Gcse Math Revised Support 6523

8/11/2019 Gcse Math Revised Support 6523

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REVISED GCSE

For First Teaching September 2010

For First Examination Summer 2011

This Unit Summer 2012

Scheme of WorkMathematics

Foundation Unit 5


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Unit T5


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Version 1: 28 April 10 2

Unit T5

This is a working document for teachers to adapt to their own specific needs.

Unit T5

Topic No. Topic Subject Content

1 Number Read, write and order numbers

2 Number The four operations

3 Number BODMAS

4 Algebra Unknowns5 Algebra Formulae

6 Geometry and Measures Area/Surface Area

7 Algebra Indices

8 Number Number Calculations

9 Algebra Graphs

10 Geometry and Measures Imperial Measures

11 Geometry and Measures Compound Measures

12 Number Ratios

13 Algebra Inequalities

14 Algebra Quadratic Functions

15 Number Estimation

16 Number Degree of Accuracy

17 Geometry and Measures 2D shapes

18 Geometry and Measures Constructions

19 Geometry and Measures Symmetry20 Geometry and Measures Transformations


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21 Number Language of Number

22 Number Multiplicative Inverses23 Number Multiplying and Dividing by multiples of ten

24 Handling Data Probability experiments

25 Handling Data Calculating probabilities

26 Handling Data Estimating probabilities

27 Handling Data Probability outcomes


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CCEA GCSE Mathematics from September 2010


TOPIC 1: NUMBER Read, write and order numbers UNIT: T5

Learning Objectives Learning and Teaching Strategies: Resources:

Pupils should be able to:

read, write and

order numbers.

How to put numbers in order. Place value of digits.

How to round off to the nearest ten, hundred, thousand.

Readings from rulers, jugs and any other measuring instrument.

Specimen P1 Q1(a)

Specimen P2 Q1


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TOPIC 2: NUMBER The four Operations UNIT: T5



understand the four

operations and the

relationshipbetween them.

Know addition and the effect it has.

Know subtraction and the effect it has.

Recognise that subtraction is the inverse of addition.Know multiplication and the effect it has.

Know division and the effect it has.

Recognise that division is the inverse of multiplication.


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TOPIC 3: NUMBER OPERATIONS AND APPLICATIONS BODMAS UNIT: T5



understand the

effects of operations

on numbers of anysize;

apply order of

precedence.

Class discussion: what effect addition, subtraction, multiplication and division

have on numbers (less than and greater than one).

Teacher demonstration: Introduce the term BODMAS. Explain what the letters

BODMAS represent and complete a number of worked examples. First without

brackets and then with brackets.

Worked example: Distinguish correctly between 3 + 2 5 and

(3 + 2) 5.

Solve problems requiring application of order of precedence.Example questions:

(a) 14 2 4 (b) 7 + 3 4 (c) (10 + 2) (14 5 + 1)

Distinguish correctly between:

7.128.9

2.7

and

8.9

2.7+ 12.7

Specimen P1, Q5


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TOPIC 4: TOPIC: ALGEBRA Unknowns UNIT: T5



understand key

concepts and terms;

appreciate the use of

letters to represent

unknowns.

Terms such as solve, simplify, substitute.

Distinguish between the different roles played by letter symbols in algebra.

Knowing that letter symbols represent: definite unknown numbers in equations (e.g. 5x+ 1 = 16),

defined quantities or variables in formulae (e.g. V = IR),

general unspecified numbers in identities (e.g. 3x+ 2x= 5xfor all values of

x)

and in functions they define new expressions or quantities by referring to

known quantities (e.g.y= 2x).

Specimen P1, Q6


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TOPIC 5: TOPIC: ALGEBRA Formulae UNIT: T5



understand key

concepts and terms;

understand,construct and

evaluate formulae

related to

Mathematics or

other subjects or

real-life situations;

change the subject

of linear formulae.

Construct simple algebraic formulae.

