NEW for Examination 2015
AQA GCSE Linear
Lower Tier
Mathematics
GCSE Content and Overview
Lower Tier
(Outcomes U – 7)
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: 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 – 7 (where 7 is the highest outcome achieved).
· Passes will be considered as 7 - 3.
· Fail will be considered as 2 – U.
Guidance for Students
· All candidates will be expected to use, but not memorise, these formulae:
ü
· All candidates will be expected to be able to use the formulae for:
ü Quadratic formula
ü Circumference and area of a circle, where r is the radius and d is the diameter.
ü Pythagoras’ Theorem
ü Trigonometric ratios (sin, cos and tan)
ü Sine rule
ü Cosine rule
NOTE: These will not be provided in the exam.
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
Pythagoras’s theorem
In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:
Trigonometry formulae
In any right-angled triangle ABC where a, b and c are the length of the sides and c is the hypotenuse:
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 / WeightingAO1 / 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%
Notes of Use
Content is to be taught to all classes, dependent upon ability.
Content highlighted in yellow is aimed at higher achieving students for the lower tier (Set 2 pupils should cover this material)
Overview
Year 10
Week 1 / Week 2 / Week 3 / Week 4 / Week 5 / Week 6 / Week 7 / Week 8Number 1
Place value and ordering / Number 2
Mental & Written Calculations / Algebra 1
Basics & Simplifying / Geometry 1
Angle Facts / Statistics 1
Data Collection / Number 3
Factors, Multiples & Primes / Geometry 2
Properties of 2D shapes / Geometry 3
Bearings
Week 9 / Week 10 / Week 11 / Week 12 / Week 13 / Week 14 / Week 15 / Week 16
Number 4
Fractions & Decimals / Algebra 2
Coordinates & Straight Lines / Number 5
Rounding & Accuracy / Statistics 2
Presenting Data / Number 6
Negative Numbers / Revision
Assessment / Algebra 3
Using Equations & Formulae
Week 17 / Week 18 / Week 19 / Week 20 / Week 21 / Week 22 / Week 23 / Week 24
Measures 1
Metric Measures / Number 7
Simple Percentages / Algebra 4
Sequences / Geometry 4
Perimeter & Area / Geometry 5
Circles / Algebra 5
Real Life Graphs / Number 8
Basic Ratio / Number 9
Ratio & Proportion
Week 25 / Week 26 / Week 27 / Week 28 / Week 29 / Week 30 / Week 31 / Week 32
Algebra 6
Expressions & Equations / Revision
Assessment / Algebra 7
Indices / Geometry 6
Polygons & Angles / Algebra 8
Linear Graphs / Geometry 7
Reflections & Translations / Geometry 8
Rotations
Week 33 / Week 34 / Week 35 / Week 36 / Week 37 / Week 38 / Week 39 / Week 40
Geometry 9
Congruence & Similarity / Geometry 10
Representing 3D Shapes / Statistics 3
Averages / Statistics 4
Simple Probability / Revision
Summer Exams / Number 10
FDP Calculations / Measures 2
Scales & Compound Measures
Year 11
Number 11
Indices & Standard Form / Number & Algebra 1
Inequalities / Geometry 11
Surface Area / Geometry 12
Volume / Number 12
Calculating with Fractions / Geometry 13
Enlargement / Algebra 9
Plotting Graphs / Number & Algebra 2
Direct & Indirect Proportion
Week 9 / Week 10 / Week 11 / Week 12 / Week 13 / Week 14 / Week 15 / Week 16
Number 13
Percentages & Finance / Revision
&
Assessment / Geometry 14
Pythagoras’ Theorem / Geometry 15
Trigonometry / Geometry 16
Angles / Statistics 5
Scatter Graphs
Week 17 / Week 18 / Week 19 / Week 20 / Week 21 / Week 22 / Week 23 / Week 24
Geometry 17
Cylinders & Cones / Algebra 10
Quadratics / Algebra 11
Other Graphs / Statistics 6
Tree Diagrams / Statistics 7
Probability Experiments / Algebra 12
Real Life Graphs / Geometry 18
Constructions / Geometry 19
Loci
Week 25 / Week 26 / Week 27 / Week 28 / Week 29 / Week 30 / Week 31 / Week 32
Algebra 13
Simultaneous Equations / Geometry 20
Pyramids (volume & s. area) / Geometry 21
Vectors / Statistics 8
Venn Diagrams / 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
Date: / Resources: / Lesson: / To be able to: / Outcome / Common mistakes and misconceptions
Week 1
Number 1
Place Value and Ordering
(Integers and decimals) / L3 pk 1 p11 -17
L3 pk 1 p 37
L3 pk 1 p43 / 1 / ü Read and write whole and decimal numbers in figures and words
ü Order positive integers
ü Compare whole numbers using the symbols =, ≠, <, >, ≤, ≥ / · Failing to understand the concept of place value and so reading 204 as 24 (20, 4 twenty-four).
Week 1 ordering and comparing decimals
L4 pk4 p 33 / 2 / ü Order decimal numbers
ü Compare decimal numbers using the symbols =, ≠, <, >, ≤, ≥ / · Thinking that the more digits in a number, the greater the value of the number.
