Download Year 11 - Heworth Grange

Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Year 11
Taught in year
9?
No
No of lessons
6
F, E, D, C
No
5
F, E, D, C
No
6
G, F, E, D, C
19. Sequences and
proof
25. Equations, formulae
and proof
No
6
G, F, E, D, C
No
3
D, C
22. Angles
Yes
5
G, F, E, D, C
24. Triangles and
constructions
26. Quadrilaterals and
other polygons
Yes
4
G, E, D, C
Yes
6
G, F, E, D, C
28. Perimeter, area and
volume
29. 3-D objects
Yes
6
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
Expressions and Equations: N5.9
Sequences, Functions and Graphs: N6.1, N6.2
The Language of Algebra: N4.2
Expressions and Equations: N5.1, N5.4, N5.6
Geometrical reasoning and calculation: G2.3
Properties of angles and shapes: G1.1, G1.2
Measures and Construction: G3.6, G3.8
Properties of angles and shapes: G1.2, G1.8
Measures and Construction: G3.9, G3.10
Expressions and Equations: N5.4
Sequences, Functions and Graphs: N6.3
Properties of angles and shapes: G1.2, G1.3, G1.4, G1.6
Mensuration: G4.1, G4.4
Yes
2
G, F, E, D
Geometrical reasoning and calculation: G2.4
30. Reflection,
translation and rotation
Yes
5
G, F, E, D, C
Properties of angles and shapes: G1.7
Vectors: G5.1
33. Enlargement
Yes
3
F, E, D
Properties of angles and shapes: G1.7
Measures and Construction: G3.2
31. Circles and
cylinders
Yes
7
G, D, C
Properties of angles and shapes: G1.5
Mensuration: G4.1h, G4.3, G4.4
37. Pythagoras’
theorem
Yes
6
C
Geometrical reasoning and calculation: G2.1
36. Constructions and
loci
Yes
4
C
Measures and Construction: G3.10, G3.11
34. Trial and
improvement
32. Measurement 2
No
2
D, C
No
3
D, C
Working with numbers and the number system: N1.14
Expressions and Equations: N5.8
Working with numbers and the number system: N1.4, N1.13h
Measures and Construction: G3.4, G3.7
13. Basic rules of
algebra
16. Equations and
inequalities
17. Indices and
formulae
© Pearson Education Limited 2010
The Language of Algebra: N4.1
Expressions and Equations: N5.1
Expressions and Equations: N5.4, N5.7
1
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
35. Quadratic graphs
21. Number skills
revisited
No
5
If time allows
D, C
Sequences, Functions and Graphs: N6.12, N6.13
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
REVISION FOR JUNE EXAMS
Linear GCSE and FSMQ Core
© Pearson Education Limited 2010
2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Year 11
Chapter 13 Basic rules of algebra
Time: 6 hours
N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation.
N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
Learning
objectives
Grade
Resource
Support and homework
Extra
support
F, E, D
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 13.1
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Writing m × 3 = m3.
Section
13.1
Section
13.1
F, E
Section 13.2
Failing to comprehend that x = 1x.
Combining unlike terms.
Section
13.2
Section
13.2
E
Section 13.3
Treating terms in m and in m as like terms
2
2
(e.g. simplifying 3m + m wrongly to 4m ).
GPW 13.3
Section
13.3
D
Section 13.4
Forgetting to multiply the second term in the
bracket by the term outside (e.g. expanding
2(x + 3) as 2x + 3), or ignoring minus signs
(e.g. writing 3(m – 2) as 3m + 6).
GPW 13.4
Section
13.4
AQA Linear
specification
reference
N4.1
N5.1
N5.1
N5.1
Write simple
expressions using
letters to represent
unknown numbers
Use the correct
notation in algebra
Simplify algebraic
expressions with
only one letter
Simplify algebraic
expressions by
collecting like
terms
Multiply together
two simple
algebraic
expressions
Multiply terms in a
bracket by a
number outside the
bracket
Multiply terms in a
bracket by a term
that includes a
letter
© Pearson Education Limited 2010
Common mistakes and misconceptions
2
3
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
N5.1
Simplify
expressions
involving brackets
D, C
Section 13.5
N5.1
Recognise factors
of algebraic terms
Simplify algebraic
expressions by
taking out common
factors
Multiply together
two algebraic
expressions with
brackets
Square a linear
expression
D
Section 13.6
C
Section 13.7
N5.1
© Pearson Education Limited 2010
Forgetting to multiply the second term in the
bracket by the term outside.
