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Key words
Length and perimeter
millimetre (mm)
centimetre (cm)
metre (m)
kilometre (km)
perimeter
Measure and draw lines to the nearest millimetre
Know and use the names and abbreviations for units of length
Understand, measure and calculate perimeters of rectangles and
regular polygons
The metre (m) is a unit of length.
All the other units we use are connected to the metre.
Units smaller than a metre are:
The millimetre (mm) . Milli means thousandth so there are 1000 millimetres in a
metre (m).
The centimetre (cm) . Centi means hundredth so there are 100 centimetres in a metre (m).
The kilometre (km) is a larger unit than the metre.
Kilo means thousand so there are a thousand metres in a kilometre.
3c
4 cm
5c
m
m
6 cm
1 cm
2 1 2 1 6 cm
Use a ruler. Measure
each side in turn and
write down the length.
Then add the lengths of
all the sides together.
3 2 3.2 1
9.2 cm
A
4 cm
4 cm
4 cm
4 cm
B
D
Calculate the perimeter of this regular hexagon:
4 cm
1 cm
2 cm
2c
Measure the perimeter of this shape:
Perimeter AB BC CD DA
Example 2
2 cm
1 cm
We can measure it or calculate it by
adding up the lengths of all the sides
of the shape in turn.
Example 1
m
Perimeter means the distance all
the way round the edge of a shape.
C
4 cm
Since it is a regular hexagon, all
the sides are the same length.
There are 6 sides and each side is
4 cm so calculate 6 4 cm.
4 cm
6 4 24 cm
Exercise 3.1 ..........................................................................................
a) How wide is your finger in mm?
b) How many finger widths is this book?
c) How many mm wide is this book?
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Maths Connect 1G
You may find it helpful to
use a calculator for
difficult multiplications.
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a) How wide is your handspan in cm?
b) How many handspan widths is your desk?
c) How many cm wide is your table?
Handspan
Write down the unit you would use to make the following measurements.
You can choose from mm, cm, m and km.
a) Distance around a football pitch
b) Length of a matchstick
c) Width of a staple
d) Distance an aeroplane flies
e) Length of a javelin throw
f) Height of a high jump.
A game for 2 players.
Estimate
Actual
Difference
My points
measurement
– Copy the table.
– One person should draw
a line using a straight edge.
– Both estimate the length of the line to the nearest mm and record your estimates.
– Now measure the length of the line. Calculate the difference between the actual length
of the line and your estimate. Repeat for your partner’s estimate.
– The person whose estimate was closest to the actual length scores 1 point. If the
estimate is exactly right, score 2 points. Repeat five times, with a different person
drawing the line each time.
Measure the perimeter of these shapes:
a)
b)
c)
d)
Calculate the perimeters of these rectangles:
a)
6 cm
b)
5.2 m
c)
2 km
2 cm
4m
d)
32 mm
5.6 km
18 mm
Calculate the perimeters of these shapes:
a)
b)
d) 10 mm
c)
7 mm
3 cm
2 cm
Rhombus
Equilateral triangle
Regular pentagon
Regular octagon
Investigation
You need squared paper.
How many different rectangles can you draw which have a perimeter of 24 cm?
Length and perimeter 27
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Key words
Area
area
square millimetre (km2)
square centimetre (cm2)
square metre (m2)
square kilometre (km2)
Understand that area is measured in square units
Use appropriate methods to measure and estimate area
Understand, count and calculate the area of a rectangle
The area is the space inside a two dimensional shape.
A square millimetre (mm2) is about this size:
A square centimetre (cm2) is about this size:
Other units of area are the square metre (m2) and square kilometre (km2) .
We can find the area of a shape by counting
the squares inside it.
If the shape is a rectangle or square we can add
up the squares row by row.
There are 4 cm squares
in each row.
1
2
3
4
2 rows
This rectangle contains 2 rows of 4 centimetre
squares so its area is 8 cm2.
Notice that this is the same as calculating the
length width:
2 cm
2 cm 4 cm 8 cm2.
4 cm
Example 1
Find the area of this rectangle by counting the squares
inside it:
There are 6 squares in the bottom row.
There are 4 rows of 6 squares, which is 4 6 24
Count the number of squares in the
bottom row and then count the
number of rows.
square units in total.
Example 2
Find the area of this rectangle:
6 cm
Area of rectangle length width
3 cm
3 cm 6 cm
18 cm2
Exercise 3.2 ..........................................................................................
What units would you use to measure the areas of the following?
Choose from:
mm2 cm2 m2 or
a) the sole of your foot
d) the floor of this room
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Maths Connect 1G
km2
b) the cover of this book
e) a mouse’s footprint
c) the top of the table
f) Spain.
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Count squares to find the areas of these shapes:
a)
b)
c)
d)
e)
f)
g)
h)
a) Calculate the areas of these rectangles by multiplying
Remember to record the units.
the lengths by the widths.
i)
ii)
iii)
3 mm
3 cm
iv)
5 12 cm
10 mm
6 cm
6 cm
Remember to
count half squares
as well as whole
squares.
2 cm
4 cm
b) Check your answers by counting the squares.
Calculate the areas of these rectangles.
a)
b)
c)
2 km
d)
4 cm
5 km
2.5 mm
10 mm
15 m
5 cm
3m
Sani wants to buy carpet for her room. It measures 3 m by 4 m.
a) What is the area of carpet she needs?
b) Sani chooses a carpet that costs £20 per square metre. How much will she have to pay?
Sani’s little brother Rajeev wants new carpet too! His room is smaller.
