and

calculate the probabilities of two intersecting circles.

Some students should be able to complete and use a Venn

diagram with three intersecting circles.

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All students should be able to draw a tree diagram for

conditional events.

Most students should be able to calculate the probability for two

conditional events using a tree diagram.

Some students should be able to calculate the probability for

two or more conditional events using a tree diagram.

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44

https://www.youtube.com/watch?v=haAAfHuDcX0

Topic: Compound Measures Duration: 5 Hours Prerequisite Knowledge

know and apply formulae to calculate:

o rectangles

o rectilinear composite shapes

o area of triangles

o volume of cuboids

use standard units of measure and related concepts

(length, area, volume/capacity, mass, time, money,

etc.)

Keywords

Density Mass

Volume Pressure

Area Force

Newton Speed

Distance Time

Gradient Acceleration

Retardation Displacement

Success Criteria

use standard units of mass, length, time, money and

other measures (including standard compound

measures) using decimal quantities where

appropriate

round numbers and measures to an appropriate

degree of accuracy (e.g. to a specified number of

decimal places or significant figures)

change freely between related standard units (e.g.

time, length, area, volume/capacity, mass) and

compound units (e.g. speed, rates of pay, prices,

density, pressure) in numerical and algebraic

contexts

use compound units such as speed, rates of pay, unit

pricing, density and pressure

calculate or estimate gradients of graphs and areas

under graphs and interpret results in cases such as

distance-time graphs and velocity-time graphs

Key Concepts

The units of measure for density, speed and pressure

originate from their calculations, i.e., Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑇𝑖𝑚𝑒=

𝑚𝑖𝑙𝑒𝑠

ℎ𝑜𝑢𝑟.

It is useful to calculate compound measures through the

unitary method where ratios are in the form 1 : n.

Distance – Time graphs can be extended to Speed-

Time/Acceleration-Time graphs.

Use algebraic techniques to manipulate the various

formulae so that other measures can also be found.


Density, pressure and time do not have to have fixed units.

For instance a speed can be m/s or mph, density can be

g/cm3 or kg/3.

Students often have difficulty remembering individual

formulae for speed, density and pressure. Labelling triangles

are helpful to recall the relationship between the various

measures.

45


Resources

Independent

Learning


Videos All students should be able to calculate speed using the S=D/T

triangle.

Most students should be able to calculate speed as a

compound measure of distance and time.

Some students should be able to convert between units of speed

using equivalent ratios.

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All students should be able to interpret a distance – time graph

Most students should be able to interpret and plot a distance –

time graph.

Some students should be able to interpret, plot and measure

speed from a distance – time graph

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All students should be able to calculate density as a compound

measure of mass and volume.

Most students should be able to calculate either a volume or

mass when given a density.

Some students should be able to calculate a population density.

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All students should be able to calculate pressure as a compound

measure of force and area.

Most students should be able to calculate a pressure, force or

area when given the other two measures.

Some students should be able to convert between metric units of

pressure.

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All students should be able to recognise a positive gradient as

increasing velocity and a negative gradient as decreasing

velocity.

Most students should be able to plot a velocity – time graph and

calculate the area under the line to measure displacement.

Some students should be able to sketch a distance – time graph

from a velocity time graph.

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Hand-out

46

Topic: Accuracy and Rounding Duration: 6 hours Prerequisite Knowledge

Recognise the value of a digit using the place value table.

Round numbers to the nearest integer or given degree of

accuracy not including decimal place or significant figure

Calculate square numbers up to 12 x 12.

Keywords

Accuracy Rounding

Nearest 10,100 & 1000 Significant Figure

Decimal Place Integer

Upper Bound Lower Bound

Maximum Minimum

Limit of accuracy

Success Criteria

use standard units of mass, length, time, money and other

measures (including standard compound measures) using

decimal quantities where appropriate

round numbers and measures to an appropriate degree of

accuracy (e.g. to a specified number of decimal places or

significant figures

estimate answers; check calculations using approximation

and estimation, including answers obtained using

technology

use inequality notation to specify simple error intervals due to

truncation or rounding

apply and interpret limits of accuracy, including upper and

lower bounds

Key Concepts

When rounding to the nearest ten, decimal place or significant

figure students need to visualise the value at a position along

the number line. For instance, 37 to the nearest 10 rounds to 40

and 5.62 to 1 decimal place rounds to 5.6.

When a value is exactly halfway, for instance 15 to the nearest

10, by definition it is rounded up to 20.

To estimate a solution it is necessary to round values to 1

significant figure in the first instance. However, students need

to apply their knowledge of square numbers when estimating

roots.


When rounding to a significant figure the values that are less

significant become zero rather than being omitted. For

instance, 435 to 1 s.f. becomes 400 rather than 4.

Students often have difficulty calculating the upper bound

of a rounded value. For instance the upper bound for a

number rounded to the nearest 10 as 20 is 25 not 24.999.

When using inequality notation to describe the limits of

accuracy there can be confusion with the direction of the

symbols.

Students often have difficulty knowing which bound to use

when calculating the limits of accuracy for division and

subtraction problems.

47


Resources

Independent

Learning


Videos

All students should be able to round a number to a single decimal place

using a number line.

Most students should be able to round to a given decimal place using

mental methods.

Some students should be able to determine the limits of accuracy when

rounded to a given decimal place.

Lesson Plan

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All students should be able to round a positive number, greater than one

to one significant figure.

Most students should be able to round any number to one or more

significant figures.

Some students should be able to calculate the limits of accuracy when

a number has been rounded to a significant figure.

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Tarsia Activity


All students should be able to estimate a solution by rounding each

number to one significant figure.

Most students should be able to estimate a solution by rounding each

number to one significant figure and the nearest square number.

Some students should be able to estimate solutions using a combination

of rounding to the nearest significant figure, square/cube number or

square root.

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Tarsia Activity


All students should be able to calculate the upper and lower bounds

using a number line.

Most students should be able to calculate the upper and lower bounds

using mental methods.

Some students should be able to calculate the limits of accuracy for

simple calculations.

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YouTube

Demonstration

48

https://www.youtube.com/watch?v=vhBRYhvQmuI


Resources

Independent

Learning


Videos

All students should be able to calculate the maximum and minimum

sum and difference using limits of accuracy.

Most students should be able to calculate the maximum and minimum

product and quotient using the limits of accuracy.

Some students should be able to calculate problems in context using

limits of accuracy.

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YouTube

Demonstration

49

https://www.youtube.com/watch?v=KLKKD0BemgU

Topic: Similarity and Congruence Duration: 5 hours Prerequisite Knowledge

use standard units of measure and related concepts (length, area,

volume/capacity, mass, time, money, etc.)

know and apply formulae to calculate: area of triangles,

parallelograms, trapezia; volume of cuboids and other right prisms

(including cylinders)

identify, describe and construct congruent and similar shapes,


translation and enlargement

Keywords

Similar Congruent

Length scale factor Volume scale factor

Area scale factor Ratio

Scale Enlargement

Success Criteria

apply the concepts of congruence and similarity, including the

relationships between lengths, areas and volumes in similar figures

compare lengths, areas and volumes using ratio notation; make

links to similarity and scale factors

Key Concepts

Similar shapes have equal angles whereas congruent shapes have

equal angles and lengths.

Students need to be able to use ratios in the form 1 : n to model the

length scale factor.

