Year 7 - Number
Term 1
1 Number systems
Ancient number systems
Numbers Bases
2 Operations
3 Fractions
X-C: Maths and music (ratio)
P&S1: Intro to probability
a) Path walking & random walks
b) Weird dice
Term 2
4 Negatives and zero
5 Primes Factor Multiples
X-C: History of Maths
P&S2: Surveys, sampling and experiments
a) Is there no such thing as a bad question?
b) Conducting a survey
c) Conducting an experiment
Term 3
6 Powers
7 Patterns and sequences
X-C: Teacher choice
P&S3: Interpreting data
a)
b)
c)
d)
e)
f)
Maths and voting (percentages)
UK by numbers
How long will you live?
Inequality
Social maths
Gapminder
Number content descriptors from Edexcel 2012 Spec
A. Add, subtract, multiply and divide any number including negatives
B. Order rational numbers
C. Use the concepts and vocabulary of factor (divisor), multiple, common factor,
Highest Common Factor
(HCF), Least Common Multiple (LCM), prime number
and prime
factor decomposition
D. Use the terms square, positive and negative square root, cube (and cube
root)
E. Use index notation for squares, cubes and powers of 10
F. Use index laws for multiplication and division of integer powers
H. Understand equivalent fractions, simplifying a fraction by cancelling
all
common factors
I. Add and subtract fractions
J. Use decimal notation and recognise that each terminating decimal is a fraction
K. Recognise that recurring decimals are exact fractions, and that some exact
fractions are recurring
decimals
L. Understand that ‘percentage’ means ‘number of parts per 100’ and use this to
compare proportions
M. Use percentage
O. Interpret fractions, decimals and percentages as operators
P. Use ratio notation, including reduction to its simplest form and
its various
links to fraction notation
Q. Understand and use number operations and the relationships between them,
including inverse operations and hierarchy of operations
T. Divide a quantity in a given ratio
U. Approximate to specified or appropriate degrees of accuracy including a given
power of ten, number of decimal places and significant figures
V. Use calculators effectively and efficiently, including statistical functions
Year 8 - Algebra
1 Rules of algebra
Binary operations; is it comm?
What is ass? Simplifying expressions
What is dist? Partitioning -> expanding/factorising.
Think of a number…
Methods for super-dist (grid, Ancient Indian, tree)
‘4-squares’ investigation; calculating 101^2, 99^2, 101.99. etc…
An introduction to proof: adding/multiplying evens/odds, sums of
consecutives (up to 4), primes 6n +-1? … Develop patterns and pictures
into algebraic proof
Difference of 2 squares
Coda: Super-super-dist… patterns in expansions, the binomial theorem,
Pascal’s triangle again…
2 Inverses
The identity element
Defining the additive inverse and subtraction (x + -x = 0)
Defining the multiplicative inverse and division (x.1/x = 1)
Div 0: What is 1/0? And 0/0?
Inverses mod n (YE1)
3 Powers
Squares, cubes
Squares of products and reciprocals
Powers of negatives and negative powers
Rules of powers
Square roots and fractional powers
P&S4: Counting and probability (Pascal’s triangle, combinatorics,
derangements, …)
4 Sequences
AP: nth terms, sum of AP, prime sequences, problems, …
GP: 5th terms, sum of infinite GP, fractals
Triangle and square numbers: identities
Pascal’s triangle and counting [link to probability]
Quadratic sequences: prime sequences, Babbage’s difference engine
Recursive functions: Fibonacci, Collatz…
5 Functions
Algebraic geometry – straight lines
Quadratics (viete’s theorem, discriminant, maxima and minima) and other
functions (reciprocals, cubics)
Pythagorean points
Zeroes and the factor theorem, Intermediate Value Theorem,
Discontinuous functions (floor/ceiling)
Absolute value
Transformations
Waves and trigonometry
Programming in python/logo, geogebra
6 Solving equations
Linear equations
Diophantine equations, Bachet’s weights
Simultaneous equations
Quadratic equations
7 Divisibility (opt)
Divisibility tests, Recurring decimals, Prime factors (Euler’s functions),
Algebraic fractions, Factorising revisited
P&S5: Correlation (gapminder, dating, straight up, bullying v absence, other?)
8 Applying algebra
Perimeter, area, volume formulae
Weird ways to work with pi
Pythagoras
Simple geometry problems and proofs – triangles, quads, circles
Physical formulae: speed/distance, electrical circuits, …
Codes
Maths and magic
Mathematical games
Graph theory
9 Inequalities
Solving inequalities
Probability using geometry
Triangle inequality
Cauchy inequality
10 Averages
AM
GM (AM > GM)
HM (AM > GM > HM)
RMS (…RMS wins!)