It measures 3 m by 3.5 m.
a) What is the area of carpet he needs?
b) Rajeev chooses a carpet that costs £22 per square metre. Look at your answers to Q5.
Does Rajeev’s carpet cost more or less than Sani’s?
Investigation
On squared paper draw these shapes and cut them out. Join
them in as many different ways as you can and record the shapes
you make. For each shape, note down the area and the perimeter.
Do you always get the same area? Does the perimeter stay the same?
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Key words
Connecting 2-D and 3-D
face
edge
vertex
vertices
cube
cuboid
net
Use squares to visualise cubes
Identify different nets for an open cube
A face is the flat surface of a solid.
Face
Vertex
An edge is where two faces meet.
Edge
A vertex or corner is where three or more edges meet.
A cube has six identical square faces. All its edges are
the same length. Three edges meet at each vertex.
Cube
A cuboid has three pairs of matching rectangular faces.
Opposite faces are the same shape and size.
A net folds up to make a 3-D shape.
This is an example of a net for an open cube.
Example 1
a) Describe this shape made from cubes.
b) What is the smallest number of extra cubes you
will need to make the shape into a cuboid?
a) The shape is made out of ten cubes. There are three rows of two cubes on
the bottom layer and two rows of cubes on the top layer. The shape has
two L-shaped faces, two square faces and four rectangular faces.
b) Two extra cubes needed to be added to the
top layer to make the shape into a cuboid.
Example 2
30
This is a net for an open cube.
The black square is the base.
Use coloured pens to show which edges will meet
when it is folded up.
Maths Connect 1G
Cuboid
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Exercise 3.3 .............................................................................................
Describe each of these shapes, made from cubes.
i)
ii)
iii)
There are no hidden
cubes in these shapes.
Predict the number of extra cubes you will need to make each of the shapes in Q1 into a
cuboid.
Work with a partner. Take a handful of cubes each. Take it in turns to make a 3-D shape
and describe it so that your partner can make it. Try to use the key words at the top of
page 30. If your cubes are coloured, try not to use colour as a clue!!
These are nets for open cubes. The black squares show the base of the cubes. Copy them
on to centimetre squared paper and use coloured pens to show which edges meet when
the nets are folded up.
a)
b)
c)
Work with a partner. You need Polydrons or Clixi and squared paper.
Make an open cube using four squares of one colour and one square in a different colour.
Use the square that is a different colour for the base.
a) Undo the open cube to make the nets shown in Q4.
b) There are eight different possible nets for an open cube. Try to find the other five nets.
Draw each net you identify on centimetre squared paper.
This puzzle cube is made from alternate green and white cubes.
a) How many squares are there on each of the faces?
b) How many green squares are there in total?
c) How many white squares are there in total?
Investigation
You need squared paper, card and sticky tape.
Choose one of your nets from Q5 and make a bigger
version of it, using the squared paper.
Use four squares for each face instead of just one.
When you have drawn the net, stick it to the card
and cut it out.
Fold up the large net and use sticky tape to hold it
together. Repeat for the small net.
How many of the smaller cubes would fit inside your larger cube?
Repeat for a different net. What do you notice?
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Cubes and cuboids
Use squares and rectangles to visualise cubes and cuboids
Count squares and calculate the surface area of cubes and cuboids
Key words
cube
cuboid
surface area
A cube has six identical square faces.
A cuboid has three pairs of matching rectangular faces.
To find the surface area of a cube, first find the area of one of the square faces. Since a
cube has six square faces, the total surface area is six times the area of one face.
We can find the surface area of a cuboid by adding up
the areas of its three pairs of rectangular faces.
Example
a) Draw the faces of this cuboid.
1 cm
1.5 cm
2 cm
b) Find the area of each face and add them together to find the total surface
area of the cuboid.
The blue faces measure 1 cm by 2 cm.
2 cm
The area of one face is 1 2 2 cm2 so the area of two faces is
2 2 4 cm2
1 cm
1.5 cm
1 cm
1.5 cm
The pink faces measure 1.5 cm by 2 cm.
The area of one face is 1.5 2 3 cm2 so the area of two
2 cm
1.5 cm
faces is 2 3 6 cm2
The green faces measure 1.5 cm by 1 cm.
1.5 cm
1 cm
The area of one face is 1.5 1 1.5 cm2 so the area of two
faces is 2 1.5 3 cm2
The total surface area is 4 6 3 13 cm2
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Exercise 3.4 .............................................................................................
For these cubes:
i) Find the area of one face.
a)
b) 2 cm
ii) Find the total surface area.
Make sure that your
answers are in the
correct units.
1 cm
1 cm
1 cm
2 cm
2 cm
a) Draw the faces of this cuboid on centimetre squared paper:
b) Find the area of each of the six faces.
c) Find the surface area of the cuboid by adding together the
areas of the six faces.
2 cm
3 cm
1 cm
a) Draw the faces of this cuboid on centimetre squared paper:
2 cm
3 cm
10 cm
b) Find the area of each of the six faces.
c) Find the surface area of the cuboid by adding together the areas of the six faces.
These nets make open cuboids. The black rectangles are the bases.
Find the total surface area for each one.
a)
b)
4 cm
5 cm
Matching faces are the
same colour and have
the same area.
1 cm
1 cm
1 cm
3 cm
3 cm
2 cm
2 cm
1 cm
1 cm
1 cm
4 cm
3 cm
3 cm
2 cm
5 cm
2 cm
Investigation
These models are made from four cubes.
a) Make each of the models and then
find the surface area by counting
the squares.
b) Make some models of your own using four cubes and record their surface areas.
Investigate which model has the largest possible surface area.
Which model has the smallest possible surface area?
Cubes and cuboids 33