To calculate the correct scale factor students need to match

corresponding dimensions, e.g., Area 1 ÷ Area 2 or Length 1 ÷ Length

2

Area Scale Factor = (Length S.F.)2, Volume S.F. = (Length S.F.)3


Students often struggle with proving congruence. Encourage them to

annotate sketch diagrams with clearly marked angles and state the

angle properties used.

Scale factors are can be incorrectly calculated using different

measures, e.g., Area ÷ Length

The incorrect scale factor can be applied to calculate an unknown

dimension. For instance, students may use the Area scale factor to

find a length.

50


Learning


Videos

All students should be able to understand that congruent shapes have

equal angles and lengths.

Most students should be able to recognise SSS, SAS, ASA properties to

prove congruency.

Some students should be able to show congruency through reasoned

algebraic proof.

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All students should be able to calculate the length scale factor for two

similar shapes.

Most students should be able to calculate missing dimensions in similar

shapes using the length scale factor.

Some students should be able to calculate missing lengths in

compound shapes by considering their similar components.

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All students should be able to calculate the area scale factor as the

square of the length scale factor.

Most students should be able to determine and apply the area scale

factor to calculate unknown areas.

Some students should be able to determine and apply the area scale

factor to calculate unknown areas and lengths.

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All students should be able to calculate the volume scale factor given

two corresponding lengths in similar solids.

Most students should be able to derive and apply the volume scale

factor to calculate unknown volumes in similar solids

Some students should be able to derive and apply the volume and

length scale factors to calculate unknown measurements in solid

shapes.

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All students should be able to use the length and volume scale factors

in similar 3D shapes.

Most students should be able to use the length, area and volume scale

factors in any similar 2D or 3D shape.

Some students should be able to use the length, area and volume

scale factors in any similar 2D or 3D shape with algebraic dimensions.

Lesson Plan

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51


Topic: Inequalities Duration: 5 hours Prerequisite Knowledge

solve linear equations in one unknown algebraically (including

those with the unknown on both sides of the equation)

Plot graphs of equations that correspond to straight-line graphs in

the coordinate plane;

Identify and interpret gradients and intercepts of linear functions

graphically and algebraically

Keywords

Inequality Set

Bounds Inequation

Variable Quadratic

Roots Linear

Success Criteria

solve linear inequalities in one or two variable(s), and quadratic

inequalities in one variable;

represent a solution set on a number line, using set notation and on

a graph

Key Concepts

When representing inequalities on a grid it is easier to plot the straight

line first and then decide which side to shade.

Students need to have a secure understanding of the <, >, ≥, and ≤

notation for defining inequalities.

When multiplying or dividing an inequality by -1 the sign changes.

Solid boundary lines do include the value on the line. Dashed

boundary lines do not.


Students tend to not interpret the "≤" and "<" signs correctly

Confusion often lies in understanding the notation using empty and

full circles on a number line.

Inequations are solved as individual values rather than sets.

Students often find it difficult to identify the correct region for linear

and quadratic inequalities on a grid.

52


Learning


All students should be able to plot an inequality on a number

line.

Most students should be able to plot and derive an inequality

using a number line

Some students should be able to plot, derive and solve an

inequality using a number line.

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All students should be able to solve a two-step linear inequation

and represent the solutions on a number line.

Most students should be able to solve a linear inequation

involving brackets and represent the solutions on a number line.

Some students should be able to solve a linear inequation

between two boundaries and represent the solutions on a

number line.

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Worksheet

Tarsia Activity

All students should be able to use a number line to represent the

solutions to two inequalities.

Most students should be able to find a set of solutions for two

inequalities.

Some students should be able to identify a set of inequalities that

have no common number sets.

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Differentiated

Worksheet

All students should be able to plot an inequality on a number

line.

Most students should be able to plot and derive an inequality

using a number line

Some students should be able to plot, derive and solve an

inequality using a number line.

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Worksheet


All students should be able to solve a quadratic inequality using

the balance method.

Most students should be able to solve a quadratic inequality in

the form 𝑥2 + 𝑏𝑥 + 𝑐 = 0 by factorising.

Some students should be able to solve a quadratic inequality

with non-integer roots using the formula.

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53



Topic: Sequences Duration: 6 hoursPrerequisite Knowledge

use simple formulae

generate and describe linear number sequences

express missing number problems algebraically

Pupils need to be able to use symbols and letters to represent variables

and unknowns in mathematical situations that they already understand,

such as:

missing numbers, lengths, coordinates and angles

formulae in mathematics and science

equivalent expressions (for example, a + b = b + a)

generalisations of number patterns

Keywords

Sequence Linear

Term to term Equation

Function Graph

Nth term Linear

Quadratic Parabola

Straight line graph Sequence

Arithmetic Geometric

Recurrence Formula Inductive relationship

Success Criteria

generate terms of a sequence from either a term-to-term or a

position-to-term rule

recognise and use sequences of triangular, square and cube

numbers, simple arithmetic progressions, Fibonacci type

sequences, quadratic sequences, and simple geometric

progressions ( r n where n is an integer, and r is a rational number >

0 or a surd) and other sequences

deduce expressions to calculate the nth term of linear and

quadratic sequences

Key Concepts

The nth term represents a formula to calculate any term a sequence

given its position.

To describe a sequence it is important to consider the differences

between each term as this determines the type of pattern.

Quadratic sequences have a constant second difference. Linear

sequences have a constant first difference.

Geometric sequences share common multiplying factor rather than

common difference.

Whereas a geometric and arithmetic sequence depends on the

position of the number in the sequence a recurrence relation

depends on the preceding terms.


Students often show a lack of understanding for what ‘n’ represents.

A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than

3n – 2.

Quadratic sequences can involve a linear as well as a quadratic

component.

Calculating the product of negative numbers when producing a

table of results can lead to difficulty.

The nth term for a geometric sequence is in the form arn-1 rather than

arn.

Students often struggle understanding the notation of recurrence

sequences. In particular, using difference values of n for a given term.

54


All students should be able to use a function machine to

determine an output of a linear function given its x value.

Most students should be able to create a table of results showing

x and y for any linear function.

Some students should be able to derive a linear function given

corresponding x and y values.

Lesson Plan

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Jigsaw Puzzle

Differentiated

Worksheet


All students should be able to generate a linear sequence from

the nth term formula

Most students should be able to generate a quadratic sequence

from the nth term formula.

Some students should be able to generate any sequence when

given the nth term formula.

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Worksheet


All students should be able to derive the nth term of a positive

sequence.

Most students should be able to derive the nth term of a positive

and negative sequence

Some students should be able to derive the nth term of a

fractional sequence.

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Jigsaw Puzzle



All students should be able to derive the formula for a quadratic

sequence in the form n2+c

Most students should be able to derive the formula for a

quadratic sequence in the form an2+c

Some students should be able to derive the formula for a

quadratic sequence in the form an2+bn+c

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Worksheet


All students should be able to find the common ratio of a

geometric sequence.

Most students should be able to find the common ratio and nth

term of a geometric sequence.

Some students should be able to solve compound percentage

problems using geometric sequences.

Lesson Plan

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All students should be able to generate the first six terms of a

recurrence sequence in the form 𝑢𝑛+1 = 𝑎𝑢𝑛 + 𝑐.

Most students should be able to generate the first six terms of a

recurrence sequence using the previous term.

Some students should be able to generate the first six terms of a

recurrence sequence in the form 𝑢𝑛+2.

