GRADE 6
MATHEMATICS
term 3
WORKBOOK
Juffrou Anri se Klaskamer
Estimate and measure 2D
shapes and 3D objects using
measuring tools
Summary and activity
We use different measuring tools to measure different lengths.
➔ For smaller lengths, such as millimetres (mm) and centimetres (cm),
we use a ruler or tape measure.
VERY IMPORTANT!
When we use a ruler/tape measure, we always start measuring at ZERO (0)!
➔ For larger lengths, such as metres (m) and kilometres (km) we use a
measuring wheel.
activity
1.
Look at the different objects and say which measuring instrument we
will use to measure the following lengths:
a)
b)
c)
2.
Estimate in centimetres (cm) the lengths of the following objects:
a)
Your nose.
b)
The length of your table.
c)
The height of your chair.
d)
Your pencil.
3.
Now use your ruler to measure the objects in question 2 and
get their actual lengths. Write your answer in centimetres (cm).
a)
b)
c)
d)
4.
Which measurement unit can we use to measure the following
lengths? Choose the correct answer from the box below.
metre (m)
millimetre (mm)
kilometre (km)
centimetre (cm)
a)
The height of a house is given in
.
b)
The distance between South Africa and Namibia is measured in
_____________.
c)
The length of your school trousers is measured in _______________.
d)
The size of your fingernail will be measured _______________.
5.
Use your ruler to measure the lengths of the following two objects.
Write the correct length in millimetres along each side.
Memorandum
1.
a)
Measuring wheel
b)
Ruler or tape measure.
c)
Ruler or tape measure.
2.
Learners' own answers.
3.
Learners' own answers.
4.
5.
a)
metre (m)
b)
kilometres (km)
c)
centimetres (cm)
d)
millimetres (mm)
Check that learners have measured lengths correctly and
used a ruler correctly.
Draw, compare and arrange
lengths
Summary and activity
Lengths have different units, namely:
➔ millimetres (mm)
➔ centimetres (cm)
➔ metre (m)
➔ kilometres (km)
Small objects are measured in mm, e.g. your sharpener.
It's important to know:
0,5 km = 500 m
0,25 km = 250 m
10 mm = 1 cm
100 cm = 1 m
1 000 m = 1 km
0,5 m = 50 cm
0,25 m = 25 cm
7 cm = 70mm, therefore we can say that:
7 cm > 60 mm.
Make the units the same before you compare them.
Example:
Use <; > or = to complete the following.
1
1 km > 1 250m
2
→
1
1 km = 1.5 km = 1 500 m
2
activity
1.
Which unit of measurement (mm; cm; m; km) would you use to
measure the following items?
a)
The length of the school bus.
b)
The distance from the shop to your home.
c)
The length your ear.
d)
The size of a ring.
2.
First estimate the length of each line and then use your ruler to
measure the actual length. Write your answer in millimetres (mm)
next to each line.
3.
Use the signs <; > and = to complete the following statements.
a)
1 m 30 cm
100.0 cm
b)
5.5 km
5 500 m
c)
190 mm
d)
1 4 km
1 750 m
e)
3.05 m
350 cm
4.
Arrange the following measurements in ascending order.
20 cm
1
10.5 m; 105 cm; 500 cm; 159mm; 1
1
2
km; 5050 m
5.
Use your ruler and draw a rectangle with the following dimensions:
a)
Length: 10 2 cm
b)
Width: 55 mm
1
Memorandum
1.
2.
a)
m
b)
km
c)
cm
d)
mm
Check that learners estimate and then write down the correct length
in mm along the line.
3.
a)
>
b)
=
c)
<
d)
<
e)
<
1
4.
159 mm; 105 cm; 500 cm; 10.5 m; 1 2 km; 5050 m
5.
Make sure the learner draws a rectangle with the correct dimensions.
Solve problems in contexts
involving length
Summary and activity
It's important to remember that we always have to make the units the same
before we can do a calculation.
When you get a problem that contains more than one unit, we have to use
the above method to make the units the same, e.g.:
200 cm + 45 m = ?
→
Here we have centimetres and metres.
Let's choose to convert the centimetres to meters:
200 cm ÷ 100 = 2 m
Now we can write the sum like this:
2 m + 45 m = 47 m → The units are now the same so we can add the
lengths together.
activity
1.
Henry goes to ride the same route every day with his horse. If he rides
3
a total distance of 35 4 km in 7 days, what is the distance of the route
that he rides every day? Round your answer to the nearest kilometre.
2.
1
Kagiso is 1,5 m tall, Riana is 105 cm tall and Rudi is 14 m tall. Who is
the tallest?
