Yearly Plan Maths Form 5

Yearly Plan – Mathematics Form 5

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Learning ObjectivesPupils will be taught to.....

Learning OutcomesPupils will be able to…

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Suggested Teaching & Learning activities/Learning Skills/Values

Points to Note

Learning Area : NUMBER BASES -- 2 weeks

First Term

1 1. Understand and use the concept of number in base two, eight and five.

2/1/2012-8/1/2012

(i) State zero, one, two, three, …, as a number in base:

a) two

b) eight

c) five

(ii) State the value of a digit of a number in base:

a) two

b) eight

c) five

(iii) Write a number in base:

a) two

b) eight

c) five

in expanded notation

1

1

2

Use models such as a clock face or a counter which uses a particular number base.

Discuss- Dicuss digits used- Place valuesin the number system with a particular number base.

Skill : Interpretation, observe connection between base two, eight and five.

Use of daily life examples

Values : systematic, careful, patient

Emphasis the ways to read numbers in variours bases. Give examples:

Numbers in base two are also know as binary numbers.

Expanded notationGive examples

2 9/1/2012-15/1/2012 (iv) Convert a number in base: a) two b) eight c) five to a number in base ten and

vice versa.

2 Use number base blocks of twos, eights and fives.

Perform repeated division to convert a number in base ten to a number in other bases.Give examples.

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(v) Convert a number in a certain base to a number in another base.

(vi) Perform computations involving :

a) addition b) subtration of two numbers in base two

3

1

Discuss the special case of converting a number in base two directly to a number in base eight and vice versa.

Skill : Interpretation, converting numbers to base of two, eight, five and then.

Use of daily life examples

Values : systematic, careful, patient

Limit conversion of numbers to base two, eight and five only.

The usage of scientific calculator in performing the computitations.

Topic 2 : Graphs of Functions II --- 3 weeks

32.1 Understand and

use the concept of graphs of functions

16/1/2012-22/1/2012

(i) Draw the graph of a: a) linear function : y = ax + b, where a and b are constant; b) quadratic function , where a, b and c are constans, c) cubic function : , where a, b, c and d are constants,

d) reciprocal function

, where a is a

constants,

2 Explore graphs of functions using graphing calculator or the GSP

Compare the characteristic of graphs of functions with different values of constants.

Values : Logical thinking

Skills : seeing connection, using the GSP

Questions for 1..2(b) are given in the form of ; a and b are numerical values.

Limit cubic functions.Refer to CS.

2

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4

23/1/2012-29/1/2012

(ii) Find from the graph a) the value of y, given a value of x b) the value(s) of x, given a value of y

(iii) Identify: a) the shape of graph given a type of function b) the type of function given a graph c) the graph given a function and vice versa

(iv) Sketch the graph of a given linear, quadratic, cubic or reciprocal function.

CHINESE NEW YEAR

1

2

2

Play a game or quiz

For certain functions and some values of y, there could be no corresponding values of x.

Limit the cubic and quadratic functions.Refer to CS.

Limit cubic functions.Refer to CS.

4 2.2 Understand and use the concept of the solution of an equation by graphical method.

30/1/2012-5/2/2012

(i) Find the point(s) of intersection of two graphs

(ii) Obtain the solution of an equation by finding the point(s) of intersection of two graphs

(iii) Solve problems involving solution of an equation by graphical

1

1

2

Explore using graphing calculator of GST to relate the x-coordinate of a point of intersection of two appropriate graphs to the solution of a given equation. Make generalisation about the point(s) of intersection of the two graphs.

Use everyday problems.

Skills : Mental process

Use the traditional graph plotting exercise if the graphing calculator or the GSP is unavailable.

Involve everyday problems.

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method.

5 2.3 Understand and use the concept of the region representing inequalities in two variables.

