STRAND 2 MESURMENT.pptx grade 6 cbc for learners

GRADE SIX MATHEMATICS
STRAND 2 MEASUREMENT

MEASUREMENT
2.1 length
• By the end of the sub strand, the learner should be able to;
• Use the millimeter (mm) as a unit of measuring length in different situations,
• Establish the relationship between the millimeter and centimetre in different situations,
• Convert centimetres and millimeters to millimeters in different situations,
• Add centimetres and millimeters in different situations,
• Subtract centimetres and millimeters in different situations,
• Multiply centimetres and millimeters by whole numbers in real life situations,
• Divide centimetres and millimeters by whole numbers in real life situations,
• Determine the circumference of a circle practically,
• Identify the relationship between circumference and diameter in different situations,
• Appreciate use of length in real life situations.

Identifying millimeter as a unit of measuring
length
• Group Activity
• In groups of four
i. Get a 30 cm ruler.
ii. Identify the centimetre markings on the ruler.
iii. Count the number of small spaces in one centimetre interval.
iv. Relate the number of small spaces counted to one centimetre.
v. Discuss the results and share with other groups.

• One of the ten small intervals in one centimetre is a millimeter (mm).
• ( A millimeter is a unit of measuring small lengths. Example I Use a ruler to
measure in millimeters the length of the line shown.
Example
Use a ruler to measure in millimeters the length of the line shown
A B
Solution

ASSESSMENT
• How long is the needle on a typical sewing machine in millimeters?
• What is the diameter of a standard pencil in millimeters?
• How thick is a typical sheet of paper in millimeters?
• What is the width of a postage stamp in millimeters?
• How deep is the groove on a vinyl record in millimeters?
• What is the thickness of a credit card in millimeters?
• How wide is a strand of human hair in millimeters?
• What is the diameter of a US dime in millimeters?

Relationship between millimeters and
centimetres
Group Activity 2
In pairs
• 3.Measure the length of line AB in millimeters.
• Measure the length of line AB in centimetres.
• Relate the length in millimeters and the length in centimetres.
• Discuss the results and share with other groups
B
A

Example
Measure the length of the following line in
(a) Centimetre
(b) millimeters
(c) P LINE PQ=50mm
LINE PQ=5cm
(a) Q LINE XY=68mm
X Y LINE XY 6cm 8 mm

ASSESSMENT
1. How many millimeters are in a centimeter?
2. How does the length of a typical small paperclip in millimeters compare to that
in centimeters?
3. When measuring the width of a book cover, would you typically use millimeters
or centimeters?
4. How would you convert a length of 25 centimeters to millimeters?
5. When discussing the height of a small plant, would it be more practical to use
millimeters or centimeters?
6. If a piece of string measures 50 millimeters, how many centimeters is that?
7. When buying fabric, would the width typically be measured in millimeters or
centimeters?
8. How many millimeters are equivalent to 2.5 centimeters

Conversion of centimetres to millimetres
• Group Activity
• A line measures 6 cm 2 mm. Convert the length to millimetres.
In groups of four:
1.Express 6 cm in millimeters.
2.Add the 2 mm to the results.
3.Discuss the results and share with other groups.
Note
• To convert centimetres to millimeters, multiple the number of
centimetres by 10.

Example
• Convert
• (a)9 cm (b)4cm 2mm
solution
a b
1 cm =10mm 1 cm =10mm
9cm=9 x10mm 4cm=4 x10mm
=90mm =40mm+10mm
=50mm

ASSESSMENT
1. If a room is 250 centimeters long, how many millimeters is that?
2. How many millimeters are in a typical 30-centimeter ruler?
3. A swimming pool is 500 centimeters wide. How many millimeters is its
width?
4. When a TV is advertised as having a 100-centimeter screen, how many
millimeters is that?
5. If a piece of wire is 15 centimeters long, how many millimeters is it?
6. A standard A4 paper is 21 centimeters wide. How many millimeters is its
width?
7. If a shelf is 80 centimeters high, how many millimeters is its height?
8. A kitchen countertop is 150 centimeters long. How many millimeters is
its length?

Conversion of millimeters to centimetres
Group Activity
• Convert 69 millimeters to centimetres and millimeters. In pairs:
1. Read 69 mm from your ruler in centimetres and millimeters.
2. Divide 69 mm by 10.
3. Write your answer in centimetres and millimeters.
4. Discuss the results and share with other groups.

Note
• To convert mm to cm divide the number of mm by 10.
• Example
• (a) 47 mm to cm and mm
Solution
10 mm =1 cm
47 mm = 47 mm ÷10
= 4 cm 7 mm

ASSESSMENT
• The length of a mathematics textbook is 295 mm. What is the length
of the textbook in centimetres and millimeters
• Philip drew a line of length 45 mm. What is the length of the line in
centimetres and millimeters?
• The perimeter of a rectangular card is 72 mm. What is the perimeter
of the card in centimeters and millimeters

Addition of centimetres and millimeters
Addition of centimetres and millimeters without conversion
• Group activity
• Work out 9cm 4mm + 7 cm 3mm
In pairs:
1. Align the measurements vertically.
2. Add the millimeters.
3. Add the centimetres.

Example
• Example
• Simiyu bought two pieces of wire. Pieces was 40 cm 5 mm and the
other other was 20cm 2mm what was the total length of the two
pieces of wire?
• Solution
cm mm
40 5
20 2
60 7

ASSESSMENT
1.If you have a piece of wood that is 25 centimeters long and you add an additional 35 millimeters to it, what is the total
length in centimeters?
2.A bookshelf is 120 centimeters wide. If you add another 25 millimeters to its width, what is the new width in
centimeters?
3.A curtain rod is 180 centimeters long. If you extend it by 50 millimeters, what is the new length in centimeters?
4.If you have a piece of string that is 50 centimeters long and you add 15 millimeters to it, what is the total length in
centimeters?
5.A table is 75 centimeters tall. If you add an extra 20 millimeters to its height, what is the new height in centimeters?
6.A piece of fabric is 2 meters long, and you cut off 35 centimeters. If you then add 75 millimeters to the remaining
length, what is the final length in centimeters?
7.A picture frame is 40 centimeters wide. If you attach a 10-millimeter border around the picture, what is the total width in
centimeters?
8.A piece of wire is 1 meter long. If you cut off 75 millimeters from it and then add 25 millimeters, what is the final length
in centimeters?

