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AQA GCSE Maths Schemes of Work writing brief D R A F T

NEW for Examination 2015

AQA GCSE Linear

Higher Tier

Mathematics

GCSE Content and Overview

Higher Tier

(Outcomes U 9)

Key Information

This syllabus is to be taught over 2 years, starting 2015.

The first examination series for this syllabus will be Summer 2017.

Fully Linear course, no modules.

Re-sit is only available in November series immediately following the initial Summer exam (i.e. for Y12 students).

Assessment will be in the form of two written examinations in the Summer examination period of the second year (for Year 11 students). Comprising one calculator and one non-calculator paper. These will total a minimum of 3.5 hours.

Assessment results will be given as an outcome ranging between U 9 (where 9 is the highest outcome achieved).

Passes will be considered as 9 - 3.

Fail will be considered as 2 U.

Assessment Objectives

The new curriculum has a greater focus on both problem solving and quality of written communication. This now comprises 25% of the total marks.

The overall weighting of each of these objectives to be assessed through the final summer examination are as follows:

Assessment Objectives

Weighting

AO1

Using and applying:

Accurately recall facts and definitions.

Use and interpret correct notation.

Accurately carry out routine calculations or tasks requiring multi-step solutions.

50%

AO2

Reason, interpret and communicate mathematically:

Make deductions and form conclusions from mathematical information.

Construct chains of reasoning to achieve a result.

Interpret and communicate information accurately.

Present arguments or proofs.

Assess the validity of an argument.

25%

AO3

Problem Solving:

Translate problems in mathematical or non-mathematical contexts into a series of mathematical processes.

Make and use connections between different parts of mathematics.

Interpret results in the context of the given problem.

Evaluate methods used and results obtained.

Evaluate solutions.

25%

Formulae Guidance

1. Formulae included in the subject content. Candidates are expected to know these formulae; they must not be given in the assessment.

The quadratic formula

The solutions of 2++= 0 where 0

Circumference and area of a circle

Where r is the radius and d is the diameter:

Circumference of a circle= 2=

Area of a circle= 2

Pythagorass theorem

In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:

Trigonometry formulae

2. The following formulae are not specified in the content but should be derived or informally understood by candidates. These formulae must not be given in the examination.

3. Formulae candidates should be able to use, but need not memorise. These can be given in the exam, either in the relevant question, or in a list from which candidates select and apply as appropriate.

Notes of Use

Teaching:

Content is to be taught to the highest achieving students in the cohort (i.e. set 1 pupils), dependent upon ability. Teachers are responsible for differentiating all lessons appropriately for the pupils in their classes.

Resources:

Any resources listed can be found on the shared Maths drive, on staff laptops, or in the resource folders. All resource folders are categorised by week and topic.

Suggested resources include:

Sumbooks worksheets

Ten Ticks worksheets

Abacus software

AQA Active Teach software (teacher examples, exercises, end of unit tests and mark schemes)

Interactive Essentials

www.mymaths.co.uk

www.worksheetworks.com

http://www.superteacherworksheets.com

http://www.tes.co.uk/maths-secondary-teaching-resources

Assessment for Learning

Time has been built in to this scheme of work at the end of every Term so that revision of topics taught can be undertaken.

Formal assessments will be implemented at the end of every Term.

Regular homework must be set in line with the mathematics department policy for all Year 10 and Year 11 students. Teachers may wish to use the GCSE homework sheets available on the shared maths drive or source a suitable alternative.

Number

Statistics

Algebra

Measures

Geometry

Number & Algebra

Revision/Exams

Topic colour codes

Overview

Year 10

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 8

Number 1

Mental & Written Calculations

Algebra 1

Simplifying & Surds

Geometry 1

Triangles, Quadrilaterals & Angles

Geometry 2

Bearings

Statistics 1

Data Collection and Simple Charts.

Number 2

Laws of Indices & Powers

Algebra 2

Plotting Coordinates & Linear Graphs

Number 3

Fractions, Decimals & Rounding

Week 9

Week 10

Week 11

Week 12

Week 13

Week 14

Week 15

Week 16

Algebra 3

Using Equations and Formulae

Measures 1

Metric Measures

Geometry 3

Circle Theorems

Number 4

Percentages

Algebra 4

Sequences

Revision & Unit Tests

Geometry 4

Perimeter & Area

Week 17

Week 18

Week 19

Week 20

Week 21

Week 22

Week 23

Week 24

Geometry 5

Circles

Algebra 5

Real Life Graphs

Number 5

Ratio and Proportion

Geometry 6

Polygons and Angles

Algebra 6

Expressions & Equations

Algebra 7

Equations: Straight Lines & Circles.

Geometry 7

Transformations:

Reflections & Translations

Geometry 8

Transformations:

Rotation

Week 25

Week 26

Week 27

Week 28

Week 29

Week 30

Week 31

Week 32

Geometry 9

Congruence & Similarity

Revision & Unit Tests

Statistics 2

Averages & Probability

Statistics 3

Charts for Grouped Data

Algebra 8

Solving Quadratic Equations

Geometry 10

Representing 3D shapes

Week 33

Week 34

Week 35

Week 36

Week 37

Week 38

Week 39

Week 40

Number & Algebra 1

Inequalities

Algebra 9

Plotting graphs

(Linear & Quadratic)

Geometry 11

Constructions

Geometry 12

Loci

Revision & Summer MOCK Exams

Number 6

FDP

Measures 2

Using scales & Compound Measures

Year 11

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

Week 7

Week 8

Geometry 13

Surface Area

Geometry 14

Volume

Number 9

Calculating with Fractions

Geometry 15

Enlargement

Geometry 16

Vectors

Number & Algebra 2

Direct & Indirect Proportion

Number 10

Percentages & Finance

Number 10


Week 9

Week 10

Week 11

Week 12

Week 13

Week 14

Week 15

Week 16

Algebra 10


Algebra 11

Algebraic Fractions

Revision & MOCK Exams

Geometry 17

Pythagoras & Trigonometry

Geometry 18


Algebra 12

Quadratic and Other Graphs

Statistics 4

Scatter Graphs & Tree Diagrams

Week 17

Week 18

Week 19

Week 20

Week 21

Week 22

Week 23

Week 24

Statistics 5

Probability: Experiments and Charts.

Geometry 19

Sine and Cosine Rule

Geometry 20

Cylinders, Cones and Spheres.

Algebra 13

More Real Life Graphs

Algebra 14

Simultaneous Equations

Geometry 21

Pyramids

Statistics 6

Probability: Venn Diagrams

Algebra 15

Inequalities: Linear and Quadratic

Week 25

Week 26

Week 27

Week 28

Week 29

Week 30

Week 31

Week 32

Revision

Revision

Revision

Revision

Revision

Revision

Revision

Revision

Week 33

Week 34

Week 35

Week 36

Week 37

Week 38

Week 39

Week 40

Revision

Summer Exams

Content: Year 10

Autumn 1

Learning Objectives:

Date:

Resources:

Lesson:

To be able to:

Outcome

Common mistakes and misconceptions

Week 1

Number 1

Mental and Written Calculations

(Integers, negatives, powers and roots)

1

Recall the squares of integers up to 15 and the cubes of 2, 3, 4, 5 and 10

Recall and use corresponding squares, cubes and their roots.

Recognise powers of 2, 3, 4, 5

Evaluate expressions involving other integer powers and roots (e.g. 23 + 42)

Estimate powers and roots of any given positive number.

Incorrectly thinking that taking a square means multiplying by 2 and a cube as multiplying by 3.

Not recognising that square roots have 2 solutions (this will become clearer when calculations with negatives are studied)

2

Calculate accurately with negative numbers.

Multiply and divide using whole and decimal numbers.

Adding and subtracting incorrectly.

Mistakes made when using negatives and powers (e.g. -33 = 27 instead of -27)

3

Solve numerical problems involving decimals.

Estimate and check answers to calculations involving decimal and negative numbers.

Not considering context.

Not rounding off numbers and working accurately when asked to estimate.

Not showing all working

4

Calculate sums using BIDMAS involving negatives, powers and decimals.

Forgetting to use the correct order.

Not writing down their working and losing track of what they have done previously in the calculation.

Week 2

Algebra 1

Simplifying & Surds

1

Multiply together two algebraic expressions with brackets.

Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments.

Not multiplying all terms in one bracket by the other.

Forgetting to simplify answers fully.