Lesson Plan

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55

https://www.youtube.com/watch?v=il0FrSbXD54

http://youtu.be/VPimhWj-Hyw

Topic: Indices and Standard Form Duration:8 hours Prerequisite Knowledge

Apply the four operations, including formal written methods, to

integers

use and interpret algebraic notation

count backwards through zero to include negative numbers

use negative numbers in context, and calculate intervals across

zero

Keywords

Indices Base

Power Prime

Prime Factors Decompose

Highest Common Factor Lowest Common Multiple

Index Notation Standard Form

Surd Rational

Rationalise the denominator Ordinary Form

Success Criteria

use the concepts and vocabulary of highest common factor,

lowest common multiple, prime factorisation, including using

product notation and the unique factorisation theorem

calculate with roots, and with integer and fractional indices

calculate with and interpret standard form A x 10n, where 1 ≤ A <

10 and n is an integer.

simplify and manipulate algebraic expressions

simplifying expressions involving sums, products and powers,


calculate exactly with surds

simplify surd expressions involving squares and rationalise

denominators

Key Concepts

To decompose integers into their prime factors students may need to

review the definition of a prime.

A base raised to a power of zero has a value of one.

Students need to have a secure understanding in the difference

between a highest common factor and lowest common multiple.

Standard index form is a way of writing and calculating with very

large and small numbers. A secure understanding of place value is

needed to access this.

Surds are square roots that cannot exactly in fraction form.

Students need to generalise the rules of indices.


One is not a prime number since it only has one factor.

𝑥2 is often incorrectly taken as 2𝑥.

Students often have difficulty when dealing with negative powers. For

instance, they assume, 1.2 × 10−2 to have a value of -120.

Multiplying out brackets involving surds is often attempted incorrectly.

√52is often confused with 2√5

56


Videos

All students should be able to use the fraction and brackets

functions on a calculator.

Most students should be able to use the fraction, root, power and

brackets functions on a calculator.

Some students should be able to use any combination of the

fraction, root, power and brackets functions on acalculator.

Lesson Plan

Smart Notebook

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Differentiated

Worksheet

All students should be able to decompose an integer using its

prime factors.

Most students should be able to decompose an integer using its

prime factors and write the product using index notation.

Some students should be able to solve equations such as 2m x 3k

= 648 using prime number factorisation.

Lesson Plan

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Worksheet

All students should be able to calculate the LCM and HCF of a

pair of integers using Prime Factors

Most students should be able to calculate the LCM and HCF of

any number of integers using Prime Factors

Some students should be able to solve real life problems through

the use of calculating the HCF or LCM.

Lesson Plan

Smart Notebook

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Microsoft

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Differentiated

Worksheet

All students should be able to simplify the products of indices

Most students should be able to simplify the products and

quotients of indices

Some students should be able to simplify combinations of indices

using products and quotients

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet Indices

Differentiated

Worksheet

Coefficient

Treasure Hunt


All students should be able to convert numbers greater than one

to and from standard form.

Most students should be able to convert numbers greater or less

than one to and from standard form.

Some students should be able to perform calculations using the

rules of indices with numbers written in standard form.

Lesson Plan

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Worksheet

Tarsia Activity


All students should be able to calculate the product and

quotient of two numbers written in Standard Index Form.

Most students should be able to calculate the total, difference,

product and quotient of two numbers written in

Standard Index Form.

Some students should be able to substitute numbers written in

Standard Index Form into formulae.

Lesson Plan

Smart Notebook

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Differentiated

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57


Videos

All students should be able to evaluate an expression in index

form with a faction of ½, 1/3, ¼ as the power.

Most students should be able to evaluate an expression in index

form with any fraction as the power.

Some students should be able to solve equations in index form

where the power is the unknown.

Lesson Plan

Smart Notebook

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Microsoft

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Differentiated

Worksheet


All students should be able to simplify and evaluate terms written

in index form where an integer base is raised to a negative

power.

Most students should be able to simplify and evaluate terms

written in index form where a decimal base is raised to a

negative power.

Some students should be able to simplify and evaluate terms

written in index form where the base is written as a fraction or

mixed number is raised to a negative power.

Lesson Plan

Smart Notebook

Activ Inspire

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Microsoft

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Differentiated

Worksheet

All students should be able to understand the meaning of an

Irrational number

Most students should be able to understand the meaning of an

Irrational number and simplify surds

Some students should be able to simplify products and quotients

involving surds

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

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Differentiated

Worksheet


brackets involving surds.

Most students should be able to substitute a surd into an

expression and evaluate the result

Some students should be able to solve problems using surds in

context.

Lesson Plan

Smart Notebook

Activ Inspire

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Microsoft

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Worksheet

All students should be able to rationalise a denominator with a

integer term as the numerator

Most students should be able to rationalise a denominator with a

surd as the numerator

Some students should be able to rationalise a denominator with

a integer and surd in the numerator

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

58

Topic: Trigonometry with Right-Angled Triangles Duration: 5 hours Prerequisite Knowledge

express a multiplicative relationship between two

quantities


know the formulae for: Pythagoras’ theorem, a2 + b2 = c2

apply angle facts, triangle congruence, similarity and

properties of quadrilaterals to conjecture and derive

results about angles and sides, including Pythagoras’

Theorem and the fact that the base angles of an isosceles

triangle are equal, and use known results to obtain simple

proofs

Keywords

Trigonometry Right-Angled Triangle

Opposite Adjacent

Hypotenuse Sine (sin)

Cosine (cos) Tangent (tan)

Theta (𝜃) Trigonometric Ratios

Pythagoras’ Theorem Surd

Success Criteria

know the trigonometric ratios, 𝑆𝑖𝑛𝜃 =𝑂𝑝𝑝

𝐻𝑦𝑝, 𝐶𝑜𝑠𝜃 =

𝐴𝑑𝑗

𝐻𝑦𝑝,

𝑇𝑎𝑛𝜃 = 𝑂𝑝𝑝

𝐴𝑑𝑗,

apply them to find angles and lengths in right-angled

triangles and, where possible, general triangles in two and

three dimensional figures

Key Concepts

Sin, Cos and Tan are trigonometric functions that are used to find lengths and

angles in right-angled triangles.

The ‘hypotenuse’ is opposite the right angle, the ‘opposite’ refers to the side

that is opposite the angle in question and ‘adjacent’ side runs adjacent to the

angle.

The inverse operations of sin, cos and tan are pronounced arcos, arcsin and

arctan.

Students need to confident using diagram notation to draw 2D diagrams from

problems in 3D.


Students often have difficulty knowing which trigonometric ratio to apply.

Encourage them to clearly label the sides to identify the correct ratio.

Use SOHCAHTOA as a memory aid as students often forget the trigonometric

ratios.

When using trigonometric ratios to calculate angles students often forget to

use the inverse functions.

59


Learning


All students should be able identify the three trigonometric ratios

of a right-angled triangle.

Most students should be able to calculate the Opposite and

Adjacent side using Sin θ or Cos θ

Some students should be able to solve real life problems involving

the lengths of any side of a right angled triangle using SOH CAH

TOA.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint


All students should be able to calculate the length of a right

angled triangle using the Sine and Cosine functions.

Most students should be able to calculate the length of a right

angled triangle using the Sine, Cosine and Tangent functions.

Some students should be able to calculate the length of a

polygon edge by considering its right-angled triangular

components.

Lesson Plan

Smart Notebook

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Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to use the Sine and Cosine function to

calculate angles in right-angled triangles.

Most students should be able to use the Sine, Cosine and

Tangent function to calculate angles in right angled triangles.

