Longman AQA GCSE Maths 1-Year MODULAR Scheme of Work – Higher

OVERVIEW

Notes:

1. Assumes 3 hours of guided teaching per week.

2. Assumes a minimum of 3 hours of personal study per week.

3. Assumes the Autumn term is based on an early September start.

4. Assumes the November, March and June exams are at the beginning of November, March and June respectively.

5. Unit 2 revision will need to include the earlier work on ratio (Chapter 7).

6. The scheme assumes teaching is on a topic basis as indicated by the Chapter/Chapter groupings. The assigned hours per topic should be flexibly implemented.

7. AQA Modular specification references: G3.1, G3.3, G3.5 are not specifically recorded. This content, at Grade E, can feature in ‘lead-in’ questions in the exams.

Chapter / Guided learning hours / Grades / AQA Modular specification reference
AUTUMN TERM / UNIT 1: Statistics and Number
1. Data collection / 3 / D, C, A, A* / The Data Handling Cycle: S1
Data Collection: S2.1, S2.2, S2.3, S2.4, S2.5
Data presentation and analysis: S3.1
2. Fractions, decimals and percentages
7. Ratio and proportion / 3 / D, C, B, A / Working with numbers and the number system: N1.14
Fractions, Decimals and Percentages: N2.5, N2.6, N2.7
Ratio and Proportion: N3.1, N3.2, N3.3, N3.3h
3. Interpreting and representing data / 3 / D, C, A, A* / Data presentation and analysis: S3.2, S3.2h
Data Interpretation: S4.2, S4.3, S4.4
4. Range and averages / 3 / D, C, A / Data presentation and analysis: S3.3
Data Interpretation: S4.1
5. Probability / 3 / D, C, B, A, A* / Probability: S5.1, S5.2, S5.3, S5.4, S5.5h, S5.6h, S5.7, S5.8, S5.9
6. Cumulative frequency / 3 / B / Data presentation and analysis: S3.2h, S3.3h
Data Interpretation: S4.4
8. Complex calculations and accuracy / 3 / C, B, A, A* / Working with numbers and the number system: N1.10h, N1.13h
Fractions, Decimals and Percentages: N2.7h
NOVEMBER: UNIT 1 EXAM (OPTION A)
REVISION: 3 GUIDED HOURS
UNIT 2: Number and Algebra
9. Estimation and currency conversion
13. Decimals / 3 / D, C, B, A / Working with numbers and the number system: N1.1, N1.2, N1.4, N1.4h
Fractions, Decimals and Percentages: N2.3, N2.4
11. Fractions / 3 / D, C, B / Working with numbers and the number system: N1.2, N1.3, N1.5
Fractions, Decimals and Percentages: N2.1, N2.2
12. Basic rules of algebra
15. Formulae / 3 / D, C, B / The Language of Algebra: N4.1, N4.2, N4.2h
Expressions and Equations: N5.1, N5.1h, N5.4, N5.6
14. Equations and inequalities / 3 / D, C, B / Expressions and Equations: N5.4, N5.4h, N5.7
10. Factors, powers and roots
16. Indices and standard form / 3 / D, C, B, A, A* / Working with numbers and the number system: N1.6, N1.7, N1.8, N1.9, N1.9h, N1.10h, N1.11h, N1.12h
17. Sequences and proof / 3 / D, C, B, A, A* / Expressions and Equations: N5.9, N5.9h
Sequences, Functions and Graphs: N6.1, N6.2
18. Percentages / 3 / D, C, B / Fractions, Decimals and Percentages: N2.6, N2.7, N2.7h
SPRING TERM / 19. Linear graphs / 3 / D, C, B, A / Expressions and Equations: N5.4h, N5.7h
Sequences, Functions and Graphs: N6.3, N6.4, N6.5h, N6.6h, N6.11, N6.12
20. Quadratic equations / 3 / B, A, A* / Expressions and Equations: N5.2h, N5.5h
21. Further algebra / 3 / B, A, A* / Expressions and Equations: N5.3h, N5.4h, N5.6
UNIT 3: Geometry and Algebra
22. Number skills / REVISION THROUGH PERSONAL STUDY / Working with numbers and the number system: N1.3, N1.4h, N1.14
Fractions, decimals and Percentages: N2.1, N2.5, N2.7
Ratio and Proportion: N3.1
23. Angles
24. Triangles, polygons and constructions / 3 / D, C / Expressions and Equations: N5.4
Properties of angles and shapes: G1.1, G1.2, G1.3, G1.4
Measures and Construction: G3.6, G3.8, G3.9, G3.10
29. Constructions and loci / 3 / C, B / Measures and Construction: G3.10, G3.11
26. Compound shapes and 3-D objects / 3 / D, C, A / Properties of angles and shapes: G1.6
Geometrical reasoning and calculation: G2.4
Mensuration: G4.1, G4.4
MARCH: UNIT 2 EXAM (OPTION A)
REVISION: 3 GUIDED HOURS
MARCH: UNIT 1 EXAM (OPTION B)
27. Circles, cylinders, cones and spheres / 3 / D, C, A, A* / Properties of angles and shapes: G1.5
Geometrical reasoning and calculation: G2.4
Mensuration: G4.1h, G4.3, G4.3h, G4.4, G4.5h
28. Measures and dimensions / 2 / D, C, B / Measures and Construction: G3.4, G3.7
25. More equations and formulae / 1 / D, C, B, A / Expressions and Equations: N5.4, N5.6, N5.8
30. Reflection, translation and rotation
31. Enlargement / 3 / D, C, A / Properties of angles and shapes: G1.7, G1.7h
Measures and Construction: G3.2
Vectors: G5.1
32. Congruency and similarity / 3 / C, B, A, A* / Properties of angles and shapes: G1.8
Geometrical reasoning and calculation: G2.3, G2.3h
Measures and Construction: G3.2h
33. Pythagoras’ theorem and trigonometry / 3 / C, B, A, A* / Working with numbers and the number system: N1.14h
Sequences, Functions and Graphs: N6.3h
Geometrical reasoning and calculation: G2.1, G2.1h, G2.2h
SUMMER TERM / 36. Further trigonometry / 3 / A, A* / Sequences, Functions and Graphs: N6.8h
Geometrical reasoning and calculation: G2.2h
Mensuration: G4.2h
34. Circle theorems / 3 / B, A, A* / Properties of angles and shapes: G1.5h
35. Non-linear graphs / 3 / D, C, B, A, A* / Expressions and Equations: N5.2h, N5.5h
Sequences, Functions and Graphs: N6.7h, N6.8h, N6.10h, N6.11h, N6.13
37. Transformations of graphs / 3 / B, A* / Sequences, Functions and Graphs: N6.9h
38. Vectors / 3 / A, A* / Vectors: G5.1h
JUNE: UNIT 3 EXAM
REVISION: 3 GUIDED HOURS
JUNE: UNIT 2 EXAM (OPTION B)