Addition of centimetres and millimetres with
conversion
Group Activity
In pairs:
1. Obtain a foolscap paper.
2. Measure the length of the paper in cm and mm.
3. Measure the width of the paper in cm and mm.
4. Add the two measurements.

Example
Add
24 cm 6mm to 19 cm 7mm
Cm mm
1241 7
+ 19 6
44 3

ASSESSMENT
1. If a piece of wood is 30 centimeters long and you add an additional 5 millimeters, what is the total length
in centimeters?
2. A shelf is 50 centimeters wide. If you add another 2 centimeters and 5 millimeters to its width, what is
the new width in centimeters?
3. A curtain is 2 meters long. If you add 30 centimeters and 5 millimeters to its length, what is the new
length in meters?
4. If you have a piece of string that is 45 centimeters long and you add 2 meters and 15 millimeters to it,
what is the total length in meters?
5. A table is 80 centimeters tall. If you add an extra 25 millimeters to its height, what is the new height in
centimeters?
6. A ribbon is 75 centimeters long. If you add 1 meter and 20 millimeters to its length, what is the total
length in meters?
7. A picture frame is 30 centimeters wide. If you add a border of 5 centimeters and 50 millimeters around
the picture, what is the total width in centimeters?
8. A piece of wire is 2 meters long. If you add 50 centimeters and 25 millimeters to it, what is the total
length in meters?

Subtraction of centimetres and millimetres
A subtraction of centimetres and millimeters without conversion
Group Activity
Subtract 49 cm 2 mm from 86 cm 4 mm
In pairs:
1. Align the lengths in a vertical form.
2. Subtract the millimeters.
3. Subtract the centimetres.

EXAMPLE
• Subtract 26 cm 6mm from 90 cm 8mm
Cm mm
90 8
26 6
64 2

Assessment
1. If a piece of wood is 75 centimeters long and you cut off 2 centimeters and 5 millimeters, what is the
remaining length in centimeters?
2. A rope is 3 meters long. If you trim 50 centimeters and 20 millimeters from it, what is the new length in
meters?
3. A curtain rod is 200 centimeters long. If you remove 1 meter and 75 millimeters from its length, what is
the remaining length in centimeters?
4. If a wire is 1.5 meters long and you cut off 30 centimeters and 5 millimeters, what is the remaining length
in meters?
5. A bookshelf is 120 centimeters wide. If you trim 5 centimeters and 2 millimeters from its width, what is
the new width in centimeters?
6. A piece of fabric is 2.5 meters long. If you cut off 75 centimeters and 20 millimeters from it, what is the
remaining length in meters?
7. A table is 90 centimeters tall. If you remove 15 millimeters from its height, what is the new height in
centimeters?
8. A rope is 5 meters long. If you shorten it by 2 meters and 50 centimeters, what is the remaining length in
meters?

Multiplication of centimetres and millimeters
Group Activity 9
Multiply 25 cm 2 mm by 4
In pairs:
1. Align the numbers vertically.
2. Multiply 2 mm by 4.
Write the answer in the mm column.
3. Multiply 25 cm by 4.
Write the result in the cm column.
4. Discuss the results and share with other groups

Example
• Cm mm
• 14 5
• x 7
101 5

ASSESSMENT
1. A chef needs to slice a loaf of bread that is 30 centimeters long into slices that are 1.5
centimeters thick. How many slices can the chef obtain?
2. A tailor has a piece of fabric that is 3 meters long, and they need strips that are 20
centimeters wide. How many strips can the tailor cut?
3. A construction worker needs to lay bricks along a path that is 4 meters long. If each
brick is 10 centimeters long, how many bricks will they need?
4. A student is building a model bridge using toothpicks. If the bridge is 60 centimeters
long, and each toothpick is 5 millimeters wide, how many toothpicks will the student
need for the length of the bridge?
5. A decorator wants to add a border around a painting that is 50 centimeters wide. If
the border is 2 centimeters wide, how many centimeters of border material will the
decorator need in total?
6. A gardener wants to plant flowers in a garden bed that is 1.5 meters wide. If they
space the flowers 10 centimeters apart, how many flowers can they plant in a row?

Division of centimetres and metres
(a) Division of centimetres and millimeters without t conversion
Group Activity
Divide 32 cm 8 mm by 4
In groups of three:
1.Write 32 cm 8 mm divided by 4 in long division form.
2. Divide 32 cm by 4.
3. Divide 8 mm by 4.
4. Discuss and share the results with other groups.
Note
When dividing cm and mm by a whole number, from cm. Division starts

Example
• Divide 36cm 9mm by 3
12cm 3mm
3 36cm 9mm
3 9mm
06 0mm
6
0

ASSESSMENT
1. If you have a rope that is 3 meters long and you need pieces that are 50 centimeters
each, how many pieces can you obtain?
2. A baker has a dough that is 1 meter long, and they need to divide it into pieces that
are 25 centimeters each. How many pieces can they make?
3. If a piece of wood is 90 centimeters long, and you need pieces that are 10 centimeters
each, how many pieces can you cut?
4. A gardener has a hose that is 15 meters long, and they need sections that are 2 meters
and 50 centimeters each. How many sections can they make?
5. A tailor has a piece of fabric that is 3 meters long, and they need strips that are 15
centimeters wide. How many strips can they cut?
6. If a shelf is 80 centimeters wide, and you need compartments that are 10 centimeters
each, how many compartments can you create?
7. A construction worker has a plank that is 4 meters long, and they need pieces that are
30 centimeters each. How many pieces can they cut?

Division of centimetres and millimeters with
conversion
Group Activity
Divide 47 cm 7 mm by 9
In groups of four
1.Write 47 cm 7 mm divided by 4 in long division form.
2. Divide 47 cm by 9.
3. Convert the remaining cm to mm and add to 7 mm.
4. Divide the sum in step 3 by 9.
5. Discuss the results and share with other groups

example
divide 80cm 5mm by 7
solution
11cm 5mm
7 80cm 5mm
-7
10
-7
3cm x 30mm ………..1cm =10mm
35mm…………(30mm+5mm)
- 35mm
00

ASSESSMENT
1. A piece of wire is 1.2 meters long, and you need sections that are 15 centimeters each.
How many sections can you obtain?
2. A gardener has a hose that is 5 meters long, and they need sections that are 50
centimeters each. How many sections can they make?
3. A baker has a dough that is 80 centimeters long, and they need pieces that are 10
centimeters each. How many pieces can they make?
4. If a shelf is 90 centimeters wide, and you need compartments that are 15 centimeters
each, how many compartments can you create?
5. A construction worker has a plank that is 2.5 meters long, and they need pieces that
are 25 centimeters each. How many pieces can they cut?
6. A tailor has a piece of fabric that is 3.6 meters long, and they need strips that are 60
centimeters wide. How many strips can they cut?
7. If a rope is 2.4 meters long, and you need pieces that are 30 centimeters each, how
many pieces can you obtain

Circumference, diameter and radius
a) Measuring circumference
Group Activity
In pairs:
1. Obtain a cylindrical container.
2. Tie a string once round the curved surface of the cylinder.
String
3. Measure the length of the string that was tied round the cylinder.

