Download Higher Level Two Tier GCSE Mathematics

GCSE EDEXCEL Linear Higher Tier SOW for W1
Functional Maths:
Functional maths must be embedded in all lessons throughout Year 10 and Year 11 – many of the new exam style questions will be functional maths
based.
The interactive textbooks have some good functional maths questions that can be used in lessons.
Functional maths tasks are hyperlinked on the SOW and can be printed directly from there – these tasks must be carried out.
Financial Capability:
All year 10 will have 4 financial capability tasks. There is one task per half term.
These are detailed below and hyperlinked to the appropriate folder. Please familiarise yourself with the content prior to delivery.
There is one per half term – it des not really matter where in the half term they are delivered; but they MUST be delivered.
First half of Autumn Term – Financial Capability task 1
Second half of Autumn Term – Financial Capability task 2
Spring Term – Financial Capability task 3
Summer Term – Financial Capability task 4
Investigations:
Using and applying mathematics is done throughout the lessons and SOW in Year 10 and Year 11; however – there are three investigations to be
carried out during Year 10 – one per term. They can be completed at any time during the term; but towards the end of each term is usually
preferable. The investigations are “Borders”, Number Stairs and Manhattan Cops
GCSE Mathematics - Medium Term Plan
GCSE EDEXCEL Linear Higher Tier SOW for W1
YEAR 10
The number of lessons allocated is a guide. It is important to enrich the curriculum and ensure Functional Mathematics is embedded throughout the topics.
Financial capability task 1 and task2 must be covered during the autumn term (Click on task for hyperlink)
Investigation – “Borders” must be completed this term
General Topic
No. of
lesson
s
Number –
Calculations:
Whole numbers
6
Number Decimals
6
Objectives






Autumn Term

Fractions: Addition
and subtraction
Fractions:
Multiplication and
division
4
6






Students should be able to …
Long multiplication and long division of positive integers, including
word problems and knowing to round up or down after a remainder.
Add, subtract, multiply and divide negative numbers and solve word
problems involving negative numbers
Round decimals to 1, 2 and 3 of decimal places
Round integers and decimals to 1, 2 and 3 significant figures
Estimate solutions by first rounding to 1 significant figure
Multiply and divide decimal numbers by whole numbers and decimal
numbers (up to 2 d.p.), e.g. 43.2 1.2 & 266.22  0.34
Know that e.g. 13.5  0.5 = 135  5
Compare the sizes of fractions using a common denominator
Add and subtract fractions, including mixed numbers – different
denominators
Convert a fraction to a decimal, or a decimal to a fraction
Find the reciprocal of whole numbers, fractions, and decimals
Multiply a fraction by an integer, by a unit fraction and by a general
fraction including finding a fraction of a quantity
Divide a fraction by an integer, by a unit fraction and by a general
fraction (expressing the answer in its simplest form)
Grade
Notes
D
D-C
FM style questions must be
taught.
D/C
C
D-C
Include calculating before
estimating, writing down all
numbers on calculator display
FM solving problems
involving money
D
D
D/C
D
C
C
C
GCSE Mathematics - Medium Term Plan
Need to be able to
communicate why one
fraction is bigger than
another using equivalence eg:
1/3 or 2.5?
Revisits simplifying,
equivalent and converting
between mixed and
improper.
Include solving word
problems using fractions
Suggested
Enrichment / FM
NRICH - Tug of war – a
game for two involving
adding / subtracting
negative numbers
GCSE EDEXCEL Linear Higher Tier SOW for W1
General Topic
Geometry &
measures Coordinates
No. of
lesson
s
4
Objectives



Grade
Students should be able to …
Identify the coordinates of the vertex of a cuboid on a 3-D grid
Writing down the coordinates of the midpoint of the line connecting
two points.
Calculate the gradient of the line segment joining two points in the
plane (all four quadrants) - change in vertical/change in horizontal.
C
D
Notes
Suggested
Enrichment / FM
Review Plotting and reading
coordinates in all four
quadrants if needed.
B
Learning Review 1
Algebra Introduction to
algebra
4-6


