THEALE GREEN COMMUNITY SCHOOL
MATHEMATICS DEPARTMENT
GCSE SCHEME OF WORK
INTERMEDIATE TIER
AUTUMN TERM
Module 1
Number
|
Aim:
Understanding place value and extending the number system |
Objectives |
Resources |
Teachers Notes |
|
Understand and use the concept of place value in
whole numbers and decimals. Relate this to computation and the metric system
of measurement. |
·
Read,
write and order whole numbers of any magnitude given in figures or words. ·
Rounding
decimals to a given number of decimal places. ·
Rounding
numbers to a given number of significant figures. ·
Write
numbers to the nearest 10, 100, 1000 etc. ·
Order
decimals and understand place values. ·
Understand
the use of decimals in measures e.g. 0.5m = 50cm |
SEG Intermediate Ch 1, 2, 3 Worksheets 4X Ex 5.10 5.11 |
|
|
Aim:
Understanding and using relationships between numbers and developing methods
of computation |
Objectives |
Resources |
Teachers Notes |
|
Consolidate knowledge of number facts, including
multiplication to 10 ΄ 10, developing use of
methods for finding quickly from known facts those which they cannot recall;
use some common properties of numbers, including multiples, factors and
primes, powers and roots. |
·
Same
as Foundation tier. ·
Relationship
between power and roots, meaning of reciprocals. ·
To
include expressing a positive integer as a product of primes; finding the
Highest Common Factor (HCF) and Lowest Common Multiple (LCM). |
SEG Intermediate Ch 5, 6 Worksheets 4X Ex 5.3 4X Ex 5.12 5.14 |
|
|
Extend mental methods of computation, to
consolidate a range of non-calculator methods of addition and subtraction of
whole numbers and multiplication and division of whole numbers by whole
numbers, understanding and using accurately the methods that they choose. |
·
The
understanding and use of a non-calculator method to multiply and divide whole
numbers up to, and including, multiplication and division of a three-digit
number by a two-digit number. ·
Understand
order of operation BODMAS. ·
Refer
to the National Numeracy Strategy. |
SEG Intermediate Ch 1 Worksheets |
|
|
Mentally estimate and approximate solutions to
numerical calculations. Leading to multiplication and division with
numbers of any size rounded to one significant figure. |
·
Use
estimation in multiplication and division problems with whole numbers to
obtain approximate answers, e.g. ·
Multiplying
and dividing mentally single digit numbers of powers of 10 with whole number
answers. |
SEG Intermediate Ch 3 Worksheets |
|
AUTUMN TERM
Aim: Solving Numerical problems
|
Objectives |
Resources |
Teachers Notes |
|
Use a variety of checking strategies and apply
them appropriately to calculations; use estimation and inverse operations,
and confirm that results are of the right order of magnitude. |
·
Use
estimation and approximation to predict and then confirm results to addition,
subtraction, multiplication and division problems involving whole numbers are
correct. ·
Use
the inverse method to check results. ·
This
includes solutions obtained using a calculator. |
SEG Intermediate Ch 1 Worksheets |
|
|
Aim:
Understanding place value and extending the number system |
Objectives |
Resources |
Teachers Notes |
|
Understand and use decimals, ratios, fractions and
percentages, and the interrelationships between them. Understand and use negative numbers. |
·
Equivalence
between decimals, fraction, percentages and ratios. ·
Round
to a given number of decimal places. ·
Use
with understanding directed numbers in practical situations. ·
Ordering
directed numbers and adding and subtracting negative numbers in context. Not
multiplying or dividing by a negative number. |
SEG Intermediate Ch 8, 9, 10 Worksheets 4X Ex 1.1 1.2 4X Ex 1.6 1.7 4X Ex 11.1 11.7 |
|
|
Understand and use index notation, leading to
standard form |
·
Reinforce
words square and cube. ·
Understand
the meaning of ·
Express
and use number in standard form, with positive and negative powers of 10. ·
Use
rules of indices using positive and negative and zero indices. |
SEG Intermediate Ch 5 Worksheets 4X Ex 5.5, 5.8 4X Ex 5.4, 5.7 |
|
AUTUMN TERM
Algebra
|
Aim:
Understanding and using functional relationships |
Objectives |
Resources |
Teachers Notes |
|
Appreciate the use of letters to represent
variables. |
|
SEG Intermediate Ch 13 Worksheets |
|
|
Explore number patterns arising from a variety of
situations, using computers where appropriate; interpret, generalise and use
simple relationships, and generate rules for number sequences; express simple
functions initially in words and then symbolically, representing them in
graphical or tabular form. |
·
Recognise,
describe, continue and explain patterns in number; e.g. recognise square and triangular numbers, generate a Fibonacci
sequence. ·
Find
the ·
Represent
the nth term