6/2/2012-12/2/2012

(i) Determine whether a given point satisfies a) or or

(ii) Determine the position of a given point relative to the equation

(iii) Identify the region satisfying or

(iv) Shade the regions representing the inequalities a) or b) or

(v) Determine the region which satisfy two or more simultaneous linear inequalities.

2

2

2

Include situations involving , , , or .

Values: Making conclusion, connection and comparison, careful

Emphasise on the use of dashed and solid line as well as the concept of region.

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Learning Outcomes Pupils will be able to…

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Topic/Learning Area :

TRANSFORMATIONS III ( 3 weeks )

13.1 Understanding

and use of the concept of combination of two transformations.

13/2/2012-19/2/2012

(i) determine the image of an object under combination of two isometric transformations.

1 using CD-Rom – interactive activities.

Everyday life example: around the school.

Recall the types of transformations:

- translation- rotation- reflection- enlargement- isometric

transformation

(ii) determine the image of an object under combination of:

a. two enlargements

b. an enlargement and and an isometric transformation.

2 using Geometer’s Sketchpad. CD-Rom Give variety of examples to

show an enlargement and isometric transformation.

5

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(iii) Draw the image of an object under combination of two transformations.

(iv) State the coordinates of the image of a point under combined transformations.

2 Give examples on the blackboard and students are asked to draw the image under 2 transformations

Tr. will state the coordinates of the image of a point under combined transformations.

220/2/2012-26/2/2012

(v) Determine whether combined transformation AB is equivalent to combined transformation BA.

3 Using Maths exercise books (grids)

Do exercises from the textbooks

(vi) specify two successive transformations in a combined transformation given the object and the image.

Outdoor activity – students are brought to specific site of the school compound and ask to identify the two successive transformations : pictures should consist of an object and an image.

327/2/2012-29/2/2012

(vii) Specify a transformation which is equivalent to the combination of two isometric transformations.

(viii) Solve problems involving transformations.

5 Classroom activities – use GSP and CD-ROM (Multimedia Gallery)

To specify isometric transformation

Different examples to be given

Various problem solving questions to be given

- limit to translation, reflation & rotation.

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1/3/2012-9/3/2012

10/3/2012-18/3/2012

FIRST SCHOOL EXAMINATION

SCHOOL HOLIDAYS

Topic/Learning Area :

MATRICES ( 4 weeks )

4 4.1 Understand and use the concept of matrix.

19/3/2012-25/3/2012

(i) Form a matrix from given information.

(ii) Determine:

a. the number of rows

b. the number of columns

c. the order of a matrix

(iii) Identify a specific element in a matrix

1 Understanding the concept of matrices through daily examples:

- price of food on a menu- a contingent of altelitic- seating of students in

class- mark sheet of students

Introduce the order (mxn) of a matrix

Class activity – students are requested to identify the students’ seating position in class

Other examples give

* m represents row * n represents column

4.2 Understand and use the concept of equal matrices.

(i) Determine whether two matrices are equal.

(ii) Solve problems involving equal matrices.

2 Teacher gives examples of two equal matrices and discusses equal matrices in terms of the corresponding elements.

Different problems given to solve equal matrices.

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4.3 Perform addition and subtraction on matrices.

(i) Relate to real life situations such as keeping score of medal tally or points in sports.

(ii) Find the sum or the difference of two matrices.

(iii) Perform addition and subtraction on a few matrices.

(iv) Solve matrix equations involving addition and subtraction.

2 Teacher shows the examples from the textbook to determine how addition or subtraction can be performed on 2 given matrices.

Examples given to find the addition and subtraction of two matrices.

Examples given to solve matrix equations involving additions and subtractions

To include finding values of unknown elements

limit to not more than 3 rows and 3 columns.

4 4.4 Perform Multiplication of a matrix by a number.

26/3/2012-1/4/2012

(i) Multiply a matrix by a number.

(ii) Express a given matrix as a multiplication of another matrix by a number.

(iii) Perform calculation on matrices involving addition, subtraction and scalar multiplication.