Note
The distance round a circular object is called circumference.
In groups of 5 use a piece of string and a ruler to measure and record the
circumference of the following circular object
object circumference
Shoe polish tin
Circular lid
Edge of a circular cup
40 shilling coin
20shilling coin

b)Measuring diameter and radius of a circle
Group Activity
In groups of three
1. Obtain a circular object. Circumference
2. Trace the circular edge of the object.
3. Cut out the circular tracing.
4. Fold the cut-out into two equal parts.
Note
• The line dividing the circular cut-out into two equal parts is called diameter.
• The line of fold divides the circular cut-out into two equal parts.
5. Fold the circular cut-out to form four equal parts. Fold
fold
centre
,

Assessment
Which one of the following shows diameter or radius of a circle

Note
The two lines of fold meet at the centre
i) The line from the centre to the circumference of the Cut-out is called the
radius.
(ii) Diameter is twice the radius.
(iii)Diameter is twice the radius
P S RS =diameter
Q=centre
QP=Radius
R

Relationship between circumference and
diameter of circle
Group Activity
In groups of four:
• Obtain four different circular objects.
• Measure the circumference of each circular objects.
• Measure the diameter of each of the circular objects.
• Divide the length of the circumference by the length of thediameter.5. Copy and complete the table shown
• Discuss and compare the values of circumference divided by the diameter
Name of the object circumference diameter Circumference
diameter
A
B
C
D

Note
The circumference divided bų the diameter in all the objects is about three.
 When measured accurately, the value of circumference divided by the diameter is about 3
1
7
or
22
7
 This number (3
1
7
) is called pi and is written as 𝜋
 Circumference (c) =𝜋
Diameter (d)
Circumference = 𝜋 x d
c= 𝜋d
diameter=2 x radius(2r)
C=𝜋d or 2𝜋r

Example
• Example
• (a) The diameter of a circle is 56 cm. Find the e circumference of the circle.
• (b) The radius of a circle is 70 mm. Calculate the of the circle. (Take 𝜋 =
22
7
)
Solution
Circumference = 𝜋d
Diameter = 56 cm
=
22
7
x 56
= 176cm

ASSESSMENT
1. What is the circumference of a pizza that has a diameter of 40 centimeters?
2. A bicycle wheel has a diameter of 70 centimeters. What is the circumference of the
wheel?
3. If a clock has a diameter of 20 centimeters, what is the circumference of its face?
4. The lid of a jar has a diameter of 12 centimeters. What is the circumference of the lid?
5. A circular table has a diameter of 120 centimeters. What is the circumference of the
table?
6. The rim of a drinking glass has a diameter of 8 centimeters. What is the circumference
of the rim?
7. A hoop used in a game has a diameter of 60 centimeters. What is the circumference of
the hoop?
8. The base of a cylindrical container has a diameter of 15 centimeters. What is the
circumference of the base?

2.2AREA
• Work out area of triangles in square centimetres (cm2),
• Work out area of combined shapes involving squares, rectangles and
triangles incm2,
• Estimate the area of circles by counting squares,
• Appreciate the use of cm2 in working out area in real life.

Establishing that area of a triangle is equal to
a half area of a rectangle
Group Activity
In groups of three:
1. Draw a rectangle measuring 8 cm by 4 cm on a paper.
2. Cut out the rectangle.
3. Find the area of the rectangle.
4. Cut the rectangle along one of the diagonals to get twotriangles.
5. Compare the sizes of the two triangles.
6. Relate the area of each triangle to that of the rectangle.
Note
I)The two triangles are equal in size.
(ii) The area of each triangle is a half of the area of the rectangle.

Example
• Find the of the shaded part show
area of a rectangle =9cmx6cm=cm2
6cm the shaded part is a triangle
area of shaded part=
1
2
area of the
9cm rectangle
1
2
x 54cm2
= 27 cm2

ASSESSMENT
1. A triangular piece of land has a base of 10 meters and a height of 6 meters.
How does the area of this triangle compare to half the area of a rectangle
with the same base and height?
2. If you cut a rectangular piece of paper in half diagonally to form two
triangles, how does the total area of the two triangles compare to the area
of the original rectangle?
3. In a room, a triangular section of the floor has a base of 8 cm and a height of
5 cm. How does the area of this triangular section compare to half the area
of a rectangle with the same base and height as the triangle?
4. A roof has a triangular gable with a base of 12 meters and a height of 8
meters. How does the area of this triangular gable compare to half the area
of a rectangle with the same base and height?

5.A rectangular sheet of metal measures 18 cm by 5 cm. The sheet was cut
along a diagonal to get two triangular parts to make a decoration, Find the
area of each triangular piece. A.
6.A rectangular piece of paper measures 30 cm by 21 cm. The paper is
divided along a diagonal. One of the parts is shaded. What is the area of the
shaded part?
7.A rectangular tile measures 20 cm by 18 cm. The tile is divided along a
diagonal and one part of the tile is shaded blue. Find the area of the part
which is shaded blue.

Establishing the area of a triangle is equal to
half area of a square
Group Activity
In groups of five
1.Draw a square of side l0 cm on a paper.
2. Cut out the square.
3. Find the area of the square.
4. Cut the square along a diagonal to get two triangles.
5. Compare the sizes of the two triangles.
6. Relate the area of each triangle to that of square.
Note
(i) The two triangles are equal in size.
(ii) The area of each triangle is equal to a half area of a square.