Week 1 adding and subtracting decimals sheet and powerpoint / 3 / ü Add whole and decimal numbers.
ü Subtract whole and decimal numbers.
(NOTE: upto 3 decimal places) / · Not recording the ‘carry over’ and forgetting to add it on.
· Not lining up the decimal points.
· Forgetting to ‘reduce’ a number when borrowing from it.
· Not using 2 decimal places when calculating with money
Week 1 multiplication - grid multiplication
Sumbooks year 9 basics p17-8
L5 pk1 p3-16 / 4 / ü Use written methods to multiply integers (up to 3-digits)
ü Multiply decimal numbers
ü Work out answers to calculations when given the answer to a related calculation. / · Forgetting to add the numbers to find the final answer when using the grid method.
· Forgetting ‘zero’ when multiplying by a power of ten
· Forgetting to put decimal points back
Week 2
Number 2
Mental and Written Calculations
(integers and decimals) / Week 2 division bus stop method ppt / 1 / ü Derive division facts from multiplication facts
ü Use written methods to divide integers
ü Divide using decimal numbers / · Incorrectly writing 3.6 for an answer of 3 remainder 6.
· Not giving an answer in the context of the problem
· Moving the decimal point back at the end of a decimal division.
Sumbooks yr 9 p21-2
L4 pk 3 p 5
L5 pk1 p 33-5 / 2 / ü Multiply whole and decimal numbers by any power of 10
ü Divide whole or decimal number by any power of 10 / · Incorrectly adding the number of zeros as and when appropriate.
· Not counting decimal places correctly when multiplying or dividing by higher powers of 10.
· Not giving answers as decimals when questions do not ask for an alternative.
Week 2 squares and cubes ppt and special numbers sheet,
‘find the quote’ / 3 / ü Recall the squares of integers up to 15 and the cubes of 2, 3, 4, 5 and 10
ü Recall corresponding squares, cubes and their roots.
ü Evaluate expressions involving other integer powers and roots (e.g. 23 + 42) / · 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)
L5 pk 5 p3 -7
Week 2 Bidmas ppt.
Magic squares / 4 / ü Calculate sums using BIDMAS involving brackets and powers. / · Forgetting to use the correct order.
· Not writing down their working and losing track of what they have done previously in the calculation.
Week 3
Algebra 1
Basics and Simplifying / L5 pk 5 p 8
Week 3 collecting like terms sheet x 2 / 1 / ü Simplify algebraic expressions by collecting like terms
ü Multiply numerical or algebraic terms by terms in a single bracket
ü Simplify any linear expressions involving brackets
e.g. 2(x +3) – 2x + 4(x+6) / · Writing m × 3 = m3.
· Failing to comprehend that x = 1x.
· Combining unlike terms.
· Incorrectly adding instead of subtracting when working with negative terms.
· Forgetting to multiply the second term in the bracket by the term outside (e.g. expanding 2(x + 3) as 2x + 3)
· Expanding the wrong part of the expression
Week 3 single bracket
Sumbooks intermediate 24
Sumbooks yr 9 p52 / 2 / ü Multiply together two algebraic expressions with brackets.
ü 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)
Week 3 double brackets / 3 / ü Square a linear expression, e.g. (x+1)2
ü Expand products of 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.
L7 to 8 pk 3 p23-5 / 4 / ü Use the addition and subtraction rule of surds.
ü Use the multiplication and division rules of surds.
ü 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.
Week 4
Geometry 1
Angle Facts / L5 pk 3 pg 17-21
L5 pk 3 pg 5 / 1 / ü Recognise and name types of angles
ü Measure angles to the nearest degree.
ü Estimate the size of an angle in degrees / · Mixing up descriptions (e.g. bigger than 90 but less than 180 degrees)
· Forgetting what acute angles look like, estimating +90o
· Ignoring mm when measuring in cm and mm.
L5 pk 3 pg3-7 / 2 / ü Measure and draw line segments to the nearest mm.
ü Identify and draw perpendicular lines.
ü Draw angles to the nearest degree. / · Labelling the wrong part of the angle once drawn.
· Using the wrong scale on the protractor.
· Not understanding that when measuring angle ABC, they are measuring at ‘B’
L5 pk 3 pg 27
L6 pk 2 pg 23-5 / 3 / ü Calculate missing angles on a straight line.
ü Calculate missing angles at a point.
ü Know and apply the fact that vertically opposite angles are equal. / · Not realising that 3 angles can sum to 180o
· Measuring rather than calculating angles.
· Confusing which angles need to be found.
L5 pk 3 pg 17-19 / 4 / ü Derive and understand that angles inside a triangle sum to 180o
ü Calculate missing angles inside triangles.
ü Solve angle problems in triangles involving algebra / · 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.
Week 5
Statistics 1
Data Collection / Week 5, data handling cycle
Whiteboard maths Discrete and Continuous Data / 1 / ü To understand the data handling cycle
NOTE: The above is not specifically tested but is useful for pupil understanding
ü 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).