Students just square what they can see

e.g. stating that (x + 3) = x2 + 9

Pupils do not show working out as proof (e.g. evidence of expanding brackets)

Pupils forget to answer the question fully (e.g. forgetting to state Yes or No when asked whether expressions are equivalent)

2

Square a linear expression, e.g. (x+1)2

Expand products of two or more binomials, e.g. (x+2)3 or (x+2)2 (x+3)3

Thinking that (x+1)2 = x2 + 1

Completing only some of the steps to fully expanding.

3

Use the addition and subtraction rule of surds.

Use the multiplication and division rules of surds.

Simplify surds fully (e.g. 12 = 23) and rationalise denominators.

Expand brackets involving surds

Adding the numbers underneath the root signs, instead of collecting together.

Not simplifying answers where possible, e.g. 4 is actually 2.

4

Manipulate surds to rationalise denominators.

Simplify and manipulate algebraic expressions (including those involving surds)

Forgetting to multiply the entire fraction by the same surd.

Not simplifying answers fully in more complicated expressions.

Week 3

Geometry 1

Triangles, Quadrilaterals & Angles

1

Solve angle problems algebraically (straight lines, around a point, opposite).

Use and apply rules for parallel lines to solve angles problems.

Not using all the information in the diagram.

Confusing alternate and corresponding angles.

2

Derive and understand that angles inside a triangle sum to 180o

Calculate missing angles inside triangles.

Solve angle problems in triangles algebraically.

Not realising when a triangle is isosceles and thinking that the problem cannot be solved.

Trying to do too many steps in one go when answering algebra-based question.

3

Identify and derive properties of special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus

Draw diagrams from written description

Not recognising, or be able to name, some of the less common quadrilaterals (e.g. the kite and trapezium).

Not reading all of the information before drawing / identifying the shape being described.

4

Calculate missing angles inside quadrilaterals

Solve angle problems in quadrilaterals involving algebra

Not realising that some of the angles asked for can simply be read off the diagram.

Trying to do too many steps in one go when answering algebra-based question.

Week 4

Geometry 2

Bearings

1

Use three-figure bearing notation

Measure the bearing from one place to another.

Plot 3-figure bearings.

Plot bearings from worded problems.

Confusing where to measure from and to.

Using the wrong scale on the protractor

Week 4

Geometry 2

Bearings

Week 5

Statistics 1


2

Draw and interpret scale diagrams to represent journeys.

Not drawing bearings for all information given.

Measuring inaccurately and intersections being in the wrong places.

3

Calculate bearings in diagrams (including return journeys)

Measuring the diagram instead of realising that the angles can be calculated.

Confusing alternate and corresponding angles.

4

Consolidation:

Use and apply knowledge of angles and bearings to complete exam questions.

1

To understand the data handling cycle

NOTE: The above is not specifically tested but is useful for pupil understanding

Identify different types of data (discreet, continuous, qualitative, quantitative, primary, secondary)

Not appreciating that some data can be treated as either discrete or continuous depending on the context (e.g. age this is really continuous, but is often treated as discrete, such as when buying child or adult tickets).

Week 5

Statistics 1


Week 6

Number 2

Laws of Indices and Powers

2

Work out methods for gathering data efficiently

Work out methods for gathering data that can take a wide range of values

Not realising that data collected by a third party (even if the results of a survey or experiment) is classed as secondary data.

3

Sort data into class intervals

Interpret and use grouped frequency tables Interpret a pie chart

Using overlapping class intervals.

Recording data which is on the boundary of a class interval in the wrong class.

Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use.

4

Draw a pie chart

Solve problems with pie charts.

Looking at the angle in a pie chart and ignoring the fact that the pie chart can represent a different number of people.

Not drawing the angles in the pie chart accurately or using the appropriate scale on the protractor.

Measuring each angle from the same starting point.

1

Use laws of indices to multiply and divide numbers written in index notation. (e.g. x2 x x3 = x5)

Calculate with roots, and with integer and fractional indices.Calculate a power of a power, e.g. (23)4

Working out 27 as 2 7.

Multiplying and dividing powers instead of adding and subtracting.

Week 6

Number 2

Laws of Indices and Powers

Week 7

Algebra 2

Plotting Coordinates and Linear Graphs

2

Simplify expressions involving negative indices.

Simplify expressions involving fractional indices.

Mixing up the rules.

Forgetting to write 1/

Not simplifying fully.

3

Combine laws of indices to evaluate more complicated expressions.

Use proof to show equivalence in expressions involving powers.

Simplifying and not evaluating fully when asked to.

Not showing all steps when simplifying or showing equivalence.

4

Write numbers in standard form.

Convert between standard form and decimal numbers.

Calculate using numbers written in standard form.

Forgetting to use a negative power when working with very small numbers.

Working out only part of the calculation, forgetting to simplify the power.

Ensuring final answers are in standard form, e.g. 1.2 x104 and not 12 x103.

Leaving answer as a decimal number, if required.

1

Identify straight-line graphs that are parallel to the x- or y- axis

Identify and interpret gradients and y-intercepts of lines in the form of y = mx + c

Use the form y = mx + c to identify parallel and perpendicular lines.

Find the equation of the line through two given points, or through one point with a given gradient.

Confusing the x- and y- axis

Mixing up the gradient and y-intercept

Not stating that the gradient is negative.

Week 7

Algebra 2

Plotting Coordinates and Linear Graphs

2

Sketch straight line graphs

Match straight line graphs to their equations

Forgetting that the bigger the gradient, the steeper the graph should look

That gradients of 2 and -2 look the same, but slope in opposite directions

Confusing the gradient and y-intercept

3

Complete a table of values for linear functions (for positive and negative values of x)

Plot graphs of linear functions using a table of values.

Plot linear functions with or without being given a table of values.

Incorrectly calculating with negative numbers

Ignoring BIDMAS.

Confusing the x- and y- coordinates

Not joining up all points.

Only plotting 2 points and joining these together, a 3rd should be used.

4

Calculate the gradient of a straight line (using change in y- / change in x- values)

Identify the equation of a line by finding the gradient and using y-intercept

Incorrectly dividing the change in x- by change in y- values.

Forgetting to check whether the gradient should be positive or negative once calculations have been done.

Mixing up the gradient and y-intercept.

Autumn 2


Level / Outcome / grade?


Date:

Resources:

Lesson:

To be able to:

Week 8

Number 3

Fractions, Decimals and Rounding

TT L5 P2 p33-34

1

Identify and understand equivalent factions

Compare fractions with different denominators using equivalence.

Multiplying the denominator but not the numerator when finding equivalent fractions.

Stating that 1/3 is smaller than as the denominator is smaller.

Week 8

Number 3

Fractions, Decimals and Rounding

Week 9

Algebra 3


Sumbooks Higher worksheet (11)page 19.

2

Identify terminating and recurring decimals

Convert fractions into terminating decimals

Convert terminating decimals into fractions

Change recurring decimals into their corresponding fractions and vice versa

Confusing 0.3 with eq \f(1,3).

Not understanding that recurring decimals are a form of exact maths and therefore rounding answers.

Giving the answer in the wrong form.

TT L9-10 p1 pg 3-5

TT L9-10 p1 pg 3-5

3

Round decimals to a given number of decimal places.

Round numbers to a given number of significant figures.

Apply and identify limits of accuracy when rounding. Including upper and lower bounds.

Treating the digits on each side of the decimal point as separate whole numbers

so giving 0.95 rounded to 1 d.p. as 0.1

Sumbooks Higher worksheet (1), page 9.

4

Estimate and approximate calculations by rounding.

Solve problems using estimation.

Use inequality notation to specify simple error intervals due to truncation or rounding

Not considering context when giving final answers to problems.

Not rounding values to the same degree of accuracy where appropriate.

1

Form simple expressions

Form expressions involving powers and brackets

Form and solve linear equations to solve problems.

Not seeing the general case.

Including brackets unnecessarily in calculations.

Week 9

Algebra 3


Week 10

Measures 1

Metric Measures

2

Substitute numbers to work out the value of algebraic expressions (including powers and indices)

Substitute numerical values into more complicated formulae.

Incorrectly substituting values into expressions (e.g. substituting a = 6 into the expression 4a, writing 46 and assuming it is forty-six).

Ignoring BIDMAS.

Not realising that eq \f(n,10) means n 10, or that eq \f(1,2) 6 means eq \f(1,2) of 6 = 3.

Giving answers irrespective of context.

Sumbooks Higher worksheet (55) page 63.

