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Targeting Maths © Blake Publishing 2012

These blackline masters provide opportunities to estimate, measure, order and compare areas using formal and informal units of measurement.

Students are involved in decision making and lateral thinking activities based on boundaries.

They investigate square metres and square centimetres and use these in problem solving activities.

There are two assessment pages and an activity, which involves manipulating shapes to fill a given area.

31

Area

32

Middle Primary

Area

Content DesCriPtionsUsing units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume.

© Australian Curriculum, Assessment and Reporting Authority 2010

Proficiency StrandsUnderstanding:

• The concept of area and boundaries.

• The square metre and the square centimetre.

• Different shaped objects can have the same area

Fluency:

• Use informal and formal units of area.

• Estimate and count areas in squares.

• Compare shapes according to area.

Languageunit of measurement, area, surface, boundary

MateriaLscoloured pencils, leaves, Base 10 materials

BLM Content• materials needed for each BLM

1.1 Looking at area – greatest area; jobs that use area• coloured pencils

1.2 Informal units – hands-on activities using informal units to measure area• leaves from the playground/home

1.3 More informal measuring – decide on the best informal units to use; true and false questions.

1.4 Boundaries – define and draw boundaries; smallest area.• coloured pencils

1.5 Thinking – increase areas; compare and order areas.

1.6 Same area – different shape – use grid paper to draw shapes of a given size and see that the same areas can be different shapes.

1.7 Assessment

1.8 Activity – manipulate shapes to fill a rectangle.

unit 1Compare areasUse formal and informal unitsBoundariesDraw objects with a given area.


Remember• Measurement is a hands-on

experience.

• Allow children plenty of time to make their own discoveries.

*

33

Area Unit 1

answersBLM 1.11 Teacher to check.2 Teacher to check.3 a painter

b farmer or gardenerc tiler/plumberd builder/quantity surveyore carpet layer

BLM 1.2Teacher to check.

BLM 1.31 cereal boxes2 cardboard3 suitcases4 sticks of chewing gum5 a true b true c false d false

e false f false g true h false


BLM 1.51 Teacher to check.2 a 3, 2, 4, 5, 1

b 3, 4, 1, 5, 2c 2, 1, 4, 5, 3

3 Teacher to check.

BLM 1.61 Teacher to check, True2 Teacher to check

BLM 1.71 a from left to right 3, 2, 5, 4, 1

b from left to right 2, 1, 4, 3c from left to right 2, 4, 3, 1, 5

2 a Teacher to check b False3 Teacher to check.4 Teacher to check.5 Teacher to check.6 a square

BLM 1.8

aDDitionaL aCtivities• Write a list of jobs or professions that use area in

their workplace.

• Compare the areas of the different continents of the world. Order these from smallest to largest.

• Make a wall hanging of every child’s hand print. Reduce the gaps between each hand print as much as possible. Calculate the total area.

• Each child draws the tiles that are on his/her bathroom or kitchen walls or floor. Discuss why these are tessellations.

• Looking for tessellating patterns in magazines, etc. Make a class poster.


Targeting Maths © Blake Publishing 2012.

Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: The concept of area and boundaries.

name Date

Looking at area Area 1.1

34

1 Circle the shape inside each box that has the greatest area.

2 Surface is another word for area. Colour the object with the greatest surface red and the smallest surface blue.

3 For many people it is important to understand area and how to work it out. Read the following statements and see if you can work out who these people are.a I use area to work out how many litres of paint I will need to paint

all the walls in Mrs Nesbitt’s house. I am a ________________________ .

b I need to understand the area of my land so I can calculate the amount of seed and fertilizer I will need to buy. I am a ________________________ .

c I want to tile Mr Gregory’s bathroom, so I must calculate the area of the walls and floor. Then I can work out how many tiles I will need for the job. I am a ________________________ .

d The cement mixer is arriving next week to pour concrete on the floor of the house I am building. I need to understand area to work out how much cement I should order. I am a ________________________ .

e Mrs Browning has chosen a lovely dark green carpet to replace the cream coloured mats in her apartment. I have to measure each room to work out the total area of carpet needed to make her apartment look smart. I am a ________________________ .