Example
• Find the area of the shaded triangle shown
12cm
12cm
Area of the square =12cm x 12cm
=144cm2
Area of the triangle=
1
2
x 144cm2
=72cm2

ASSESSMENT
1. A triangular piece of fabric has a base of 8 cm and a height of 6 cm.
How does the area of this triangle compare to half the area of a
square with the same side length as the base of the triangle?
2. If you have a triangular piece of land with a base of 12 meters and a
height of 10 meters, how does the area of this triangle compare to
half the area of a square with each side measuring 12 meters?
3. In a kitchen, a triangular cutting board has a base of 15 centimeters
and a height of 12 centimeters. How does the area of this triangle
compare to half the area of a square with each side measuring 15
centimeters?

4.A roof has a triangular gable with a base of 20 cm and a height of 16 cm. How
does the area of this triangular gable compare to half the area of a square with
each side measuring 20 cm?
5.If you have a triangular piece of paper with a base of 5 cm and a height of 4 cm,
how does the area of this triangle compare to half the area of a square with each
side measuring 5 cm?
6.A triangular flag has a base of 3 meters and a height of 2 meters. How does the
area of this flag compare to half the area of a square with each side measuring 3
meters?

Area of a triangle
• Area of a right-angled triangle
• Group Activity
• In groups of four
• Draw a rectangle measuring I2 cm by 6 cm.
• 2. Cut out the rectangle and label the rectangle as shown.
D C
A B
3. Find the area of the rectangle ABCD
4. Cut the rectangle along the diagonal BD to form two triangles.
5. Find the area of each triangle.
6. Compare the area of triangle ABD and that of triangle CDB.

NOTE
i) Two right angled triangles, ABD and CDB are formed.
ii)Area of the rectangle is
1
2
of the rectangle
(iii) If the length of the rectangle is L and width is W
Area of a triangle =
1
2
l x w
L is the base of the triangle
W is the height of the triangle
The base can be represented by letter b.
The height can be represented by letter h.

Area of combined shapes
Combined shapes involving rectangles and squares
Group Activity
Work out the area of the shape shown.
12cm
8cm
4cm
4cm 4cm

In groups of four:
1. Copy the shape shown.
2. Divide the shape into rectangles and squares.
3. Determine the measurements of each part.
4. Find the area of each part.
5. Find the total area of the combined shapes.
Note
The total area of the shapes is the area of the combined shapes.

Example
• The diagram below shows a plan of a house
10cm Area of rectangle A=15cm x 5cm=77 cm2
5cm Area of a square =5cm x 5cm =25 cm2
15cm 5cm total =75cm2+25cm2 =100cm
5cm

ASSESSMENT
1.Find the area of each of the following
6cm
10cm 4cm
14cm 4cm 6cm
6cm 2cm
12cm

2. Practically use some rectangles, squares and triangular cut-outs to form
combined shapes. Find the area of the combined shapes.
3. Use IT devices to learn more on area of combined shapes involving
rectangles, squares and triangles.
4. Digital time: https://www.youtube.com/watch?v=TCsnufMCWUc

2.8 capacity
By the end of the sub strand, the learner should be able to;
• Identify the relationship among cubic centimetres (cm3), millilitres
and litres in real life,
• Convert litres to millilitres in different situations,
• Convert capacity in millilitres to litres in different situations,
• Appreciate use of cm3 and litres in measuring capacity in real life.

Cubic centimetres, millilitres and litres
(a) Cubic centimetres and millilitres
Group Activity
In groups of five
1. Obtain a wooden block measuring 10 cm by 10 cm by l0 cm.
Calculate its volume.
2. Fill a tin with water completely.
3. Obtain an empty basin.
4. Put the tin full of water in the basin as in A.

• 5. Submerge the wooden block as in B. Some water will spillinto the basin.
• 6. Transfer the water displaced by the block cube into ameasuring jar C,
marked in millilitres.
• 7. Compare the amount of water displaced with the volumeof the block.
• 8. Discuss your findings and share with the other groups.
Note
i)The volume of the wooden block is I 000 cm3.
(ii) The amount of water in millilitres displaced is I 000 ml.
(iii) The volume of the block is equal to the volume of the water displaced
Example
write a) 200ml in cm3
1ml=1cm3
200ml= 200 x 1cm3 = 200cm3

ASSESSMENT
1. How many cubic centimeters are in a milliliter, and how is this conversion used in measuring liquid
medications?
2. If a cube-shaped box has dimensions of 5 centimeters by 5 centimeters by 5 centimeters, what is its
volume in cubic centimeters and milliliters?
3. When measuring the capacity of a syringe, why is it often expressed in both cubic centimeters and
milliliters?
4. A medicine bottle contains 250 milliliters of cough syrup. What is the volume of the syrup in cubic
centimeters?
5. A cube-shaped aquarium has dimensions of 30 centimeters by 20 centimeters by 15 centimeters. What
is its volume in cubic centimeters, and how does this relate to its capacity in milliliters when filled with
water?
6. If a perfume bottle holds 50 milliliters of perfume, what is the volume of perfume in cubic centimeters?
7. When measuring the displacement of an engine, why is it often reported in both cubic centimeters and
milliliters?

Cubic centimetres
Group Activity
In groups of five:
1.Fillallbottle with water.
2. Transfer the water into a measuring jar marked in cubic centimetres.
3. Read the level of the water in cubic centimetres.
4.Relate the amount of water in the jar with the amount of water that was in the bottle
Discuss and share your results with other groups.
Note
1000 cm = 1000 ml
Example
Joseph had a 2l bottle full of water. He transferred the water intoa measuring jar marked in cm'.
What was the reading of the water level?
The mark of the water level was 2 000 cm3 .

Assessment
1. How many cubic centimeters are in a liter?
2. If a swimming pool has dimensions of 10 meters by 5 meters by 2
meters, what is its volume in cubic meters?
3. A soda can has a capacity of 355 milliliters. What is its volume in
cubic centimeters?
4. If a bathtub can hold 150 liters of water, what is its volume in cubic
centimeters?
5. A jug contains 2.5 liters of milk. What is the volume of the milk in
cubic centimeters?