3

Find approximate solutions to equations using trial and improvement.

Not showing all stages of working.

Not understanding the concept of rounding to get the final solution.

Sumbooks Higher worksheet 41 (pg 49).

4

Find approximate solutions to equations using iteration.

Not showing enough stages of working out to show how the answer tends to a given solution.

L5 p 3 pg 27-34

L5 p3 pg 35- 37

1

Change freely between related standard units (time, length, area, volume, mass, capacity, money)

Change freely between metric units of area and volume.

Ignoring the different units when comparing measurements.

Not considering the relative size of units when deciding whether to multiply or divide.

Week 10

Measures 1

Metric Measures

Week 11

Geometry 3

Circle Theorems

2

Know and use approximate metric equivalents of pounds, feet, miles, pints and gallons

Note: This is no longer in the GCSE subject content but still may be useful for students.

Forgetting the equivalent values.

Multiplying instead for dividing.

L5 p 3 pg 29-33

3

Estimate measures.

Solve problems involving measures and conversion.

Ignoring context when estimating.

4

Identify upper and lower limits of numbers rounded to a given degree of accuracy.

Solve problems involving limits of accuracy and measures.

Misinterpreting the rounding that has taken place.

Using the wrong limit when performing calculations.

1

Identify and:

Use the tangent / radius theorem.

Use the two tangent theorem.

Use the chord / bisector theorem.

Forgetting that angles are equal when using the two-tangent theorem.

Forgetting that bi-sect means cut in half.

Week 11

Geometry 3

Circle Theorems

Week 12

Number 4

Percentages

apply and prove the standard circle theorems

2

Identify and:

Use the angle subtended by an arc theorem.

Use the semi-circle theorem.

Use the same-segment theorem.

Using the angle subtended by an arc theorem the wrong way around, i.e. the angle at the edge is twice the one at the centre, instead of the other way around.

Doubling instead of halving.

3

Identify and:

Use the cyclic quadrilateral theorem.

Use the alternate segment theorem.

Assuming that opposite angles in cycling quadrilaterals are equal.

Not being able to spot the alternate segment rule.

4

Apply combinations of circle theorems concerning angles, radii, tangents and chords, and use them to prove related results.

Prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results.

Students not able to see the bigger picture.

Pupils forget to apply simple angles rules to help prove more complicated circle theorems.

1

Convert between fractions, decimals and percentages.

Order fractions, decimals and percentages.

Forgetting that fraction lines mean divide

Multiplying by the wrong power of 10 to change between decimals and percentages.

Show their working out, forgetting to order their final answer.

Week 12

Number 4

Percentages

Week 13

Algebra 4

Sequences

2

Find a percentage of an amount without using a calculator

Find percentages of amounts in more complex situations

Compare two quantities using percentages

Students divide by 10 to get 10%, so therefore divide by 1 to find 1%.

Treating a percentage such as 0.05% as though it were 5%.

3

Find a percentage of an amount with a calculator

Write one quantity as a percentage of another

Not using the original amount as the denominator, when finding a percentage difference.

Working with quantities in different units, forgetting to convert.

4

Calculate a percentage increase or decrease

Calculate percentage increase or decrease using VAT

Adding the percentage to the cost when finding a percentage increase (e.g. 315 + 15% VAT = 330).

Thinking that percentages over 100% cannot exist.

Giving the actual increase/decrease as the answer, not the final total.

Using the multiplier as 1.5 rather than 1.05 for an increase of 5%.

1

Recognise sequences of triangular, square and cube numbers.

Recognise and use sequences such as Fibonacci, quadratic and involving powers (e.g. 21, 22, 23, 24, 25)

Find any term in a sequence given the nth term

Show something is false using a counter-example

Writing 3 squared as 2 x 3

Writing powers as 2x1, 2x2, 2x3

Not identifying an appropriate counter-example.

Not appreciating that a proof shows something works for all values.

Week 13

Algebra 4

Sequences

Week 14 / 15

2

Find the nth term of a linear sequence

Find the nth term for pattern sequences

Identify and use sequences involving surds.

Not showing every step of working out

Not making the connection between the structure of the physical pattern and the form the nth term takes.

3

Find the nth Term rule for a simple quadratic sequence.

Not showing all steps in working out.

Confusing whether they need to add or subtract a value to get from one part of a sequence to another.

4

Find the nth Term rule for any quadratic sequence.

Missing out steps in working out.

Mixing up n2 with 2n, for example.

Revision & Unit Tests / Exam Question focus?


Spring 1

Resources:

Lesson:

To be able to:

Outcome


Week 16

Geometry 4

Perimeter and Area

10 ticks L5 P4 p36-40

Abacus

Sumbooks (Y9 basics) p83

1

Calculate the perimeter of rectangles, triangles, parallelograms and trapezia

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.

Counting squares instead of the number of edges exposed around the outside.

Not adding all side lengths together

Assuming that everything is in cm and not checking the correct units

Week 16

Geometry 4

Perimeter and Area

Week 17

Geometry 5

Circles

10 ticks L5 P4 p36-40

http://www.worksheetworks.com/math/geometry/measuring-figures.html

Abacus

Sumbooks (Exercises in Numeracy) p32

2

Identify missing measurements on compound shapes.

Calculate the perimeter of compound shapes.

Stating a measurement because it looks the same as another one

Not converting lengths into the same units before adding

Only adding the measurements given, ignoring unlabelled sides

10 ticks L5 P4 p36-40

Abacus


3

Calculate the area of rectangles, triangles, parallelograms and trapezia

Writing cm instead of cm2

For triangles, forgetting to halve

Not using the vertical height

Multiplying all measurements together, instead of the ones they need

10 ticks L5 P4 p36-40

http://www.worksheetworks.com/math/geometry/measuring-figures.html

Abacus


4

Calculate the area of compound shapes made from rectangles.

Calculate the area of compound shapes involving triangles, parallelograms and trapezia.

Forgetting to add all areas together to get a total

Not identifying the correct measurements to use when there are more than they need

Multiplying all given measurements together

Abacus

1

Recall the definition and properties of circles (inc. symmetry)

Know and label parts of a circle (centre, radius, chord, diameter, circumference, tangent, arc, sector and segment)

Draw circles accurately

Forgetting there are an infinite number of lines of symmetry

Confusing radius and diameter

Confusing segment and sector

Forgetting to divide by 2 when the diameter is given and the radius is needed.

Week 17

Geometry 5

Circles

Week 18

Algebra 5

Real Life Graphs

10 ticks L6 P5 p33-38

Abacus

Sumbooks (Foundation book) p54

2

Calculate the circumference of a circle using 2r or d

Calculate the perimeters of compound shapes involving circles or parts of circles

Leave answers in terms of

Not multiplying by 2 when the radius is given and the diameter is needed.

Forgetting to add all lengths to get final answers.

Adding measurements to the perimeter that are inside the shape

Not leaving answers incorrect form.

10 ticks L6 P5 p33-38

Abacus


3

Calculate the area of a circle using r2

Calculate the areas of compound shapes involving circles or parts of circles.

Leave answers in terms of .

Multiplying by ( before squaring.

Using the diameter instead of radius.

Not leaving answers in correct form.

Abacus

4

Calculate arc lengths .

Calculate the area of a sector.

Calculate angles inside sectors of circles.

Using the angle for the major sector when the minor is needed, and vice versa.

Not being able to rearrange calculations to find the angle inside the sector

1

Read and interpret distancetime graphs

Draw distance-time graphs

Read and interpret velocity-time graphs

Draw velocity-time graphs

Solve problems involving speed, distance and acceleration

Drawing and labelling axes before working out the axes range appropriate to the problem.

Confusing the formula for calculating acceleration

Forgetting that a positive slope is acceleration and negative slope is deceleration

Week 18

Algebra 5

Real Life Graphs

Week 19

Number 5


2

Read and interpret real-life graphs

Sketch real-life graphs

Read and interpret conversion graphs

Plot conversion graphs

Sketch and interpret reciprocal and exponential graphs of real-life functions.

Not realising that the intercept represents a fixed cost.

Not recognising that a straight line represents constant change, curves show rates vary

Inaccurately reading from one value on a conversion graph to find another value.

Drawing out axes using an unsuitable scale

Not being able to use their graph to work out a solution to a problem not represented on the graph (e.g. axes go up to 200g, need to use 800g)

3

Interpret the gradient at a point on a curve as the instantaneous rate of change.