For example:

Mr Smith bought aapples and some oranges. He had 4 times as manyoranges as apples. How many oranges did he have?

He used half the apples in a pie and his son ate one. How many apples were

left?

To cook a chicken, allow 20 minutes per lb plus 20 minutes. A chicken

weighsxlb. Write an expression to show the number of minutes mto cook a

chicken.

Find an unknown where it is not the subject of the formula and where an equationmust be solved. For example, the formula for the change Cfrom 50 for d

compact discs at 7 each is C = 50 7d.If C = 15, what is d?

Change the subject of a formula using inverse operations. For example:

Make R the subject of V = IR

Make u the subject of v = u+ at

Specimen P2 Q3


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TOPIC 6: GEOMETRY AND MEASURESArea/Surface Area UNIT: T5



recall and use the

formula for the area

of squares andtriangles;

calculate the surface

areas of cubes and

cuboids.

Use to calculate the areas of compound shapes, parallelograms, rhombuses, kites

and trapezia.

Calculate the surface area of a box.

Illustrate the net of a cube as 6 joined squares. Calculate the area of one square

and hence the surface area of the cube.

Illustrate the net of a cuboid as 6 rectangles/squares, calculate area of each and

hence the surface area.

Specimen P2, Q8 (c)

Specimen P2, Q10


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TOPIC 7: ALGEBRA Indices UNIT: T5



use the rules of

indices for integral

values.

Use index notation for positive integer powers.

Know that expressions involving repeated multiplication of the same number,

such as nn; nnn; nnnnare written as n2, n3and n4and are referred to as

nsquared, ncubed and nto the power of 4, etc.

Understand the different meanings of expressions such as 2nand n2, 3nand n3.

Simplify expressions such as 2x2+ 3x2, n2 n3,p3p2

Know and use the general forms of the index laws for multiplication and divisionof integer powers:

pa pb= pa+b

pa pb= pa-b

(pa)b= pab

Specimen P2, Q11


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TOPIC 9: ALGEBRA Graphs UNIT: T5



interpret and display

information on

graphs that describe

real-life situations.

Conversion graphs

Discuss practical examples such as:

The number of euros you can exchange for pounds sterling

The number of km equal to miles

The cost of books at 3 each

Draw a graph of such information.

Observe that the points lie in a straight line.

Discuss, plot and interpret graphs (which may be non-linear) modelling real

situations.

Distance-time graphs including intersecting travel graphsPlot a simple distance-time graph.

Interpret a simple distance-time graph, giving plausible reasons for each section.

Specimen P2 Q5


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TOPIC 10: GEOMETRY AND MEASURES Imperial Measures UNIT: T5



know imperial

measures still in

common use

including foot, yard,

mile, pound and

pint and their

approximate metric

equivalents.

Recall that 1 kg is about 2.2 lb, 8 km is approximately 5 miles, 1 litre is about

1.75 pints.

Specimen P2, Q6


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TOPIC 11: TOPIC: GEOMETRY AND MEASURES Compound Measures UNIT: T5



understand and use

compound measures

including speed and

density.

Work out average speed (distance/time) density (mass/volume)

30 mph for 3 hours = 90 miles

120 miles in 3 hours = 40 mph

400 miles at 50 mph = 8 hours


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TOPIC 12: NUMBER OPERATIONS AND APPLICATIONS Ratios UNIT: T5



use unitary ratios

and calculate with

ratios in a variety of

situations;

divide a quantity in

a given ratio.

Unitary ratios: for example: 1:n or n:1. Know that if the ratio of cement to sand

is 1:3 then the ratio of sand to cement is 3:1. The order of the objects is very

important. Remember that the ratios are numbered in the same order as they are

written.

Example questions:

In a recipe, the ratio of flour to currants is 5:1. If you need 10 ounces of flour,

how many ounces of currants will you need?

Simplify ratios.

Use the approximation of 5 miles to 8 km to find the equivalent of 12 miles.