Problems
P&S6: Location and spread investigations (mean value theorem, mean
game, which mean do you mean, converging means, wisdom of the crowds, …)
11 Strange algebras (opt)
Group theory, Congruences, Other algebraic structures eg. Logic, Sets,
Matrices, Quaternions, …
Algebra content descriptors from Edexcel 2012 Spec
A. Distinguish the different roles played by letter symbols in
algebra, using the
correct notation
B. Distinguish in meaning between the words ‘equation’, ‘formula’ ‘identity’ and
‘expression’
C. Manipulate algebraic expressions by collecting like terms, by multiplying a
single term over a bracket, and by taking out common factors, multiplying two
linear expressions, factorise quadratic expressions including the
difference of two squares and simplify rational expressions
D. Set up and solve simple equations including simultaneous equations in
two unknowns
E. Solve quadratic equations
F. Derive a formula, substitute numbers into a formula and change the subject
of a formula
G. Solve linear inequalities in one or two variables, and represent the solution
set on a number line or co-ordinate grid
H. Use systematic trial and improvement to find approximate solutions of
equations where there is no simple analytical method of solving them
I. Generate terms of a sequence using term-to-term and position- to-term
definitions of the sequence
th
J. Use linear expressions to describe the n
term of an arithmetic sequence
K. Use the conventions for coordinates in the plane and plot points in all four
quadrants, including using geometric information
L. Recognise and plot equations that correspond to straight-line graphs in the
coordinate plane, including finding gradients
M. Understand that the form
y = mx + c represents a straight line and that
m is the gradient of the line and c is the value of the y- intercept
R. Construct linear functions from real-life problems and plot their corresponding
graphs
S. Discuss, plot and interpret graphs (which may be non-linear) modelling real
situations
T. Generate points and plot graphs of simple quadratic functions, and use these
to find approximate solutions
Plus lots of other criteria from other areas of the curriculum, such as:
Geometry
B. Understand and use the angle properties of parallel and intersecting lines,
triangles and quadrilaterals
C. Calculate and use the sums of the interior and exterior angles of polygons
G. Use Pythagoras’ theorem in 2-D
I. Distinguish between centre, radius, chord, diameter, circumference, tangent,
arc, sector and segment
X. Calculate perimeters and areas of shapes made from triangles and rectangles
Z. Find circumferences and areas of circles
Stats
H. Calculate median, mean, range, mode and modal class
Probability
M. List all outcomes for single events, and for two successive events, in a
systematic way and derive relative probabilities
Year 3 – Geometry
As per popplet… TBA
P&S7 – experimental probability (codes/language, randomness, games)
P&S8 – theoretical probability (probability as area, games and game theory)
P&S9 – gender stereotypes (experiments, collecting and interpreting data)
Probability and stats – GCSE criteria from Edexcel 2012 spec.
YEAR 7
1 Intro to probability
M. Understand and use the vocabulary of probability and probability scale
N. Understand and use estimates or measures of probability from theoretical
models (including equally likely outcomes), or from relative frequency
O. List all outcomes for single events, and for two successive events, in a
systematic way and derive relative probabilities
P. Identify different mutually exclusive outcomes and know that the sum of the
probabilities of all these outcomes is 1
Q. Know when to add or multiply two probabilities: when A and B are mutually
exclusive, then the probability of A or B occurring is P(A) + P(B), whereas when A
and B are independent events, the probability of A and B occurring is P(A) × P(B)
R. Use tree diagrams to represent outcomes of compound events,
recognising
when events are independent
2 Surveys, sampling, bias and experiments
A. Understand and use statistical problem solving process/handling data cycle
B. Identify possible sources of bias
C. Design an experiment or survey
D. Design data collection sheets for different types of data
G. Produce charts and diagrams for various data types
3 Interpreting data
E. Extract data from printed tables or lists
G. Produce charts and diagrams for various data types
I. interpret a wide range of graphs and diagrams and draw
conclusions
J. Look at data to find patterns and exceptions
YEAR 8
4 Counting and probability
M. Understand and use the vocabulary of probability and probability scale
N. Understand and use estimates or measures of probability from theoretical
models (including equally likely outcomes), or from relative frequency
O. List all outcomes for single events, and for two successive events, in a
systematic way and derive relative probabilities
P. Identify different mutually exclusive outcomes and know that the sum of the
probabilities of all these outcomes is 1
Q. Know when to add or multiply two probabilities: when A and B are mutually
exclusive, then the probability of A or B occurring is P(A) + P(B), whereas when A
and B are independent events, the probability of A and B occurring is P(A) × P(B)
R. Use tree diagrams to represent outcomes of compound events,
recognising
when events are independent
5 Correlation
I. Interpret a wide range of graphs and diagrams and draw
conclusions
J. Look at data to find patterns and exceptions
K. Recognise correlation and draw and/or use lines of best fit by eye,
understanding what these represent
6 Location and spread
H. Calculate median, mean, range, quartiles and interquartile range, mode and
modal class
L. Compare distributions and make inferences
Year 9
7 Experimental probability
M. Understand and use the vocabulary of probability and probability scale
N. Understand and use estimates or measures of probability from theoretical
models (including equally likely outcomes), or from relative frequency
S. Compare experimental data and theoretical probabilities
T. Understand that if they repeat an experiment, they may − and
usually will −
get different outcomes, and that increasing sample size generally leads to better
estimates of probability and population characteristics
8 Theoretical probability
M. Understand and use the vocabulary of probability and probability scale
N. Understand and use estimates or measures of probability from theoretical
models (including equally likely outcomes), or from relative frequency
O. List all outcomes for single events, and for two successive events, in a
systematic way and derive relative probabilities
P. Identify different mutually exclusive outcomes and know that the sum of the
probabilities of all these outcomes is 1
Q. Know when to add or multiply two probabilities: when A and B are mutually
exclusive, then the probability of A or B occurring is P(A) + P(B), whereas when A
and B are independent events, the probability of A and B occurring is P(A) × P(B)
R. Use tree diagrams to represent outcomes of compound events,
recognising
when events are independent
9 Gender stereotypes
C. Design an experiment or survey
D. Design data collection sheets for different types of data
G. Produce charts and diagrams for various data types
I. interpret a wide range of graphs and diagrams and draw
conclusions
J. Look at data to find patterns and exceptions