Some students should be able to calculate an angle in an

isosceles triangle using Trigonometrical functions.

Lesson Plan

Smart Notebook

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Microsoft

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Differentiated

Worksheet


All students should be able to calculate an angle in a right

angled triangle using trigonometrical relationships.

Most students should be able to calculate a combination of

angle and length in a right angled triangle using trigonometrical

relationships.

Some students should be able to demonstrate geometrical

properties of a right angled triangle using trigonometrical

relationships.

Lesson Plan

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Microsoft

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Worksheet




60

https://www.youtube.com/watch?v=Ct7ZwoAZ0eo

https://www.youtube.com/watch?v=PxCqduk4d3c


Learning


All students should be able to calculate a length in a 3D shape

using 2D representations of right angled triangles

Most students should be able to calculate an angle in a 3D

shape using 2D representations of right angled triangles.

Some students should be able to calculate a combination of

length and angle in a 3D shape using 2D representations of right

angled triangles.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



61

https://www.youtube.com/watch?v=7Ksc4KqpAQU

Topic: Volume and Surface Area Duration: 8 hoursPrerequisite Knowledge

use standard units of measure and related concepts (length, area,

volume/capacity

know and apply formulae to calculate: area of triangles,

parallelograms, trapezia;

know the formulae: circumference of a circle = 2πr = πd, area of a

circle = πr2; calculate: perimeters of 2D shapes, including circles;

areas of circles and composite shapes

Keywords

Volume Surface Area

Capacity Cylinder

Cuboid Prism

Prism Cross-Section

Compound Shape

Success Criteria

know and apply formulae to calculate the volume of cuboids and

other right prisms (including cylinders)

know the formulae to calculate the surface area and volume of

spheres, pyramids, cones and composite solids

Key Concepts

To calculate the volume of a prism identify the cross-section and

calculate its area. The volume is a product this area and its depth.

When calculating surface areas encourage students to illustrate their

working by either writing the area on the faces of the 3D

representation or create the net diagram so all individual faces can

be seen.

While students are not necessarily required to derive the formulae for

the volume and surface area of complex shapes they do need to be

proficient with substituting in known values.


Students often forget to include units when calculating volumes and

areas.

It is important to differentiate between those which are prisms and

those which are not. Encourage students to identify the cross-section

whenever possible.

Pyramid

62


Videos

All students should be able to calculate the volume of a cuboid

using the cross sectional area and depth

Most students should be able to calculate the volume of a

cylinder and triangular prism using the cross sectional area and

depth.

Some students should be able to calculate the volume of any

prism by identifying the area of the cross section.

Lesson Plan

Smart Notebook

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Microsoft

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Differentiated

Worksheet

Interactive Geogebra

File

All students should be able to calculate a Total Surface Area

when given a cuboid’s volume.

Most students should be able to calculate multiple Total Surface

Areas when given a fixed volume.

Some students should be able to calculate the multiple total

surface areas when given a fixed volume of a compound prism.

Lesson Plan

Smart Notebook

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Microsoft

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Differentiated

Worksheet


File

All students should be able to calculate a Total Surface Area

when given a cuboid’s volume.

Most students should be able to calculate multiple Total Surface

Areas when given a fixed volume.

Some students should be able to calculate the multiple total

surface areas when given a fixed volume of a compound prism.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint


File

All students should be able to calculate the volume of a cylinder.

Most students should be able to calculate the volume and total

surface area of a cylinder.

Some students should be able to calculate the volume and total

surface area of compound shapes involving cylinders.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


File


All students should be able to calculate the volume and total

surface area of a sphere.


surface area of a hemisphere.

Some students should be able to calculate the volume and total

surface area of compound shapes involving spheres.

Lesson Plan

Smart Notebook

Activ Inspire

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Microsoft

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Differentiated

Worksheet



Spheres


Hemispheres.






63









https://www.youtube.com/watch?v=oTpxXMjO6s4

https://www.youtube.com/watch?v=Fp_LjTRaWM0

https://www.youtube.com/watch?v=Fp_LjTRaWM0



Videos

All students should be able to calculate the volume of a cone

using the formula.


surface area of a cone using formulae.

Some students should be able to change the subject of the

formulae associated to cones to calculate other variables.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


File

All students should be able to calculate the volume of a square

based pyramid

Most students should be able to calculate the volume of a

compound shape involving a square based pyramid.

Some students should be able to calculate the volume of a

frustum.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


File

All students should be able to calculate the curved surface area of a cone using the formula.

Most students should be able to calculate the total surface area of a cone using Pythagoras’ Theorem to calculate the slant.

Some students should be able to manipulate the formula for the area of a cone to calculate the radius, slant or perpendicular height.

Lesson Plan

Smart Notebook

Activ Inspire

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Microsoft

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Differentiated

Worksheet


File




64




Topic: Formulae Duration: 6 hours Prerequisite Knowledge

solve linear equations in one unknown algebraically (including


translate simple situations or procedures into algebraic expressions

deduce expressions to calculate the nth term of linear sequence

use compound units such as speed, rates of pay, unit pricing,

density and pressure

Keywords

Formula(e) Rearrange

Balance Method Substitution

Subject of the formula Expression

Equation Identity

Factorise Kinematics

Acceleration Speed

Displacement MotionSuccess Criteria

substitute numerical values into formulae and expressions, including

scientific formulae

understand and use the concepts and vocabulary of expressions,

equations, formulae, identities inequalities, terms and factors

understand and use standard mathematical formulae; rearrange

formulae to change the subject

use relevant formulae to find solutions to problems such as simple

kinematic problems involving distance, speed and acceleration

know the difference between an equation and an identity; argue

mathematically to show algebraic expressions are equivalent, and

use algebra to support and construct arguments

Key Concepts

When substituting known values into formulae it is important to follow

the order of operations.

Students need to have a secure understanding of using the balance

method when rearranging formulae. Recap inverse operations,

e.g. 𝑥2 => √𝑥.

When generating formulae it is important to associate mathematical

operations and their algebraic notation with key words.

Sketching a diagram to model a motion enables students to identify

the key information and choose the correct Kinematic formula.


Students often consider 2𝑎3 to be incorrectly calculated as (2𝑎)3.

Recap the order of operations to avoid this.

Students often have difficult generating formulae from real life

contexts. Encourage them to carefully break down the written

descriptions to identify key words.

Knowing which Kinematics formula to use often causes students to

drop mark in examinations.

65


Learning


All students should be able to write a formula involving the sum

and difference of two or more terms.

Most students should be able to write a formula involving the

product and quotient of two of more terms.

Some students should be able to write a formula involving a

products, quotients, differences and sums.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Treasure Hunt

All students should be able to substitute integers into simple

formulae involving addition, subtraction and multiplication.

Most students should be able to substitute integers into simple

formulae using the standard order of operations (BODMAS)

Some students should be able to derive formulae and evaluate

by substituting integers using the standard order of operations

(BODMAS)

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Tarsia Activity


All students should be able to rearrange a formula involving

addition and subtraction terms.

Most students should be able to rearrange a formula involving a

combination of product, division, addition and subtraction terms.

Some students should be able to rearrange a formula involving

powers using the balance method.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Jigsaw Activity

All students should be able to sketch a diagram to ascertain the

key variables of motion.

Most students should be able to identify and apply the correct

kinematic formula to solve problems involving motion.

Some students should be able to derive the three kinematic

formulae from first principals.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to rearrange a formula in the form

ax + bx = c by factorising to make x the subject.