(iv) Solve matrix equations involving addition, subtraction and scalar multiplication.

2 Teacher shows examples on scalar multiplication of matrix:- give examples of real life

situations such as in industrial productions.

examples given on the calculation of matrices involving addition, subtraction, and scalar multiplication.

Examples given on problem solving questions.

To include finding values of unknown elements.

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4.5 Perform multiplication of two matrices.

(i) determine whether two matrices can be multiplied and state the order of the product when the two matrices can be multiplied.

(ii) Find the product of two matrices.

(iii) Solve matrix equations involving multiplication of two matrices.

3 Teacher gives real life situations. Examples:-

- to find the cost of meals in the restaurant

- teacher shows how 2 matrices can be multiplied.

Examples given for the product of two matrices.

Examples given on problem solving involving multiplication of 2 matrices.

Limit to not more than 3 rows and 3 columns

Limit to 2 unknown elements

5 4.6 Understand and use the concept of identify matrix.

2/4/2012-8/4/2012

(i) determine whether a given matrix is an identity matrix by multiplying it to another matrix.

(ii) Write identity matrix of any order.

(iii) Perform calculation involving identity matrices.

2 Teacher discusses the property of the number as an identity for multiplication of a number.

Teacher introduces identity matrix or unit matrix.

Teacher gives examples of identity matrix of any order.

Teacher discusses the properties:

- AI = A- IA = A

Unit matrix is denoted by I.

Limit to 3 rows and 3 columns.

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4.7 Understand and use the concept of inverse matrix.

(i) Determine whether a

2 X 2 matrix is the

inverse matrix of

another 2 X 2

matrix.

(iii) Find the inverse matrix of a 2 X 2 matrix using:

a. the method of solving simultaneous linear equations

b. a formula

3 teacher introduces the concept of inverse matrix and its denotion.

Examples given on problem solving questions involving matrix:

- using simultaneous linear equations

- using a formula

-1 AA = I

6 4.8 Solve simultaneous linear equations by using matrices.

9/4/2012-15/4/2012

(i) Write simultaneous linear equations in matrix form.

(ii) Find the matrix in

using

the inverse matrix.

(iii) solve simultaneous linear equations by the matrix method.

(iv) Solve problems involving matrices.

5 Teacher shows examples how to write simultaneous linear equations in matrix form

To solve simultaneous linear equations by using inverse matrix

Project involving matrices using electronic spreadsheet to be given to students.

* limit to 2 unknowns.

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Topic/Learning Area : 5. VARIATIONS

(1 Weeks)

5.1 Understand and use the concept of direct variation16/4/2012-22/4/2012

(i) State the changes in a quantity with respect to the changes in another quantity, in everyday life situations involving direct variation.

(ii) Determine from given information whether a quantity.

(iii) Express a direct variation in the form of equation

Discuss the characteristics of the graph of y agains x when y x.

Relate mathematical variation to Charles’s Law or the mation of the simple pendulum.

Discuss the characteristics of the graphs of y against xn.

Communicative skills

Y varies directly as x , y x.y x n , limit n to 2, 3 and ½

Y = kx where k is the constant of variation.

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involving two variables.(iv) Find the value of a

variable in a direct variation when sufficient information is given.

(v) Solve problems involving direct variation for the following cases:

y x ; y x2 ; y x3 ; y x1/2 .

1

1

Coorperation an d systematic

5.2 Understand and use the concept of inverse variation

i) State the changes in a quantity with respect to changes in another quantity, in everyday life situations involving inverse variation.

ii) Determine form given information whether a quantity vaqries inversely as another quantity.

iii) Express an inverse variation in the form of equation involving two variables.

iv) Find the value of a

1

Discuss the the form of the graph and relates it to science, eg. Boyle’s Law.

Y varies inversely as x if and only if xy is a constant.

y 1/x

For the cases y 1/xn, limit n to 2,3 and ½

If y 1/x, then y = k/x, where k is the constan t of variation.