State the lengths 8cm and 12cm in a drawing are in the ratio 2:3

Adapt a recipe for six people to one for eight people.

Understand the relationship between fractions and ratios. Divide 10 between

two people in the ratio 2:3

Specimen P1, Q9


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TOPIC 13: ALGEBRA Inequalities UNIT: T5



understand key

concepts and terms;

solve inequalities on

a number line.

Solve linear inequalities in one variable.

Represent the solution set on a number line.

For example:

List the values of the integer nsuch 10 < 2n20

Solve the inequality 2n 3 7 illustrating the solution on a number line.

Solvex3x 5 wherexis a real number.

Specimen P2 Q12


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TOPIC 14: ALGEBRA Quadratic Functions UNIT: T5



explore the

properties of

quadratic functions.

Make tables of such functions.

Sketch and interpret their graphs using graphical calculators and computers to

understand their behaviour.

To include drawing graphs of y = ax2+ bx + c


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TOPIC 15: NUMBER Estimation UNIT: T5



approximate

numbers to the

nearest unit, 10 or

100;

estimate within

calculations

(initially with

numbers within 100

and extending to all

whole numbers).

Estimate that 1472 383 is about 1100 (1500 400)

Estimate that 278 39 is about 7 (280 40)

Understand that 32.24 9.75 is approximately 30 10

Recognise that7.5

4.8325.0 is about 3 or 4

Specimen P1 Q1(b)


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TOPIC 16: NUMBER Degree of Accuracy UNIT: T5



give solutions in the

context of a

problem to an

appropriate degree

of accuracy,

recognising

limitations on the

accuracy of data and

measurements.

Comment on the upper and lower bounds of data.

e.g. 10.5cm correct to the nearest tenth means a range from 10.45cm to 10.55cm.


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TOPIC 17: GEOMETRY AND MEASURES 2D Shapes UNIT: T5



explore shape

through drawing

and practical work

using a wide range

of materials.

Recognise and describe 2-D shapes.

Recognise right-angled corners in 2-D shapes.

Specimen P1, Q8


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TOPIC 18: GEOMETRY AND MEASURES Constructions UNIT: T5



use ruler and

compasses for

standard

constructions;

construct loci.

To include triangles, quadrilaterals, the mid-point and perpendicular bisector of a

line segment, the perpendicular from a point to a line, the perpendicular from apoint on a line and the bisector of an angle.

Region bounded by a circle and an intersecting line.


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TOPIC 19: GEOMETRY AND MEASURES Symmetry UNIT: T5



recognise symmetry

properties in a

variety of shapes in

two dimensions;

recognise line

symmetry;

draw the axes of

symmetry;

reflect shapes in a

mirror line;

recognise rotationalsymmetry, its order

and centre;

know and use

symmetry properties

of triangles,

quadrilaterals and

other polygons;

recognise planes of

symmetry in

practical situations.

Find the centres and axes of symmetry in a variety of shapes.

Rotate shapes using tracing paper.

Reflection to include rectilinear figures only.

Study shapes and identify some lines and planes of symmetry.

Specimen P1, Q4


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TOPIC 20: GEOMETRY AND MEASURES Transformations UNIT: T5



understand

transformation of

shapes;

reflect shapes in a

line,

[for example,x= 1];

rotate shapes about a

given centre;

translate shapes;

enlarge a shape

through a given centreof enlargement

recognise that

enlargements preserve

angle but not length;

distinguish properties

that are preserved

under particular

transformations.

Transformations will include single or combined enlargements, reflections,

rotations and translations.

Rotations will be limited to 90oand 180oabout a point.

Reflections will be limited to reflections in lines parallel to the co-ordinateaxes.

Vector notation for translation.

Enlarge a shape by a whole number scale factor only.

Use transformations to create and analyse spatial patterns.