Conversion of litres to millilitres
Group Activity
In groups of five:
1. Take a number less than 10.
2. Multiply the number by 10, 100 and I 000. What do you notice?
3. Take another number less than 100.
4.Multiplų the number by I 000.
5. Share your results with other groups.
Note
To multiply a number by 1000, the result is the number with zero in the ones,
tens and hundreds place values.5

Example
Convert 6l to milliliter
1l=1000ml
6l=6 x 1000=6000ml

Assessment
1. A bottle of water contains 1.5 liters. How many milliliters is this?
2. If a car's fuel tank can hold 60 liters of gasoline, how many milliliters of gasoline
does it contain?
3. When purchasing a gallon of paint, it is often sold in liters. If a gallon of paint is
equivalent to approximately 3.785 liters, how many milliliters is this?
4. A jug of juice contains 2.5 liters. How many milliliters of juice does it hold?
5. If a shampoo bottle contains 750 milliliters of shampoo, how many liters is this?
6. A bottle of cooking oil contains 2.2 liters. How many milliliters of oil does it
contain?

Conversion of millilitres to litres
Group Activity
In groups of four
1. Write the relationship of the liter and millilitres.
2. Use the relationship to find the number of I 000 ml into7000 ml
3. Discuss and share your results with other groups.

EXAMPLE
Convert
5000ml to litres
1000ml = 1l
5000ml=5000÷ 1000l
=5l

Assessment
1. If a water bottle contains 500 milliliters of water, how many liters is this?
2. A medicine bottle holds 250 milliliters of liquid medication. How many liters is
this?
3. When buying a carton of milk, it is often sold in liters. If a carton contains
1,200 milliliters of milk, how many liters is this?
4. A bottle of soda contains 750 milliliters of soda. How many liters is this?
5. A jug of juice contains 1,500 milliliters. How many liters of juice is this?
6. If a bottle of shampoo holds 300 milliliters, how many liters of shampoo is
this?

Conversion of litres and millilitres to millilites
Group Activity
Convert 4 l 240 ml to millilitres
In groups of five:
1.Write the relationship of the liter and millilitres.
2. Convert 4 l to millilitres.
3. Add 240 ml to the result of (2) above.
4. Discuss your results and share with other groups.

Example
• Convert 9l 125ml to millilitres
solution
1l=1000ml
9l=9x1000ml
=9000ml
9000ml+125ml
=9125ml

Assessment
1. The capacity of a container is 2 125 ml. What is the capacity of the
container in millilitres?
2. Three litres three hundred and eighty millilitres of water leaked out
of a tank. Write this amount in millilitres.
3. A jerrycan can hold 5l 790 ml of a detergent. Write this amount in
millilitres.
4. The capacity of a can is 20 400 ml. What is the capacity of the can in
millilitres?

Conversion of millilitres to litres and millilitres
Group Activity
In pairs:
I. Write the relationship of the litres and millilitres.
2. Estimate the complete number of times I000 will divide3 570 ml.
3. Multiply the estimated number by 1000 and subtract the product
from 3570 ml.
4. Write the answer in litres and millilitres.
5. Discuss your results and share with other groups

Example
Convert 65440 ml to litres and millilitres.
Solution
1000ml=1l
6540ml=6540ml÷1000
=6l 540ml

Assessment
1. The capacity of a container is 4 500 ml. Write the capacityin litres
and millilitres
2. A bottle contained one 125 millilitres of mango juice. Howmuch was
the juice in litres and millilitres?
3. Convert to litres and millilitres:
(a) 1500 ml (b) 7 205 ml
(c)3400ml

Conversion involving millilitres, litres and
cubic centimetres.
Group Activity
Convert
(a) 250 ml to cm3 (b)740cm to ml
(c)3l to cm3 ()2730 cm3 to ml
In groups of five:
1. Write a relationship of the ml and cm?.
2. Use the relationship to convert:
(a) 250 ml to cm³ ? (b) 740 cm³ to ml
1. Write a relationship of the liter and cubic centimetres.
2. Use the relationship in (3) above to convert:
3. (c) 3l to cm³ and (b) 2730 cm³ to l and ml
5, Discuss and share the results with other groups.

Example
Convert
150ml to cm³
150ml=150x1 cm³
=150 cm³

Assessment
1. A water tank has a capacity of 5,000 liters. How many milliliters is this,
and how does it compare to its volume in cubic centimeters?
2. A bottle of detergent contains 1.5 liters. How many milliliters is this, and
what is its volume in cubic centimeters?
3. A swimming pool has a capacity of 100,000 liters. How many cubic
centimeters is this, and how many milliliters of water does it hold?
4. If a bottle of soft drink contains 2 liters and is shaped like a cylinder with
a diameter of 10 centimeters and a height of 20 centimeters, what is its
volume in cubic centimeters?
5. A container of cooking oil holds 3,500 milliliters. How many liters is this,
and what is its volume in cubic centimeters?

2.4 MASS
• Identify the tonne as a unit for measuring mass in real life,
• Identify items measured in tonnes in real life,
• Identify the relationship between the kilogram and the tonne,
• Estimate mass in tonnes in different situations,
• Convert kilograms to tonnes and tonnes to kilograms in real life situations,
• Add tonnes and kilograms in real life situations,
• Subtract tonnes and kilograms in real life situations,
• Multiply tonnes and kilograms by whole numbers in real life situations,
• divide tonnes and kilograms by whole numbers in real life situations,
• appreciate use of the kilogram and tonne in measuring mass

Identifying the tonne
Group Activity
In groups of three
I. Write down objects whose mass can be measured in grams
2. Write down objects whose mass can be measured in kilograms.
3. Estimate the mass, in kilograms, of large objects such as lorry, a car, a
pickup, fifty bags of maize, seventy bags of cement and a tractor.
Note
• The unit for measuring mass of large objects is called a tonne (t).

ASSESSMENT
• In pairs, copy and complete the table
Note
The unit for measuring mass of lrge object is called a tonne(t)
item Unit of measuring mass
1. A packet of tea leaves
2. A lorry
3. A packet of unga
4. . A car
5. A bag of maize
6. A bag of cement
7. A pickup
8. 20 bags of sugar

Items where mass can be measured in tonnes
(t)
• Group Activity
• In groups of three:
• I. Write five (5) large items whose mass can be measured intonnes in;
• (a) the school compound.
• (b) the neighborhood of your home.
• (c) the marketplace.
• 2. Discuss your results and share with other groups.