Most students should be able to rearrange a formula in the form𝑎

𝑥+ 𝑐 = 𝑦 to make x the subject

Some students should be able to rearrange a formula in the form𝑎

𝑥+𝑑=

𝑏

𝑥−𝑐 to make x the subject

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Treasure Hunt

66

All students should be able to manipulate the formula for the arc

length of a sector.

Most students should be able to manipulate the formula for the

arc length and area of sectors.

Some students should be able to derive known facts for problems

involving sectors through manipulating the formulae.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Geogebra File

https://www.youtube.com/watch?v=BKbDJ4BgrTU

Topic: Graphical Functions Duration: 8 hours Prerequisite Knowledge

plot graphs of equations that correspond to straight-line graphs inthe coordinate plane

recognise, sketch and interpret graphs of linear functions

Keywords Function Quadratic Cubic Reciprocal Linear Graph Scale Approximate Exponential Equation of a Circle Tangent Gradient

Success Criteria Recognise, plot and interpret graphs of quadratic functions, simple

cubic functions and the reciprocal function 𝑦 =1

𝑥with 𝑥 ≠ 0.

solve quadratic equations by finding approximate solutions using agraph

plot and interpret graphs exponential graphs recognise and use the equation of a circle with centre at the origin find the equation of a tangent to a circle at a given point.

Key Concepts To generate the coordinate’s students need to have a secure

understanding of applying the order of operations to substitute andevaluate known values into equations.

Quadratic, Cubic and Reciprocal functions are non-linear andtherefore do not have straight lines. All graphs of this nature shouldbe drawn with smooth curves.

When solving equations graphically students should realise solutionsare only approximate.

Students need to gain an understanding of the shape of eachfunction in order to identify incorrectly plotted coordinates.

The equation of a circle relates very closely to Pythagoras’ theorem.

Exponential graphs can be increasing as well as decreasing. Students need to understand the equivalence between linear graphs

in the form y = mx + c and ax + by + c = 0.Common Misconceptions Students often have difficulty substituting in negative values to

complex equations. Encourage the use of mental arithmetic. Identifying the correct type of function from graphs is often a source

of confusion. By creating the table of results students will be more able to choose a

suitable scale for their axes. Students who complete the table of results correctly often have little

difficulty plotting the graph correctly. Students often have difficulty drawing the equation of a circle

correctly in examinations. Students often have difficulty stating the equation of a linear graph in

the form ax + by + c = 0.

67


All students should be able to plot a quadratic graph in the form𝑥2 ± 𝑎

Most students should be able to plot a quadratic in the form 𝑥2 ±𝑎𝑥

Some students should be able to plot and solve quadraticequations graphically.


Flipchart Microsoft

PowerPoint

Differentiatedworksheet

QuadraticFunctions Activity

Interactive Excel File Hand-out

All students should be able to complete a table of results from acubic equation.

Most students should be able to plot the graph of a cubicequation.

Some students should be able to plot a cubic equation and usethat to solve equations graphically


Flipchart Microsoft

PowerPoint


Interactive Excel File Hand-out

All students should be able to complete a table of results for areciprocal function.

Most students should be able to plot the graph of a reciprocalfunction in all four quadrants.

Some students should be able to model a real life reciprocalfunction graphically.


Flipchart Microsoft

PowerPoint


Hand-out

All students should be able to plot an exponential graph in theform y=kx where x ≥ 0.

Most students should be able to plot and recognise theproperties of an exponential graph in the form y=kx.

Some students should be able to model and solve exponentialfunctions graphically.


Flipchart Microsoft

PowerPoint


Geogebra File

All students should be able to recognise the equation of a circlein the form x2 + y2 = r2.

Most students should be able to plot the equation of a circle. Some students should be able to use the equation of a circle to

solve simultaneous equations graphically.


Flipchart Microsoft

PowerPoint


68

Geogebra Activity

Geogebra File

Geogebra File

Geogebra File


http://web.geogebra.org/app/?id=709735





All students should be able to calculate the gradient of atangential line to a circle.

Most students should be able to calculate the equation of a linetangential to a circle.

Some students should be able to use algebra to prove a line istangential to a circle.


Flipchart Microsoft

PowerPoint


All students should be able to use graphical methods to solve theroots of a quadratic equation.

Most students should be able to use a linear function to solve aquadratic equation graphically.

Some students should be able to derive and solve the resultantquadratic equation from linear and quadratic graphs.


Flipchart Microsoft

PowerPoint


Hand-out

All students should be able to solve cubic equations graphically Most students should be able to solve cubic and reciprocal

equations graphically Some students should be able to derive an equation that can be

solved graphically by a cubic or reciprocal function


Flipchart Microsoft

PowerPoint


Hand-out

69

Geogebra Activity


Topic: Trigonometry in Non-Right Angled Triangles Duration: 4 hours Prerequisite Knowledge

know the trigonometric ratios, 𝑆𝑖𝑛𝜃 = 𝑂𝑝𝑝


𝐴𝑑𝑗

𝐻𝑦𝑝, 𝑇𝑎𝑛𝜃 =

𝑂𝑝𝑝

𝐴𝑑𝑗,

apply them to find angles and lengths in right-angled triangles and,

where possible, general triangles in two and three dimensional

figures

Keywords

Cosine Rule Sine Rule

Included Angle Area Rule

Success Criteria

know and apply the sine rule 𝑎

𝑆𝑖𝑛 𝐴=

𝑏

𝑆𝑖𝑛𝐵=

𝑐

𝑆𝑖𝑛 𝐶 and cosine rule 𝑎2 =

𝑏2 + 𝑐2 − 2𝑏𝑐𝐶𝑜𝑠𝐴 to find unknown lengths and angles

know and apply the formula for the Area of Triangle 𝐴 =1

2𝑎𝑏𝑆𝑖𝑛𝐶 to

calculate the area, sides or angles of any triangle.

Key Concepts

The Sine rule is used when:

o Any two angles and a side is known.

o Any two sides and an angle is known

The Cosine rule is used when:

o All three sides are known

o When two sides and the adjoining angle is known

Students should have the opportunity to derive the three formulae

from first principals.

This topic is often linked with problems involving bearings and map

sketches.


Students often have difficulty choosing the correct formula.

A common mistake is attempting to use Pythagoras’ Theorem to find

a length in a non-right angled triangle.

Marks are often lost when breaking down the Cosine Rule using the

order of operations.

70


Resources

Independent

Learning


All students should be able to substitute known values into the

Sine rule formula to calculate an unknown angle.

Most students should be able to substitute known values into the

Sine Rule formula to calculate an unknown angle or length.

Some students should be able to solve problems involving non

right-angled triangles by deriving and applying the Sine Rule.

Lesson Plan

Smart

Notebook

Activ Inspire

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Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to calculate an unknown length in a

non-right-angled triangle using theCosine rule.

Most students should be able to calculate a magnitude of

direction using bearings and a length in a non-right-angled

triangle using the Cosine rule.

Some students should be able to derive and apply the Cosine

Rule to calculate unknown lengths in triangular shapes.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to calculate an unknown angle in a

triangle using the Cosine rule.

Most students should be able to calculate an unknown angle or

bearing using the Cosine rule.

Some students should be able to derive and apply the Cosine

rule for triangular shapes.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



All students should be able to calculate the area of a non-right-

angled if the value of two sides and the adjoining angle are

known.

Most students should be able to calculate the area of a triangle

using a combination of the Cosine and Area formulae.

