THEALE GREEN COMMUNITY SCHOOL

MATHEMATICS DEPARTMENT

 

 

GCSE SCHEME OF WORK

 

HIGHER 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 Higher Ch 3, 7

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 Higher Ch 4

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.

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. » 6000.

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

SEG Higher 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 Higher Ch 3

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 Higher Ch 1

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

·   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 Higher Ch 4

Worksheets

4X – Ex 5.5, 5.8

4X – Ex 5.4, 5.7

 

 

 

 

 

Further Material

Objectives

Resources
Teachers Notes

Understand and use direct and inverse proportion.

·   For example:,  ,  ,  ,  .

SEG Higher Ch 5

Worksheets

4Y – Ex 9.1 – 9.5

 

 

Distinguish between rational and irrational numbers, and appreciate that irrational numbers complete the real number system.

·   Converting recurring decimals to fractional forms.

·   Simplification of expressions involving surds, but excluding rationalising the denominator of a form such as .

SEG Higher Ch 6

Worksheets

4Y – Ex 3.1 – 3.3

 

 

 

 

AUTUMN TERM

Algebra

Aim: Understanding and using functional relationships

Objectives

Resources

Teachers Notes

Appreciate the use of letters to represent variables.

 

SEG Higher Ch 8

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  term of the sequence where the rule is linear or quadratic

·   Represent the nth term graphically, and predict further terms from the graph.

SEG Higher Ch 9

Worksheets

 

 

Aim: Understanding and using equations and formulae

Objectives

Resources

Teachers Notes

Appreciate the use of letters to represent unknowns.

·          Simplify expressions for example

         

 

 

SEG Higher Ch 9

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 Higher Ch 8

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 Higher Ch 8

Worksheets

 

 

 

Further Material

Objectives

Resources

Teachers Notes

Generate rules for number sequences

·   Find the rule for the nth term of a sequence (linear or quadratic)

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.

·   Perimeters of squares, rectangles, triangles and circumference of circles;

·   Areas of squares, rectangles, right-angled triangles, circles and composite figures

·   Volumes of cubes and cuboids.

SEG Higher Ch 23

Worksheets

 

 

Further Material

Objectives

Resources
Teachers Notes

Extend measurement, including distances and angles, to more complex plane shapes and solids, including circular arcs, cylinders, cones and spheres; understand and use relationships between similar figures and solids.

·   Calculate lengths of arcs, areas of sectors and segments; prisms and pyramids should be covered.

·   Similar figures (including solids)

SEG Higher Ch 19

Worksheets

4Y – Ex 4.1 – 4.3

4Y – Ex 4.4

 

Use angle and tangent properties of circles.

·   Know and use angle and tangent properties of circles.  Angles in the same segment are equal; angle at the centre is twice the angle at the circumference; opposite angles of a cyclic quadrilateral sum to 180°; angle between tangent and radius is 90°; angle between the tangent and the chord is equal to the angle in the alternate segment; tangents from an external point are equal.

SEG Higher Ch 18

Worksheets

5Y – Ex 8.1 – 8.5

ICT: Cabri (booklets)

 

 

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 Higher Ch 28

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).

SEG Higher Ch 28

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 Higher Ch 29

Worksheets

4X – Ex 10.1 – 10.7