Assessment
Use the IT device to find the mass. in tonnes, of each of the following:
(a) a lorry
(d) a whale
(b) an elephant
(e) a giraffe
(c) a rhino
(f) a trailer

The relationship between the kilograms and
the tonne
Group Activity
In groups of four:.
1.Measure a 20 kg of sand or soil.
2. Put the sand in a baq.
3. Work out the mass of sand or soil in 50 such bags
Note
(i) The mass of the 50 bags of sand or soil is 20 kg x 50 = 1000 kg
(ii) 1000 kg = I tonne (t)

Assessment
• Copy and complete the table below
Number of 20kg bags Mass in kg Mass in tonne
50 1000 1
100 2000 2
200
300
400
500 10

Estimating mass in tonnes
• Group Activity
In groups of five:
1.Estimate the mass, in tonnes, of items in the school compound.
2.Visit the market centre. Identify and estimate the mass, in tonnes, of the
following items:
(a) A pile of crates of soda.
(b) A pile of bags of cement
(c) A pickup.
(d) A lorry.
(e) A heap of sand.
(f) Discuss your results and share with other groups.

ASSESSMENT
• In pairs, estimate the mass in tonnes of objects of your choice.Record
in a table such as one shown.
ITEM Estimated mass in tonne
A A pickup 2
B
C
D
e

Conversion of tonnes to kilograms
Group Activity
Multiply each of the following by 1000:
(a) 2 (b)3 (c)5 (d)
In pairs:
1Multiply 2 by 1000.
2Multiply 3 by 1000..
3Multiply 5 by I000
4. Multiply 8 by l000.
5. Discuss the results with other groups.

Example
Convert
(a) 7tonne to kilograms
(b)5 tonne 460 kg to kg
Solution
(a) 1tonne =1000kg
7tonne=7 x 1000kg
=7000
(b)1tonne = 1000kg
5t 640kg=5x1000kg+640
=5000kg+640kg
=5640kg

Assessment
1. Kasanga had 5 tonnes of potatoes. He repacked the potatoes into 2
kg packets. How many 2 kg packets did he obtain?
2. The mass of an elephant was estimated to be 4 tonnes850 kg. What
was this mass in kilograms?
3. A shopkeeper had 2 tonnes 750 kg of rice in the store. What was
the mass of the rice in kilograms?
4. A supermarket repacked 8 tonnes of sugar into 2 kg packets. How
many 2 kg packets of sugar were obtained?
5. A seed company repacked 3 t 420 kg of a seed into 5kg plackets.
How many 5 kg packets of seeds were obtained?

Conversion of kilograms to tonne
Group Activity
In groups of three
1.Divide each of the following number 2000,4000 and 1000
2Discuss your result and result and share with other groups
Note
1Thousand can be written as a product of a number and 1000
2 6000=6x 1000
Therefore 6000÷ 1000 = 6

Example
Convert 5
(a)3000kg to tonne (b)5600kg=1000 5600
5600kg to tonne and kilograms 5000
Solution 600
3000kg =3000÷1000tonne therefore 5600kg =5tonne 600kg
= 3tonnes

assessment
1. A pickup carried a load of 1360 kg. What was this mass in tonnes and
kilograms?
2. A lorry carried s 6 800 kg of sand. What was the mass of the sand in
tonnes and kilograms?
3. A hardware shop stored 7 850 kg of cement. What was the mass of
cement in tonnes and kilograms?
4. Gacagua bought 12 500 kg of ballast. What was this mass in tonnes and
kilograms?
5. Three lorries carried 8 560 kg. 16 800 kg and 20 600 kg of sugar. What
was the total mass in tonnes and kilograms of sugar carried by the
lorries?

Addition of tonnes and kilograms without
conversion
Group Activity
In groups of three:
Add 35 t 360 kg to 7 t 235 kg.
lign the working vertically.
2. Add the kilograms first.
3. Add the tonnes next.
Example
A lorry was loaded with 4 t 350 kg of sugar and3t 530 kg of rice. What was
the total mass of the sugar and rice?

Mass of sugar was 4t 350 kg
Mass of rice was 3t 520kg
Total mass was 4t 350kg + 3t 520kg
t kg
4 350
+ 3 520
7 870

Assessment
1. A cargo ship is carrying 8 tonnes of bananas and 600 kilograms of pineapples. How much fruit is being
transported in total, in kilograms?
2. Imagine you have 3 tonnes of grain and you need to add 500 kilograms of a different type of grain to the
mix. How much grain will you have in total?
3. A construction project requires 8 tonnes of steel beams. If you already have 4,500 kilograms of steel on
site, how much more steel in kilograms do you need to procure to meet the requirement?
4. You're organizing a charity event where you need to distribute food supplies. You have 2 tonnes of rice and
700 kilograms of lentils. How much food in total do you have available to distribute?
5. A farmer is stocking up animal feed for the winter. He currently has 5 tonnes of hay and wants to add 300
kilograms of oats to the stock. What will be the total weight of feed once the oats are added?
6. A shipping company needs to load containers onto a cargo ship. If each container weighs 2 tonnes and
they've already loaded 15,000 kilograms of cargo, how many more containers can they load without
exceeding the ship's capacity?
7. You're managing inventory for a warehouse. If you have 7 tonnes of electronics and you receive a shipment
of 600 kilograms of new products, what will be the total weight of electronics in the warehouse?

Addition of tonnes and kilograms with
conversion
Group Activity
In groups of four:
Add 8t 560 kg to 5t 735 kg.
Arrange the working vertically.
2. Add the kilograms first.
3. Convert the kilograms into tonnes and kilograms.
4. Take the tonnes to tonnes column and write the kilograms in the kilograms
column.
5. Add the I tonne obtained in (4) above to the tonnes column.

Example
Add 25t 785kg to 30t 512kg
solution
Arrange the working vertically and add
t kg
25 785
30 512
56 297

Assessment
1. Nasokho bought 5 t 649 kg of cabbages and 15 t 975 kg of
potatoes. What was the total mass of the items he bought?
2. A lorry carried 7 t 498 kg of sugar and 5 t 839 kg of maize. What was
the total mass of the load?
3. At a construction site, 11t 600 kg of cement, 33 t 450 kg ofsand and
45 t 725 kg of ballast were required. What was the total mass of the
materials required?