AUTUMN TERM

Geometry: Lines,
angles and
reasoning:
Angles, properties
of triangles and
quadrilaterals
Statistics Representing &
interpreting data.
Algebra Factors and
multiples
6-8



8
o
o
o
o


4





Simplify algebraic expressions in one or more like terms by addition and
subtraction
Multiply and divide powers of the same letter to simplify algebraic
expressions (e.g. a x a x a = a3, 2a x 3a2 = 6a3, a3/a2 = a)
Expand a single bracket and factorise algebraic expressions involving
one pair of brackets
D
Use angle properties of quadrilaterals to calculate unknown angles.
(Include algebra to find missing angles).
Identify and list the properties of special quadrilaterals (including kites)
and use these to find missing angles.
Find missing angles on parallel lines using properties of corresponding
angles, supplementary angles and alternate angles, giving reasons.
D-C
Draw and read information from an ordered stem-and-leaf diagram.
Draw pie charts (for categorical data) working out angle sizes, and
percentages.
Draw a Frequency polygon for grouped data
Calculate and use the mean and range to compare distributions.
Draw and produce a scatter graph
Appreciate that correlation is a measure of the strength of association
between two variables and distinguish between positive, negative and
no correlation.
Draw a line of best fit by eye and understand what it represents
Use a line of best fit to interpolate/ extrapolate
Find the HCF and the LCM of numbers by listing factors or multiples.
Write a number as a product of its prime factors, e.g. 108 = 22  33
Find the HCF and LCM of two numbers from their prime factor
decompositions.
Review 2
XMAS BREAK
D
C
3(y + 4) and 2y(3y – 4) type
12a – 18 and 20a2 + 35a type.
Remind (-2)2 must go in
brackets in calculator
C
D
Reason: Candidates do poorly
on explanations. Cannot give
Z, F, C angle as reasons –
must use correct
terminology.
Use ICT to draw charts and
graphs too.
C
C
C
GCSE Mathematics - Medium Term Plan
If asked for relationship in
exam – word correlation
must appear.
Note – check understanding
of what a prime number, a
factor and a multiple is.
FM: Reporting the
weather and FM
Teacher notes
GCSE EDEXCEL Linear Higher Tier SOW for W1
Financial capability task 3 must be completed during the Spring term (Click on task for hyperlink)
Investigation – “Number Stairs” must be completed this Spring term
General Topic
Geometry:
Constructions and
loci
Spring Term
Statistics Collecting data
No. of
lesson
s
4-6
2
Objectives
Grade
Suggested
Enrichment / FM
Students should be able to …

o
o
o
o
o
o
o
o
o
Construct:
An equilateral triangle with a given side
The mid-point and perpendicular bisector of a line segment
The perpendicular from a point on a line
The bisector of an angle
The angles 60, 30 and 45 degrees
A regular hexagon inside a circle, etc
A path equidistant from 2 points or 2 line segments, etc
Draw a locus for a given rule.
Solve practical problems using loci.

Design a suitable question for a questionnaire and criticize a
questionnaire.
Understand the difference between: primary and secondary data;
discrete and continuous data
Choose and justify an appropriate sampling scheme, including random
and stratified sampling, including understanding about bias in sampling


3

Understand and use bearings
Algebra:
Patterns and
sequences
3–4

Find the nth term of a number sequence as an algebraic expression and
use this to find any term in the sequence.
Find the nth term from a sequence of patterns
Investigate special number sequences (Fibonacci)
Geometry &
Measures:
Properties of
polygons
4-6
Geometry: Lines,
angles and
reasoning:
Notes







D
C
C
C
D
Remind candidates
construction lines must not
be erased
FM: Intruder – uses loci
and constructions to
secure premises
C
C
C
D
Candidates generally answer
poorly in exams on criticising
questionnaires and writing
better question / responses
C
D/C
Calculate and use the sums of the interior angles of polygons of sides 3,
4, 5, 6, 8, 10
Know, or work out, the relationship between the number of sides of a
polygon and the sum of its interior angles
Know that the sum of the exterior angles of any polygon is 360 degrees
Find the size of each exterior/interior angle of a regular polygon
Solve problems involving angles of regular and irregular polygons
NCETM-The Ant –
Visualising and
constructing the loci of
an ant
C
C
C
D
D
D
C
Review 3
GCSE Mathematics - Medium Term Plan
FM: Get OS maps from
Geography, using
bearings plan a route
from A to B.
Students could be able to give a
reasoned argument to support
conclusions.
NRICH – Fibs –
investigating the
Fibonacci sequence
GCSE EDEXCEL Linear Higher Tier SOW for W1
General Topic
Number Percentages
No. of
lesson
8
Objectives






