Leicestershire KS4 Pilot Framework
The National Numeracy Strategy
Leicestershire Key Stage 4 Pilot
1st draft medium-term plans
for mathematics
Year 10 - Foundation
Written to 2000/01 dates.
06/02/16
Leicestershire KS4 Pilot Framework
Framework for teaching mathematics
Year 10: Autumn
Objectives for Oral and mental starter:
recall all positive integer complements to 100
recall all multiplication facts to 10 X 10, and derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10
recall the fraction-to-decimal conversion of familiar simple fractions
round to the nearest integer and to 1sf
distinguish between acute, obtuse, reflex and right angles
estimate the size of an angle in degrees
Week
Hours
Topic
Fractions & Decimals
Objectives: pupils will be taught to
order fractions & understand equivalent fractions
use decimal notation and order decimals
recognise that each terminating decimal is a fraction
Equations 1
distinguish the different roles played by letter symbols in algebra
distinguish in meaning between the words 'equation', 'formula', 'identity' and
'expression'
solve linear equations with integer coefficients
recall and use properties of angles around a point and on a straight line
use parallel lines, alternate angles and corresponding angles
calculate and use the sums of the int. and ext. angles of quadrilaterals
1
2
A Angles 1
3
4
Transformations 1reflection & translation
5
Mental Methods Decimals
Probability 1
6
7
understand that reflections are specified by a mirror line
understand that translations are specified by a distance and direction
recognise and visualise reflections and translations, including reflection
symmetry of 2-D and 3-D shapes,
transform 2-D shapes by translation, and reflection
add and subtract mentally numbers with up to 2dps
multiply and divide numbers with no more than one decimal digit using the
commutative, associative, and distributive laws and factorisation where possible,
or place value adjustments
estimate answers to problems involving decimals
understand and use the probability scale
understand and use estimates or measures of probability from theoretical models
(including equally likely outcomes), & from relative frequency
list all outcomes for single events
Assess and review
Objectives for oral and mental starter:
develop a range of strategies for mental calculation
derive unknown facts from those they know
NB extra content will be provided by pupil responses to & understanding of previous work
8
Calculator Methods 1
? Topic / context
Symbols & Formulae 1
9
Co-ordinates & Graphs 1
10
Measures of Average
11
Measures 1
12
Perimeter & Area
13
14
understand and interpret the calculator display
know not to round during the intermediate steps of a calculation
make mental estimates of the answers to calculations
use checking procedures
distinguish in meaning between the words 'equation', 'formula', 'identity' and
'expression'
use formulae expressed in words, letters and symbols
substitute numbers into a formula
use axes and coordinates to specify and locate points in all four quadrants
know y = mx + c is a straight-line graph
plot graphs of functions in which y is given explicitly or implicitly
calculate mean, range and median of small data sets with discrete then
continuous data; identify the modal class for grouped data
compare distributions and make inferences, using distribution shape, averages
and range
interpret scales on a range of measuring instruments, including those for time
and mass
know that measurements using real numbers depend on the choice of unit
convert measurements from one unit to another
recall and use the formula to find areas of rectangles, parallelograms and
triangles
calculate perimeters and areas of shapes made from triangles and rectangles
Assess and review
06/02/16
Leicestershire KS4 Pilot Framework
Framework for teaching mathematics
Year 10: Spring
Objectives for Oral and mental starter: estimating, explaining methods …
break down a complex calculation into simpler steps
make sensible estimates of a range of measures in everyday settings
understand angle measure using the associated language
Week
Hours
Topic
Percentages
1
2
3
4
5
6
Fractions, Decimals and
Percentages 1
Objectives: pupils will be taught to
use percentage, in real-life situations, as an operator and to compare
proportions
understand the multiplicative nature of percentages as operators
solve simple percentage problems, including increase
perform short division to convert a simple fraction to a decimal
convert simple fractions of a whole to percentages of the whole and vice versa
Transformations 2 - Rotation understand that rotations are specified by centre and angle
rotate a shape about the origin, or any other point
recognise and visualise rotations incl. rotation symmetry of 2-D shapes;
transform 2-D shapes by rotation
measure the angle of rotation
measure and draw lines to the nearest millimetre, and angles to the nearest
Construction 1
degree
draw triangles and other 2-D shapes using a ruler and protractor
understand that inscribed regular polygons can be constructed by equal
division of a circle
Written Methods 1
use brackets and the hierarchy of operations
use standard column procedures for addition and subtraction of integers and
decimals
use standard column procedures for multiplication of integers and decimals
Assess and review
Objectives for oral and mental starter:
add and subtract mentally numbers with up to 2dps
multiply and divide numbers with no more than one decimal digit using the commutative, associative, and distributive laws and
factorisation where possible, or place value adjustments
estimate answers to problems involving decimals
Representing Data
draw and produce graphs, charts and diagrams using paper and ICT
find the median and an estimated mean for large data sets (grouped)
Inequalities
solve simple linear inequalities in one variable, and represent the solution set
on the number line
Symbols & Formulae 2
manipulate simple algebraic expressions
derive a formula and change its subject
Ratio
use ratio notation, including reduction to simplest form and its various links to
fraction notation
divide a quantity in a given ratio
Quadrilaterals
recall the essential properties of special types of quadrilateral
classify quadrilaterals by their geometric properties
explain why the angle sum of any quadrilateral is 360 degrees
understand the properties of parallelograms
7
8
9
10
11
12
Assess and review
06/02/16
Leicestershire KS4 Pilot Framework
Framework for teaching mathematics
Year 10: Summer
Objectives for Oral and mental starter:
recall the essential properties of special types of quadrilateral
recognise and visualise rotations, reflections and translations
use arbitrarily large positive numbers and round them to a given power of 10
understand, order and use positive numbers
use the concepts and vocabulary of factor (divisor), multiple and common factor
Week Hours
Topic
Index Notation
Objectives: pupils will be taught to
use the terms square, positive square root, cube;
use index notation for squares, cubes and powers of 10
use index notation for simple integer powers, and simple instances of index laws
substitute positive and negative numbers into expressions
enter complex calculations and use function keys for reciprocals, squares and
powers
Applying Statistical
Methods
GCSE coursework ?
design an experiment or survey & discuss how data relate to a problem
identify source and format of primary and secondary data
design and use data-collection sheets
relate summarised data to the initial questions
interpret a wide range of graphs and diagrams and draw conclusions
look at data to find patterns and exceptions
generate terms of a sequence using term-to-term and position-to-term definitions
use linear expressions to describe & justify the nth term of an arithmetic
sequence
1
2&3
Sequences
4
5
Assess and review
Objectives for Oral and mental starter:
Week Hours
Topic
Probability 2
Objectives: pupils will be taught to
list all outcomes for two successive events, in a systematic way
identify different mutually exclusive outcomes and know these sum to 1
Solving Numerical
Problems 1
select appropriate operations, methods and strategies to solve number problems
inc Trial & Improvement
use a variety of checking procedures
give solutions in the context of the problem
Angles 2
calculate and use the sums of the int. and ext. angles of quads, pentagons and
hexagons
calculate and use the angles of regular polygons
Perimeter, Area & Volume
1
find the surface area of simple shapes using the area formulae for triangles and
rectangles
recall and use the formula to find volumes of cuboids
calculate volumes of right prisms and of shapes made from cubes and cuboids
recall the definition of a circle and the meaning of related terms
recall and use formulae to find circumference and area of circles
6
7
8
9
Circles
10
11
Assess and review
06/02/16