4.A grocery store receives a shipment of 4 tonnes of potatoes and 800 kilograms of
tomatoes. How many kilograms of produce did they receive in total?
5.A shipping container can hold a maximum of 10,000 kilograms. If the container currently
contains 6 tonnes of cargo, how many more kilograms of cargo can be loaded before
reaching the limit?
6.A farmer harvests 3.5 tonnes of wheat and 1,200 kilograms of barley. How many
kilograms of grains did the farmer harvest in total, if both wheat and barley are considered
together?
7.A construction project requires 15 tonnes of concrete. If the contractor has already used
7,500 kilograms of concrete, how many more tonnes of concrete do they need to complete
the project?
8.A warehouse manager needs to organize inventory. They have 9 tonnes of steel beams
and receive a shipment of 500 kilograms of aluminum sheets. After converting everything
to kilograms, what is the total weight of metal inventory in the warehouse?

Subtraction of tonnes and kilograms without
conversion
Group Activity
Subtract 7 t 635 kg from 12 t 464 kg.
1.Write the working in a vertical form.
2. First subtract the kilograms in the kg column.
3. Subtract the tonnes in the tonnes column.

Example
Subtract 12t 735kg from 25t 876kg
t kg
25 876
-12 735
13 141

Assessment
1. A shopkeeper had 2 t 670 kg of sugar. She sold I t 575 kg to schools.
What. Was the amount of sugar that remained?
2. A businessman had l6 t 920 kg of maize in his store. He sold12t 870
kg of the maize to millers. Work out the amount of maize he was
left with.
3. A construction company ordered for 15 t 750 kg of building
materials. The company used some of the materials and was left
with 4 t 645 kg of it. What was the total mass of the material the
company used?

Subtraction of tonnes and kilograms with
conversions
Group Activity
In group of 5
Subtract 56t 532 kg from 87t 348 kg.
1. Arrange the masses vertically.
2. Subtract the kilograms first. Regroup I t from the 87 t andconvert it
into kilograms.
3. Add I 000 kg to 348 kg and subtract 532 kg.
4. Subtract 56 t from 86 t.

Example
Work out
5t 376kg – 3t 870kg
t kg
5 376
-3 870
1 506

Assessment
1. Mary had 56 t 835 kg of maize. She sold 46 t 400 kg of the maize.
How much maize was she left with
2. There was 575 t 367 kg of coffee in a warehouse. Later, 264 of the
coffee was sold. What was the mass of coffee left?
3. Philip had 12 t 635 kg of sugar. He sold some of the sugar. He was
left with 4t 800 kg. How much sugar did he sell?

• Group Activity
Multiply 9t 32 kg by 9
In groups of three:
1.Align the working vertically.
2. Multiply 32 kg by 8.
3. Multiply 4 t by 8.

Example
7 Multiply l6 t 70 kg by 12
arrange vertically
t kg
16 70
12
192 840

Assessment
1. The mass of a loaded trailer was l2 t 250 kg. What was the mass of
3 such trailers?
2. Four lorries carried a load of 9t 220 kg each. What was the total
mass of the load carried
3. There were 8 buses packed in a garage. The mass of each bus was 2
t 100 kg. What was the total mass of the buses?

Multiplication of tonnes and kilograms by
whole numberswith conversion
Group Activity
Work out 8 t 472 kg x 5In groups of three:
1. Arrange in vertical form.
2. Multiply kilograms by the whole numbers.
3. Convert the results to tonnes and kilograms.
4. Multiply tonnes by the whole number. add the results to the tonnes
obtained in (3) above.

Example
Multiply
7t 362kg
X 6
44t 172kg

Assessment
1. A pickup carried I t 650 kg of animal feeds in one trip. If the pickup
made 8 such trips, what was the total mass of the animal feeds
carried by the pickup?
2. A wholesaler supplied 5 t 750 kg of goods everyday for 9 days. What
mass of goods did the wholesaler supply in the q days?
3. A factory produced 65 t 355 kg of a product daily. What mass of the
product did the factory produce for 15 days

Division of tonnes and kilograms by whole
numberswithout conversion
Group Activity
Divide 72 t 480 kg by 6
In groups of three:
1. Divide 72 tonnes by 6.
2. Divide 480 kilograms by 6.

Example
Divide 10t 615kg by 5
Arrange in the long division form
2t 123kg
5 10t 615
-10 5
0 11
10
15
15 =2t 123kg
0

assessment
1. A charitable organisation shared 84 t 384 kg of rice equal among 12
villages. How much rice did each village get?
2. A lorry transported 32 t 568 kg of sand in 4 trips. If it carried equal
amounts of sand in each trip, how much sand did i carry in a trip?
3. A factory packed 280 t 427 kg of sugar in 7 days. If the factory packed
equal day, how much sugar did it pack daily?
4. A train was connected with 11 coaches. The coaches were parked with
equal masses of goods. The total mass of the goods was 122 t I44 kg.
Work out the mass contained in each coach.
5. The total mass of 6 pickups of equal mass was |4 t 124 kg. Work out the
mass of each pickup.
6. The total mass of 7 tractors was 30 t 555 kg. The tractors were of the
same mass. Find the mass of each tractor.

2.5 TIME
i. By the end of the sub- strand, the learner should be able to;
experiences,
write time in a.m. and p.m. in day to day life
ii. relate time in a.m. and p.m. to the 24h clock system,
iii. convert time from 12h to24h and 24h to 12h system,
iv. interpret travel timetable in different situations,
v. appreciate use of time in both 12h and 24h systems.

Time in a.m. and p.m
There are two 12 hour period in a day.
The first 12hour period starts from midnight to midday
This period is called ante meridian (am)
This second period starts from midday to midnight
This period is the post meridian (pm)

midnight midday
midnight
Ante meridian (am) Post meridian (pm)

Identifying time in a.m and p.m
In group of five
1. write the activities that you do between midnight and midday
2.Discuss the activities and share with other groups

Assessment
1. Complete the statements:
(a) A day has…………. twelve hour periods
(b) A day starts from……..to………
(c) There are …… ante meridian hours and……… post meridian hours
2. Write a.m. or p.m.
(b) Time from midday to midnight is a Writing time in a.m.
(c) Time from breakfast to school time is
(d) Time from end of lessons to bedtime is

Writing time in am
Group Activity
In groups of four:
1. Draw and label 3 clock faces.
2. On the clock faces, show:
(a) the time you take breakfast.
(b) the time you go to school
(c) the time you go for the morning break.
3. Draw a digital clock to show the time for each activity in(2) above
4. Discuss and share your results with other groups.