Collect 10 leaves from one of the trees in your school playground.

1 Cover the following objects with the leaves and record how many were needed.

Number of Leaves

a your desk top ________________________

b your pencil case ________________________

c your exercise book ________________________

d Did everyone in the class choose leaves of the same size and shape?

______________________

e Did everyone in the class get the same answers? ______________________

f Why? ___________________________________________________________________________________________

___________________________________________________________________________________________________

2 Use your to cover the same objects. Record your answers.

Number of Hands

a your desk top ________________________



d Were these results more alike? ___________________________________________________________

3 Now use ‘hundreds’ blocks to cover the same 3 objects.

Number of Hundreds

a your desk top ________________________



d Which was the best and easiest measuring tool? Circle your choice.

leaves hands hundreds

e Why? ___________________________________________________________________________________________

___________________________________________________________________________________________________


Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Fluency: Use informal and formal units of area.

name Date

informal units Area 1.2

35


Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Fluency: Use informal and formal units of area.36

Tick the easier one.

1 Measuring the area of your classroom with a cereal boxes

b pencils

2 Measuring the area of the playground with a matchsticks

b sheets of cardboard

3 Measuring the area of a tennis court with a pins

b suitcases

4 Measuring the area of a Christmas card with a sticks of chewing gum

b exercise books

5 Write true or false for these statements.

a Using Base 10 tens as a measuring tool is a good choice because each one is exactly the same. _______________________

b Measuring the area inside a curved shape is much harder than measuring the area inside a shape with straight sides. _______________________

c It doesn’t matter if we measure area using our hands because everybody’s hand is almost the same size. _______________________

d Centicubes or ones are not good area measuring tools because they are different colours. _______________________

e The area inside a shape is always the same as the distance around the outside of the shape. _______________________

f We can only find the area of square shapes. _______________________

g Area can be measured in square metres or square centimetres. _______________________

h The bigger the area, the easier it is to measure. 00000 _______________________

name Date

informal units Area 1.3


Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: The concept of area and boundaries. 37

name Date

Boundaries Area 1.4

1 Use a coloured pencil to draw a dotted line around the outside boundary of these shapes.

2 Join the dots in anyway you like to make 2 different shapes. In the first box the sheep should be inside the boundary of one of your shapes. In the second box place the sheep outside the boundary of your shapes.

3 Join some dots so that the sheep is inside the boundary of 2 different shapes. ie The two shapes should overlap.

4 Write three examples of boundaries: eg boundaries in a cricket game.

a ____________________________________________________________________________________________________

b ____________________________________________________________________________________________________

c ____________________________________________________________________________________________________

go back and look at all the shapes you have

created. Colour the one with the smallest area.

a b

*

*


Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: The concept of area and boundaries. Fluency: Compare shapes according to area.38

name Date

thinking Area 1.5

1 Finish the boundaries of these shapes so the areas increase in each frame.

a

b

2 Order these shapes from the smallest to the largest area. Use the numbers 1–5.

a

b

c

3 Draw a shape on the left that has a smaller area and one on the right that has a greater area.

a b

c d


Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: Different shaped objects can have the same area. 39

1 Draw three different straight sided shapes with an area of 24 squares.

True or False? Shapes with the same area do not have to be the same

length or width. _______________________

2 Draw five different shapes with one curved side each, with an area of about 16 squares. Count part squares where there are curved sides.

Place a tick on the widest shape and a cross on the narrowest shape.

What do you know about shapes with the same area?

____________________________________________________________________________________________________

name Date

same area – Different shape Area 1.6


40

name Date

assessment • Area Area 1.7

1 Order these shapes from largest to smallest area.

2 a Draw three rectangles of 10 squares.

b True or false? Three shapes that have the same area will all look the same.

_________________________

3 Name 4 objects that could be used as informal measuring units, eg leaves.

____________________ ____________________ ____________________ ____________________4 Name 2 objects that would be good measuring tools.