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variable in an inverse variation when sufficient information is given.

v) Solve problems involving inverse variation for the following cases:

y 1/x; y 1/x2

y 1/x3 ; y 1/x1/2

1For cases y 1/xn , n = 2,3 and ½, discuss the characteristics of the graph of y against 1/xn

Graph drawing skill

Be straight and honest.

Use:Y = k/x orx1y1=x2 y2

to get the solution.

5.3 Understand and use the concept of joint variation

23/4/2012-24/4/2012

(i) Represent a joint variation by using the symbol for the following cases:

a) two direct variations b) two inverse variations c) a direct variation and an inverse variation.

(ii) Express a joint variation in the form of equation.

(iii) Find the value of a

1

1

Discuss joint variation for the three cases in everyday life situations.

Relate to science, eg. Ohm’s Law.

For the cases y xn zn,Y 1/ xn zn and y xn / zn,Limit n to 2,3 and ½.

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variable in a joint variation when sufficient information is given.

(iv) Solve problems involving joint variation.

1

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Topic/Learning Area 6: GRADIENT & AREA UNDER A GRAPH --- 3½ weeks

15

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6.1 Understand and use the concept of quantity represented by the gradient of a graph

25/4/2012-29/4/2012

30/4/2012-6/5/2012

(i) State the quantity represented by the gradient of a graph

(ii) Draw the distance-time graph, given:

a) a table of distance-time values

b) a relationship between distance and time

(iii) Find and interpret the gradient of a distance-time graph

(iv) Find the speed for a period of time from a distance-time graph

(v) Draw a graph to show the relationship between two variables representing certain measurements and state the meaning of its gradient

1

2

2

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2

Use examples in various areas such as technology and social science

Use of daily life examples like speed of a car, Formula One Grand Prix, a sprinter

Compare and differentiate between distance-time graph and speed-time graph

Use real life situations such as traveling from one place to another by train or by bus.

Use examples in social science and economy, for example, the increase in population in certain years

Limit to graph of a straight line.

The gradient of a graph represents the rate of change of a quantity on the vertical axis with respect to the change of another quantity on the horizontal axis. The rate of change may have a specific name for example ‘speed’ for a distance-time graph.

Emphasise that: Gradient = change of distance Time = speed

Include graphs which consists of a combination of a few straight lines.For example,

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Distance, s

Time, t

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6.2 Understand the concept of quantityrepresented by the area under a graph

7/5/2012-10/5/2012

11/5/2012-25/5/2012

26/5/2012-10/6/2012

(i) State the quantity represented by the area under a graph

(ii) Find the area under a graph

(iii) Determine the distance by finding the area under the following of speed-time graphs:a. v=k (uniform speed)b. v=ktc. v=kt + hd. a combination of the above

(iv) Solve problems involving gradient and area under a graph.

SECOND SCHOOL EXAMINATION

SCHOOL HOLIDAYS

1

2

4

2

Discuss that in certain cases, the area under a graph may not represent any meaningful quantity.For example:The area under the distance-time graph. Discuss the formula for finding the area under a graph involving: A straight line which is parallel to

the x-axis A straight lien in the form of

y=kx+ hA combination of the above.

Include speed-time and acceleration-time graphs.

Limit to graph of a straight line or a combination of a few straight lines.

V represents speed, t represents time, h and k are constants. For example:

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Speed, v

time, t

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Topic/Learning Area : PROBABALITY II

Second Term --- 2 weeks

1 7.1 Understand and use the concept of probability of an event.

11/6/2012-17/6/2012

(i) Determine the sample space of an experiment with equally likely outcomes.

(ii) Determine the probability of an event with equiprobable sample space.

(iii)Solve problems involving probability of an event.

1

1

1

Discuss equiprobable sample space through concrete activities and begin with simple cases such as tossing a fair coin.