Getting the wrong signs when multiplying
negative values.
2
Not realising that x is a factor of x and x .
Not taking out the highest common factor.
Identifying the common factor but forgetting
to work out one of the terms inside the
bracket.
Confusing methods.
Forgetting to multiply pairs of terms.
4
Section
13.5
GPW 13.6
Section
13.6
GPW 13.7
Section
13.7
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 16 Equations and inequalities
Time: 5 hours
N5.4 Set up and solve simple linear equations.
N5.7 Solve linear inequalities in one variable and represent the solution set on a number line.
Learning
objectives
Grade
Resource
Solve equations
involving addition
or subtraction
Solve equations
involving
multiplication and
division
Solve two-step
equations
F, E
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 16.1
E, D
Section 16.2
N5.4
Write and solve
equations
E, D
Section 16.3
N5.4
Solve equations
involving brackets
D, C
Section 16.4
N5.4
Solve equations
with an unknown
on both sides
D, C
Section 16.5
AQA Linear
specification
reference
N5.4
N5.4
© Pearson Education Limited 2010
Common mistakes and misconceptions
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Not appreciating that an equation can be
written in different but equivalent formats
(e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7).
GPW
16.1a16.5a,
16.1b-16.5b
Section
16.1
Section
16.1
Not appreciating that an equation can be
written in different but equivalent formats
(e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7).
Incorrectly combining number work involving
fractions and decimals with equation
solving.
Not appreciating that an equation can be
written in different but equivalent formats
(e.g. 2a + 7 = 9 → 7 + 2a = 9 → 9 = 2a + 7).
Not following a question carefully when
writing an equation to represent a problem.
Forgetting to multiply the second term in the
bracket by the term outside.
Getting the wrong signs when multiplying
negative numbers.
Incorrectly simplifying after expanding the
bracket.
Introducing errors when there are a negative
number of unknowns on either side of the
equation.
GPW
16.1a16.5a,
16.1b-16.5b
Section
16.2
GPW
16.1a16.5a,
16.1b-16.5b
Section
16.3
GPW
16.1a16.5a,
16.1b-16.5b
Section
16.4
GPW
16.1a16.5a,
16.1b-16.5b
Section
16.5
5
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
N5.7
N5.7
Show inequalities
on number lines
Write down whole
number values for
unknowns in an
inequality
Solve simple
inequalities
© Pearson Education Limited 2010
E, D
Section 16.6
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.
Section
16.6
C
Section 16.7
Not reversing the sign when multiplying or
dividing by a negative.
Section
16.7
6
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 17 Indices and formulae
Time: 6 hours
N1.8 Index notation for squares, cubes and powers of 10.
N1.9 Index laws for multiplication and division of integer powers.
N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.6 Derive a formula, substitute numbers into a formula and change the subject of a formula.
Learning
objectives
Grade
Resource
Support and homework
Extra
support
G, F
AQA GCSE
Maths
Foundation
sets Student
Book;
Foundation
sets Teacher
Guide
Section 17.1
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Substituting the wrong values for letters.
Section
17.1
Section
17.1
E, D
Section 17.2
Not seeing the ‘general’ case.
E, D,
C
Section 17.3
Not realising that x means x , or that a number
divided by 1 gives the number itself (e.g. 6 ÷ 1
= 6).
Section
17.2
Section
17.3
C
Section 17.4
Forgetting that a letter on its own in a
2
calculation, such as p in p × p, is raised to the
power 1.