Some students should be able to derive and solve equations

using the Area of Triangle formula.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Geogebra File

Hand-out

71

Geogebra File

Geogebra File

Geogebra File

http://youtu.be/212cOMEzQdk

http://youtu.be/7vT103aGy-0





Topic: Proportion and Variation Duration: 3 Hours Prerequisite Knowledge

use ratio notation, including reduction to simplest form

express a multiplicative relationship between two quantities

as a ratio


relate ratios to fractions

express the division of a quantity into two parts as a ratio

apply ratio to real contexts and problems (such as those

involving conversion, comparison, scaling, mixing,

concentrations)


Keywords

Variation Direct

Indirect Proportion

Varies Formula

Constant of proportionality Squared

Cube Square root

Cube root Inverse(ly)

Success Criteria

understand that X is inversely proportional to Y is equivalent to X is

proportional to 1/Y;

construct and interpret equations that describe direct and inverse

proportion.

Key Concepts

The symbol ∝ is used to represent ‘is proportional to’.

Direct proportion and varies directly both include 𝑦 ∝ 𝑥, 𝑦 ∝ 𝑥2 and 𝑦 ∝𝑥3.

Indirect proportion and varies inversely both include 𝑦 ∝1

𝑥 and 𝑦 ∝

1

𝑥2.

k is used as the constant of proportionality.

Students need to be able to associate the graphical representations

with the various proportions.


Students often struggle with writing the correct proportional formula

from the written description. Writing indirect proportions is particularly

difficult for most students.

Modelling the variation as a formula with the correct value of k is key

to accessing this topic.

When students do write the correct formula they are often unable to

correctly manipulate it to calculate unknown values.

72


Resources

Independent

Learning


All students should be able to derive a formula using the constant

of proportionality to describe how two measurements are in

proportion.

Most students should be able to derive and use a formula with

the constant of proportionality to calculate measurements that

are in direct proportion.

Some students should be able to solve problems in context by

deriving and using the constant of proportionality.

Lesson Plan

Smart

Notebook

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Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to calculate the constant of variation

that models how two measurements are in direct proportion.

Most students should be able to derive and use the formula that

models how two measurements are in direct proportion.

Some students should be able to model how two measurements

are in nonlinear direct proportion using a formula and graph.

Lesson Plan

Smart

Notebook

Activ Inspire

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Microsoft

PowerPoint

Differentiated

Worksheet


All students should be able to derive a formula in the form 1/x to

model inverse proportion.

Most students should be able to derive a formula to model

inverse proportion and use it to calculate unknown values.

Some students should be able to derive and use a formula to

model when one unit is inversely proportion to the square or

cube of another.

Lesson Plan

Smart

Notebook

Activ Inspire

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Microsoft

PowerPoint

Differentiated

Worksheet

Jigsaw Activity


73

Topic: Circle Theorems Duration: 3 hours Prerequisite Knowledge

understand and use alternate and corresponding angles on

parallel lines;

derive and use the sum of angles in a triangle (e.g. to deduce use

the angle sum in any polygon, and to derive properties of regular

polygons)

measure line segments and angles in geometric figures, including

interpreting maps and scale drawings and use of bearings

Keywords

Circle Sector

Angle Radius

Radii Tangent

Diameter Circumference

Proof Chord

Segment Alternate segments

Success Criteria

identify and apply circle definitions and properties, including:

centre, radius, chord, diameter, circumference, tangent, arc,

sector and segment

apply and prove the standard circle theorems concerning angles,

radii, tangents and chords, and use them to prove related results

Key Concepts

Students need a solid understanding of the properties for angles in

parallel lines, vertically opposite, angles in a polygon and on a

straight line.

Understanding the various parts of a circle is critical to fully defining

the various circle theorems.

Students need to spend time breaking down the problem by

considering the various angle properties that may be relevant.

Taking time to prove the various theorems illustrates how

interconnected all the properties are.

Encourage students to annotate and draw on the diagrams.


Students often struggle with precisely defining the various angle the

appropriate angle properties.

Incomplete angle properties are a common source for losing marks in

examinations.

Angle and line notation often confuses students to an extent they

may calculate an angle that was not asked for.

Students need to relate their written work with the relevant angle

rather than writing detached paragraphs.

74


Resources

Independent

Learning


All students should be able to discover the relationships between

the angles at the centre and circumference of a circle, opposite

angles in cyclic quadrilaterals and angles at the circumference

in the same segment.

Most students should be able to discover the three theorems and

apply them individually to calculate missing angles.

Some students should be able to discover and apply the three

properties and apply them to calculate angles involving multiple

theorems.

Lesson Plan

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Notebook

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Microsoft

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Worksheet


Proof – Angle at the centre & angle at the circumference

Proof – Cyclic quadrilaterals

Proof – Angles in the same segment

All students should be able to discover that a tangent and radius

intersecting at the circumference of a circle and perpendicular.

Most students should be able to discover that a tangent and

radius intersecting at the circumference of a circle are

perpendicular and that angles in alternate segments are equal.

Some students should be able to derive both theorems relating

to tangents at the circumference of a circle and apply them to

solve complex problems involving multiple circle theorems.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Geogebra - Alternate segment YouTube Demonstration

Proof – Angles is alternate segments

Geogebra 2 - Cyclic QuadsGeogebra 1 - Same segment

75

https://www.youtube.com/watch?v=NqaZYOJMqn4

https://www.youtube.com/watch?v=1lN28_cgS-c


https://www.youtube.com/watch?v=PV80HfP6Ai4

https://www.youtube.com/watch?v=r1bNnOb0RjQ


https://www.youtube.com/watch?v=O5u4jmCSz-s

https://www.youtube.com/watch?v=oMJIbtiBlKc





Topic: Quadratics Duration: 6 hours Prerequisite Knowledge

Simplify and manipulate algebraic expressions by:

expanding products of two or more binomials

factorising quadratic expressions of the form x2 + bx + c,

including the difference of two squares

simplifying expressions involving sums, products and

powers, including the laws of indices

factorising quadratic expressions of the form ax2 + bx + c.

Keywords

Quadratic Root

Completing the square Factorise

Quadratic Formula Expressions

Identity Equation

Turning point Parabola

Intersection Coefficient

Success Criteria

know the difference between an equation and an

identity; argue mathematically to show algebraic

expressions are equivalent, and use algebra to support

and construct arguments and proofs

simplify and manipulate algebraic expressions by

factorising quadratic expressions of the form ax2 + bx + c

understand and use standard mathematical formulae;

rearrange formulae to change the subject

identify and interpret roots, intercepts, turning points of

quadratic functions graphically

deduce roots algebraically and turning points by

completing the square

recognise, sketch and interpret graphs of quadratic

functions

solve quadratic equations (including those that require

rearrangement) algebraically by factorising, by

completing the square and by using the quadratic

formula; find approximate solutions using a graph

solve two simultaneous equations in two variables

linear/quadratic algebraically; find approximate solutions

using a graph

Key Concepts

Check brackets have been factorised correctly by multiplying them back out.

To solve quadratics by factorising students need to identify two numbers that

have a product of c and a sum of b. Roots are found when each bracket is

made to equal zero and are solved for x.

When a quadratic cannot be solved by factorising students should use

completing the square or the quadratic formula.

Students should be able to derive the quadratic formula from the method of

completing the square.

A sketched graph is drawn freehand and includes the roots, turning point and

intercept values.

