l2 numeracy shape workbook 1

8/2/2019 L2 Numeracy Shape Workbook 1

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Everyday Maths Skills

Shape and space

Name:

Date:

Shape and space

All objects in the world are 3-D. They have three dimensions: height, widthand depth. However, when we look at a picture, a diagram or even aphotograph of an object, what we see is not 3-D. These are 2-D (two-dimensional) representations of 3-D objects.

In this topic you will learn about 2-D and 3-D and how to read and use 2-Drepresentations of 3-D objects.

What you will learn about

how 2-D drawings represent 3-D objects viewfrom above (plan view) view from the side (front, rear, left side, right side) combining views nets how to solve problems involving 2-D drawings and parallel lines.

You will find suggestions and answers for the Activities,Practices and Mini-test in the Answerpages.

1/20 Ufi Ltd February 2010. All rights reserved. learndirect is a registered trademark of Ufi Ltd. All information correct at time of publication.

Cecilia Nicoleta Trasca

22.09.2011


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Learning

How 2-D drawings represent 3-D objects

We often see two-dimensional drawings of three-dimensional objects. Although we visualisethem as solid objects, they are in fact drawn on a flat piece of paper, so they only have twodimensions height and width. What we see is a representation of an object from aparticular angle. This angle can give us the illusion of depth, but if we touch the object in thedrawing, it is flat.

Whatever angle it is taken from, a single drawing cannot show the whole of a 3-D object.For example, the back and underneath of each of these objects could be different coloursto the front and top. The left sides of objects 1 and 4 could be different colours to the rightsides. A single drawing cannot show this information.

Three or more views are often necessary to provide all the details about a 3-D object.Over the next pages we will learn about some of these different views.

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1

23

4

A Activity 1

a. All drawings are 2-D (two-dimensional) because they have two dimensions heightand width. Real-life objects are 3-D (three-dimensional) because they have threedimensions.What are the three dimensions?

Ufi Ltd February 2010. All rights reserved. learndirect is a registered trademark of Ufi Ltd. All information correct at time of publication.

height, width and depth


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Learning

View from above (plan view)

Drawings 1 to 6 each depict a 3-D object in plan view. Match each drawing to the object itdepicts. Type the corresponding letter in the box next to each number.

Plan view

1 2 3 4 5 6

a b c d e f

One viewpoint that is frequently used in drawings is plan view. This is a view from directlyabove. It is as though you are seeing a birds-eye view of the object. From this view, you seehorizontal surfaces. You cannot tell if part of a surface is closer or further away, though thedrawing may indicate that there are variations in height/depth (see example d).

Plan view

a b c d

a b cd

A Activity 2


b d f e c a


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Learning

Side view (front, rear, left side or right side view)

Side views look directly at oneside of a 3-D object.

If the object has different details on each side (e.g. a house with windows and doors), thedrawing will give a view of each side the front, the rear, the left side and the right side.If opposite sides of the object are exactly the same (e.g. the front and rear are the same,and the left and right side are the same, as in the example below) then just two side viewsare given.

Side views show vertical surfaces. You cannot tell if part of a vertical surface is closer orfurther away, but by piecing the drawings together, you can gather information aboutdepth. Check this out in the example below.

Front view Right side view

a

ba

b



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Learning

A Activity 3

Drawings 1 to 6 each depict a front view or a right side view of the 3-D objects below.

1 2 3 4 5 6

a b c

Match each drawing to the correct object and the correct side. Enter the letters in theboxes below. The first one is done for you.

Drawing Object Side

1 c front

2

3

4

5

6


a front

b right side

c right side

b front

a right side


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Learning

Combining views

Because it is impossible to give every detail of a 3-D shape in a single drawing, severaldrawings are made each from a different viewpoint. By combining the different viewstogether, it is possible to visualise a single 3-D object. It takes practice to develop the visualskills required to do this.