SPRING TERM

Geometry &
measures:
2D shapes –
perimeter, area
including circles.
6-8







Algebra:
Solving linear
equations
6
Grade
Notes
…




Write a percentage as a decimal; or as a fraction in its simplest terms
Write one number as a percentage of another number
Calculate the percentage of a given amount – using multiplier
Find a percentage increase/decrease of an amount – using multiplier
Calculate simple and compound interest for two, or more, periods of
time.
Find a reverse percentage, e.g. find the original cost of an item given
the cost after a 10% deduction
Given two quantities – find the percentage change.
D
C
C
C
Students need to learn how
to use a multiplier.
B
B
Need to be able to compare
two saving / borrowing
options where one uses
simple interest and the other
compound.
Must solve FM problems
involving area and
perimeter.
Solve problems of compound shapes involving rectangles, triangles.
Calculate the area of a trapezium, areas of more complex shapes that
involve trapeziums.
Convert between units of area (e.g. 4m2 into cm2).
Use and recall formulae to calculate perimeters and areas of circles, and
parts of circles (semi circle, quarter circle – not arc length and sector
area)
Find the perimeter and area of shapes made up from triangles,
rectangles and parts of circles
Solve word problems involving area and circumference of circles –
including working backwards to find ‘r ‘or‘d’ if area or circumference
given.
Calculate circumference and area of circles, giving answers in terms of
∏
D/C
C
Solve linear equations with one, or more, operations (including
fractional coefficients) with unknowns on both sides.
Solve linear equations involving a brackets
Solve quadratic and cubic equations using trial and improvement
method to 1 d.p.
Set up and solve linear equations
Easter Break
C
Must solve FM style
questions
D/C
C
Check students can name all
parts of circles, tangents too.
Review expanding a single
bracket
D
Year 10 Exams are a few weeks after Easter break
GCSE Mathematics - Medium Term Plan
Suggested
Enrichment / FM
FM – Get job section of
local paper. Obtain
income tax rates, NI rates
and ask students to use
these to work out take
home pay.
FM: Understanding VAT
& FM: Teacher notes
NRICH
Race track – A good
problem involving
circumference
of
circles.
FM: Plan a bedroom.
Give area, use Argos
catalogues for cost /
dimensions of items
including carpet; draw
2D plan of bedroom –
include cost.
FM: Naismith’s Rule and
FM – Teacher notes
GCSE EDEXCEL Linear Higher Tier SOW for W1
Spri
ng
Ter
m
General Topic
No. of
lesson
s
Objectives
Grade
Notes
Suggested
Enrichment / FM
Students should be able to …
Year 10 Exams are 2nd week back
Financial capability task 4 must be completed during the Summer term (Click on task for hyperlink)
Investigation – “Manhattan Cops” must be completed this Summer term
Geometry &
measures:
3-D shapes and
tessellation
Transformations
4-6
5–7




Draw and interpret plans and elevations
Draw 3D solids onto isomeric paper.
Draw planes of symmetry in 3-D shapes
Tessellate a shape and recognise which regular polygons tessellate.