DETAIL

Chapter 1 Data collection GLH: 3 hours

S1 Understand and use the statistical problem solving process which involves

·  specifying the problem and planning

·  collecting data

·  processing and presenting the data

·  interpreting and discussing the results.

S2.1 Types of data: qualitative, discrete, continuous. Use of grouped and ungrouped data.

S2.2 Identify possible sources of bias.

S2.3 Design an experiment or survey.

S2.4 Design data collection sheets distinguishing between different types of data.

S2.5 Extract data from printed tables and lists.

S3.1 Design and use two-way tables for grouped and ungrouped data.

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework / Extension
AQA Modular specification reference / AQA GCSE Maths Higher sets Student Book; Higher sets Teacher Guide / Higher sets Teacher Guide / Higher sets Practice Book / A-A* Practice Book
S1 / Learn about the data handling cycle
Know how to write a hypothesis / D / Section 1.1 / Formulating a hypothesis that cannot be tested.
Thinking that a hypothesis is not valuable if it is eventually proved false. / Section 1.1
S2.4 / Know where to look for information / D / Section 1.2 / Not realising that data collected by a third party (even if the results of a survey or experiment) is classed as secondary data. / Section 1.2
S2.1 / Be able to identify different types of data / D / Section 1.3 / 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). / Section 1.3
S2.4 / Work out methods for recording data that can take a wide range of values / D / Section 1.4 / Using overlapping class intervals.
Recording data which is on the boundary of a class interval in the wrong class. / Section 1.4
S2.5, S3.1 / Work out methods for recording related data / D / Section 1.5 / Not checking that the totals in two-way tables add up. / Section 1.5
S2.2, S2.3, S2.4 / Learn how to write good questions to find out information / C / Section 1.6 / Using overlapping classes, or gaps between classes, for response options. / Section 1.6
S2.4 / Know the techniques to use to get a reliable sample / C / Section 1.7 / Mistaking biased samples for random samples. / Section 1.7
S2.4 / Know how to take a stratified sample / A, A* / Section 1.8 / Inaccurately calculating the sampling fraction.
Incorrectly rounding. / Section 1.8 / Section 1.1


Chapter 2 Fractions, decimals and percentages GLH: 3 hours

N1.14 Use calculators effectively and efficiently, including statistical functions.