3.
Round off to the nearest metre (m):
a)
312,6 m ≈
b)
1 003,3 m ≈
4.
Convert to metre (m):
a)
10 2 km =
m
b)
55,25 km =
m
5.
Thato has a busy day. She rides 5.75 km to school with her bicycle in
1
the
.
.
morning.
1
After school she rides another 35 km to extra classes. After the extra
class, she rides 2 150 m to Themba to pick something up. After that
she rides 1.6 km home again. How far did she ride for the day? Give
your answer as a decimal fraction.
6.
1
Bingo wants to wrap presents. He uses 25 2 cm of ribbon per present.
He currently has 400 cm. How much more ribbon will he have to buy if
he wants to wrap 20 presents?
Memorandum
3
1.
354 km = 35 750 m
35 750 m ÷ 7 = 5 107,14 m
5 107,14 m ÷ 1 000 = 5,10714 km ≈ 5 km
The route is 5 km.
2.
Make the units the same.
Kagiso: 1.5 m x 100 = 150 cm
Riana = 105 cm
1
Rudi = 14m = 1 m 25 cm = 125 cm
Kagiso is the tallest.
3.
4.
5.
a)
312,6 m ≈ 313 m
b)
1 003,3 m ≈ 1 003 m
a)
102 km = 10 500 m
b)
55,25 km = 55 250 m
1
Make the units the same:
To school: 5,75 km
1
Extra class: 3 5 km = 3,2 km
Themba’s house: 2 150 m = 2,15 km
Home: 1,6km
Total = 5,75 km + 3,2 km + 2,15 km + 1,6 km = 12,7 km
6.
(20 x 25,5 cm) - 400 cm
= 510 cm - 400 cm
= 110 cm
He still has to buy 110cm.
Conversions between units
Summary and activity
Before we can convert lengths, we need to know the following:
1 km = 1 000 m
1 m = 100 cm
1 cm = 10 mm
It is very important to memorize this information.
We can use the following methods to convert from one unit to another:
Example:
Convert 20.75 km to metres (m).
20.75 km x 1 000 = 20 750 m
activity
1.
Fill in the correct answer:
a)
0.75 km is
b)
A 4 m is equivalent to
c)
We can say that 1 km is equal to 1000
d)
There is
2.
Convert the following lengths to kilometres (km):
a)
4 500 m =
km
b)
2 750 m =
km
c)
10 900 m =
3.
Say whether the following is true or false:
a)
8.25 km = 8 025 m
b)
1 5 m = 150 cm
c)
300 cm 5 mm = 3005 mm
d)
1 km = 10,000 cm
m.
1
cm.
mm in one metre.
km
1
.
4.
Solve:
a)
213.55 km + 650 2 km
b)
10 025 m + 105 km
c)
50.4 cm + 1500 mm
d)
80 5 km + 25 050 m
5.
Fill in the correct operation to make the conversion true:
a)
35.3 km
= 35 300 m
b)
705 cm
= 7050 mm
c)
50 m
d)
100 000 m
1
1
= 5 000 cm
= 100 km
Memorandum
1.
2.
3.
4.
a)
750 m
b)
25 cm
c)
metre (m)
d)
1 000 mm
a)
4 500 m 1 000 = 4.5 km
b)
2 750 m 1 000 = 2.75 km
c)
10 900 m 1 000 = 10.9 km
a)
False
b)
False
c)
True
d)
False
a)
213.55 km + 650 2 km
1
Units are the same:
1
650 2 km = 650.5 km
213.55 km + 650.5 km = 864.05 km
b)
10 025 m + 105 km
Make units the same:
105 km x 1 000 = 105 000 m
10 025 m + 105 000 m = 115 025 m
c)
50.4 cm + 1500 mm
Make units the same:
50.4 cm x 10 = 504 mm
504mm + 1500mm = 2004mm
d)
1
80 5 km + 25 050 m
Make units the same:
1
80 5 = 80.2 km = 80 200 m
80 200 m + 25 050 m = 105 250 m
5.
a)
35.3 km x 1 000 = 35 300 m
b)
705 cm x 10 = 7 050 mm
c)
50 m x 100 = 5 000 cm
d)
100 000 m ÷ 1 000 = 100 km
regular and irregular
polygons
Summary and activity
Here are examples of regular shapes that you should know by heart:
Circle
Triangle
Trapezium
Square
Parallelogram
Rectangle
Rhombus
Pentagon
Hexagon
Heptagon
You also get irregular forms:
The shape has 6 angles, but does not look
like a regular hexagon. This is an irregular
hexagon.