GPW 17.4
Section
17.4
F, E, D
Section 17.5
Incorrectly substituting values into expressions
(e.g. substituting a = 6 into the expression 4a,
GPW 17.5
Section
17.5
AQA Linear
specification
reference
N4.2, N5.6
N4.2, N5.6
N1.8, N4.2
N1.9
N4.2, N5.6
Substitute
numbers into a
simple formula
written in words
Use simple
formulae that are
written using
letters
Use algebra to
derive formulae
Use index
notation in
algebra
Use index
notation when
multiplying or
dividing algebraic
terms
Use index laws to
multiply and
divide powers in
algebra
Substitute
numbers to work
© Pearson Education Limited 2010
Common mistakes and misconceptions
1
7
Section
17.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
N4.2, N5.6
N5.6
out the value of
simple algebraic
expressions
Substitute
numbers into
expressions
involving brackets
and powers
Substitute
numbers into a
variety of
formulae
Changing the
subject of a
formula
writing 46 and assuming it is forty-six).
Ignoring BIDMAS.
E, D
Section 17.6
n
1
Not realising that 10 means n ÷ 10, or that 2 ×
GPW 17.6
Section
17.6
GPW 17.7
Section
17.7
1
6 means 2 of 6 = 3.
C
© Pearson Education Limited 2010
Section 17.7
Not using brackets or a clear division (e.g.
rewriting c = 2a + 5 as a = c − 5 ÷ 2).
Not using the inverse operation (e.g. x + y = z
becomes x = z + y).
8
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 19 Sequences and proof
Time: 6 hours
N5.9 Use algebra to support and construct arguments.
N6.1 Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.
th
N6.2 Use linear expressions to describe the n term of an arithmetic sequence.
Learning
objectives
Grade
Resource
G, F, E
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 19.1
E
Section 19.2
Expecting all sequences to have common
differences.
Looking at the first two numbers and
assuming that the rest follow this pattern.
E, D, C
Section 19.3
Mistaking x for 2x.
G, F,
E, C
Section 19.4
Not making the connection between the
structure of the physical pattern and the
form the nth term takes.
AQA Linear
specification
reference
N6.1
N6.1
N6.2
N6.2
Find the next term
in a sequence
Describe the termto-term rule for
continuing a
sequence
Find the next term
in a sequence
including negative
values
Continue
sequences by
finding differences
between
consecutive terms
Explain the termto-term rule
Find any term in a
sequence given
the nth term
Find the nth term
of a linear
sequence
Draw the next
pattern in a
sequence
Find the nth term
© Pearson Education Limited 2010
Common mistakes and misconceptions
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Section
19.1
Section
19.1
Expecting all sequences to ascend.
Looking at the first two numbers and
assuming that the rest follow this pattern.
2
9
GPW 19.2
Section
19.2
GPW 19.3
Section
19.3
Section
19.4
Section
19.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
N5.9
N5.9
for pattern
sequences
Show step-by-step
deduction when
solving problems
Use notation and
symbols correctly
Show something is
false using a
counter-example
© Pearson Education Limited 2010
E, D
Section 19.5
Not appreciating that a proof shows
something works for all values.
C
Section 19.6
Assuming that ‘number’ means positive
whole number.
Not identifying an appropriate counterexample.
10
Section
19.5
GPW 19.6
Section
19.6
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 25 Equations, formulae and proof
Time: 3 hours
N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
N5.4 Set up and solve simple linear equations.
N5.6 Derive a formula, substitute numbers into a formula.
G2.3 Justify simple geometrical properties.
Learning
objectives
Grade
Resource
Common mistakes and misconceptions
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
AQA Linear
specification
reference
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
G-F
Practice
Book
Foundation
sets
Practice
Book
Section
25.1, 25.2,
25.3
Algebra skills: expressions (N4.2, N5.1); brackets (N5.1); solving equations (N5.4); formulae (N5.6)
N5.4, N5.6
G2.3
Write your own
formulae and
equations
Set up and solve
equations
Substitute into a
formula to solve
problems
Change the subject
of a formula
Prove simple
results from
geometry
© Pearson Education Limited 2010
D, C
Section 25.1
Failing to consider the different terms of an
expression when changing the subject of a
formula (e.g. W = 12 x + 3 ⇒ 2W = x + 3).
GPW 25.1
Section
25.1
Not using brackets or a clear division (e.g.
rewriting c = 2a + 5 as a = c − 5 ÷ 2).
Not using the inverse operation (e.g. x + y =
z becomes x = z + y).