N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.

N2.6 Interpret fractions, decimals and percentages as operators.

N2.7 Calculate with fractions, decimals and percentages.

Chapter 7 Ratio and proportion

N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.

N3.2 Divide a quantity in a given ratio.

N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.

N3.3h Repeated proportional change. Direct and indirect proportion and exponential growth.

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework / Extension
AQA Modular specification reference / AQA GCSE Maths Higher sets Student Book; Higher sets Teacher Guide / Higher sets Teacher Guide / Higher sets Practice Book / A-A* Practice Book
N2.6, N2.7 / Find a fraction of an amount with a calculator in complex situations / D / Section 2.1 / Incorrectly inputting numbers on the calculator.
Being unsure of what to work out when a fraction calculation is set in context.
/ GPW 2.1 / Section 2.1
N2.7 / Write one quantity as a fraction of another / D / Section 2.2 / Not making the denominator the total in questions involving a number of quantities.
Working with quantities in different units.
Incorrectly cancelling down. / GPW 2.2 / Section 2.2
N1.14 / Use the fraction key on a calculator with mixed numbers / D, C / Section 2.3 / Not recognising or know how to use the fraction key on a calculator.
Misinterpreting a mixed number on a calculator display. / Section 2.3
N2.5, N2.7 / Write one quantity as a percentage of another
Write one quantity as a percentage of another in more complex situations / D, C / Section 2.4 / Not using the original amount as the denominator, when finding a percentage difference.
Working with quantities in different units. / Section 2.4
N2.6, N2.7 / Calculate a percentage increase or decrease
Perform calculations using VAT / D / Section 2.5 / Giving the actual increase/decrease as the answer when the amount after the increase/decrease is what is required.
Using the multiplier as 1.5 rather than 1.05 for an increase of 5%. / Section 2.5
N2.7 / Understand and use the retail prices index
Understand and use the retail prices index in more complex situations / D, C / Section 2.6 / Using a previously found price instead of the base year price. / GPW 2.6 / Section 2.6
N3.1, N3.3 / Use a ratio in practical situations / D / Section 7.1 / Not multiplying or dividing all quantities by the same amount when scaling quantities up or down.
Simplifying ratios without ensuring the quantities are in the same units. / GPW 7.1 / Section 7.1
N3.1, N3.3 / Write a ratio as a fraction
Use a ratio to find one quantity when the other is known / D, C / Section 7.2 / Turning a ratio into a fraction (e.g. the ratio 4 : 5 becomes ).
Failing to find the value of the unit fraction in more complex problems. / GPW 7.2 / Section 7.2
N3.3 / Write a ratio in the form 1 : n or n : 1 / C / Section 7.3 / Ignoring different units in a ratio (e.g. simplifying 2 days : 15 hours to 1 : 7½) .
Giving a ratio as 1 : n when n : 1 is asked for. / Section 7.3
N3.2, N3.3 / Share a quantity in a given ratio
Solve word problems involving ratio / D, C / Section 7.4 / Not multiplying both sides of the ratio by the same number.
Giving an answer without considering the context. / GPW 7.4 / Section 7.4
N3.3 / Understand direct proportion
Solve proportion problems, including using the unitary method
Work out which product is the better buy / D, C / Section 7.5 / Not always seeing the relationships between numbers (e.g. if the cost of 4 items is given, and the price of 8 is asked for).
Not making the units the same for each item. / GPW 7.5 / Section 7.5
N3.3 / Understand inverse proportion / C, B / Section 7.6 / Dividing instead of multiplying when finding the time taken for fewer people. / Section 7.6
N3.3, N3.3h / Write and use an equation to solve proportion problems / A / Section 7.7 / Writing the initial statement y = kx or y = kx2 incorrectly.
Forgetting to substitute the found value of k into the original statement. / GPW 7.7 / Section 7.7 / Section 3.1, 3.2
N3.3, N3.3h / Write and use an equation to solve inverse proportion problems / A / Section 7.8 / Writing the initial statement y = or y = etc. incorrectly.
Forgetting to substitute the found value of k into the original statement. / GPW 7.8 / Section 7.8 / Section 3.3


Chapter 3 Interpreting and representing data GLH: 3 hours

S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals.

S3.2h Histograms with unequal class intervals, box plots, cumulative frequency diagrams, relative frequency diagrams.

S4.2 Look at data to find patterns and exceptions.

S4.3 Recognise correlation and draw and/or use lines of best fit by eye, understanding what they represent.