AQA GCSE Maths Schemes of Work Writing Brief D R a F T s2

Longman AQA GCSE Mathematics Two-year Modular Scheme of Work – Starting with Unit 1 – for Foundation sets

OVERVIEW

Notes to Teacher:

1. At a minimum, aim for completion of Chapters 1–3 by the end of Year 9.

2. At a minimum, aim for completion of Chapters 4–9 by the October half-term of Year 10.

3. The assumption is that the March and June exams are at the beginning of March and June respectively.

4. Unit 2 revision will need to include the earlier work on ratio (Chapters 4 and 10).

Chapter / Teaching hours / Grades / AQA Modular specification reference
Y9 SUMMER TERM / UNIT 1: Statistics and Number
1. Data collection / 5 / F, E, D, C / The Data Handling Cycle: S1
Data Collection: S2.1, S2.2, S2.3, S2.4
Data presentation and analysis: S3.1
2. Interpreting and representing data 1 / 3 / G, F, C / Data presentation and analysis: S3.2
Data Interpretation: S4.1, S4.4
3. Number skills 1 / 4 / G, F, E, D / Working with numbers and the number system: N1.1, N1.2, N1.3, N1.4, N1.5, N1.14
Fractions, Decimals and Percentages: N2.1, N2.3, N2.7
Measures and Construction: G3.4
4. Fractions, decimals, percentages and ratio / 5 / G, F, E, D, C / Fractions, Decimals and Percentages: N2.5, N2.6, N2.7
Ratio and Proportion: N3.1, N3.3
Y10 AUTUMN TERM
5. Interpreting and representing data 2 / 5 / F, E, D, C / Data presentation and analysis: S3.2
Data Interpretation S4.1, S4.2, S4.3
6. Range and averages / 4 / G, F, E / Data presentation and analysis: S3.3
Data Interpretation: S4.1
7. Probability 1 / 4 / G, F, E, D / Probability: S5.1, S5.2, S5.3, S5.4
8. Probability 2 / 4 / E, D, C / Data Collection: S2.5
Data presentation and analysis: S3.1, S3.2
Probability: S5.2, S5.5h, S5.7, S5.8, S5.9
9. Range, averages and conclusions / 4 / F, E, D, C / Data presentation and analysis: S3.3
Data Interpretation: S4.1, S4.4
10. Ratio and proportion / 4 / D, C / Ratio and Proportion: N3.1, N3.2, N3.3
UNIT 2: Number and Algebra
11. Number skills 2 / 5 / G, F, E, D, C / Working with numbers and the number system: N1.2, N1.3, N1.4, N1.5
12. Multiples, factors, powers and roots / 6 / G, F, E, D, C / Working with numbers and the number system: N1.6, N1.7, N1.8, N1.9
13. Basic rules of algebra / 6 / F, E, D, C / The Language of Algebra: N4.1
Expressions and Equations: N5.1
14. Fractions / 7 / G, F, E, D, C / Working with numbers and the number system: N1.3
Fractions, Decimals and Percentages: N2.1, N2.2, N2.7
Y10 SPRING TERM
15. Decimals / 5 / F, E, D, C / Working with numbers and the number system: N1.2
Fractions, Decimals and Percentages: N2.3, N2.4
16. Equations and inequalities / 5 / F, E, D, C / Expressions and Equations: N5.4, N5.7
UNIT 1 REVISION FOR MARCH EXAM (6 HOURS)
17. Indices and formulae / 6 / G, F, E, D, C / Working with numbers and the number system: N1.8, N1.9
The Language of Algebra: N4.2
Expressions and Equations: N5.6
18. Percentages / 5 / E, D, C / Fractions, Decimals and Percentages: N2.5, N2.7, N2.7h
19. Sequences and proof / 6 / G, F, E, D, C / Expressions and Equations: N5.9
Sequences, Functions and Graphs: N6.1, N6.2
Y10 SUMMER TERM
20. Coordinates and linear graphs / 7 / G, F, E, D, C / Sequences, Functions and Graphs: N6.3, N6.4, N6.11, N6.12
UNIT 2 REVISION FOR JUNE EXAM (8 HOURS)
Y11 AUTUMN TERM / UNIT 3: Geometry and Algebra
21. Number skills revisited / 3 / Working with numbers and the number system: N1.3, N1.4, N1.14
Fractions, decimals and Percentages: N2.1, N2.5, N2.7
Ratio and Proportion: N3.1
22. Angles / 5 / G, F, E, D, C / Properties of angles and shapes: G1.1, G1.2
Measures and Construction: G3.6, G3.8
23. Measurement 1 / 4 / G, F, E / Working with numbers and the number system: N1.3
Measures and Construction: G3.3, G3.5
24. Triangles and constructions / 4 / G, E, D, C / Properties of angles and shapes: G1.2, G1.8
Measures and Construction: G3.9, G3.10
25. Equations, formulae and proof / 3 / D, C / The Language of Algebra: N4.2
Expressions and Equations: N5.1, N5.4, N5.6
Geometrical reasoning and calculation: G2.3
U1/U2 REVISION FOR NOVEMBER RE-SITS (5 HOURS)
26. Quadrilaterals and other polygons / 6 / G, F, E, D, C / Expressions and Equations: N5.4
Sequences, Functions and Graphs: N6.3
Properties of angles and shapes: G1.2, G1.3, G1.4, G1.6
27. Units and scale / 2 / E / Measures and Construction: G3.1, G3.4
28. Perimeter, area and volume / 6 / F, E, D, C / Mensuration: G4.1, G4.4
29. 3-D objects / 2 / G, F, E, D / Geometrical reasoning and calculation: G2.4
30. Reflection, translation and rotation / 5 / G, F, E, D, C / Properties of angles and shapes: G1.7
Vectors: G5.1
Y11 SPRING TERM / 31. Circles and cylinders / 7 / G, D, C / Properties of angles and shapes: G1.5
Mensuration: G4.1h, G4.3, G4.4
32. Measurement 2 / 3 / D, C / Working with numbers and the number system: N1.4, N1.13h
Measures and Construction: G3.4, G3.7
33. Enlargement / 3 / F, E, D / Properties of angles and shapes: G1.7
Measures and Construction: G3.2
34. Trial and improvement / 2 / D, C / Working with numbers and the number system: N1.14
Expressions and Equations: N5.8
U1/U2 REVISION FOR MARCH RE-SITS (5 HOURS)
35. Quadratic graphs / 5 / D, C / Sequences, Functions and Graphs: N6.12, N6.13
36. Constructions and loci / 4 / C / Measures and Construction: G3.10, G3.11
37. Pythagoras’ theorem / 6 / C / Geometrical reasoning and calculation: G2.1
UNIT 3 REVISION FOR JUNE EXAM (19 HOURS)
Y11 SUMMER TERM