Use a vector to describe and draw a translation.
Rotate a 2D shape about a point and fully describe a rotation
Reflect shapes in a given mirror line; parallel to the coordinate axes and
then y = x or y = –x
Enlarge shapes by a given scale factor from a given point; using positive
and negative scale factors greater than one
Enlarge shapes by a given fractional scale factor, e.g. 1/2, 3/2, 1/4
Understand that shapes produced by translation, rotation and
reflection are congruent to its image
Combine transformations and describe combined transformations.
Use the relationship between distance, speed and time to draw,
interpret and solve problems of distance–time graphs including finding
the gradient and knowing that average speed is the gradient of the line.
Convert between hours and fractions of an hour to minutes, and form
fractions of a minute to seconds.
Convert between metric units of speed e.g. km/h to m/s
Draw and solve problems using real life graphs (Car hire, bills with fixed
charges, conversion graphs etc)
Know that density is found by mass ÷ volume
Use the relationship between density, mass and volume to solve
problems, e.g. find the mass of an object with a given volume and
density
Convert between metric units of density e.g. kg/m to g/cm
Substitute positive and negative numbers into simple algebraic
formulae including formulae involving powers and roots
Change “word” formulae into algebra
Change the subject of a formula (Use function machine to help)
Generate a formula by working backwards through a problem
e.g. given y = 3d + 4, find d.

Summer Term


Measures:
Speed, density and
conversion graphs
6-8







Algebra:
Formulae
4–6





C
D
D
D/C
C
Candidates must tessellate at
least 6 shapes
Candidates lose marks
because they do not describe
properly or fully, or they
confuse transformation.
C
NRICH
Tessellating
transformations a very
interesting activity on
combined
transformations
C
C
C
B
C
B
GCSE Mathematics - Medium Term Plan
Link to science – gradient
gives average speed or
velocity.
Candidates frequently cannot
convert 3.4 hrs into hours
and minutes, or 3.4 minutes
into minutes and seconds.
Like wise – they also have
difficulty with km/h to m/s
It is important that students
know where formula are
used, and the cross curricular
link with science is made
FM: Mobile phones and
FM: Teacher notes
GCSE EDEXCEL Linear Higher Tier SOW for W1
General Topic
Summer Term, Year 10
Number:
Ratio, proportion
and scale
No. of
lesson
8-10







Geometry &
measures:
Surface area and
volume
6







Objectives
Students should be able to …
Appreciate that e.g. the ratio 1:2 represents 1/3 and 2/3 of a quantity
and write a ratio as a fraction.
Divide quantities in a given ratio, e.g. divide £20 in the ratio 2:3
Work backwards to find a quantity e.g. Jack and Jill shared a lottery win
in the ratio of 4:7; Jill got £560, what was the total lottery win?
Write ratio’s in the form 1:n and n:1
Solve problems involving unitary ratio, e.g. Best buys and recipes.
Solve problems involving indirect proportion.
Work out the real distance from a map, e.g. Find the real distance
represented by 4 cm on a map with scale 1:25 000
Work out the distance on a map for a given real distance and scale
Solve problems involving scale drawing.
Use formulae to calculate the volumes of cuboids and right-prisms.
Use formulae to calculate the surface area of cuboids and right-prisms.
Use formulae to calculate the volume and surface area of a cylinder.
Solve a range of problems involving surface area and volume, e.g. given
the volume and length of a cylinder find the radius
Convert between units of volume (e.g. m3 to cm3)
Grade
D/C
Notes
FM style questions must be
practiced.
D/C
Suggested
Enrichment / FM
NRICH
The Garrison – problem
involving direct
proportion
C
FM: Planning a dinner
party and Teacher
notes
C
B
B
B
YEAR 10 WORK EXPERIENCE – 1 WEEK
Summer Holiday
GCSE Mathematics - Medium Term Plan
FM questions – best
packaging, better volume.
Candidates classically convert
m3 to cm3 wrong. They think
they just add two zeros.
GCSE EDEXCEL Linear Higher Tier SOW for W1
YEAR 11
The number of lessons allocated is a guide. It is important to enrich the curriculum and ensure Functional Mathematics is embedded throughout the topics.
YEAR 11
Mock Exams are first week of December
General Topic
Statistics:
Averages for large
sets of data.
Probability
No. of
lesson
4-5
6-8