Quadratic identities in the form (𝑥 + 𝑎)2 + 𝑏 ≡ 𝑎𝑥2 + 𝑏𝑥 + 𝑐 can be solved either

through completing the square to RHS = LHS or by expanding the brackets to

LHS = RHS and equating the unknowns.

Quadratic and linear simultaneous equations should be sketched before

solved algebraically to ensure students know to find and the x and y values.


The method of trial and improvement is often incorrectly used to try and solve

quadratics.

When solving quadratic and linear simultaneous equations students often

forget to find the y values as well the x.

When using the formula to solve quadratics students often forget to evaluate

the negative solution. Some students also incorrectly apply the division by

reducing the terms it covers.

Students tend to struggle deriving quadratic equations from geometrical facts.

76


Learning



form x2 + bx + c = 0 using factorisation.

Most students should be able to solve a quadratic equation by

rearranging to the form x2 + bx + c = 0 using factorisation.

Some students should be able to derive and solve an equation

using known geometrical facts.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



form ax2 + bx + c = 0 when ‘a’ is prime using factorisation.


form ax2 + bx + c = 0 when ‘a’ is not prime using factorisation.

Some students should be able to derive and solve an equation in

the form ax2 + bx + c = 0 using known geometrical facts.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet



form x2 + bx + c = 0 using the method of completing the square.

Most students should be able to solve a quadratic equation in

the form ax2 + bx + c = 0 where a ≠1 using the method of

completing the square.

Some students should be able to use completing the square to

solve equivalent quadratic identities.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Treasure hunt

All students should be able to use the quadratic formula to solve

equations where the coefficient of a = 1.

Most students should be able to use the quadratic formula to

solve equations where the coefficient of ‘a’ ≠ 1

Some students should be able to derive the quadratic equation

by completing the square and use it to solve complex problems.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

YouTube derivation of the

formula

All students should be able to sketch a parabola in the form x2 +

bx = 0 to illustrate the roots and intercept.

Most students should be able to sketch a parabola in the form x2

+ bx + c = 0 to illustrate its roots, intercept and turning point.

Some students should be able to sketch a parabola in the form

ax2 + bx + c = 0 to illustrate its roots, intercept and turning point.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Geogebra File

77

https://www.youtube.com/watch?v=sJvc7S3VTp4



Learning


All students should be able to solve a pair of simultaneous

equations where one is quadratic and the other is linear through

the method of substitution.

Most students should be able to find intersecting points from a

quadratic and linear graph using the method of substitution to

solve equations simultaneously.

Some students should be able to find the intersecting point

between a reciprocal and linear equation.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

78

Topic: Vectors Duration: 2 hours Prerequisite Knowledge

describe translations as 2D vectors

use and interpret algebraic notation, including:

o ab in place of a × b

o 3y in place of y + y + y and 3 × y

Keywords

Vector Magnitude

Parallel Direction

Success Criteria

apply addition and subtraction of vectors, multiplication of vectors

by a scalar, and diagrammatic and column representations of

vectors

use vectors to construct geometric arguments and proofs

Key Concepts

A scalar has direction only whereas a vector has direction and

magnitude.

A vector has a magnitude and direction but its starting point is

variable.

Parallel lines have vectors that are multiples of each other.

To add and subtract vectors is similar to collecting like terms.

Multiplying vectors is similar to expanding brackets.

The third side of a triangle is the resultant of two vectors.


Students often forget to multiply a vector by a negative when

reversing direction.

Writing vectors in their simplest form by collecting like terms is often a

problem in examinations.

Incorrect application of ratio notation leads to difficulty when proving

geometrical properties.

Students often fail to label the diagrams sufficiently to identify known

paths.

Providing a proof of geometrical facts tends to separate the most

able from the majority.

79


Resources

Independent

Learning


All students should be able to use vectors to describe the position

of one object in respect of another.

Most students should be able to use geometrical properties of

parallelograms and trapezia to add and subtract given vectors.

Some students should be able to prove the geometrical

properties of shapes using vector addition.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to use the geometrical properties of

polygons to define vectors.

Most students should be able to prove the geometrical

properties of polygons using vectors.

Some students should be able to use ratio and the geometrical

properties of polygons to prove two lines are parallel.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

80

Topic: Trigonometrical Graphs Duration: 2 hours Prerequisite Knowledge

know the trigonometric ratios, 𝑆𝑖𝑛𝜃 = 𝑂𝑝𝑝


𝐴𝑑𝑗

𝐻𝑦𝑝, 𝑇𝑎𝑛𝜃 =

𝑂𝑝𝑝

𝐴𝑑𝑗,

apply them to find angles and lengths in right-angled triangles and,

where possible, general triangles in two and three dimensional

figures

Keywords

Asymptotes Amplitude

Period Frequency

Success Criteria

know the exact values of 𝑆𝑖𝑛𝜃 and 𝐶𝑜𝑠𝜃 for 𝜃 = 0°, 30°, 45°, 60° and

90°; know the exact value of 𝑇𝑎𝑛𝜃 for = 0°, 30°, 45°, 60°

recognise, sketch and interpret graphs of trigonometric functions

(with arguments in degrees) y = sin x , y = cos x and y = tan x for

angles of any size

Key Concepts

Trigonometric graphs have lines of symmetry at that can be used to

find additional solutions equations.

Trigonometric ratios of 30°, 45° and 60° have exact forms that can be

calculated using the special triangles.

The relationship 𝑇𝑎𝑛𝜃 =𝑆𝑖𝑛𝜃

𝐶𝑜𝑠𝜃 can be seen from the asymptotes in the

tan graph.


Students often forget to rationalise Sin45° and Cos45°.

When solving trigonometric equations students often forget to use the

graphs to include all solutions.

In examinations students often confuse the coordinates, e.g., (0,180)

with (180,0)

81


All students should be able to draw the trigonometric graphs of

sine, cosine and tangent functions.

Most students should be able to use the symmetrical properties of

trigonometrical graphs to solve simple trigonometric equations.

Some students should be able to identify equivalent

trigonometric functions using sine, cosine and tangent

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Geogebra File

All students should be able to calculate the exact values of Sin

and Cos 30°, 45°, 60° and 90°.

Most students should be able to solve trigonometric equations

such as 2Cos45°.

Some students should be able to use trigonometric graphs to find

alternative solutions to Sin, Cos and Tan 30°, 45°, 60° and 90°.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Hand-out

Hand-out

82


Topic: Algebraic Fractions Duration: Prerequisite Knowledge

solve linear equations in one unknown algebraically(including


apply the four operations, including formal written methods, simple

fractions (proper and improper)

calculate exactly with fractions

simplify and manipulate algebraic expressions by factorising quadratic expressions of the form ax2 + bx + c

Keywords

Algebraic fraction cross-multiply

quadratic expression

linear factorise

solve identity

equivalent

Success Criteria

simplify and manipulate algebraic fractions by:

o collecting like terms

o multiplying a single term over a bracket

o taking out common factors

o expanding products of two or more binomials

o simplifying expressions involving sums, products and powers,


know the difference between an equation and an identity; argue

mathematically to show algebraic expressions are equivalent, and

use algebra to support and construct arguments and proofs

solve quadratic equations (including those that require

rearrangement) algebraically by factorising, by completing the

square and by using the quadratic formula

Key Concepts

Students need to apply the same numerical techniques with

algebraic fractions as they have done with numerical ones.

Like numerical fractions algebraic fractions need to have a common

denominator when performing addition or subtraction.

Simplifying algebraic fractions involves factorising the expression into

either one or more brackets.