C
Section 25.2
Not laying out answers in an organised way.
Not providing reasons for each stage of the
working.
11
Section
25.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 22 Angles
Time: 5 hours
G1.1 Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex.
G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G3.6 Understand and use bearings.
G3.8 Measure and draw lines and angles.
Learning
objectives
Grade
Resource
G
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 22.1
G, F
F, E
AQA Linear
specification
reference
G1.1, G3.6
G1.1, G3.8
G1.1
Describe angles as
turns and in
degrees
Understand
clockwise and
anticlockwise
Know and use
compass directions
Use letters to name
angles
Recognise and
name types of
angles
Draw angles using
a protractor
Measure angles
using a protractor
Estimate the size of
an angle in degrees
Calculate angles on
a straight line and
angles around a
point
Recognise
vertically opposite
angles
© Pearson Education Limited 2010
Common mistakes and misconceptions
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Confusing clockwise and anticlockwise.
Section
22.1
Section
22.1
Section 22.2
Using the wrong scale on the protractor.
Section
22.2
Section
22.2
Section 22.3
Not realising that angles marked with the
same letter are equal.
Measuring rather than calculating angles.
Section
22.3
Section
22.3
12
GPW 22.3
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
G1.2
G3.6
Recognise
corresponding and
alternate angles
Calculate angles in
diagrams with
parallel lines
Use three-figure
bearing notation
Measure the
bearing from one
place to another
Plot a bearing
Calculate bearings
in diagrams
© Pearson Education Limited 2010
D
Section 22.4
Confusing alternate and corresponding
angles.
GPW 22.4
Section
22.4
E, D, C
Section 22.5
Confusing which angles need to be found.
Not realising that some of the angles asked
for can simply be read off the diagram.
GPW 22.5
Section
22.5
13
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 24 Triangles and constructions
Time: 4 hours
G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G1.8 Understand congruence and similarity.
G3.9 Draw triangles and other 2D shapes using a ruler and protractor.
G3.10 Use straight edge and a pair of compasses to do constructions.
Learning
objectives
Grade
AQA Linear
specification
reference
G1.2
G3.9, G3.10
G1.8
Recognise and
draw the four main
types of triangle
Solve angle
problems in
triangles
Solve angle
problems in
triangles involving
algebra
Draw triangles
accurately when
given the length of
all three sides
Draw triangles
accurately when at
least one angle is
given
Recognise and
explain how
triangles are
congruent
© Pearson Education Limited 2010
G, E,
D
Resource
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 24.1
Common mistakes and misconceptions
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 questions.
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW 24.1
Section
24.1
Section
24.1
E, D
Section 24.2
Inaccurately using a protractor or
compasses.
Not completing the triangle by drawing the
third side.
Rubbing out construction lines.
Section
24.2
C
Section 24.3
Thinking that two triangles are congruent
when they are not (due to the relative
positions of side lengths or angles being in
different positions).
Section
24.3
14
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 26 Quadrilaterals and other polygons
Time: 6 hours
N5.4 Set up and solve simple linear equations.
N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including geometric information.
G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G1.3 Calculate and use the sums of the interior and exterior angles of polygons.
G1.4 Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.
G1.6 Recognise reflection and rotation symmetry of 2D shapes.
Learning
objectives
Grade
Resource
E, D
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 26.1
F, E, D
Section 26.2
Giving correct answers but not explaining
the properties used.
D, C
Section 26.3
Forgetting the formula for the exterior angles
of a polygon and how to apply it.
GPW 26.3
Section
26.3
D, C
Section 26.4
Incorrectly splitting the polygon into
triangles.
GPW 26.4
Section
26.4
AQA Linear
specification
reference
G1.2, N5.4
G1.2, G1.4
G1.3
G1.3
Calculate interior
angles of
quadrilaterals
Solve angle
problems in
quadrilaterals
involving algebra
Identify
quadrilaterals given
their properties
Make quadrilaterals
from two triangles
Use parallel lines
and other angle
properties in
quadrilaterals
Use the exterior
angles of polygons
to solve problems
Calculate interior
angles of polygons
Solve more
complex angle
problems involving
© Pearson Education Limited 2010
Common mistakes and misconceptions
Working things out mentally without writing
down the calculations.