Drawing a tangent to the curve inaccurately.

Dividing the change in x- by y-

Ignoring whether it should be a positive or negative gradient.

4

Calculate the gradients of chords and tangents numerically and algebraically.

Drawing tangents to curves inaccurately.

1

Write a ratio as a fraction.

Interpret ratios in practical situations.

Identify and work with fractions in ratio problems.

Divide a given quantity into a ratio.

Use a ratio to find one quantity when the other is known.

Turning a ratio into a fraction (e.g. the ratio 4:5 becomes eq \f(4,5)).

Giving an answer without considering the context.

Dividing by 2 as there are two parts to the ratio.

Failing to find the value of the unit fraction in more complex problems.

Week 19

Number 5


Week 20

Geometry 6

Polygons and Angles

2

Write a ratio in the form 1 : n or n : 1

Use a ratio when comparing a scale model to the real-life object

Dividing by the wrong amount to find the unit value.

Writing the ratios the wrong way around.

3

Understand direct proportion

Solve problems involving direct proportion.

Understand value for money.

Work out which product is the better buy.

Giving an answer without considering the context.

Not multiplying or dividing both sides of the ratio by the same amount.

Not finding the unit cost.

Dividing by the wrong amount to find unit cost.

4

Understand indirect proportion.

Solve problems involving indirect proportion.

Not considering real-life context before answering questions.

Incorrectly multiplying instead of dividing.

10 ticks L5 P3 p19-21


Sumbooks (Intermediate book) p42

1

Angles re-cap:

Calculate angles inside a triangle

Calculate angles inside quadrilaterals

(including special quadrilaterals, and algebraically)

Not showing working.

Not stating the angles rule they have used.

Not remembering properties of regular / irregular polygons and other properties of shapes.

Confusing the rule for triangles and quadrilaterals.

Week 20

Geometry 6

Polygons and Angles

Week 21

Algebra 6

Expressions and Equations

10 ticks L6 P5 p27-29

2

Use properties of triangles to find the sum of interior angles inside polygons.

Calculate interior angles of polygons.

Incorrectly splitting the polygon into triangles.

Working things out mentally without writing down the calculations.

10 ticks L6 P5 p27-29

3

Understand that exterior angles on polygons always sum to 360o

Use exterior angles of polygons to solve problems.

Thinking that exterior angles are only 360o on quadrilaterals.

Confusing the rules for interior and exterior angles.

Forgetting the formula for the exterior angles of a polygon and how to apply it.

10 ticks L6 P5 p27-29

4

Solve more complex angle problems involving exterior and interior angles of polygons.

Failing to spot that all angles are equal on a regular polygon when only one angle is given.

Forgetting that interior and exterior sum to 180o

Pupils do not use the correct notation for angles (e.g. angle ABC = angle DEF because)

1

Know the difference between and equation, expression and an identity

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.

Solve two-step equations.

Solve equations involving brackets.

Incorrectly combining number work involving fractions and decimals with equation solving.

Getting the wrong signs when multiplying negative numbers.

Incorrectly simplifying after expanding the bracket.

Week 21

Algebra 6

Expressions and Equations

10 ticks L6 P1 p6-8

http://www.worksheetworks.com/math/pre-algebra.html

Sumbooks (Y9 basics) p5310 ticks L6 P1 p6-8

http://www.worksheetworks.com/math/pre-algebra.html

Abacus

2

Solve equations with an unknown on both sides.

Solve equations with unknown on both sides and brackets.

Introducing errors when there are a negative number of unknowns on either side of the equation.

3

Solve equations involving fractions on one side.

Solve equations involving fractions on both sides.

Not multiplying by the denominator of the fraction.

Not multiplying by the LCM of each fraction when they appear o both sides.

Inaccurately multiplying so having errors in final answer.

4

Rearrange formulae to change the subject.

Rearrange formulae where the subject appears twice.

Not using the inverse operation (e.g. x + y = z becomes x = z + y).

Not using brackets or a clear division (e.g. rewriting c = 2a + 5 as a = c 5 2).

Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs

Week 22

Algebra 7


1

Find the equation of a straight line through two points

Incorrectly working out the change in x- or y- values when finding the gradient.

Forgetting that they needs to substitute in values for x- and y- using the coordinates given.

Not being able to solve the equation to find the y-intercept.

Week 22

Algebra 7


2

Find the equation of the line through one point with a given gradient

Solve problems involving equations of straight lines.

Forgetting that when x=o, y is the intercept.

3

Recognise and use the equation of a circle centre (0,0)

Substituting in the wrong values into the equation.

Forgetting the formula.

Not square rooting to find the radius.

4

Find the equation of a tangent to a circle at a given point.

Abacus


Spring 2

Resources:

Lesson:

To be able to:

Outcome


Week 23

Geometry 7

Transformations:

Reflections and Translations

10 ticks L4 P7 p29-36


1

Recognise and draw lines of symmetry in plane shapes.

Draw a reflection of a shape in a mirror line (horizontal, vertical or diagonal)

Draw reflections in the x- or y- axis on a coordinate grid.

Only drawing on one line of symmetry when there are several

Drawing the image a different distance from the mirror line than the object.

Week 23

Geometry 7

Transformations:

Reflections and Translations

10 ticks L6 P2 p11-12


2

Identify lines that are parallel to the x- or y- axes.

Reflect shapes on coordinate grids in lines parallel to the x- or y- axis

Reflect shapes in lines such as y = x

Mixing up x = and y = lines

Confusing whether the line is horizontal or vertical when drawing on the line of reflection.

Automatically reflecting in the x- or y- axes.

10 ticks L7-8 P4 p32

3

Identify lines of reflection on a coordinate grid by finding midpoints.

Describe fully reflections on a coordinate grid.

Assuming the mirror line is either the x- or y- axis.

Incorrectly identifying mirror lines parallel to the x- or y-axis.

Forgetting to give enough information, i.e. reflection in the line)

10 ticks L5 P4 p31-32

10 ticks L6 P2 p3-10


4

Translate shapes according to a given vector.

Describe translations fully using vectors.

Only finding the new location of one corner of the shape and then drawing in the rest incorrectly.

Forgetting that negative numbers mean left or down.

Confusing the left/right value for the up/down value in column vectors.

Using coordinate notation instead of vector notation.

Describing the translation of shape A to shape B, when the opposite was required.

Describe the changes and invariance achieved by combinations of rotations, reflections and translations.

Week 24

Geometry 8

Transformations:

Rotation

10 ticks L4 P7 p37-38



1

Recognise rotational symmetry in regular 2-D shapes.

Recognise rotational symmetry in other shapes.

Complete images to give a given order of rotational symmetry.

Forgetting the definition of regular polygons.

Stating order 4 for shapes with 4 sides.

Pupils make images symmetrical, instead of giving order of rotational symmetry.

Week 24

Geometry 8

Transformations:

Rotation

Week 25

Geometry 9

Congruence and Similarity

10 ticks L6 P2 p13-16


2

Use fractions of turns, angles and compass directions (e.g. turn clockwise, 90o anticlockwise, turn through 180o)

Rotate simple shapes on a grid around a given point.

Mixing up clockwise and anticlockwise.

Not realising 180o turns end in the same position independent of direction.

Rotating the shape around the wrong point.

10 ticks L6 P2 p13-16

3

Draw the position of a shape after rotation about the origin (0,0) on a coordinate grid.

Rotate a shape on a coordinate grid given any centre of rotation.

Working out the angle of rotation incorrectly.

Assuming that (0,0) is the centre of rotation instead of reading the question carefully.

10 ticks L6 P2 p13-16

4

Identify the centre of rotation between two shapes.

Describe a rotation fully giving the size and direction of turn and the centre of rotation.

Not giving enough information, i.e. centre, direction and angle.

If not using tracing paper:

Not joining up corresponding corners.

Perpendicular lines not drawn accurately, crossing in the wrong place.

10 ticks L7-8 P5 p11-14

Abacus

1

Understand the meaning of congruence.

Identify congruent shapes (squares, circles, regular polygons)

Identify congruent shapes on coordinate grids (i.e. that have been rotated, reflected, translated or enlarged including fractional and negative scale factors)

Not realising that shapes are still congruent even if they have been rotated or reflected.

Week 25

Geometry 9

Congruence and Similarity

Week 26/27

10 ticks L7-8 P5 p11-14

Abacus


2

Know the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

Recognise and explain how triangles are congruent.

