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Transcript
MATHEMATICS Schemes of Learning
Year 9 Progression Route:
Term Autumn HT1
Unit of Work: 1
Time
NC/Specification
content:
NUMBER
2 weeks
 understand and use place value (e.g. when working with very large or
very small numbers, and when calculating with decimals)
 apply the four operations, including formal written methods, to integers
and decimals
 solve problems involving addition, subtraction, multiplication and division
Unit of Work:2
Time
NC/Specification
content:
Indices & Powers
3 weeks





use roots (square, cube and higher), recognise powers of 2, 3, 4, 5 (
estimate powers and roots of any given positive number
calculate with roots, and with integer indices
Be able to write very large and very small numbers presented in a
context in standard form
calculate with standard form A × 10n, where 1 ≤ A < 10 and n is an
integer
Unit of Work: 3
SOLVING EQUATIONS
Time
3 weeks
NC/Specification
content:





solve linear equations in one unknown algebraically
solve linear equations with the unknown on both sides of the equation
Factorise algebraic expressions by taking out common factors
Expand the product of two linear expressions
Factorise quadratic expressions of the form x2 + bx + c including the
difference of two squares
 Solve quadratic equations
Term Autumn HT2
Unit of Work: 4
Time
NC/Specification
content:
ALGEBRA PROFICIENCY
2 weeks
Unit of Work: 5
Time
NC/Specification
content:
PROPORTIONAL REASONING
2 weeks
Unit of Work: 6
Time
NC/Specification
content:
SEQUENCES
2 weeks
Unit of Work: 7
Time
NC/Specification
content:
VISUALISING & CONSTRUCTING
(2 week)
 simplifying expressions involving sums, products and powers, including the
laws of indices
 substitute numerical values into scientific formulae
 rearrange formulae to change the subject
 use ratio notation, including reduction to simplest form
 apply ratio to real contexts and problems (such as those involving
conversion, comparison, scaling, mixing, concentrations)
 understand and use proportion as equality of ratios
 solve problems involving direct and inverse proportion including graphical
and algebraic representations
 apply the concepts of congruence and similarity, including the relationships
between lengths in similar figures
 use compound units (such as speed, rates of pay, density and pressure)
 recognise and use sequences of triangular, square and cube numbers,
simple arithmetic progressions
 generate terms of a sequence from either a term-to-term or a position-toterm rule
 deduce expressions to calculate the nth term of linear sequences
 recognise and use Fibonacci type sequences, quadratic sequences
 use the standard ruler and compass constructions (perpendicular bisector
of a line segment, constructing a perpendicular to a given line from/at a
given point, bisecting a given angle)
 use these to construct given figures and solve loci problems; know that the
perpendicular distance from a point to a line is the shortest distance to the
line
Term SPRING HT1
Unit of Work: 8
Time
NC/Specification
content:
CALCULATING SPACE
3 weeks
Unit of Work: 9
Time
NC/Specification
content:
PROOF / PROPERTIES OF SHAPES
3 weeks
 know and apply formulae to calculate area of triangles, parallelograms,
trapezia
 identify and apply circle definitions and properties, including: centre,
radius, chord, diameter, circumference, tangent, arc, sector and segment
 calculate perimeters of 2D shapes, including circles
 know the formulae: circumference of a circle = 2πr = πd, area of a circle =
πr²
 calculate areas of circles and composite shapes
 know and apply formulae to calculate volume of cubes, cuboids, right
prisms (including cylinders)
 calculate arc lengths, angles and areas of sectors of circles
 calculate surface area of cuboids, right prisms (including cylinders)
 calculate exactly with multiples of π
 know the formulae for: Pythagoras’ theorem, a² + b² = c², and apply it to
find lengths in right-angled triangles in two dimensional figures
 understand and use alternate and corresponding angles on parallel lines
 derive and use the sum of angles in a triangle (e.g. to deduce and use the
angle sum in any polygon, and to derive properties of regular polygons)
 use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
 apply angle facts, triangle congruence, similarity and properties of
quadrilaterals to conjecture and derive results about angles and sides,
including Pythagoras’ Theorem and the fact that the base angles of an
isosceles triangle are equal, and use known results to obtain simple proofs
Term SPRING HT2
Unit of Work:10
Time
NC/Specification
content:
ALGEBRA – DRAWING GRAPHS
3 weeks
 understand and use lines parallel to the axes, y = x and y = -x
 plot graphs of equations that correspond to straight-line graphs in the
coordinate plane
 identify and interpret gradients and intercepts of linear functions
graphically and algebraically
 recognise, sketch and interpret graphs of linear functions and simple
quadratic functions
 use the form y = mx + c to identify parallel lines
 find the equation of the line through two given points, or through one
point with a given gradient
 interpret the gradient of a straight line graph as a rate of change
 recognise, sketch and interpret graphs of quadratic functions, simple cubic
functions and the reciprocal function y = 1/x with x ≠ 0
 plot and interpret graphs (including reciprocal graphs) and graphs of nonstandard functions in real contexts, to find approximate solutions to
problems such as simple kinematic problems involving distance, speed and
acceleration
Unit of Work:11
Time
NC/Specification
content:
SOLVING EQUATIONS & INEQUALITIES 2
3 weeks




solve linear inequalities in one variable
represent the solution set to an inequality on a number line
solve linear inequalities in two variables
solve, in simple cases, two linear simultaneous equations in two variables
algebraically
 derive an equation (or two simultaneous equations), solve the equation(s)
and interpret the solution
 find approximate solutions to simultaneous equations using a graph
Term SUMMER HT1
Unit of Work:12
Time
NC/Specification
content:
PROBABILITY
2 WEEKS
 apply the property that the probabilities of an exhaustive set of outcomes
sum to one; apply the property that the probabilities of an exhaustive set
of mutually exclusive events sum to one
 apply systematic listing strategies
 record describe and analyse the frequency of outcomes of probability
experiments using tables and frequency trees
 construct theoretical possibility spaces for combined experiments with
equally likely outcomes and use these to calculate theoretical probabilities
 apply ideas of randomness, fairness and equally likely events to calculate
expected outcomes of multiple future experiments
 calculate the probability of independent and dependent combined events,
including using tree diagrams and other representations, and know the
underlying assumptions
 enumerate sets and combinations of sets systematically, using tables,
grids, Venn diagrams and tree diagrams
 understand that empirical unbiased samples tend towards theoretical
probability distributions, with increasing sample size
Unit of Work:13
Time
NC/Specification
content:
PRESENTATION OF DATA
2 WEEKS
 interpret and construct tables, charts and diagrams, including frequency
tables, bar charts, pie charts and pictograms for categorical data, vertical
line charts for ungrouped discrete numerical data and know their
appropriate use
 cumulative frequency graphs and box plots
 scatter graphs
YEAR 9 EXAM
Term SUMMER HT2
(7 weeks)
Year 10 SOL