Not showing full working for the algebra
questions.
15
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW 26.1
Section
26.1
Section
26.2
Section
26.1
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
N6.3
G1.6
exterior and interior
angles of polygons
Plot all points of a
quadrilateral given
geometric
information
Find the mid-point
of a line segment
Recognise and
draw lines of
symmetry in simple
shapes
Recognise
rotational symmetry
in 2-D shapes
© Pearson Education Limited 2010
E
Section 26.5
G, F
Section 26.6
Plotting the numbers on the x- and y-axes
the wrong way round.
Not recognising, or be able to name, some
of the less common quadrilaterals (e.g. the
kite and trapezium).
Averaging only the x- or y-coordinate and
not both when finding the mid-point.
Incorrectly thinking that, for example, a
rectangle has 4 lines of symmetry, a kite has
2 lines of symmetry, and a parallelogram
has 2 lines of symmetry.
16
Section
26.5
Section
26.6
Section
26.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 28 Perimeter, area and volume
Time: 6 hours
G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles.
G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.
Learning
objectives
Grade
Resource
F, E, D
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 28.1
D
Section 28.2
Incorrectly calculating missing lengths.
Adding areas instead of subtracting.
E, D, C
Section 28.3
Confusing volume and surface area.
AQA Linear
specification
reference
G4.1
G4.1
G4.4
Find the perimeter
and area of
rectangles,
parallelograms,
triangles and
trapezia
Find the perimeter
and area of
compound shapes
Find the volume
and surface area of
a prism
© Pearson Education Limited 2010
Common mistakes and misconceptions
Not making rough estimates of areas as a
check to avoid arithmetical errors.
Incorrectly converting between units.
Using measurements in different units.
17
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW 28.1
Section
28.1
Section
28.1, 28.2
Section
28.2
GPW 28.3
Section
28.3
Section
28.3
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 29 3-D objects
Time: 2 hours
G2.4 Use 2D representations of 3D shapes.
Learning
objectives
Grade
Resource
G, F
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 29.1
E, D
Section 29.2
AQA Linear
specification
reference
G2.4
G2.4
Recognise the net
of a 3-D object
Draw the net of a
3-D object
Make a drawing of
a 3-D object on
isometric paper
Draw plans and
elevations of 3-D
objects
Identify planes of
symmetry of 3-D
objects
© Pearson Education Limited 2010
Common mistakes and misconceptions
Incorrectly visualising 3-D objects in 2-D.
Missing out hidden cubes when converting
from a 3-D view to a plan or elevation.
Using isometric paper in landscape not in
portrait.
18
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Section
29.1
Section
29.1
Section
29.1
Section
29.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 30 Reflection, translation and rotation
Time: 5 hours
G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that
are preserved under particular transformations.
G5.1 Understand and use vector notation for translations.
Learning
objectives
Grade
AQA Linear
specification
reference
G1.7
G1.7, G5.1
G1.7
Resource
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 30.1
Draw a reflection of
a shape in a mirror
line
Draw reflections on
a coordinate grid
Describe reflections
on a coordinate
grid
Translate a shape
on a grid
Use column vectors
to describe
translations
G, F,
E, D, C
D, C
Section 30.2
Draw the position
of a shape after
rotation about a
centre
Describe a rotation
fully giving the size
and direction of
turn and the centre
of rotation
D, C
Section 30.3
© Pearson Education Limited 2010
Common mistakes and misconceptions
Drawing the image a different distance from
the mirror line than the object.
Incorrectly identifying mirror lines parallel to
the x- or y-axis.
Forgetting what the two values in the
column vector mean.
Using coordinate notation instead of vector
notation.
Confusing the terms ‘transformation’ and
‘translation’.
Working out the angle of rotation incorrectly.
Turning in the wrong direction.
19
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW 30.1
Section
30.1
Section
30.1
Section
30.2
GPW 30.3
Section
30.3
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 33 Enlargement
Time: 3 hours
G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that
are preserved under particular transformations.
G3.2 Understand the effect of enlargement for perimeter, area and volume of shapes and solids.