____________________ ____________________

5 a What is a boundary? ______________________________________________________________

_______________________________________________________________________________________

b Give 2 examples. _________________________________________________________________

6 Tick one answer. The best shape to use to measure area is:

a rectangle a leaf a square

a

b

c


41

name Date

activity • Area Area 1.8

1 Draw a rectangle 12 cm long and 8 cm wide.

2 Cut out these pieces. Put them together to fill your rectangle.Remember — no gaps and no overlaps!

42Targeting Maths © Blake Publishing 2012

Middle Primary

Area

Content DesCriPtionsUsing units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume.

© Australian Curriculum, Assessment and Reporting Authority 2010

Proficiency StrandsUnderstanding:

• The square centimetre and the square metre.

• The need for a formal unit to measure area.

• Shapes with the same area can have a different perimeter.

Fluency:

• Apply knowledge of square centimetres to design shapes.

• Calculate area with formal units.

• Record area using the short form.

• Record area using numerals and abbreviations.

Languagecalculate, formal, informal, units, square metre, square centimetre, increase, decrease

MateriaLsscissors, large sheets of paper, sticky tape

BLM Content• materials needed for each BLM

2.1 Calculating area – an introduction to formal units; count squares covered by shapes.

2.2 Area of irregular shapes – count squares and half squares.

2.3 The square metre – create a square metre; calculate and estimate.• sticky tape and scissors, • large sheets of paper

2.4 The square centimetre – draw square centimetres; choose the best unit of measure.

2.5 Square centimetres – put knowledge of a square centimetre to work by constructing shapes with a given area.

2.6 Different shapes, same area – construct shapes of a given area, realise that they can have different shapes and therefore different perimeters.

2.7 Assessment

unit 2Calculating area in formal unitsCalculating area of irregular shapesSquare metreSquare centimetreDifferent shapes can have the same area.

Remember

*

• All lines should be ruled with a sharp pencil.

• Reinforce difference between area and perimeter.

43Targeting Maths © Blake Publishing 2012

Area Unit 2

answersBLM 2.1 1 9 2 22 3 23 4 425 30

BLM 2.21 8 2 19 3 18 4 19

1

5 20 6 11 7 30

BLM 2.31 Teacher to check.2 Teacher to check.3 Teacher to check.4 a 307 m2 b 26

1 m2 c 88 m2

d 511 m2 e 1.6 m2

5 yes

BLM 2.41 Teacher to check.2 Teacher to check.3 a 22 cm2 b 19 m2 c 4 m2

d 17 cm2 e 131 cm2 f 85 cm2

4 a m2 b m2 c m2 d cm2

e cm2 f cm2 g cm2 h cm2

i m2


BLM 2.61 a Teacher to check. b Teacher to check.2 a Teacher to check. b Teacher to check.

BLM 2.71 a < b > c <

d > e > f >2 a 13 squares b 21 squares c 10 squares3 Teacher to check.4 a m2 b m2 c cm2

d cm2 e cm2 f cm2

aDDitionaL aCtivities• Research the areas of other countries. The

Internet could be used. What other units of measure are used for large areas?

• Place a square metre of paper on the ground and see how many students can be squeezed onto this space.

• Ask a member of the local council to visit to explain council boundaries and the population per square metre/kilometre.

• Research when it first became important to measure area and why. What were early measuring tools and measurements?

2

2

2

Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Fluency: Calculate area with formal units.

name Date

Calculating area Area 2.1

44Targeting Maths © Blake Publishing 2012.

Calculate the areas of each shape by counting the number of squares.

1

3

4

5

2

Area = __________ squares



Area = __________ squaresArea = __________ squares

Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Fluency: Calculate area with formal units.

name Date

area of irregular shapes Area 2.2


Carefully calculate the number of squares that each of these shapes cover. Don’t forget to add the half squares.