[Full detail begins on next page]
Chapter 1 Data collection Time: 5 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.

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

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework / Extra support
AQA Modular specification reference / AQA GCSE Maths Foundation sets Student Book; Foundation sets Teacher Guide / Foundation sets Teacher Guide / Foundation sets Practice Book / G-F 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
S2.3, 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). / GPW 1.3 / Section 1.3
S2.4 / Work out methods for gathering data efficiently / F, E / Section 1.4 / Using shortcuts in the tallying process – counting up the items in each class, rather than tallying items one by one. / Section 1.4 / Section 1.1
S2.4 / Work out methods for gathering data that can take a wide range of values / D / Section 1.5 / Using overlapping class intervals.
Recording data which is on the boundary of a class interval in the wrong class. / Section 1.5
S3.1 / Work out methods for recording related data / D / Section 1.6 / Not checking that the totals in two-way tables add up. / Section 1.6
S2.3, S2.4 / Learn how to write good questions to find out information / C / Section 1.7 / Using overlapping classes, or gaps between classes, for response options. / Section 1.7
S2.2, S2.3, S2.4 / Know the techniques to use to get a reliable sample / C / Section 1.8 / Mistaking biased samples for random samples. / Section 1.8

Chapter 2 Interpreting and representing data 1 Time: 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.

S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.

S4.4 Compare distributions and make inferences.

Chapter 3 Number skills 1 Time: 4 hours

N1.1 Understand integers and place value to deal with arbitrarily large positive numbers.

N1.2 Add, subtract, multiply and divide any number.