Activity
1.
Say whether the following shapes are regular or irregular.
a)
.
b)
.
c)
.
d)
.
2.
a)
Write down the names of the following shapes:
b)
c)
3.
Look at the pattern below and identify all the regular and
irregular 2D shapes you can see.
4.
Draw an irregular pentagon in the block below:
Memorandum
1.
a)
b)
c)
d)
Regular
Irregular
Irregular
Regular
2.
a)
b)
c)
Octagon
Heptagon
Parallelogram
3.
Triangle; trapezium; irregular quadrilateral; square.
4.
Learner's own sketches.
Characteristics of shapes
Summary and activity
Each 2D shape possesses different properties or characteristics. We look at
the characteristics of a shape to determine what shape it is.
Properties such as the number of sides, straight or curved sides, size of each
angle and length of the sides.
Let's look at a Trapezium:
Features of the shape:
★ Four sides – quadrilateral.
★ One pair of opposite sides are equal in length.
★ Top two adjacent angles are greater than 90°.
★ Bottom two adjacent angles are smaller than 90°.
activity
1.
Circle all the shapes with curved sides.
A
2.
B
C
E
Look at the shapes below and write down 3 characteristics of each.
a)
b)
3.
D
State whether the following is true or false:
a)
A trapezium has two pairs of opposite sides that are equal in length.
b)
A square's angles are all right angles.
c)
A circle is not a polygon.
d)
A parallelogram has only straight sides.
e)
A rectangle only has acute angles.
4.
Draw the following two shapes in the block below.
a)
A 2D shape that has two pairs of opposite sides of equal length and
all angles are 90°.
b)
A 2D shape with five straight sides of equal length and all angles
greater than 90°.
Memorandum
1.
A; C; E
2.
a)
Rectangle
● Four sides
● All sides are straight.
● Two pairs of opposite sides are equal in length.
● All four angles are right angles.
b)
Parallelogram
● Four sides.
● All sides are straight.
● Two pairs of opposite sides are equal in length.
● One pair of opposite angles is less than 90°.
● One pair of opposite angles is greater than 90°.
3.
4.
a)
False
b)
True
c)
True
d)
True
e)
False
a)
Learner must draw a rectangle.
b)
Learner must draw a pentagon.
Describe, sort and compare
2D shapes
Summary and activity
We can describe 2D shapes by looking at the number of sides, size of angles
and lengths of the sides.
Most 2D shapes have angles. We get different types of angles:
90°
Right angle
greater than 90°
smaller than 90°
Obtuse angle
Acute angle
Look at the angles in the shapes below.
Rectangle:
• Four sides
• Two pairs of opposite sides are the
same length.
• All the angles are right angles.
Rhombus:
• Four sides
• All the sides are the same length.
• Two pairs of opposite angles that are
equal in size.
activity
1.
Give the name of each of the following shapes:
a)
b)
2.
Fill in the correct answers in the questions below.
a)
A rectangle's angles are all
b)
A heptagon has
sides.
c)
A trapezium has
and
3.
Describe each of the following shapes in terms of number of sides,
.
lengths of sides and sizes of angles.
a)
b)
angles.
c)
d)
4.
Provide the name of the following shape:
Polygon with four sides of which one pair of opposite sides
are equal in length. One pair of angles are acute angles and one pair
is greater than 90°
5.
Draw a polygon with six sides that are the same length and six angles
that are all greater than 90°.
Memorandum
1.
2
3.
a)
Parallelogram
b)
Trapezium
a)
right angles /90°/equal size
b)
seven
c)
acute angles and obtuse angles
a)
Four sides; two pairs of opposite sides are equal in length; one
pair of opposite angles are acute angles and one pair of opposite
angles are obtuse angles.
b)
Eight sides; sides all the same length; angles are all obtuse
angles.
c)
Four sides; sides are all the same length; one pair of opposite
angles are acute angles; one pair of opposite angles are obtuse
angles.
d)
Four sides; one pair of sides are of equal length; one pair of
adjacent angles are obtuse angles and one pair of adjacent
angles are acute angles.
4.
Trapezium
5.
Learners must draw a hexagon.
Draw circles
Summary and activity
When we want to draw circles, we can use a compass to help us.
For example, when the radius should be 4cm, then you use your compass
to measure the length on the ruler and then draw the circle.
We can also form patterns with circles.
Below is an example of patterns inside a circle.
activity
1.
Use your compass to draw a circle with a radius of 30 mm.
2.
Use the block below and draw your own pattern with 2D shapes. You
must use circles in your pattern.
3.
Look
at
the
circle
below
and
use
draw patterns of your choice inside the circle.