Here are some tips to get you started:

look at each view in turn, thinking carefully about the positionit is drawn from (e.g.are you looking from the top, front or side?)

think about the appearance of opposite sides (front and rear, right side and leftside) remember, if only two side views are shown in the drawing, then oppositesides are the same

imagine cutting out and piecing the different views together this may involveplacing some views at right angles to other views.

Try out these tips on the example below. Use your visualisation skills to piece togetherthe three drawings so that they make the 3-D object.

a

bc

Plan view

a

b


c

Hints and tips:Remember, you cannot tell if part of asurface is closer or further away usingjust one view. You gather informationabout depth by piecing the drawingstogether.



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Learning

AActivity 4

a. Which 3-D object is depicted in this drawing?

Object 1 Object 2

Object 3 Object 4Right side viewFront view

Plan view

b. Which 3-D object is depicted in this drawing?

Object 3 Object 4

Object 1 Object 2

Plan view



object 2

object 4


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Learning

A Activity 5

What would this 3-D object look like from the top (plan view) and from the right side?Insert a tick in the box beside the set that correctly represents the object.

a. plan view side view

b. plan view side view

c. plan view side view



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Learning

Nets

Another way of representing 3-D objects in 2-D is by drawing the net.

A net is a drawing of all the faces of the 3-D object arranged in such a way that when folded,they become the faces of a solid 3-D object.

To visualise a 3-D object from its net, you have to: look carefully at the sizes and shapes of the faces that make up the net imagine folding a cut-out version of the net along the edges of the faces.

Try this out using the example below. Use your visualisation skills to piece together the

net so that it makes the 3-D object.

Net 3-D object

Activity 6A

Drawings 1 to 3 are nets of the 3-D objects below. Use your visualisation skills to piecetogether each net so that it makes a 3-D object. Match each net to the 3-D object it depictsby typing the corresponding number in the box under each 3-D object.

1 2 3

a b c


2 3 1


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Learning

Solving problems involving 2-D drawings and parallel lines

So far we have looked at different ways that 2-D drawings represent 3-D objects.

To save space on the drawing, a measurement is not shown against every single line. Iftwo setsofparallel linesjoin together at right angles (as in the example below), it is onlynecessary to show twomeasurements on the drawing, because the line that is parallel isexactly the same length.In this example:

side A represents a length of 5.25 m, as does side B which is parallel to A side C represents a length of 2.75 m, as does side D which is parallel to C.

Parallel lines are lines that never cross each other. Theyre a bit like railway lines withoutthe points they always keep the same distance apart from each other. You will have comeacross parallel lines in many everyday situations, such as when laying carpet tiles or puttingup wallpaper. Wallpaper strips are parallel to each other so they fit neatly together and thejoin cant be seen.

In most practical contexts, measurements are also shown on these drawings to give a

complete understanding of the object depicted. Measurements are shown by a double-headed arrow against the side which it relates to.

Plan of garden

Hints and tips:Every square andrectangle has two setsof parallel lines that jointogether at right angles.

A

B

DC

5.25 m

2.75 m



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Learning

Use the ground floor plan below to answer the following questions:

a. The store room is 6.1 metres long. How wide is the store room?

b. The main office is 3.7 metres wide. What is the length of the main office?

c. What are the length and width of the conference room?

Length

Width

Activity 7A

Ground floor plan

3.7 m

2.2 m

8.5 m 6.1 m

Reception

Conference room

Store room

Main office

Now try the practice questions.


2.2 m

8.5 m

6.1 m

3.7 m


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Practice

Zak has made some drawings of the bird box, but he has not labelled them. Label eachdrawing to show which view point it is taken from. Type your labels into the boxes below.

Practice 1P

Zak wants to make a nesting box for birds and has found adesign that he likes in a magazine. Here is a picture of it.