Mixing up the rules of congruence (e.g. thinking that AAS = ASA)

Stating congruence even when corresponding sides / angles are not equal.

10 ticks L7-8 P5 p23-24

Abacus

3

Understand the meaning of similar shapes.

Calculate scale factors in similar shapes.

Identify similarity in simple shapes.

Not checking that all lengths are similar.

Dividing measurements that are not corresponding.

10 ticks L7-8 P5 p23-29

Abacus

4

Describe and construct similar shapes (e.g. circles, squares, rectangles)

Use similarity when working with area

Apply the concepts of congruence and similarity to solve problems.

Using the wrong scale factor.

Dividing lengths that are not corresponding to check similarity.

Not using a squared scale factor when working with area.

Revision & Unit Tests / Exam Question focus? (Easter)


Summer 1

Resources:

Lesson:

To be able to:

Outcome


Week 28

Statistics 2


1

Find MMR from a frequency table.

Find the modal class and median from a grouped frequency table.

Adding up the total frequency incorrectly.

Forgetting to divide by the total by the number of data items.

Week 28

Statistics 2


Week 29

Statistics 3


2

Find an estimate of the mean for grouped data.

Compare a set of discreet data using mode, range, median and mean.

Not using the midpoint of a class interval.

Adding the frequencies together before multiplying by the midpoint.

Selecting an inappropriate measure for the data provided.

Showing calculations without making a conclusion or proving a hypothesis.

3

Understand the meaning of independent events.

Systematically list all outcomes for combined independent events (in a list or table).

Calculate the probability of combined independent events.

Construct theoretical possibility spaces (sample space) combined events.

Calculate probabilities using possibility spaces (sample space).

Working in a haphazard way when giving possible combinations, thus missing one or more combinations.

Not simplifying fractions where required.

Not listing all outcomes of each event.

Miscounting the number of possibilities in the sample space.

4

Set up tree diagrams for combined independent events.

List outcomes using tree diagrams.

NOTE: (you may wish to calculate simple probabilities from a tree diagram here)

Not including enough branches for outcomes.

Not reading across every possible combination of branches and therefore missing outcomes.

1

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

Assuming that all column widths should be equal.

Forgetting that bar height represents frequency density and not frequency.

Multiplying or dividing incorrectly when trying to find missing values needed.

Using unsuitable scales on the axes.

Week 29

Statistics 3


Week 30

Algebra 8


2

Interpret and solve problems involving histograms.

Not being able to identify the scale that has been used.

3

Plot cumulative frequency curves.

Interpret cumulative frequency curves.

Forgetting to add frequencies together.

Plotting coordinates and joining together like a frequency polygon.

Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)

4

Draw box plots from cumulative frequency curves.

Interpret box blots.

Understand and discuss the effect of outliers.

Drawing the box inaccurately, so it represents the lowest and highest value instead of the interquartile range.

Placing the median in the middle of the axes, instead of at the correct value.

Not finishing off whiskers.

Not showing outliers where required.

10 ticks L7-8 P3 p9


1

Expand and simplify expressions involving brackets and surds.

Factorise linear expressions.

Factorise expressions involving surds.

Errors made when working with negative numbers.

Not multiplying all terms in the bracket by the number / term on the outside.

Forgetting basic rules of surds.

Not taking out the highest common factors.

Forgetting that x2 is a factor of x3

Forgetting that 2 is a factor of 10 and 12, for example.

Week 30

Algebra 8


Week 31

Algebra 8


10 ticks L7-8 P3 p9


Sumbooks (Higher book) p34

2

Factorise quadratic expressions.

Factorise using the difference of two squares.

Factorise quadratic expressions with coefficients greater than 1 (e.g. starting 2x2)Factorise quadratic expressions of the form ax2 + bx + c including the difference of two squares.

Errors made when multiplying out brackets to check answers.

3

Plot graphs of quadratic functions (re-cap)

Solve quadratic equations graphically.

Solve quadratic equations by factorising algebraically (including those that need rearranging).

Forgetting to write the opposite sign when writing the solution, e.g. (x + 1) gives solution of x= -1 not x=1.

Not writing down both solutions.

4

Complete the square.

Solve quadratic equations by completing the square.

Forgetting to halve the value in front of the x

Errors made when multiplying out what is inside the bracket.

Incorrectly writing add or subtract after the bracket, when the opposite is necessary.

Forgetting there are always 2 solutions.

1

Substitute into formulae (including negatives and indices) (re-cap)

Recognise and interpret the quadratic formula.

Substitute into the quadratic formula.

Errors made when squaring or multiplying with negatives.

Forgetting to change the sign in from of the b value to a positive or negative where required.

Week 31

Algebra 8


Week 32

Geometry 10


2

Solve quadratic equations using the quadratic formula, finding both solutions.

Not writing both solutions on the answer line.

Miscalculating with negatives.

3

Consolidation

4

Consolidation

10 ticks L4 P8 p22-28

1

Identify 3D shapes: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

Describe 3D shapes by their properties.

Identify planes of symmetry of 3-D objects.

Giving correct answers but not explaining the properties used.

Using incorrect terminology, e.g. corners instead of vertices.

Week 32

Geometry 10


Week 33

Number & Algebra 1

Inequalities

10 ticks L4 P8 p22-28

10 ticks L6 P4 p33-40



2

Recognise the net of a 3-D object

Draw the net of a 3-D object

Incorrectly visualising 3-D objects in 2-D.

10 ticks L6 P2 p37-42



3

Make a drawing of a 3-D object on isometric paper.

Make isometric drawings of a 3-D object when given certain criteria (e.g. 24 cubes, draw a cube that has 125 cubes, draw a cuboid)

Using isometric paper in landscape not in portrait.

Not joining lines dot-to-dot.

Forgetting that there are cubes on the inside of a shape (e.g. asked to draw a cuboid that has 24 cubes) and only considering the cubes you can see.

10 ticks L5 P6 p30-34

10 ticks L6 P2 p37-42


4

Construct and interpret plans and elevations of 3-D objects

Missing out hidden cubes when converting from a 3-D view to a plan or elevation.

Confusing the different views.

L 6 p 1 p9

1

Set up linear equations.

Solve linear equations.

Misinterpreting the problem.

Not making links between one part of the question and another.

Correct equation formed but solved incorrectly.

Week 33

Number & Algebra 1

Inequalities

Week 34

Algebra 9

Plotting graphs

(Linear and Quadratic)

L6 p 6 pg 7

L7-8 p 4 pg 13-15

2

Use the symbols , , to show numerical inequalities.

Write down integer values that satisfy inequalities.

Show inequalities on a number line.

Confusing the convention of an open circle for a strict inequality and a closed circle for an included boundary.

Not remembering how to use inequality symbols.

Not reversing the sign when multiplying or dividing by a negative.

Sumbooks higher p 24- 5

3

Solve linear inequalities in one variable.

Solve linear inequalities and show solutions on a number line.

Colouring in the circle when it is not needed.

Misinterpreting the symbols given in the inequality.

Not changing the symbols around when multiplying or dividing by a negative.

Sumbooks higher p 24- 5

4

Solve linear inequalities in one or two variables and represent solutions on a number line.

Writing x= on answer lines instead of using the appropriate symbol.

L6 p 1 pg25

1

Plot graphs of linear functions (with or without a table of values)

Plot graphs of two linear functions and identify points of intersection.

Solve linear equations graphically.

Substituting incorrectly.

Not using BIDMAS.

Making mistakes when calculating with negative numbers.

Not using a third point as a check when drawing a straight line.

Week 34

Algebra 9

Plotting graphs

(Linear and Quadratic)

L6 p 1 pg27-29

L6 p 1 pg 35

L7-8 p 3 pg 29

2

Plot graphs of quadratic functions.

Solve linear or quadratic equations graphically.

Not plotting enough points.

Not joining points together.

Joining coordinates with a straight line instead of a smooth curve.

AQA Higher book, Ex. 35D, page 551.

3

Solving problems with quadratic equations (graphically or algebraically).

Not visualising the problem.

Incorrectly setting up equations.

Students do not apply basic knowledge of mathematics to help solve problems (e.g. multiplying out algebraic expressions given as lengths, to find an expression or equation for area).

4

Plot graphs of other functions (e.g. cubic, reciprocal, exponential for positive values of k)

NOTE: This is not specifically tested, but is useful for when students need to sketch graphs of various functions.

Joining non-linear graphs with straight lines.