2D
shapes
to
Memorandum
1.
Learner's own sketch. Make sure radius is 30 mm.
2.
Learner's own pattern. Make sure learner has used circles.
3.
Learner's own pattern.
Recognize and name angles in
2D shapes
Summary and activity
Most 2D shapes have angles. We get different types of angles:
Obtuse angle
Right angle
Acute angle
Straight angle
Reflex angle
Full rotation angle
Let's look at the angles of a Rhombus:
The BLUE angles are greater than 90°, therefore they are obtuse angles.
The GREEN angles are smaller than 90°, therefore they are acute angles.
activity
1.
Identify the following angles:
a)
.
b)
.
c)
.
d)
.
2.
Look at the following shapes and colour all the right angles red.
3.
Give the names of the following angles:
a)
Greater than 90° but less than 180°
b)
Greater than 180° but less than 360°
c)
360°
.
.
.
4.
a)
Name the angles indicated in the shapes below
.
.
b)
.
c)
.
5.
Draw the following angles in the box below.
a)
Full rotation angle.
b)
Straight angle.
Memorandum
1.
a)
b)
c)
d)
Acute angle
Reflex angle
Obtuse angle
Straight angle
3.
a)
b)
c)
Obtuse angle
Reflex angle
Full rotation angle.
4.
a)
b)
c)
Reflex angle
Acute angle
Right angle
2.
5.
Learners' own sketches.
1Composite 2D Shapes
Summary and activity
We can transform 2D shapes in different ways:
Translation: We just move the shape as it is up, down, left or right.
Rotation: We rotate the shape a certain number of degrees.
Reflection: We ' flip ' the shape to get its mirror image.
Here is an example of reflection. A trapezium is reflected
here.
activity
1.
Complete the following picture:
2.
Identify the following types of transformations:
a)
b)
.
.
c)
3.
a)
b)
.
Reflect the following shapes:
Memorandum
1.
2
3.
Learner's own sketch.
a)
Translation
b)
Rotation
c)
Reflection
Make sure the learner uses the right transformation.
create tessellated patterns
Summary and activity
A tessellation or tessellated pattern is when you use one or more shapes
through reflection, translation or rotation to form a pattern without any spaces
between the shapes.
Here is an example of a tessellation:
Here we can see that squares and triangles are used which are reflected,
translated and rotated to form the pattern.
activity
1.
Use reflection to make a pattern with the following shape:
2.
Look at the tessellation below and identify all the 2D shapes in the
pattern.
3.
Look at the pattern and say which transformations are used.
Memorandum
1.
Learner's own pattern.
2.
Quadrilaterals and squares.
3.
Reflection and rotation.
Describe patterns
Summary and activity
All around us in nature we see all kinds of patterns formed by reflecting,
rotating and translating 2D shapes or 3D objects.
For example, look at the skin of a giraffe.
Many patterns also form lines of symmetry. Look at our African culture and
all the beautiful symmetrical patterns that are formed.
We can see that the left side is a mirror image of the right side, even though
the colours are different.
activity
1.
a)
2.
Look at the pictures below and describe the pattern you see
b)
c)
Use your knowledge of tessellation and transformations and make your
own African pattern that can be painted on the wall of a hut.
Memorandum
1.
2.
a)
Hexagons that are reflected and translated.
b)
Quadrilaterals/diamonds that are reflected and translated.
c)
Squares and triangles that are reflected.
Learner's own sketches.
Recognize, visualize and name
3D objects.
Summary and activity
A 3D object has three dimensions: length, width and height.
Below are some 3D objects that you need to know and identify.
Cube
Square
Sphere
Pyramid
Cylinder
Cone
Triangular
Prism
Rectangular
Prism
activity
1.
Name each 3D object below:
a)
.
b)
.
c)
.
2.
Match the correct object to the description. Write the letter and name
of the object next to the correct description.
A
a)
B
C
I have a round base and form a point.
D
b)
I have a rounded surface with two circles on each side.
c)
I have four triangular faces with a square as a base.
d)
I have six faces and they all look like rectangles.
3.
a)
What 3D shapes do you see in the pictures below?
b)
What do all three shapes have in common?
4.
What 3D shape is a tent?
5.
Use your knowledge of 3D objects and draw the shape that
has six faces that are all the same size.
Memorandum
1.
2.
3
a)
Triangular prism
b)
Rectangular prism
c)
Cylinder
a)
Cone - D
b)
Cylinder - B
c)
Square pyramid - A
d)
Rectangular prism - C
a)
Sphere; Cone; Cylinder
b)
All three of them are rounded shapes.