Learning
objectives
Grade
Resource
F, E, D
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 33.1
AQA Linear
specification
reference
G1.7, G3.2
Identify the scale
factor of an
enlargement
Enlarge a shape on
a grid
Enlarge a shape
using a centre of
enlargement
© Pearson Education Limited 2010
Common mistakes and misconceptions
Inaccurately counting squares.
Adding the scale factor instead of multiplying
by the scale factor.
Not using the centre of enlargement.
20
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW
33.1a,
33.1b
Section
33.1
Section
33.1
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 31 Circles and cylinders
Time: 7 hours
G1.5 Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
G4.1h Extend to other compound shapes. [Note: Extending work on circumference and area of circles to include semicircles, quadrants, etc. will help Foundation tier students
attempt C-grade questions towards the end of a Foundation paper.]
G4.3 Calculate circumferences and areas of circles.
G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.
Learning
objectives
Grade
Resource
G
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 31.1
D, C
Section 31.2
Not multiplying by 2 when the radius is given
and the diameter is needed.
D, C
Section 31.3
Multiplying by π before squaring.
Section
31.3
C
Section 31.4
Multiplying by π before squaring.
Section
31.4
AQA Linear
specification
reference
G1.5
G1.5, G4.1h,
G4.3
G1.5, G4.1h,
G4.3
G4.3, G4.4
Recall the
definition of a circle
and the meaning of
related terms
Calculate the
circumference of a
circle
Calculate the
perimeters of
compound shapes
involving circles or
parts of circles
Calculate the area
of a circle
Calculate the areas
of compound
shapes involving
circles or parts of
circles
Calculate the
volume of a
cylinder
Solve problems
involving the
surface area of
© Pearson Education Limited 2010
Common mistakes and misconceptions
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Section
31.1
Section
31.1
Forgetting to divide by 2 when the diameter
is given and the radius is needed.
21
GPW 31.2
Section
31.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
cylinders
Chapter 37 Pythagoras’ theorem
Time: 6 hours
G2.1 Use Pythagoras’ theorem.
Learning
objectives
Grade
Resource
Understand
Pythagoras’
theorem
Calculate the
hypotenuse of a
right-angled
triangle
Solve problems
using Pythagoras’
theorem
Calculate the
length of a shorter
side in a rightangled triangle
Solve problems
using Pythagoras’
theorem
C
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 37.1
C
Section 37.2
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.
GPW 37.2
Section
37.2
C
Section 37.3
GPW 37.3
Section
37.3
Calculate the
length of a line
segment AB
C
Section 37.4
Not correctly identifying the hypotenuse.
Forgetting to take the square root to find the
final answer.
Forgetting that Pythagoras’ theorem only
applies to right-angled triangles.
Not identifying the appropriate information
when problems are set in context.
Not being able to identify the position of the
right angle.
Subtracting instead of adding the two pairs
of coordinates.
AQA Linear
specification
reference
G2.1
G2.1
G2.1
G2.1
© Pearson Education Limited 2010
Common mistakes and misconceptions
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Section
37.1
Section
37.1
2
Forgetting that x means x × x, not x × 2.
22
Section
37.4
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 36 Constructions and loci
Time: 4 hours
G3.10 Use straight edge and a pair of compasses to do constructions.
G3.11 Construct loci.
Learning
objectives
Grade
Resource
C
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 36.1
C
Section 36.2
AQA Linear
specification
reference
G3.10
G3.11
Construct the
perpendicular
bisector of a line
segment
Construct the
bisector of an angle
Construct loci
Solve locus
problems, including
the use of bearings
© Pearson Education Limited 2010
Common mistakes and misconceptions
Failing to keep the settings of compasses
constant.
Rubbing out construction lines.
Not using compasses.
Confusing a distance from a point with the
distance from a line.
Making inaccurate constructions.
Shading the wrong region.
23
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW 36.1
Section
36.1
Section
36.1
Section
36.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 34 Trial and improvement
Time: 2 hours
N1.14 Use calculators effectively and efficiently.
N5.8 Use systematic trail and improvement to find approximate solutions of equations where there is no simple analytical method of solving them.