graphically, and predict further terms from the graph. |
SEG Intermediate Ch 15, 16 Worksheets |
|
|
Aim:
Understanding and using equations and formulae |
Objectives |
Resources |
Teachers Notes |
|
|
·
Simplify
expressions for example |
SEG Intermediate Ch 13 Worksheets |
|
|
Construct, interpret and evaluate formulae and
expressions, given in words or symbols, related to mathematics or other subjects,
or real-life situations, using computers and calculators where appropriate. |
·
Substitution
of positive and negative whole numbers, fractions and decimals into simple
formulae expressed in words and symbols. |
SEG Intermediate Ch 15 Worksheets 4X Ex 4.1 4.2 |
|
|
Solving Equations |
·
Solve
equations, for example 2x + 2 = 4.7
and x2 3 = 6. Using
decimal values encourages the pupils to adopt an appropriate strategy, and
will reinforce work on decimals. ·
Pupils
check the solution by substitution. |
SEG Intermediate Ch 15, 19 Worksheets |
|
AUTUMN TERM
Shape, space and
measures
|
Aim:
Understanding and using measures |
Objectives |
Resources |
Teachers Notes |
|
Read and interpret scales, including decimal scales. |
|
Worksheets |
|
|
Find perimeters, areas and volumes of common
shapes, including circles and cylinders, by counting and dissection methods
and use of standard formulae. |
·
Areas
of composite figures ·
Perimeters
of squares, rectangles, triangles and circumference of circles; ·
Areas
of squares, rectangles, right-angled triangles and circles; ·
Volumes
of cubes and cuboids. |
SEG Intermediate Ch 27, 28, 29 Worksheets |
|
Handling
data
|
Aim:
Processing and interpreting data |
Objectives |
Resources |
Teachers Notes |
|
Design and use data collection sheets, access
required information from tables, lists and computer databases. Make frequency tables for grouped data, where
appropriate. |
·
Sort,
classify and tabulate qualitative (categorical) data and discrete or
continuous quantitative data.
Grouping of discrete data or continuous data into class intervals of
equal width. |
SEG Intermediate Ch 33 Worksheets |
|
|
Design a questionnaire or an experiment to capture
the data needed to follow lines of enquiry. |
·
Design
and criticise questions for a questionnaire.
Includes simple notion of 'fairness' (in experimental design). |
Worksheets |
|
|
Construct appropriate diagrams and graphs to
represent discrete and continuous data, including bar charts, line graphs,
pie charts, frequency polygons, scatter diagrams. |
·
Construct
and interpret pictograms, bar charts and pie charts for qualitative
data. ·
Construct
frequency polygons for grouped discrete data. ·
Understand
and know that intermediate values in a line graph may or may not have
meaning. |
SEG Intermediate Ch 34 Worksheets 4X Ex 10.1 10.7 |
|
SPRING TERM
Module 2
Number
|
Aim:
Understanding and using relationships between numbers and developing methods
of computation |
Objectives |
Resources |
Teachers Notes |
|
Calculate with negative numbers, decimals,
fractions, percentages and ratio, understanding the effects of operations, e.g. squaring, multiplying and dividing by
numbers between 0 and 1, and selecting an appropriate non-calculator or
calculator method. |
·
Use
the four rules applied to decimals, fractions and negative numbers. ·
Calculate
fractions and percentages of quantities.
·
Convert
fractions to decimals and percentages. ·
Express
one number as a fraction or percentage of another. ·
Calculate
using ratios in a variety of situations in context. ·
Simple
Proportional division |
SEG Intermediate Ch 1, 2, 8, 9,10 Worksheets 4X Ex 1.3 1.5 4X Ex 1.8 1.9 |
|
|
Aim: Solving
numerical problems |
Objectives |
Resources |
Teachers Notes |
|
Select suitable sequences of operations and
methods of computation, including trial-and-improvement methods to solve
problems involving integers, decimals, fractions, ratios and percentages. Using a spreadsheet to consider sets of
numbers that have a given sum and find the set that has the maximum product. |
·
Give
approximate answers to a specified number of significant figures. ·
Understand
how to use trial and improvement to solve numerical problems. ·
Decimals,
Fractions, Ratio and Percentages. |
SEG Intermediate Ch 3 Worksheets |
|
SPRING TERM
Algebra
|
Aim:
Understanding and using equations and formulae |
Objectives |
Resources |
Teachers Notes |
|
Manipulate algebraic expressions; form and
manipulate equations in order to solve problems. |
Recap, reinforce and develop work from beginning
of course. · Collect like terms, find
common factors, multiply out two brackets · · Factorise · Simplify algebraic
expressions involving sums, differences, products and powers. · Use the rules of indices
for positive integer values. · Simplify expressions such
as |
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