Not checking rogue coordinates they have plotted (e.g. they can see what the graph should look like, but do not check working out when there is a coordinate that does not fit with the rest).


Summer 2

Resources:

Lesson:

To be able to:

Outcome


Week 35

Geometry 11

Constructions

10 ticks L7-8 P5 p5-7

10 ticks L6 P4 p32

1

Construct acute, obtuse angles.

Construct reflex angles.

Construct the bisector of an angle.

Labelling the wrong part of the angle once drawn.

Using the wrong scale on the protractor.

Not keeping the arms of compasses an equal distance apart when bisecting.

Week 35

Geometry 11

Constructions

Week 36

Geometry 12

Loci

10 ticks L6 P4 p31-32

2

Draw triangles accurately when at least one angle is given.

Draw triangles accurately when given the length of all three sides.

Not completing the triangle by drawing the third side.

Rubbing out construction lines.

Not completing the triangle by drawing the third side.

10 ticks L6 P4 p31-32

10 ticks L7-8 P5 p3-4

3

Know that the perpendicular bisector of a line segment is the shortest route between two points.

Construct a perpendicular bisector of a line.

Construct a perpendicular to a given line from/at a given point.

Not opening the compasses so that they are greater than the midpoint.


Not keeping a consistent distance between the points of the compass when drawing arcs.


Sumbooks (Year 9 basics) p69-70

4

Make an accurate drawing of given shapes using constructions.

Using the wrong type of construction.

Not using compasses and drawing freehand

Not drawing according to all given criteria.

Worksheet in resources folder

1

Construct a locus around a point.

Construct a locus around a line of points.

Failing to keep the settings of compasses constant.


Week 36

Geometry 12

Loci

Week 37/38

Worksheet in resources folder

2

Construct a locus that is equidistant between two points.

Construct a locus that is equidistant between two lines.

Confusing a distance from a point with the distance from a line.

Sumbooks (Intermediate book) p57-58

10 ticks L7-8 P5 p7-10

3

Solve problems involving constructions and loci.

Not using compasses.

Making inaccurate constructions.

Shading the wrong region.

Sumbooks (Intermediate book) p57-58

10 ticks L7-8 P5 p7-10

Sumbooks (Higher book) p51 (including bearings)

4

Solve locus problems, including the use of bearings and scale.

Forgetting that bearings use 3-figures.

Not using a North line.

Confusing clockwise and anti-clockwise.

Revision & Summer MOCK Exams?

Week 39

Measures 2

Using scales & Compound measures (speed, rates of pay, area)

10 ticks L5 P3 p29-34

10 ticks L4 P3 p27-42

1

Read and interpret scales (mass, capacity, length)

Solve problems involving metric scales and measures.

Misreading the scale.

Incorrectly calculating the intervals shown by the scale.

Incomplete calculations shown or steps taken when solving problems.

Week 39

Measures 2

Using scales & Compound measures (speed, rates of pay, area)

Week 40

Number 6

FDP

2

Calculate amounts such as daily or weekly wages.

Calculate rates of pay (including overtime rates)

Solve problems involving salaries and pay.

Assuming that rates of pay are the same each day or time.

Doubling rates of pay instead of multiplying by 1.5, for example.

Incomplete calculations, e.g. working weekly pay but forgetting the weekend hours worked.



3

Know the formula linking speed, distance and time.

Perform calculations involving speed, distance and time.

Not remembering the formula.

Dividing instead of multiplying, where appropriate.

Not checking that measurements are using the same units (e.g. distance in Km but time in metres per hour)

10 ticks L4 P3 p27-42

4

Change freely between related standard units and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts.

Convert metric units of measurement (re-cap)

Convert between units of compound measures such as area, rates of pay and speed.

Use compound measures such as area, rates of pay and speed.

Multiplying or dividing by the wrong power of 10.

Assuming that area in m2 need to be x100 to convert into cm2.

Forgetting to convert both sets of units, e.g. when converting km per hour into metres per minute.


http://www.worksheetworks.com/math/percent.html

Abacus

Sumbooks (Y9 basics) p29-

1

Calculate percentages of amounts.

Calculate with percentages in real-life contexts.

Calculate percentage increase and decrease.

Dividing by the wrong power of 10.

Mistaking 0.3 for 3%, for example.

Calculating the increase / decrease but forgetting to add it to original amount to get a total.

Week 40

Number 6

FDP

10 ticks L6 P3 p13-16

Abacus


Sumbooks (Foundation book) p9-11

2

Use decimals as multipliers and to calculate quantities (with or without a calculator)

Convert between decimals and percentages.

Forgetting to put decimal places back in when performing without calculator.

Multiplying or dividing by the wrong power of 10.

10 ticks L6 P3 p13-16

Abacus




3

Convert between fractions and terminating decimals.

Order fractions, decimals and percentages.

Not realising that 1/10 = 10/100.

Writing 0.1 as 1%, for example.

Forgetting to convert into the same type of number before trying to compare.

10 ticks L5 P2 p3

10 ticks L6 P3 p13-16

Abacus


4

Recognise fractions as multipliers.

Calculate fractions of amounts.

Compare quantities using fractions, decimals and percentages.

Not spotting that = 0.5, so multiplying by 0.5 is the same as multiplying by

Multiplying by the denominator instead of the numerator, and vice versa.

Multiplication or division errors made but method correct.

Content: Year 11

Autumn 1


Date:

Resources:

Lesson:

To be able to:

Outcome


Week 1

Geometry 13

Surface Area

(Cubes, cuboids, other prisms)

NOTE: Not cylinders

Sumbooks Higher worksheet (92-93) page 100-101.

(includes parts of circles)

1

Calculate the areas of compound shapes.

Not being able to visualise how to split shapes up into smaller components.

Using the incorrect units or measurements.

L7-8 p 6 p3-11

2

Calculate the surface area of a cube.

Calculate the surface area of a cuboid.

Calculate the surface area of triangular prisms.

Calculate the surface area of other prisms.

Not accounting for every side of the shape.

Forgetting to divide by 2 for triangles, or dividing the area of the whole shape by 2 to get final answers.

L5 p 6 pg 36

3

Convert between metric units of area.

Solve problems involving surface area.

Not giving answers in the units required.

Not being able to rearrange a formula or calculation to find missing measurements.

Working with a mixture of units instead of converting them to the same type.

Whiteboard maths mensuration 93

4

Apply properties of similarity and congruence when working with area.

Not comparing corresponding sides of shapes to check similar lengths.

Week 2

Geometry 14

Volume

(Cubes, cuboids, other prisms)

NOTE: Not cylinders

L5 p 3 pg 31-3

1

Calculate the volume of a cube or cuboid.

Calculate the volume of a triangular prism.

Calculate the volume of other prisms.

Confusing volume and surface area.

Not splitting shapes up into smaller parts to find cross-sectional area.

2

Solve problems involving volume and capacity.


3

Convert between units when working with area and volume.

Compare lengths, areas and volumes using ratio notation.

Make links to similarity (including trigonometric ratios) and scale factors

Writing ratios in the wrong order.

Not simplifying ratios.

Using linear ratios when they should be squared or cubed.

4

Consolidation

Week 3

Number 9

Calculating with Fractions

Calculate exactly with fractions, surds and multiples of

calculate exactly with fractions, surds ) and rationalise denominators and multiples of

simplify surd expressions involving squares (e.g. 12 = 43 = 4 3 = 2 3

1

Write amounts as one fraction of another (e.g. 2/5 shaded, 3/5 not shaded)

Add and subtract fractions with the same denominator.

Add and subtract mixed numbers.

Incorrectly converting a mixed number to an improper fraction.

Not converting the final answer back to a mixed number where required.

2

Write two or more fractions with the same denominator.

Add and subtract fractions when one or more denominators need to be changed.

Not multiplying numerator and denominators by the same thing.

3

Multiply a fraction by a fraction

Multiply a fraction by a whole number.

Multiply a fraction by a mixed number, or a mixed number by a mixed number.

Multiplying diagonally as though cross-multiplying is being done,

e.g. eq \f(2,3) eq \f(5,6) = eq \f(12,15)

Multiplying the numerator and the denominator by the whole number

e.g.

1

4

20 =

20

80

.

4

Divide a whole number or a fraction by a fraction

Divide mixed numbers by whole numbers.

Find the reciprocal of a whole number, a decimal or a fraction

Leaving denominators as decimal numbers.

Not simplifying answers when asked to do so.