Autumn Term Year 11





Objectives
Students should be able to …
Find the mean and median of data given - ungrouped frequency table
Find an estimate for the mean of data - grouped frequency table
Find the modal class and the class which the median lies in a grouped
frequency table.
List all the outcomes from mutually exclusive events, e.g. from two
coins, two dice using sample space diagrams (SSD)
Know that if the probability of an event occurring is p than the
probability of it not occurring is 1 – p
Find estimates of probabilities by considering relative frequency in
experimental results and know that the more an experiment is
repeated the better the estimate of probability
Complete two way tables and calculate probabilities from these.
Know that the probability of A or B is P(A) + P(B)
Know that the probability of A and B is P(A)  P(B)
Draw and use tree diagrams to solve probability problems (including
examples of non-replacement)
Grade
D
C
C
Notes
Estimated mean from
grouped frequency –
candidates of ten lose marks
as they forget to do the mid
class interval
C
Candidates often give
probabilities as a ratio – they
lose all marks for this
C
D
B
B
Need to know that SSD and
tree diagrams are ways of
recording all outcomes, and
can be used to find
probabilities
Suggested
Enrichment / FM
FM: Fishing competition
NRICH
The Better Bet
NCETM
Fair game? – Activity
involving a game where
relative frequency can be
calculated.
FM: Fairground and
FM: Teacher notes
Candidate may have to draw
tree from scratch now
Geometry:
Pythagoras’
theorem
4-6



Use Pythagoras’ theorem to find unknown lengths in right angled
triangles.
Use Pythagoras to find the height of an isosceles triangle.
Solve word problems involving right angled triangles, including height of
isosceles triangles.
C
Review squares and square
roots.
B
Teacher discretion for h of
triangle in isosceles.
GCSE Mathematics - Medium Term Plan
One old Greek –
discovering Pythagoras
GCSE EDEXCEL Linear Higher Tier SOW for W1
General Topic
Algebra:
Linear functions
y = mx + c
No. of
lesson
8





Algebra:
Index notation
4–5







Autumn Term
Number:
Standard form
4-6





Objectives
Students should be able to …
Substitute values of x into linear functions to find corresponding values
of y, by completing a table of values.
Plot points for linear functions on a coordinate grid and draw the
corresponding straight lines where y is given explicitly in terms of x (y =
3x + 4), x + y = k, and ax + by = K types using cover up method.
Interpret m and c as gradient and y-intercept in linear functions, and
understand effects of changing these values.
Understand that the graphs of linear functions are parallel if they have
the same value of m
Name equation of line direct from graph, draw graph using gradient and
intercept method.
Calculate the gradient using difference in y/difference in x
Identify if points lie on a given straight line
Solve simultaneous equations graphically.
Know squares and roots up to 20, and cubes and roots up to 10
Know that square numbers have two square toots, one positive and one
negative.
Use index notation for squares, cubes and powers of 10.
Use index rules to simplify and calculate numerical expressions involving
powers, e.g.33  35 = 38, (23  25)  24, (4a3 b2c)/2a2 bc, 40, (2a2)3, etc
Grade
Notes
C
(Note – there may not be a table
given in the exam, so students
must be able to do this
themselves)
Understand the standard form convention
Convert large and small numbers to, and from, standard form
Calculate with numbers given in standard form with, and without, a
calculator.
Solve word problems involving standard index form
Round numbers given in standard form to a given number of significant
figures
B
B
B
C
Suggested
Enrichment / FM
Use Autograph to investigate
straight line graphs.
B
Link gradient of line as being
average speed or velocity in
speed or velocity graphs –
used commonly in science.
D/C
B
B
Mock Exams First week of December
XMAS BREAK
GCSE Mathematics - Medium Term Plan
Link to use in science.
Ensure students can read
standard form answers from
calculators, as some give 4-5
as answer – candidate needs
to know this means 4 x 10-5
FM: Oil crisis and teacher
notes
GCSE EDEXCEL Linear Higher Tier SOW for W1
General Topic
No. of
lesson
Statistics:
Representing and
interpreting data –
cumulative
frequency & box
plots
5–7
Algebra:
drawing quadratic,
cubic graphs




