.

THEALE GREEN COMMUNITY SCHOOL

MATHEMATICS DEPARTMENT

 

 

GCSE SCHEME OF WORK

 

FOUNDATION 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.

·   Understand decimal places.

·   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 GCSE Foundation

Worksheets Ch 1, 2

4W – Ex 1.4, 1.5, 1.16

 

4W – Ex 5.19 – 5.22

4W – Ex 3.16, 3.17,

          5.16,  5.2 – 5.7

 

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.

·   Know all tables upto 10 ΄ 10

·   Odd, even, prime, square and cube numbers

·   Factor, multiples, powers and roots.

·   Find LCM and HCF.

·   Number patterns, including square, triangular and rectangular numbers.

SEG GCSE Foundation Ch 4,14

Worksheets

4W – Ex 6.8 – 6.12

4W – Ex 5.29 – 5.35

 

 

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 GCSE  Foundation Ch 1

Worksheets

4W – Ex 3.22, 5.12

 

Mentally estimate and approximate solutions to numerical calculations.

 

(Leading to multiplication and division with numbers of any size rounded to one significant figure – not assessed)

·   Use estimation in multiplication and division problems with whole numbers to obtain approximate answers, e.g. » 6000.

·   Multiplying and dividing mentally single digit numbers of powers of 10 with whole number answers.

SEG GCSE

Foundation Ch 2

Worksheets

4W – Ex 3.13

4W – Ex 3.10 – 3.12,

           3.15

 

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 that the results to addition, subtraction, multiplication and division problems involving whole numbers are correct.

·   Use the inverse method to check results.

SEG GCSE

Foundation Ch 2

Worksheets

4W – Ex 3.18, 5.16,

           5.17

 

 

 

AUTUMN TERM

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, fractions, ratios and percentages; e.g. know that.

  

·   Round to a given number of decimal places.

·   Introduce Ratio.

·   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 GCSE

Foundation Ch 3, 5, 7, 8

Worksheets

 

 

Understand and use index notation.

 

(Leading to standard form – not assessed)

·   Understanding and use of index notation for positive integral index.

·   Reinforce words ‘square’ and ‘cube’.

·   Understand the meaning of  where  and n is a positive integer, in the context of a calculator display.

SEG GCSE

Foundation Ch 4

Worksheets

 

 

 

AUTUMN TERM

Algebra

Aim: Understanding and using functional relationships

Objectives

Resources

Teachers Notes

Appreciate the use of letters to represent variables.

·   Understand reasons for using letters.

SEG GCSE

Foundation Ch 11

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. 

·   Describe in words the rule for the next term in the sequence. 

·   Recap and reinforce mappings.

·   Find the  term of the sequence where the rule is linear.

·   Represent the nth term graphically (straight-line graph).

SEG GCSE

Foundation Ch 14

Worksheets

4W – Ex 6.13 – 6.15

 

 

 

Aim: Understanding and using equations and formulae

Objectives

Resources

Teachers Notes

Appreciate the use of letters to represent unknowns.

·          Simplify expressions for example

          3a + b – a + 3b

 

SEG GCSE

Foundation Ch 11

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 GCSE

Foundation Ch 11

Worksheets

4W – Ex 4.5 – 4.8

4W – Ex 4.14

 

Solving Simple Equations

·   Solve simple equations, for example x + 2 = 4.7 and x – 3 = 3.5. Using decimal values encourages the pupils to adopt an appropriate strategy, and will reinforce work on decimals.

·   Pupils check the solution by substitution.

SEG GCSE

Foundation Ch 12

Worksheets

 

 

AUTUMN TERM

Shape, space and measures

Aim: Understanding and using measures

Objectives

Resources

Teachers Notes

Read and interpret scales, including decimal scales.

 

 

 

 

SEG GCSE

Foundation Ch 24

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 GCSE

Foundation Ch 21,22

Worksheets 4W – Ex 11.17, 11.18

 

 

 

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.

·   Understand and use tallying methods.

·   Understand meaning of Frequency.

·   Able to select an appropriate group interval for grouped data.

SEG GCSE

Foundation Ch 25

Worksheets

4W – Ex 6.24 – 6.28

 

 

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).

SEG GCSE

Foundation Ch 25

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 GCSE

Foundation Ch 26

Worksheets

4W – 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. 

·   Calculate fractions and percentages of quantities. 

·   Convert fractions to decimals and percentages.

·   Find one number as a percentage of another. 

·   Calculate using ratios in a variety of situations in context.

SEG GCSE

Foundation Ch 3, 6, 7, 8

Worksheets

 

 

 

 

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;

E.g. 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 decimal places.

·   Understand how to use trial and improvement to solve numerical problems.

·   Decimals, Fractions, Ratio and Percentages.

 

SEG GCSE

Foundation Ch 3

Worksheets

 

 

 

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.

·   Understand basic conventions; e.g.

·

·   Multiply out  where