N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.

N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.

N1.5 Order rational numbers.

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

N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.

N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.

N2.7 Calculate with fractions, decimals and percentages.

G3.4 Convert measurements from one unit to another.

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework / Extra support
AQA Modular specification reference / AQA GCSE Maths Foundation sets Student Book; Foundation sets Teacher Guide / Foundation sets Teacher Guide / Foundation sets Practice Book / G-F Practice Book
N1.1, N1.5 / Read and write whole numbers in figures and words
Use place value
Compare and order whole numbers / G / Section 3.1 / Failing to understand the concept of place value and so reading 204 as 24 (20, 4 twenty-four). / Section 3.1 / Section 3.1
N1.5, N2.3 / Read and write decimal numbers in figures and in words
Use decimal notation and place value
Compare and order decimal numbers / F, E / Section 3.2 / Thinking that the more digits in a number, the greater the value of the number. / GPW 3.2 / Section 3.2 / Section 3.2
N1.4 / Round positive numbers to the nearest 10, 100 or 1000
Round decimals to the nearest whole number
Round decimals to a given number of decimal places
Round numbers to one significant figure / G, F, E / Section 3.3 / 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. / Section 3.3 / Section 3.3
G3.4 / Convert between different metric units of length, mass and capacity / F / Section 3.4 / Ignoring the different units when comparing measurements. / GPW 3.4 / Section 3.4 / Section 3.4
N2.1, N2.7 / Use fraction notation
Identify equivalent factions
Simplify fractions
Find fractions of quantities and measurements / G, F / Section 3.5 / Not understanding that the denominator of a fraction represents the ‘number of parts in the whole’. / GPW 3.5 / Section 3.5 / Section 3.5
N1.2, N1.3, N1.14 / Understand and use the order of operations
Use the four rules with whole numbers, decimals and fractions
Develop calculator skills and use a calculator effectively / G, F, E, D / Section 3.6 / Forgetting to use BIDMAS when using calculators to perform calculations. / Section 3.6 / Section 3.6

Chapter 4 Fractions, decimals, percentages and ratio Time: 5 hours

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.

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

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

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework / Extra support
AQA Modular specification reference / AQA GCSE Maths Foundation sets Student Book; Foundation sets Teacher Guide / Foundation sets Teacher Guide / Foundation sets Practice Book / G-F Practice Book
N2.5, N2.6, N2.7 / Find a percentage of an amount without using a calculator
Find a percentage of an amount with a calculator
Find percentages of amounts in more complex situations / F, E, D / Section 4.1 / Thinking that percentages over 100% cannot exist.
Treating a percentage such as 0.05% as though it were 5%.
Adding the percentage to the cost when finding a percentage increase (e.g. £315 + 15% VAT = £330). / Section 4.1 / Section 4.1
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 4.2 / Not using the original amount as the denominator, when finding a percentage difference.
Working with quantities in different units. / Section 4.2
N2.7 / Convert between fractions, decimals and percentages / G / Section 4.3 / Incorrectly multiplying numbers with one decimal place by 10, rather than 100, when converting a decimal to a percentage. / GPW 4.3 / Section 4.3 / Section 4.2
N2.7 / Understand and use a retail prices index
Understand and use a retail prices index in more complex situations / D, C / Section 4.4 / Using a previously found price instead of the base year price. / Section 4.4
N3.1, N3.3 / Simplify a ratio to its lowest terms
Use a ratio when comparing a scale model to the real-life object
Use a ratio in practical situations / E, D / Section 4.5 / Swapping over the numbers in the ratio (e.g. 2 : 5 becomes 5 : 2).
Simplifying ratios without ensuring the quantities are in the same units. / GPW 4.5 / Section 4.5
N3.1 / Write a ratio as a fraction
Use a ratio to find one quantity when the other is known / D, C / Section 4.6 / 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 4.6 / Section 4.6
N3.3 / Write a ratio in the form 1 : n or n : 1 / C / Section 4.7 / Ignoring different units in a ratio (e.g. simplifying 2 days : 15 hours to 1 : 7½) . / GPW 4.7 / Section 4.7

Chapter 5 Interpreting and representing data 2 Time: 5 hours