Leicestershire KS4 Pilot Framework
The National Numeracy Strategy
Leicestershire Key Stage 4 Pilot
1st draft medium-term plans
for mathematics
(Autumn term only)
Year 10 – Higher
Written to 2000/01 dates.
06/02/16
Leicestershire KS4 Pilot Framework
The Higher Programme of study requires all of the foundation too. The format of this
document includes ALL of the foundation objectives, however many are listed under assumed
prior knowledge within the half term schedule. This enables teachers to refer to such topics in
passing / introductions without using up teaching time which is extremely tight. Clearly
weaknesses / gaps will need to be responded to, perhaps in oral and mental work.
Work from 2nd / 3rd visits to topics is therefore brought forward within the 2 year course and
the additional higher objectives are slotted in appropriately, but with a tendency towards the
end of the Key Stage.
The teaching order follows that of the foundation syllabus to allow student movement
between sets within Key Stage 4.
Constructive feedback needed before continuing in this style. It is so dependent on the
Foundation framework that I wanted that agreed and sorted too before doing too much work
on this!
06/02/16
Leicestershire KS4 Pilot Framework
Framework for teaching mathematics
Year 10: Autumn 1 st Half term
Assumed prior knowledge, skills and understanding:
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
distinguish the different roles played by letter symbols in algebra
understand that reflections are specified by a mirror line
understand that translations are specified by a distance and direction
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
Objectives for Oral and mental starter:
order fractions & understand equivalent fractions
use decimal notation and order decimals
distinguish in meaning between the words 'equation', 'formula', 'identity' and 'expression'
recall and use properties of angles around a point and on a straight line
use parallel lines, alternate angles and corresponding angles
recognise and visualise reflections and translations, including reflection symmetry of 2-D and 3-D shapes
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
Week
Hours
Topic
Fractions & Decimals
1
Equations 1
2
A Angles 1
3
calculate and use the sums of the int. and ext. angles of quads, pentagons and
hexagons
calculate and use the angles of regular polygons
Transformations 1
transform 2-D shapes by translation, rotation and reflection
transform shapes by combinations of transformations
use congruence to show that translations, rotations and reflections preserve
length and angle distinguish properties that are preserved under particular
transformations
Mental Methods
recall integer squares from 2 X 2 to 15 X 15 and the corresponding square roots
recall the cubes of 2, 3, 4, 5 and 10
use powers of 0, -1 and fractions for common roots
round to a given number of significant figures
convert between ordinary and standard index form representations
convert to standard index form to make sensible estimates for calculations
involving multiplication and/or division
Probability 1
list all outcomes for two successive events, in a systematic way
identify different mutually exclusive outcomes and know these sum to 1
know when to add or multiply two probabilities
4
5
6
7
Objectives: pupils will be taught to
recognise that each terminating decimal is a fraction
recognise that recurring decimals are exact fractions, and that some exact
fractions are recurring decimals
distinguish between fractions representable as terminating decimals and those
by recurring decimals
convert a recurring decimal to a fraction
solve linear equations with integer coefficients
set up and solve simple equations
solve linear equations with brackets
Assess and review
06/02/16
Leicestershire KS4 Pilot Framework
Framework for teaching mathematics
Year 10: Autumn 2 nd Half term
Assumed prior knowledge, skills and understanding:
understand and interpret the calculator display
know not to round during the intermediate steps of a calculation
use formulae expressed in words, letters and symbols
substitute numbers into a formula
plot graphs of functions in which y is given explicitly
calculate mean, range and median of small data sets with discrete then continuous data
identify the modal class for grouped data
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
calculate perimeters and areas of shapes made from triangles and rectangles
Objectives for oral and mental starter:
develop a range of strategies for mental calculation
derive unknown facts from those they know
make mental estimates of the answers to calculations
use axes and coordinates to specify and locate points in all four quadrants
know y = mx + c is a straight-line graph
recall and use mean, median, mode and range
convert measurements from one unit to another
recall and use the formula to find areas of rectangles, parallelograms and triangles
Calculator Methods 1
use checking procedures
* Trial & Improvement
enter complex calculations and use function keys for reciprocals, squares and
powers
use calculators, or written methods, to calculate the upper and lower bounds of
calculations
Symbols & Formulae
manipulate simple algebraic expressions
derive a formula and change its subject
using the correct notational conventions for multiplying or dividing by a given
number,
expand the product of two linear expressions
Co-ordinates & Graphs 1
plot graphs of functions in which y is given implicitly
find the coordinates of the midpoint of the line segment AB, given A &B &
calculate length AB
understand that the point of intersection of two different lines solves a
simultaneous equation
Measures of Average
compare distributions and make inferences, using distribution shape, averages
and range
find the median and an estimated mean for large data sets
Measures 1
convert between area measures and also volume measures
understand and use compound measures, including speed
recognise that measurements given to the nearest whole unit may be inaccurate
by up to one half in either direction
13
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
14
Assess and review
8
9
10
11
12
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
Algebraic Skills
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
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