4-5






Spring term

Geometry:
Similar shapes
4-5







Algebra:
Inequalities &
regions
6
Algebra:
Quadratic
functions
4


Geometry:
Sine, cosine and
tangent
6



Objectives
Students should be able to …
Draw a cumulative frequency table for grouped data (using the upper
class boundary) and understand the rationale for using one.
Draw a cumulative frequency curve for grouped data
Use a cumulative frequency diagram to find estimates for the median,
quartiles and interquartile ranges of a distribution
Use a cumulative frequency diagram to solve problems, e.g. how many
greater than a particular value.
Draw a box plot from a cumulative frequency diagram
Be able to draw a box plot directly from given data.
Compare dual box lots to make inferences about distributions
Know and recognise the general shapes of quadratic, cubic graphs.
Accurately draw quadratic, cubic curves.
Know the points where the quadratic curve crosses the axis are the
solutions.
Given an x or y value – be able to find the other co-ordinate by reading
from the quadratic graph.
Use integer and non-integer scale factors to find the length of a missing
side in each of two similar shapes, given the lengths of a pair of
corresponding sides including similar triangles
Communicate clearly whether two 2D shapes are mathematically
similar or not.
Know when two triangles are congruent
Identify the solution set on a number line for linear inequalities.
Write down the integer solutions that satisfy a linear inequality.
Rearrange and solve linear inequalities in one variable.
Draw the graphs of linear inequalities in two variables and interpret the
solution sets given by regions in the coordinate plane, or to identify all
the integer coordinates with crosses
Expand and simplify expressions involving two pairs of brackets
Solve quadratic equations by factorising a = 1
Use trigonometric ratios (sin, cos and tan) to calculate angles in rightangled triangles
Use the trigonometric ratios to calculate unknown lengths in rightangled triangles
Calculate the angle of elevation and depression using the trigonometric
ratios.
Grade
Notes
C
B
Use of ICT for drawing
graphs.
B
B
When comparing: Emphasise
that actual statistics must be
given in answers, e.g. boys
had bigger median – 0 marks.
Boys had larger median at 23
to girls 19 – 1 mark.
B
B
B
Often lose a mark as curve
has a “flat” or “pointed”
bottom
C
Suggested
Enrichment / FM
Algebra:
Simultaneous equations;
drawing quadratic, cubic
and reciprocal graphs
FM: Scale models and
teacher notes
B
C
B
NRICH
Marbles – how many of
each in the bag? Uses
inequalities to set up the
problem.
C
B
B
Trig beginnings –
worksheet investigating
RA triangles in circles. (1)
B
GCSE Mathematics - Medium Term Plan
Make a clinometer – then
take them outside (1)
GCSE EDEXCEL Linear Higher Tier SOW for W1
Optional
Target teaching topics from mock examination analysis here.
Following targeting teaching from Mock results – either begin Note: Teacher’s must ensure 4 weeks available for
GCSE revision OR use Teacher discretion for teaching the
revision before examinations begin.
following topics:
Algebra:
Simultaneous
equations
Geometry:
Circle theorems
Number:
Limits of accuracy
3-4

4-6

3
Solve algebraically two simultaneous equations
Use circle theorems to find unknown angles and explain their methodquoting the appropriate theorem
Students need to be able to find and explain:

The angle subtended at the centre of the circle is double that
subtended at the circumference, when from the same arc.

Angles subtended at the circumference from the same arc are equal.

Angles subtended at the circumference from a diameter are 90˚

Opposite angles in a cyclic quadrilateral add up to 180˚

Tangents from an external point are equal in length.


Understand and calculate the limit of accuracy, knowing it is +/half a unit.
Find when numbers are given to a specific degree of accuracy,
the upper and lower bounds of perimeters and areas of shapes.
B
B
B
In exam – candidates often
lose marks for inappropriate
explanations. They cannot
say “arrowhead”, “bow” to
explain their answers– they
must be specific.
NRICH
 Partly Circles
 Triangles in Circles
 Subtended Angles
Right Angles
B
Ensure they are familiar with the
“sneaky” arrowhead – it is an
examiners favourite.
B
Mainly knowing +/- half a unit
at this level
B/A
Summer Term – Examination revision. GCSE Exams begin mid-may so many students will not be in lessons.
The mathematics examinations are usually the first week after half term.
GCSE Mathematics - Medium Term Plan