Multiply the fractions through by a common denominator to cancel

out the division when solving fractions.


Students who understand the need for common denominators when

adding or subtracting fractions are often let down by their poor

algebraic skills. Particularly when multiplying out by a negative.

When attempting to simplify fractions students tend to cancel down

incorrectly thus losing marks for final accuracy.

Students can forget to use the difference of two squares when finding

common denominators.

Students struggle with factorising quadratics when the coefficient of x2

is greater than one.

It is common for students to try and solve for the unknown when they

have only been asked to simplify.

83


Resources

Independent

Learning


All students should be able to simplify an algebraic fraction

involving linear terms.

Most students should be able to simplify algebraic fractions

involving linear and quadratic terms in the form 𝑎𝑥2 + 𝑏𝑥 +𝑐 where 𝑎 = 1 by factorising.

Some students should be able to simplify algebraic fractions

involving quadratics in the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 where 𝑎 ≠ 1.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to add and subtract a pair of

algebraic fractions with numerical denominators.

Most students should be able to add and subtract a pair of

algebraic fractions in the form 2

𝑥+

3

𝑦.

Some students should be able to add and subtract a pair of

algebraic fractions in the form 2

𝑥+1+

3

𝑥−2.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet


algebraic fractions.

Most students should be able to calculate the product and

quotient of two or more algebraic fractions,

Some students should be able to calculate the product and

quotients of algebraic fractions and mixed numbers.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able calculate the difference and total of

algebraic fractions.

Most students should be able to solve an equation involving a

linear algebraic fraction.

Some students should be able to solve an equation involving a

quadratic algebraic fraction.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

84

Topic: Functions and Transformations of Graphs Duration: 7 hours Prerequisite Knowledge

Plot graphs of equations that correspond to straight-line graphs

in the coordinate plane

Recognise, sketch and interpret graphs of linear and non-linear

functions

Identify, describe and construct congruent and similar shapes,


translation and enlargement.

Keywords

Function Reflection

Scale factor Stretch

Transform Vector

Translation Composite

Inverse Gradient function

Iteration Iterative formula

Differentiation Instantaneous rate of change

Success Criteria

Where appropriate, interpret simple expressions as functions with

inputs and outputs; interpret the reverse process as the ‘inverse

function’; interpret the succession of two functions as a

‘composite function’.

Sketch translations and reflections of a given function

calculate or estimate gradients of graphs (including quadratic

and other non-linear graphs),

find approximate solutions to equations numerically using

iteration

Key Concepts

A function is any algebraic expression in which x is the only variable. It is

denoted as f(x) = x ….

Understanding the notation for transformation of functions is critical to

accessing this topic.

o f(x) ±a = Vertical Translation

o f(x ± a) = Horizontal Translation

o af(x) = Horizontal stretch

o f(ax) = Vertical stretch

Composite functions combine more than one function to an input.

Inverse functions perform the opposite operation to a function.

A gradient function calculates and approximate the instantaneous rate

of change for given values of x.

Iterative solutions can diverge or converge.


-f(x) is often incorrectly taken as a reflection in the y axis rather than the

x.

f(x + a) is a translation of ‘a’ units to the left rather than to the right.

Students often struggle with writing the equation of the new function

after a transformation.

Students need to be precise when drawing the transformed function.

Students can confuse f-1(x) with f’(x).

The order of a composite function is often confused, fg(x) -> g acts on x

first then f acts on the result.

Students are often able to differentiate functions with little

understanding of how to apply the gradient function correctly.

85


All students should be able to calculate the numerical output of

a function when given an input.

Most students should be able to calculate an algebraic output of

a function.

Some students should be able to use algebra to determine valid

inputs for a function.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to use a function machine to break

down the composite functions in the form gf(x).

Most students should be able to generate outputs from

composite functions and realise that fg(x) does not give the

same output as gf(x).

Some students should be able to use algebra to determine the

input of a composite function when given the output.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to use function machines to find an

inverse function.

Most students should be able to find an inverse function using

algebraic methods.

Some students should be able to draw the graph of an inverse

function using a reflection on y = x.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to recognise a horizontal and vertical

translation from function notation.

Most students should be able to perform and describe a vertical

and horizontal translation using function notation.

Some students should be able to derive the equation of a

transformed function in terms of y.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to use function notation to perform a

horizontal and vertical stretch.

Most students should be able to use function notation to perform

a horizontal and vertical stretch and reflection.

Some students should be able to calculate the transformed

coordinate pairs using function notation.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

86

Geogebra File

Geogebra File




Videos

All students should be able to find the gradient function of a

parabola.

Most students should be able to find the gradient function as in

instantaneous rate of change for equations in the form = 𝑎𝑥𝑛 .

Some students should be able to derive the gradient function

from first principals.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

All students should be able to calculate the root of a quadratic

equation using iteration.

Most students should be able to solve a non-linear equation using

iteration.

Some students should be able to identify the limits of x when

solving equations using iteration.

Lesson Plan

Smart Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

87

Geogebra Activity


Topic: Proof Duration: 2 hours Prerequisite Knowledge

know the difference between an equation and an identity;

simplify and manipulate algebraic expressions by factorising

quadratic expressions of the form ax2 + bx + c

understand and use standard mathematical formulae; rearrange

formulae to change the subject

identify and apply circle definitions and properties, including:

centre, radius, chord, diameter, circumference, tangent, arc,

sector and segment

Keywords

Proof Demonstration

Show that

Success Criteria

apply angle facts, triangle congruence, similarity and properties of

quadrilaterals to conjecture and derive results about angles and

sides, including Pythagoras’ Theorem and the fact that the base

angles of an isosceles triangle are equal, and use known results to

obtain simple proofs

argue mathematically to show algebraic expressions are

equivalent, and use algebra to support and construct arguments

and proofs

apply and prove the standard circle theorems concerning angles,

radii, tangents and chords, and use them to prove related results

Key Concepts

Students need to understand the difference between a

demonstration using numerical examples and an algebraic proof.

Algebraic competence is essential for this topic.

Students may need to be reminded of the various geometrical

properties in order to apply them in a proof.


A common incorrect approach is to attempt to prove an algebraic

and geometrical property through numerical demonstrations.

Students often struggle generalising the rules of arithmetic to produce

a reasoned mathematical argument.

Some students expand brackets incorrectly when proving a quadratic

identity.

Students often lose marks when attempting to prove geometrical

properties due to not connecting the various angle properties.

88


Resources

Independent

Learning


All students should be able to prove angle properties involving

triangles and straight lines.

Most students should be able to prove angle properties involving

parallel lines and circle theorems.

Some students should be able to use geometrical properties to

prove congruence.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Alternate segment proof

Angle at the circumference and centre proof

Angles in the same segment proof

Cyclic quadrilaterals proof

All students should be able to use algebra to prove a linear

relationship.

Most students should be able to expand the product of two or

more brackets to prove a quadratic identity.

Some students should be able to prove number properties

through algebraic manipulation.

Lesson Plan

Smart

Notebook

Activ Inspire

Flipchart

Microsoft

PowerPoint

Differentiated

Worksheet

Deriving the quadratic formula proof

Sine rule proof

Cosine rule proof

Area of a trapezium proof

89






https://www.youtube.com/watch?v=PV80HfP6Ai4



https://www.youtube.com/watch?v=Ox1Uludv4T8

https://www.youtube.com/watch?v=ajWrU2uqx6g

https://www.youtube.com/watch?v=t1Vv_D3F42c

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