The nesting box has an entrance at the front and a perchwhere the birds can land. There is a board at the rear of thenesting box that is used for attaching it to a wall.

a b

e

c

d

f


plan view of base front

left hand side

plan view of top right hand

side

rear


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Practice

Sara is making some furry dice for the children at playgroup. She has found threedifferent ways to make a 3-D cube, and she has marked the nets out on some squaredpaper.

Sara has found out that opposite sides of dice always add up to 7. She has worked outwhere she will place some of the numbers. Can you help her figure out how many dotswill go on all the remaining sides? Type in the number of dots on each remaining side.

Practice 2P

Hints and tips:Imagine folding a cut-out version of each netalong the edges of the faces, to see how itmakes a 3-D object.


3 5 3

2

1 4

6 5 1


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Practice

P Practice 3

Troy is making an open-topped compost bin for his garden. This is his design.

1 m

1.5 m

2 m

1.5 m

2 m

1 m

Open-topped compost bin

Plan view Front view Right side view

a. What is the area of the base of the compost bin? m2

b. What is the area of the right side of the compost bin? m2

c. What is the area of the front of the compost bin? m2

d. What volume of compost will the bin hold when filled to the top? m3

Hints and tips:area of a rectangle = length width

volume of a cuboid = length width height.

Go on to the Skills review checklist on the next page.


2

1.5

3

3


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Skills review

Now you have completed the topic, how do you feel about the skills you havelearnt? Insert a tick in the box that is true for you.

Topic: Shape and space

Im OK Id like morepractice

I needsome help

Using 2-D representations of 3-Dobjects

Interpreting views from above (planview)

Interpreting views from the side

Combining views

Using nets

How did you get on?

If you feel confident, have a go at the Mini-test questions.

If you need more practice, work through the learning activities again.

If you feel you need more help, speak to your tutor.



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Mini-test

M Mini-test

Insert a tick in the box next to the right answer to these questions.

1. The D in 2-D and 3-D stands for:

a. difficult

b. directions

c. decimetres

d. dimensional.

2. A plan view shows you:

a. how something will look when it is finished

b. how a 3-D object would appear if you looked at it directly from above

c. how a 3-D object looks from the front or rear

d. all of the above.

3. Which of the following is the net of this triangular prism?

a. b. c. d.

a.

b.

c.

d.



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Mini-test

4.Which of the following is the plan view of this 3-D object?

a. b. c. d.

a.

b.

c.

d.

5. What is the area of the computer suite?

a. 16.25 m2

b. 20 m2

c. 26 m2

d. 32 m2

Reception

Library

Archives

8 m6.5 m

2.5 m

4 m

Please tell your tutor that you have completed this workbook.

Computer suite



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Answers

Topic activities:

Activity 1 (pages 2 and 3)a. Height, width and depth.b. 1. cube (or cuboid) 2. cylinder 3. sphere 4. triangular prismc. The underneath, left side and back.

Activity 2 (page 4)1= b 2 = d 3 = f 4 = e 5 = c 6 = a

Activity 3 (page 6)

1 = front view of c 2 = front view of a 3 = side view of b4 = side view of c 5 = front view of b 6 = side view of aActivity 4 (page8)a. Object 2b. Object 4

Activity 5 (page 9)c. Plan view Side view

Activity 6 (page 10)1 = c 2 = a 3 = b

Activity 7 (page 12)a. 2.2 m b. 8.5 m c. length = 6.1 m, width = 3.7 m



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Answers

Practice activities:

Practice 1a = plan view of base b = front c = left-hand side d = plan view of tope = right-hand side f = rear

Practice 2

Practice 3a. 2 m

2b. 1.5 m

2c. 3 m

2d. 3 m

3

Mini-test1. d2. b3. a

4. b5. c

3

2

5 3

1 4

6 5 1

Cecilia

Trasca

Digitally signedby Cecilia Trasca

DN: cn=Cecilia

Trasca, o, ou,

email=prof.caline

scucecilia@yahoo

.com, c=RO

Date: 2011.09.22

15:35:30 +01'00'

l2 numeracy shape workbook 1

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