Use tree diagrams to obtain sample

space for tossing a fair coin or

tossing or tossing a fair dice

activities. The Graphing calculator may also be used to simulate these activities.

Discuss events that produce

P(A) = 1 and P(A) = 0

Limit to sample space with equally likely outcomes.

A sample space in which each outcomes is equally likely is called equiprobable sample space.

The probability of an outcome A, with equiprobable sample space

S, is P(A) = Use tree diagram where appropriate.

Include everyday problems and making predictions.

7.2 Understand and used the concept of probability of the complement of an event.

(i) State the complement of an event in :

(a) words (b) set notations (ii) Find the probability of the

complement of an event.

1

1

Include events in real life situations such as winning or losing a game and passing or failing an exam.

The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A.

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2 7.3 Understand use the concept of probability of combined event.

18/6/2012-24/6/2012

(i) List the outcomes for events: (a) A or B as elements of set A B (b) A and B as elements of set A B

(ii) Find the probability by listing the outcomes of the combined events : (a) A or B (b) A and B

(iii) Solve problems involving probability of combined events.

2

2

1

Use real life situations to show the relationship between

A or B and A B A and B and A B.

An example of a situation is being chosen to be a member of an exclusive club with restricted conditions.Use tree diagram and coordinate planes to find all the outcomes of combined events.

Use two-way classification tables of events from newspaper articles or statistical data to find probability of combined events. Ask students to create tree diagrams from these tables. Example of a two-way classification table :

Means of going to workOfficers Car Bus OthersMen 56 25 83Women 50 42 37

Discuss : situations where decisions

have to be made on probability, for example in business, such as determining the value for aspecific insurance policy and time the slot for TV advertisements

the statement “probability is the underlying language of statistics”

Emphasise that : knowledge about probability is

useful in making decisions. prediction based on probability

is not definite or absolute.

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Topic/Learning Area : BEARING --- 1 week

18.1. Understand and use the concept of bearing.

25/6/2012-1/7/2012

(i) Draw and label the eight main compass directions:

a) north, south, east, west

b) north – east, north – west, south – east, south – west

ii) State the compass angle of any compass direction.

(iii) Draw a diagram of a point which shows the direction of B relative to another point A given the bearing of B from A.

(iv) State the bearing point A from point B based on given information.

(v) Solve problems involving bearing.

1

1

1

2

Carry out the activities or games involving finding directions using a compass such as treasure hunt or scravenger hubt. It can also be about locating several points on a map, finding the position of students in class.

Discuss the use of bearing in real life situations. For example, a map reading and navigation.

Compass angle and bearing are written in three digit form, from 0000 to 3600. They are measured in a clockwise direction from north. Due north is considered as bearing 0000. For cases involving degrees up to one decimal point.

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Topic 9Learning Area: EARTH AS SPHERE ( 1 weeks )

9.1 Understand and use the concept of longitude

2/7/2012-8/7/2012

(i) Sketch a great circle through the north and south poles.

(ii) State the longitude of a given point.

(iii) Sketch and label a meridian with the longitude given.

(iv) Find the difference between two longitudes

1

1

Model such as globes should be used.

Introduce the meridian through Greenwich in England as the Greenwich Meridian with longitude 0°

Discuss that:

All points on a meridian have the same longitude

There are two meridians on a great circle through both poles.

Meridians with longitude x°E(or W) and (180°- x°)W(or E) form a great circle through both poles.

Emphasise that longitude 180°E and longitue 180°W refer to the same meridian.

Express the difference between two longitudes with an angle in the range of 0° ≤ x ≤ 180°

9.2 Understand and use the concept of latitude

(i) Sketch a circle parallel to the equator.

(ii) State the latitude of a given point.

(iii) Sketch and label a parallel of latitude.

(iv) Find the difference between two latitudes.

1

1

Discuss that all the points on a paralell of latitude have the same latitude.