Specimen P1, Q2

Specimen P1, Q12


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TOPIC 21: NUMBER Language of Number UNIT: T5



understand and use

the language of

number.

Reciprocal: understand the meaning of reciprocal and its place in number

patterns. If the product of two numbers is 1 then each number is called the

reciprocal of the other.

Example: You know that 2 = 1, so you say 2 is the reciprocal of and isthe reciprocal of 2.

Questions: What is the reciprocal of

(a) 7 (b) 10 (c) (d)

Specimen P1 Q11(a)

CCEA GCSE M th ti f S t b 2010


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TOPIC 22: NUMBER Multiplicative inverses UNIT: T5



use unit fractions as

multiplicative

inverses;

understand

reciprocal as

multiplicative

inverse.

Know that multiplication by5

1is equivalent to division by 5

Know that any non-zero number multiplied by its reciprocal is one and that zero

has no reciprocal, because division by zero is not defined.



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TOPIC 23: NUMBER Multiplying and Dividing by multiples of ten UNIT: T5



multiply and divide

mentally single digit

multiples of any

power of ten.Realise that, when

multiplying by a

number less than

one, multiplication

has a decreasing

effect, and division

an increasing effect.

Multiply by numbers less than 1. Divide by numbers less than 1 (using and not

using a calculator).

Work out mentally 80 0.2 and 600 0.2



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TOPIC 24: HANDLING DATA Probability experiments UNIT: T5



understand possible

outcomes of random

trials or experiments;

understand that there

is a degree of

uncertainty about the

occurrence of some

events, and others are

certain or impossible;

know that when

repeating the same

experiment, different

outcomes may result

and that the possible

outcomes may not be

equally likely;

understand and use 0

and 1 as the limits of

the probability scale.

Know what the term probability means. Know that you do not always get 5

heads in 10 tosses of a fair coin and very occasionally there will be none.

Discussions as to whether or not all outcomes are equally likely.

Place events in order of likelihood and use appropriate words to identify

chance. Mark the likelihood of events on a probability scale.

Specimen P2, Q9(a)

Specimen P1 Q10(c)

Specimen P2, Q7



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TOPIC 25: HANDLING DATA Calculating Probability UNIT: T5



know that for

equally likely

outcomes, the

probability of anevent is the number

of desirable

outcomes divided

by the number of

possible outcomes.

Know that if there are six identical beads numbered 1, 1, 2, 2, 3 and 4, the

probability of selecting a bead labelled 1 is 2/6 = 1/3

Calculate probabilities.

Write probabilities as fractions and simplify answers.Use probability to calculate expected frequency.

Specimen P1 Q7(a),(b)

Specimen P1 Q10(b)

Specimen P2, Q9(b)



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p


TOPIC 26: HANDLING DATA Estimating Probability UNIT: T5



recognise situations

where probabilities

can be based on

equally likelyoutcomes and others

where estimates

must be based on

sufficient

experimental

evidence and make

these estimates;

understand and use

relative frequency

as an estimate of

probability.

Experimental probability. Experiment to find the contents of a bag to introduce

relative frequency.

Find relative frequency.



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TOPIC 27: HANDLING DATA Probability outcomes UNIT: T5



identify all the

outcomes when

dealing with a

combination of twoindependent events

using diagrams or

tables, and use these

to find probabilities;

know that if there

are several possibleoutcomes

(exhaustive and

mutually exclusive),

the total of these

probabilities is 1.

understand that the

probability ofsomething

happening is 1

minus the

probability of it not

happening.

Complete sample space diagrams for various events. List all the outcomes when

tossing two coins; HH, TT, TH, HT.

Make a table of all the outcomes when throwing two dice and show the totalsums arising.

Find probabilities using sample spaces.

Calculate the probability that an event will not happen. Recognise that if theprobability of a machine failing is 0.05 then the probability of it not failing is

0.95

Specimen P1 Q10(a)Specimen P1 Q7(c)

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Gcse Math Revised Support 6523