4.
Triangular prism
5.
Learner must draw cube.
Describe, sort and compare
3D objects
Summary and activity
3D objects all have different properties, in the form of number of faces, flat
or curved faces and the shape of the faces, as well as the number of vertices.
The face of an object is the sides or surface of the object.
Flat face
All the faces of the cube are flat and square.
Curved face
We can see that the base of the cylinder is the shape of a circle.
activity
1.
Look at the 3D objects and write down the number of vertices for each.
a)
.
b)
.
c)
.
2.
Look at the two objects below and answer the questions that follow.
a)
Give the name of each objects on the lines provided.
____________________
b)
_____________________
List three things that are the same about the two objects.
3.
Describe the following objects in terms of surfaces (faces) and shapes.
a)
Number of faces:
.
Flat or curved surfaces:
.
Shape of surfaces:
.
Number of vertices:
.
b)
Number of faces:
.
Flat or curved surfaces:
.
Shape of surfaces:
.
Number of vertices:
.
4.
Read the following descriptions and identify the following shapes.
a)
I have five flat faces. Four are triangular and one square base.
What am I?
b)
I have five flat faces. Two are triangular and three are rectangular.
What am I?
c)
I have six square flat surfaces, all of which are the same size.
What am I?
Memorandum
1.
2
a)
6 vertices
b)
8 vertices
c)
5 vertices
a)
Left: Cube
Right: Rectangular prism
b)
1 - Both have flat surfaces.
2 - Both have 6 faces.
3 - Both are prisms.
4 - Both have 8 vertices.
3
a)
Number of faces: 4
Flat or curved: flat
Shape of surfaces: triangles
Number of vertices: 4
b)
Number of faces: 5
Flat or curved: flat
Shape of faces: Rectangles and triangles.
Number of vertices: 6
4
a)
Square pyramid
b)
Triangular prism
c)
Cube
Perimeter and area of
squares and rectangles
Summary and activity
When working with perimeter and area, it is very important not to get
confused between the two.
Make sure you understand each one and know the definition of each.
Perimeter of a shape:
This is the total distance right around a shape.
Surface/Area:
This is the size of the floor of a shape.
Activity
1.
Look at each shape below.
a)
If I walk right around each shape, how far will I travel?
4 km
4 km
4 km
4 km
.
800 m
500 m
500 m
800 m
.
b)
How did you get your answer?
c)
Which rule would you use to determine the perimeter of a square?
d)
Which rule would you use to determine the perimeter of a rectangle?
2.
Look at the square below and answer the questions.
5 cm
5 cm
5 cm
5 cm
a)
How many squares are inside the square?
b)
How can I use the lengths of the sides to
arrive at the same answer?
c)
Which rule can you use to work out the area of a square?
3.
Look at the rectangle below and answer the questions that follow:
8m
4m
4m
8m
a)
How many squares are inside the rectangle?
b)
How can I use the lengths of the sides to
arrive at the same answer?
c)
Which rule can you use to work out the area of a rectangle?
Memorandum
1
a)
Square - 16 km
Rectangle – 2 600 m
2
3
b)
All the sides of the shape added together.
c)
side + side + side + side or side x 4
d)
(l + w) x 2 or (2 x l) + (2 x w) or l + w + l + w
a)
25 squares
b)
5 x 5 = 25
c)
A = side x side or side²
a)
32 squares
b)
8 x 4 = 32
c)
A=lxw
Volume
Summary and activity
Volume can be worked out when an object has three dimensions:
length, width and HEIGHT.
Volume is the amount that a container/object
holds or can hold.
Volume can be worked out as follows:
activity
1.
Look at the rectangular prism and answer the questions below.
10 cm
3 cm
4 cm
a)
Use
your
knowledge
of
surface
area
and
work
out the surface area of the top face of the prism.
b)
Now multiply your answer by the height of the prism to
get the volume of the prism.
2.
Work out the volume for each of the following prisms.
20 mm
5 mm
10 mm
a)
10 cm
10 cm
10 cm
b)
5 cm
4 cm
25 cm
c)
300 mm
30 mm
d)
50 mm
Memorandum
1.
a)
A = 10 cm x 3 cm
= 30 cm²
b)
V = 30 cm² x 4 cm
= 120 cm³
2.
a)
V = 20 mm x 5 mm x 10 mm
= 1 000 mm³
b)
V = 10 cm x 10 cm x 10 cm
= 1 000 cm³
c)
H = 4 cm x 5 cm x 25 cm
= 500 cm³
d)
V = 30 mm x 300 mm x 50 mm
= 450 000 mm³