Emphasise that o the latitude of the equator is 0°o latitude ranges from 0° to 90°N

( or S )

Involve actual places on the earth.

Express the diffrence between two latitudes with an angle in the range of 0° ≤ x ≤ 180°.

9.3 Understand the concept of locations of a

Use a globe or a map to find locations of cities around the world. 1

i. State the latitude and longitude of a given place

A place on the surface of the earth is represented by a point.

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place. Use a globe or map to name a place given its location.

1

ii. Mark the location of a place

iii. Sketch and label the latitude and longitude of a given place.

iv.

The, location of a place A at latitude x°N and longitude y°E is written ,as A(x°N, y°E).

9.4 Understand and use the concept of distance on the surface on the earth to solve problems.

(i) Find the length of an arc of a great circle in nautical mile, given the subtended angle at the centre of the earth and vice versa.

(ii) Find the distance between two points measured along a meridian, given the latitudes of both points.

(iii)Find a latitude of a point given the latitude of another point and the distance between the two points along the same meridian.(iv) Find the distance between two points measured along the equator, given the longitude of both points.(v) Find the longitude of a point given the longitude of another point and the distance between the two points along the equator.

(vi) State the relation betwen the radius of the earth and the radius of a parallel of latitude.

(vii) State the relation between the length of an arc on the equatoq between two meridian and the lengthe of the corresponding arc on a parallel of latitude.

(viii) Find the distance between two points measured along a parallel of latitude.

(ix) Find the longitude of a point given the longitude of another point and the distance between the two points along a parallel of latitude.

(x) Find the shortest distance between two points on the surface of the earth.

(xi) Solve problems involving : (a) distance between two points.

(b) travelling on the surface of the earth.

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Use the globe to find the distance between two cities or town on the same meridian.

Sketch the angle at the centre of the earth that is subtentded by the arc between two given points along the equator. Discuss how to find the value of this angle.

Use models such as the globe to find relationship between the radius of the earth and radii parallel of latitudes.

Find the distance between two cities or town on the same parallel of latitude as a group project.

Use the globe and a few pieces of string to show how to determine the shortest distance between two points on the surface of the earth.

Limit to nautical mile as the unit for distance.

Explain one nautical mile as the length of the arc of a great circle subtending a one minute angle at the centre of the earth.

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Limit to two points on the equator or the great a cirle through the polas.

Use knot as the unit for speed navigation and aviation.Week

NoLearning Objectives

Pupils will be taught to.....


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Topic 10

Learning Area: PLANS AND ELEVATIONS

2 weeks

1 10.1 Understand and use the concept of orthogonal projection.

9/7/2012-15/7/2012

i. Identify orthogonal projections.

ii. Draw orthogonal projections, given an object and a plane.

iii. Determine the difference between an object and its orthogonal projections with respect to edges and angles.

1

2

2

Use models, blocks or plan and elevation kit.

Emphasise the different uses of dashed lines and solid lines.

Begin wth the simple solid object such as cube, cuboid, cylinder, cone, prism and right pyramid.

2 10.2 Understand and use the concept of plan and elevation.

16/7/2012-22/7/2012

i. Draw the plan of a solid object.

ii. Draw- the front elevation- side elevation

of a solid object

1

2

Carry out activities in groups where students combine two or more different shapes of simple solid objects into interesting models and draw plans and elevation for thes models.

Limit to full-scale drawings only.

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STARY FROM23/7/2012

iii. Draw the plan of a solid object.

iv. Draw- the front elevation- side elevation

of a solid object

REVISION

1

1

Use models to show that it is important to have a plan and at least two side elevation to construct a solid object.

Carry out group project:Draw plan and elevations of buildings or structures, for example students’ or teacher’s dream home and construct a scale model based on the drawings. Involve real life situations such as in building prototypes and using actual home plans.

Include drawing plan and elevation in one diagram showing projection lines.

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Documents

Yearly Plan Maths Form 5