Finding the reciprocal of the wrong fraction, or finding the reciprocal of both fractions.

Week 4

Geometry 15

Enlargement

L6 p 2 pg 19-21

L7-8 p 4 pg 34-37

1

Identify the scale factor of an enlargement (including fractional / decimal)

Enlarge a shape on a grid

Enlarge a shape by a fractional scale factor.

Dividing the measurements of the original by the image, instead of image by original.

Inaccurately counting squares.

Adding the scale factor instead of multiplying by the scale factor.

Not using the centre of enlargement.

L7-8 p 4 pg 34-37

L9-10 p 3 pg 3-5

2

Enlarge a shape using a centre of enlargement.

Enlarge a shape on a coordinate grid, using a centre of enlargement as (0,0) or another coordinate.

(as above, including fractional scale factors)

Not enlarging all sides of the shape by the same scale factor.

Using the wrong centre of enlargement.

L7-8 p 4 pg 34-37

L9-10 p 3 pg 3-5

3

Find a centre of enlargement.

Describe enlargements fully, giving scale factor and centre.

Not joining corresponding corners of shapes.

Giving only part of the information required.

L9-10 p 3 p6-18

4

Construct similar or congruent shapes on a coordinate grid using rotation, reflection, translation or enlargement.

Understand and describe the effects of enlargement on perimeter, area and volume of shapes.

Assuming that a scale factor of 2 doubles the area of the shape.

Not carrying out multiple transformations where required.

Week 5

Geometry 16

Vectors

1

Understand vector notation.

Represent column vectors pictorially.

Describe vectors using column notation.

Writing vectors as coordinates.

Mixing up the left right direction with the up / down.

Not writing left / down as a negative value.

2

Apply addition and subtraction of column vectors.

Draw the result vector after an addition or subtraction of vectors.

Mistakes made when adding or subtracting with negative numbers.

Not drawing the resultant vector to show final answer.

3

Use multiplication of vectors by a scalar.

Use diagrammatic and column representations of vectors.

Identify parallel vectors from column vectors or diagrams.

Not multiplying both values by the scalar multiple.

Not sketching the vectors to help identify which ones are parallel.

Failing to identify common factors of vectors written in column notation.

4

Consolidation:

Solve simple problems involving vectors.

Use vectors to construct geometric arguments and proofs.

Mixing up the rules of adding / subtracting or using multiples of vectors.

Not understanding that if we travel the wrong way across a vector, it changes it into a negative, for example.

Week 6

Number & Algebra 2

Direct and Indirect Proportion

L 7-8 p 1 pg 35

Sumbook higher 17

1

Know that when y is directly proportional to x, y x and y = k x

Interpret the gradient of a straight line graph as a rate of change.

Calculate the constant of proportionality (k) given values for x and y.

Write a formula in terms of x and y for direct proportion problems.

Forgetting the formula.

Multiplying instead of dividing to find k.

Mixing up the value of x and y when substituting.

Not substituting the value of k back in to original formula.

Sumbook higher 17

2

Know that when y is inversely proportional to x, y 1/x and y = k/x

Calculate the constant of proportionality (k) given values for x and y when they are inversely proportional.

Write a formula in terms of x and y for inverse proportion problems.

Using the formula for direct instead of indirect (inverse) proportion.

Dividing instead of multiplying to find k.

Not substituting the value of k back in to original formula.

3

Recognise and sketch graphs of direct and indirect proportion.

Construct and interpret equations that describe direct and inverse proportion.

Confusing graphs of direct and inverse proportion.

Not substituting values into equations to check the effect on the shape of the graph.

L9-10 p 1 pg 11

4

Solve problems involving direct and indirect proportion algebraically and graphically.

Misinterpreting a problem as direct proportion, when it is inverse.

?

interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts

?

Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.

Week 7

Number 10


1

Calculate percentages of amounts. (re-cap)

Calculate percentage increase and decrease. (re-cap)

Find the original value after a percentage increase or decrease.

Dividing by the wrong power of 10.

Forgetting to add on the increase or deduct the decrease.

Using the wrong multiplier, i.e. 1.2 for 2% increase.

Not understanding that it is possible to have more than 100% when using percentages in context.

2

Solve problems involving percentage increase / decrease or overall percentage change.

Assuming that an increase of 30%, then a decrease of 10% is equal to an increase of 20%.

3

Calculate using simple interest.

Solve problems involving credit.

Not seeing that 17.5% = 10% + 5% + 2.5%.

Forgetting to add on the initial deposit in credit calculations.

4

Calculate repeated percentage change.

Solve problems involving repeated percentage change / compound interest.

Incorrectly calculating 1.5 x 2 instead of 1.52.

Not checking whether it is a repeated increase or decrease.

Week 8

Number 10


1

Calculate a percentage profit or loss

Calculate original values using profit or loss.

Writing the profit or loss in a monetary value instead of a final percentage.

Dividing by the selling price instead of the original cost price.

2

Understand the Retail Price Index and its use in real-life context.

Interpret changes in the retail price index in terms of the base year (i.e. +5%, -10%, +23%).

Interpret and make comparisons in the changes in the value of goods using the Retail Price Index (e.g. price of food has increased by 10%, but this is below the expected increase for that year).

Forgetting that the base year always has an index of 100 (100%)

105 means an increase of 5%, not 105% from the base year.

An index less than 100 means a decrease in value.

Using the last price in the table to calculate an increase, instead of the base year price.

3

Calculate simple price changes using the Retail Price Index (increase or decrease)

Calculate base year prices given the relevant price index.

Not understanding when the multiplier should be greater than or less than 1.

Using the multiplier as 1.5 rather than 1.05 for an increase of 5%.

4

Solve more complex problems involving the Retail Price Index.


Not showing all stages or working out, or missing stages of working out not believing they are relevant.

Week 9

Algebra 10

Solving Quadratic Equations (re-cap)

1

Re-cap:

Solve equations with unknowns on both sides.

Solve equations involving brackets or fractions.

Errors made when working with negative numbers.

Not multiplying all terms in the bracket by the number / term on the outside.

2

Factorise quadratic expressions.

Solve quadratic equations by factorising (including coefficients greater than 1).

Forgetting that x2 is a factor of x3

Forgetting to change the sign around when giving solutions.

Not multiplying out brackets to check factorisation has been done correctly.

3

Complete the square.

Solve equations by completing the square.

Not halving the coefficient in front of the x.

Incorrectly rearranging.

Not writing down both solutions.

4

Solve quadratic equations graphically.

Solve quadratic equations using the formula.

Forgetting to write the opposite sign when writing the solution, e.g. (x + 1) gives solution of x= -1 not x=1.

Incorrectly substituting in values for a, b and c.

Not changing the sign of the b value where necessary.

Week 10

Algebra 11

Algebraic Fractions

TT L 9 to 10, Pack 4, Page 28.

1

Use basic laws of indices (re-cap)

Simplify algebraic fractions

Mixing up the multiplication and division laws of indices.

Not simplifying fully.


2

Multiply and divide algebraic fractions, simplifying fully

Forgetting the rules of multiplying with simple fractions.

Not switching the second fraction upside down when dividing.



3

Add or subtract algebraic fractions, simplifying answers fully

Not making denominators match before trying to add or subtract.

Forgetting to simplify answers where possible.


4

Solve equations involving algebraic fractions.

Mixing up the rules for adding, subtracting, multiplying and dividing.

Week 11/12

Revision & MOCK Exams?

Week 13

Geometry 17


L7-8 p 2 pg 3

L7-8 p 2 pg 5-7

1

Know and understand Pythagoras theorem a2 + b2 = c2

Calculate the length of the hypotenuse of a right-angled triangle.

Calculate the length of shorter sides in a right-angled triangle.

Use Pythagoras Theorem to solve problems in real-life context.

Forgetting to take the square root to find the final answer.

Not correctly identifying the hypotenuse.

Drawing a scale diagram to calculate the length of a hypotenuse.

Adding instead of subtracting to find the shorter sides.

Thinking that square root is not needed when finding shorter sides.

Failing to identify whether they are finding the longer or shorter side when problem solving.

Students do not sketch out the problem to help them visualise it.


2

Calculate the length of a line segment AB (e.g. on a coordinate grid) using Pythagoras Theorem.

Calculate lengths in other geometrical figures using Pythagoras Theorem.

Pupils do not sketch out the problem to visualise it.

Trying to make an accurate drawing and measure lengths instead of calculating it.

TT L7-8 p5 pg 28-31.

