Longman AQA GCSE Maths 1-Year MODULAR Scheme of Work – Middle Sets taking 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. Blue type shows content that will only be examined at Higher Tier GCSE.

8. Middle sets students are often entered at Higher for Unit 1 and Unit 2, and at Foundation for Unit 3. A ‘good Grade C’ should be achievable by this route’.

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


DETAIL

Chapter 1 Data collection GLH: 3 hours [H]

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
AQA Modular specification reference / AQA GCSE Maths Middle sets Student Book; Middle sets Teacher Guide / Middle sets Teacher Guide / Middle sets 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). / Section 1.3
S2.4 / Work out methods for gathering data efficiently / 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
S2.4, S2.5 / 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
S2.5, 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 Fractions, decimals and percentages GLH: 3 hours [H]

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

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.

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework
AQA Modular specification reference / AQA GCSE Maths Middle sets Student Book; Middle sets Teacher Guide / Middle sets Teacher Guide / Middle sets Practice Book
N2.7 / Find a fraction of an amount with a calculator
Find a fraction of an amount with a calculator in more complex situations / E, 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
Use the fraction key on a calculator with mixed numbers / E, D / 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
N2.7 / Find a percentage of an amount with a calculator
Find percentages of amounts in more complex situations / E, D / Section 2.4 / 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 2.4
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 2.5 / Not using the original amount as the denominator, when finding a percentage difference.
Working with quantities in different units. / Section 2.5
N2.6, N2.7 / Calculate a percentage increase or decrease / D / Section 2.6 / 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 2.6
N2.7 / Understand and use a retail prices index
Understand and use a retail prices index in more complex situations / D, C / Section 2.7 / Using a previously found price instead of the base year price. / GPW 2.7 / Section 2.7
N3.1, N3.2 / Simplify a ratio to its lowest terms
Use a ratio in practical situations / E, D / Section 7.1 / 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 7.1a, b / 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) . / GPW 7.3 / Section 7.3
N3.3 / Share a quantity in a given ratio / D, C / Section 7.4 / Forgetting to work out the total number of parts first.
Using a ratio as a fraction. / GPW 7.4 / Section 7.4
N3.3 / Solve word problems involving ratio / C / Section 7.5 / Not multiplying both sides of the ratio by the same number.
Giving an answer without considering the context. / Section 7.5
N3.3 / Understand direct proportion
Solve proportion problems, including using the unitary method / D / Section 7.6 / 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). / Section 7.6
N3.3 / Work out which product is the better buy / D / Section 7.7 / Not making the units the same for each item.
Comparing unlike unit rates (e.g. price per gram for one item but amount for 1p for the other). / GPW 7.7 / Section 7.7
N3.3 / Solve word problems involving direct and inverse proportion
Understand inverse proportion / D, C, B / Section 7.8 / Dividing by the wrong quantity in conversion problems. / GPW 7.8 / Section 7.8


Chapter 3 Interpreting and representing data GLH: 3 hours [H]

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.

S4.2 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.

Learning objectives / Grade / Resource / Common mistakes and misconceptions / Support and homework
AQA Modular specification reference / AQA GCSE Maths Middle sets Student Book; Middle sets Teacher Guide / Middle sets Teacher Guide / Middle sets Practice Book
S3.2 / Draw a pie chart / E / Section 3.1 / 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. / GPW 3.1 / Section 3.1
S3.2 / Draw stem-and-leaf diagrams / D / Section 3.2 / Forgetting to put a key and order the leaves.
Forgetting to recombine the stem and leaf and just giving the leaf as the value. / Section 3.2
S3.2, S4.2 / Draw a scatter diagram on a given grid
Interpret points on a scatter diagram / D / Section 3.3 / Assuming that all the plotted points must be joined with a line.
Drawing the diagram without spending time working out the best scale. / Section 3.3
S4.3 / Draw a line of best fit on a scatter diagram
Describe types of correlation
Use the line of best fit / D, C / Section 3.4 / Trying to make the line of best fit go through the origin, rather than drawing it appropriately.
Not appreciating correlation in terms of ‘positive’ and ‘negative’. / Section 3.4
S3.2 / Draw frequency diagrams for grouped data / D / Section 3.5 / Using grouped labels on the data axes (e.g. 15–20, rather than the ends of the bar being clearly marked with a 15 at one end and a 20 at the other end). / Section 3.5
S3.2 / Draw frequency polygons for grouped data / C / Section 3.6 / Using a grouped label on the horizontal axis rather than a continuous scale.
Plotting the upper bound instead of the mid-point. / GPW 3.6 / Section 3.6


Chapter 4 Range and averages GLH: 3 hours [H]