Learning
objectives
Grade
Resource
N1.14
Use a calculator
efficiently
D
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 34.1
N5.8
Use trial and
improvement to
find solutions to
equations
C
Section 34.2
AQA Linear
specification
reference
© Pearson Education Limited 2010
Common mistakes and misconceptions
Including brackets unnecessarily in
calculations.
Not giving answers as decimals when
questions do not ask for an alternative.
Not checking the mid-point to determine
which of two values is correct (e.g. choosing
between x = 3.3 and x = 3.4 based on the
value of the function and the desired
output).
Using the value of the equation as the
answer rather than the value of the variable.
24
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW
34.1/34.2
Section
34.1
Section
34.1
GPW
34.1/34.2
Section
34.2
Section
34.1
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 32 Measurement 2
Time: 3 hours
N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.
N1.13h Calculate and use upper and lower bounds. [Note: It is reasonable to expect a Foundation candidate to understand that measures given to the nearest whole number
can be inaccurate by up to half a unit either way. This also links to the concept of rounding (N1.4).]
G3.4 Convert measurements from one unit to another.
G3.7 Understand and use compound measures.
Learning
objectives
Grade
Resource
D, C
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 32.1
C
Section 32.2
D
Section 32.3
AQA Linear
specification
reference
G3.4, G3.7
N1.4, N1.13h
G3.7
Convert between
different units of
area
Convert between
different units of
volume
Recognise that
measurements
given to the
nearest whole unit
may be inaccurate
by up to one half
unit in either
direction
Calculate average
speeds
© Pearson Education Limited 2010
Common mistakes and misconceptions
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW
32.1/32.2
Section
32.1
Section
32.1
Difficulty comprehending the definition of the
upper bound, since, for example, 146.5
rounds to 147.
GPW
32.1/32.2
Section
32.2
Section
32.1
Not remembering the formulae.
Confusing the decimal parts of an hour with
hours and minutes (e.g. using 1 hour 45
minutes as 1.45 hours).
GPW 32.3
Section
32.3
Section
32.2
Multiplying by 100 when converting from m
3
to cm .
25
3
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 35 Quadratic graphs
Time: 5 hours
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations.
N6.13 Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.
Learning
objectives
Grade
Resource
D, C
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Section 35.1
C
Section 35.2
AQA Linear
specification
reference
N6.12, N6.13
N6.13
Draw quadratic
graphs
Identify the line of
symmetry of a
quadratic graph
Draw and interpret
quadratic graphs in
real-life contexts
Use a graph to
solve quadratic
equations
© Pearson Education Limited 2010
Common mistakes and misconceptions
Drawing the bottom of the graph flat when a
graph has its vertex between two plotted
points.
Forgetting to write down all the solutions.
26
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
GPW 35.1
Section
35.1
Section
35.1
Section
35.2
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
Chapter 21 Number skills revisited
Time: 3 hrs
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.
N1.14 Use calculators effectively and efficiently.
N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.
N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
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.
Learning
objectives
Grade
AQA Linear
specification
reference
Understand
equivalent fractions
Simplify a fraction
by cancelling all
common factors
Recognise that
each terminating
decimal is a
fraction
Convert simple
fractions to
percentages and
vice versa
Use percentages to
compare
proportions
Understand
‘reciprocal’ as
multiplicative
inverse
Use ratio notation
Use brackets and
the hierarchy of
© Pearson Education Limited 2010
G, F,
E, D
Resource
Common mistakes and misconceptions
AQA GCSE
Maths
Foundation sets
Student Book;
Foundation sets
Teacher Guide
Chapter 21
27
Support and homework
Extra
support
Foundation
sets
Teacher
Guide
Foundation
sets
Practice
Book
G-F
Practice
Book
Chapter 21
Section
21.1
Longman AQA GCSE Maths Two-year Linear Scheme of Work for Foundation sets
operations
Add, subtract,
multiply and divide
integers
Use calculators
effectively and
efficiently; use
function keys for
squares
Use inverse
operations
Round to the
nearest integer, to
one significant
figure and to one,
two or three
decimal places
Give solutions in
the context of the
problem to an
appropriate degree
of accuracy
© Pearson Education Limited 2010
28