TT L7-8 p 5 pg 33-35.


3

Identify and label sides of triangles in terms of Trigonometric ratios (i.e. opposite, adjacent and hypotenuse)

Know and use the trigonometric ratios. (SOHCAHTOA) to find missing lengths.

Mixing up the ratios and not following SOHCAHTOA.

Using the right-angle as a starting point instead of another given angle.

Multiplying instead of dividing where necessary.

Using the wrong ratio.

TT L7-8 p 5 pg 36-37.


4

Calculate missing angles inside right-angled triangles using Trigonometry.

Solve problems involving trigonometry.

Know the formulae for Pythagoras and trigonometry ratios and apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

Forgetting whether to multiply or divide, dependent upon whether calculating a side or an angle.

Week 14

Geometry 17


1

Solve problems involving Pythagoras and Trigonometry.

Trying to apply Pythagoras when there are not enough side lengths given.

Using the wrong trigonometric ratio.

2

Use and apply the rules of Pythagoras and Trigonometry in 3D problems.

Not being able to visualise the problem.

Pupils do not sketch the problem they are working on to help see what length or angle they are finding.

3

Know the exact values of sin and cos for = 00, 300, 450 , 600 and 900;

Know the exact value of tan for = 00, 300, 450 and 600

Use exact values for sin, cos or tan when solving Trigonometry problems.

Confusing the values of the different ratios.

Not being able to apply the knowledge to the problem in front of them.

4

Recognise, sketch and interpret graphs of trigonometric functions (y=sinx, y=cosx, y=tanx) for angles in any size.

Confusing what each graph should look like with another.

Week 15

Algebra 11

Quadratic and Other Graphs

1

Recognise and sketch graphs of quadratic functions.

Recognise lines of symmetry in quadratic graphs.

Sketch translations and reflections of a given function (eg quadratic functions).

Moving the parabola across the x-axis instead of up or down the y-axis.

Not realising parabolas should be symmetrical.

Not considering how wide the curve should be depending on the coefficient, and sketching graphs that look too similar.

2

Interpret and use graphs of quadratic functions in real-life context.

Identify and interpret intercepts, turning points and roots of quadratic functions graphically.

Deduce roots algebraically and turning points by completing the square.

Not applying context when using quadratic graphs (e.g. not recognising that the turning point is where a ball stops climbing in height and stops moving).

3

Draw graphs of cubic and reciprocal functions.

Sketch and recognise graphs of cubic and reciprocal functions (e.g. y = 1/x with x 0)

Confusing what quadratic, cubic or reciprocal graphs should look like.

Not plotting a few points to remind themselves of what each type of graph might look like before sketching.

Forgetting that 1/x means 1 x.

4

Interpret graphs of quadratic, cubic and reciprocal functions.

Draw and interpret cubic and reciprocal graphs in real-life contexts.


Not thinking about how the change in x- affects the change in y-, and vice versa.

Week 16

Statistics 4

Scatter Graphs & Tree Diagrams

1

Identify types of correlation graphically.

Describe the correlation between two data sets (not from a graph)

Make predictions about bivariate data.

Interpret points on a scatter graph.

Identify points that may be classed as outliers.

Not understanding that correlation does not imply causation between two data sets.

Not considering real-life context when considering whether it is a positive or negative correlation.

2

Plot bivariate data as a scatter diagram.

Draw estimated lines of best fit.

Estimate using a line of best fit.

Understand and describe interpolation and extrapolation as a method of estimation.

Plotting as (y, x) instead of (x, y) coordinates.

Missing off points as not working systematically.

Assuming the line of best fit has to go through (0,0).

Not attempting to split the points evenly either side of the line.

Not using a suitable scale for each axis.

3

Re-cap:

Represent the outcomes of two independent events using a tree diagram.

Calculate the probability of two independent events from a tree diagram.

Work out the probability of an event that can happen in more than one way using a tree diagram (the AND OR rules).

Incorrectly setting up the two events.

Adding instead of multiplying across branches.

Not simplifying fractions where required.

4

Represent the outcomes of dependent events using a tree diagram (conditional probability)

Calculate probabilities of dependent events from a tree diagram.

Not recognising when a question involves independent events and so adding rather than multiplying the fractions.

Adding across branches, multiplying at the end.

Week 17

Statistics 5

Probability: Experiments and Charts.


1

Understand that the greater the number of experimental trials the more reliable the results.

Estimate probability from a set of experimental data.

Compare estimated probability with theoretical probability (using appropriate language and the probability scale).

Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size.

Incorrectly stating that the more trials means there is less bias.

Not understanding that as it is based on an experiment; the probability can change with each experiment and is therefore only ever an estimate.

10 ticks L7 P1 p11-13

2

Calculate relative frequency of an outcome from an experiment.

Predict the likely number of successful events of an outcome.

Comparing theoretical probability with relative frequency without taking into account the number of trials carried out.

Whiteboard maths: Bar charts, pictograms, pie charts, two-way tables.

3

Calculate probability of single events from charts (e.g. bar chart, pictograms, pie charts, two way tables).

Calculate the probability of two or more events from charts.

Incorrectly reading the vertical axis of bar charts

4

Calculate probabilities from a set of grouped data (e.g. grouped frequency tables.

Not understanding a grouped frequency table.

Week 18

Geometry 18

Sine and Cosine Rule (non-right-angled triangles)

TT L9-10 P2 p7.

1

Know and apply the sine rule to find lengths and angles.

Labelling up their triangle incorrectly (not naming corresponding angles and sides with the same letter).

Not switching the formula around depending on whether you want to find a length or an angle.

Using the wrong ratio (e.g. cos instead of sin)

TT L9-10 P2 p8.

Mixed Sine & Cosine activities:


TT L9-10 P2 p

2

Know and apply the cosine rule to find lengths and angles.

Not realising that the cosine rule can also be applied to right-angled triangles.

Not sketching out the problem given.

Rearranging incorrectly to find alternative lengths or angles.

Rounding off calculations before getting to final answers, making it inaccurate.


3

Know and apply ab sin C to find the area or sides of any triangle.

Substituting in values in the wrong places.

Rearranging the formula incorrectly.


Exam style questions:

TT L9-10 P2 p13-16.

4

Solve geometrical problems.

NOTE: Includes Pythagoras, trigonometry, Sine and Cosine rules, area of triangles.

Not being able to identify which method to use to solve a problem (i.e. Pythagoras, Trigonometry, sine or cosine rules).

Not sketching out the problem to help visualise it.

Forgetting to use inverse sin, cos or tan where necessary.

Not showing all stages of working out.

Making rounding errors.

Week 19

Geometry 19

Cylinders, Cones and Spheres.

10 ticks L6 P5 p33-38

10 ticks L9-10 P4 p10-25 (mix of surface area and volume of 3D shapes)


Abacus

1

Calculate the circumference and area of a circle (re-cap).

Calculate the volume of a cylinder.

Calculate the surface area of a cylinder.

Solve problems involving the volume and surface area of cylinders

Forgetting to divide by 2 when the diameter is given and the radius is needed.

Multiplying by ( before squaring.

Using the wrong measurement for the radius or diameter.

Not being able to identify the measurements they need to use.

10 ticks L9-10 P4 p10-25 (mix of surface area and volume of 3D shapes)

Abacus

2

Calculate the volume of a cone.

Calculate the surface area of a cone.

Forgetting to divide by 3 (or x 1/3) when finding volume.

Using the vertical or slanted height the wrong way around.

3

Calculate the volume of a frustum.

Solve problems involving cones or frustums.

NOTE: Ratio or similarity may also be included in these problems.

Calculating only part of the problem, forgetting to finish it off or show final answers.

Using incorrect measurements.

Not being able to work backwards or rearrange formulae to find missing measurements.

10 ticks L9-10 P4 p15

4

Calculate the volume of a sphere.

Calculate the surface area of a sphere.

Solve problems involving spheres.

Students often forget to apply the 4/3 of

Multiplying by 3 and dividing by 4.

Incorrectly substituting measurements into the formulae.

Week 20

Algebra 13

More Real Life Graphs

TT Level 7 to 8, Pack 6, Start Page 37.

1

Read and interpret graphs for time series data and know their appropriate use.

Calculate averages using time series data.

Using a grouped label on the horizontal axis rather than a continuous scale.

AQA Methods & Applications PDF file, page 212.

2

Calculate gradients of linear graphs.

Use and interpret gradients of linear graphs.

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