21

4


3


5

6 7






Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: The square centimetre and the square metre. Fluency: Records area using the short form.

name Date

the square Metre Area 2.3


1 Using a metre ruler and large sheets of paper, create a square metre. Use this to estimate the following.

How many square metres would cover: a your classroom floor? _____________

b your assembly floor? _____________

c the board? _____________

d the classroom door? _____________

2 List 5 things in your classroom that have an area of less than 1 square metre.

a __________________________ b __________________________ c __________________________

d __________________________ e __________________________

3 Fold your square metre into quarters. Find 5 things outside your classroom that have an area of less than a quarter of a square metre.

a __________________________ b __________________________ c __________________________

d __________________________ e __________________________

4 Rewrite these the short way.

eg seventeen square metres = 17 m2

a three hundred and seven square metres = ______________________

b twenty-six and a half square metres = ______________________

c eighty-eight square metres = ______________________

d five hundred and eleven square metres = ______________________

e one point six square metres = ______________________

5 Cut your square metre into 6 pieces. Using sticky tape, stick it back together in a different way. Is it still a square metre? ______________________ 0

tHinKing?what would be a

bigger unit of measure than a square metre?

_____________________what would be smaller

than 1 cm2?_____________________

Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: The square centimetre and the square metre.

name Date

the square Centimetre Area 2.4


1 Draw one square centimetre.

2 a In the oval draw 6 square centimetres that are joined in any way you like.

b What is the area of the shape you have drawn?

________________________________________

3 Increase or decrease these areas by the amount shown. Watch the units being used.

eg 5 cm2 increase > 2 cm2 = 7 cm2

a 15 cm2 increase > 7 cm2 = ____________ b 25 m2 decrease > 6 m2 = ____________

c 61 m2 decrease > 2

1 m2 = ____________ 0 d 26 cm2 decrease > 9 cm2 = ____________

e 21 cm2 increase > 11 cm2 = ____________ f 106 cm2 decrease > 21 cm2 = ____________

4 Choose the best unit of measure (cm2 or m2) for the area of each of these:

a picnic blanket ________________

b football field ________________

c Old Joe’s farm ________________0000

d computer screen ________________

e video tape box ________________

f a page out of a novel ________________

g slice of bread ________________

h father’s bald patch ________________

i carpet in Buckingham Palace ________________

A square centimetre is much smaller than a square metre.A square centimetre is used to measure the area of smaller objects.

2

2

2

Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: Shapes with the same area can have a different perimeter. Fluency: Applies knowledge of square centimetres to design shapes.

name Date

square Centimetres Area 2.5


*remember to use a ruler for all straight lines.

1 On the grid paper below design a shape that: a has an area of 4 square centimetres. b has an area of 10 square centimetres. c has an area of 16 square centimetres.2 a Draw 2 different shapes that have an area of 20 square centimetres. b What are their perimeters?

Using units of measurement: ACMMG290 Compare objects using familiar metric units of area and volume. Understanding: Shapes with the same area can have a different perimeter.

name Date

Different shapes, same area Area 2.6


1 a Use the grid paper and draw 4 different shapes each covering an area of 12 squares.

b Write what you found about an area of 12 squares. __________________________

____________________________________________________________________________________

2 a Use the grid paper to draw a rectangle with an area of 20 squares.

What is its perimeter? _______________

b Draw other shapes of 20 squares which have a greater or lesser perimeter. Record the perimeters and compare.

name Date

assessment • Area Area 2.7


1 Use greater than (>) or less than (<) to make these statements true.

a The area of a matchbox is ______________ than the area of a blanket.

b The area of the school hall is ______________ than the area of my bed.

c The area of the football field is ______________ than the total area of Australia.

d The area of a 50c coin is ______________ than the area of a 5c coin.

e The area of this page is ______________ than the area of a $100 note.

f The area of a desk is ______________ than the area of a video box.

2 Calculate the areas of these shapes and their perimeters.

3 On the grid paper above, draw:

a a shape with straight sides that covers 111 cm2.

b a shape with curved sides that covers approximately 7 cm2.

4 Would you use m2 or cm2 for the area of:

a the local council parkland? ______________ b the bathroom floor? _____________

c a ruler? ______________ 000000 d a tea towel? ______________

e a slippery-slide? ______________ f a book cover? ______________

b

ca

A = ________

P = ________

A = ________

P = ________

A = ________

P = ________

2

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