Example
Write the time in a.m.
(a) 2 hours after midnight.
(b) 8 hours after midnight.
(c) 4 hours before midday.
Solution
mid night midday
(a) 2 hours after midnight is 2:00 a.m.
(b) (b) 8 hours after midnight is8:00 a.m.
(c) (c) 4 hours before midday is8:00 a.m.
1 2 3 4 5 6 7 8 9 10 11 12

Assessment
1. A meeting started 10 hours 40 minutes after midnight. Writethe
time the meeting started
2. A train left a station 5 h 20 min after midnight. At whattime did the
train leave the station?
3. A taxi driver left her home 4 h 19 min after midnight. Atwhat time
did she leave home?

Writing in pm
Writing time in p.m. Time in p.m. is counted from midday to midnight.
Three hours after midday is 3:00 p.m.
In groups of four:
1. Draw and label three clock faces.
2. On the clock faces show the following:
(a) the time first lesson starts in the afternoon.
(b) the time for games after lessons.
(c) the time you take supper.
3.Discuss your results and share with other groups.

Example
Waliaula took 8h 43 minutes to drive from town to his home. He
started his journey at midday. At what time did he arrive at home?
Solution
Midday 8h 43min midnight
He arrived at the home at 8:43pm
1 2 3 4 5 6 7 8 9 10 11 12

Assessment
1. Ken went to bed 10 h 30 min after midday. At what time in p.m. did
he go to bed?
2. A meeting on HIV awareness started 2 h 15 min after midday.Write
the time in p.m. when the meeting started.
3. A group of volunteers started distributing relief food3 h 40 min after
midday. Write this time in p.m.
4. Walibora closed his shop 5 h 30 min before midnight. Write this
time in p.m.
5. Nafula finished her homework 3 h 45 min before midnight. Write
the time she finished the homework in p.m.

Writing time in a.m and p.m
Goup activity
In groups of four:
1. Write time in the afternoon shown on the clock face.
2. Write the time it will be:
(a) 10 hours after
(b) 12 hours after

Example
A watch shows the time as 10:25pm.What time will be 2
1
4
h later?
Solution
10:25pm=10h 25 min after midday
2
1
4
h = 2h 15min
2
1
4
h after 10:25 is 12h 40 min =12:40am

Assessment
1. A child was fed after every 5 hours. The child was last fed at 10:20
a.m. At what time will the child be fed again?
2. The temperature of a patient was taken after every six hours. The
temperature was last taken at 6:30 a.m. Write the time in a.m. or
p.m. when the temperature will again be taken.
3. A business was closed at I2:55 pm. The business had been opened
for 4 h 35 min. At what time was the business opened?
4. A bus driver arrived at his destination at 12:05 p.m. He had driven
for 8 h. At what time did he start the journey?

Converting time from 12h system to 24 clock
system
Converting time from 12 h system to 24 h clock system
Group Activity
In groups:
1. Take a time in a.m. or p.m.
2. Write the time in 24 h system.
3. Take a time in p.m.
4. Convert the time to 24 h system.
5. Discuss the conversion process and share with other
Note
To convert time in p.m. to time in 24h system, add 12 hours to the time in
p.m.

Example
Convert to 24h system
7:30 a.m 11:50pm
Solution
(a) 7:30 a.m. is 7h 30 min after midnight.
(b) Therefore, 7:30 am is 0730 h.
(c) (b) I1:50 p.m. is 11h 50 min after midday and midday is 12 h before
midnight.
(d) 11:50 p.m. is 11 h 50 min + 12 h in 24 h system. Therefore, 11:50 p.m. is
2350 h.

1. A flight is scheduled to depart at 11:45 PM. What time is it in the 24-hour clock
system?
2. An employee's shift starts at 8:30 AM. What time does their shift begin in the 24-hour
clock system?
3. A train is expected to arrive at 3:15 PM. Convert this time to the 24-hour clock system.
4. A business meeting is scheduled for 10:00 AM. What time is the meeting in the 24-
hour clock system?
5. A movie is scheduled to start at 5:20 PM. Convert this time to the 24-hour clock
system.
6. A store closes at 9:00 PM. What is the closing time in the 24-hour clock system?
7. the 24-hour clock system.
8. A school assembly begins at 2:45 PM. What time does the assembly start in the 24-
hour clock system?

Converting time from 24 h system to time in
12 h system
Group Activity
In groups of five:
1.Take any time in 24 h.
2. Use a chart to convert the time to 12 h system.

Example
Convert to 12 h system
(a) 0648
(b) 2134h
Solution
(a) 0648 is 6 h 48 min after midnight
6 h l48 min after midnight is 6:48 a.m.
(b) 2139h is 21 h 39 min after midnight
21 h 39 min - 12h= 9h39 min after midday.
Therefore, 2134 h is 4:39 p.m.

Assessment
1. A train is scheduled to depart at 15:30. What time is it in the 12-hour clock system?
2. A restaurant reservation is at 19:45. Convert this time to the 12-hour clock system.
3. A flight is expected to arrive at 21:15. What time does it arrive in the 12-hour clock
system?
4. A store opens at 08:00. Convert this time to the 12-hour clock system.
5. A business meeting concludes at 14:45. What time is it in the 12-hour clock system?
6. An employee's lunch break is scheduled for 12:30. Convert this time to the 12-hour
clock system.
7. A movie is scheduled to start at 18:20. What time does the movie begin in the 12-hour
clock system?
8. School dismisses at 15:00. Convert this time to the 12-hour clock system.

Tavel time tables
Group activity
The table below shows Nambuyes journey from Akoli to Bilali through Daabu
1. In pairs, use the table to answer the following questions:
(a) Where did Mutua start his journey?
(b) At what time did he:
(i) arrive at Bilali?
(ii) Daabu
station arrival Depature
Akoli 8:30a.m
Daabu 9:15 10:50 a.m
Bilali 11:45 a.m 12:30p.m

(c) Where was Mutua
(i) at 10:30 a.m. ?
(ii) at II:00 p.m. ?
2. Discuss your answers and share them with other groups.
Example
A motor cyclist travelled from Jua to Kali through Moto. The table below shows the journey of the cyclist.
Use the table to answer the following questions:
(a) At what time did the motorist start the journey?
(b) (b) Where was the motorist at 8:30 a.m.?
(c) (c) Where was the motorist at 8:45 a.m.?
Solution
(a) (a) 8:00 a.m. (b) Moto (c) On the journey from Moto to Kali.
station arrival Depature
Jua 8:00 a.m
Moto 8:30 a.m 8:40 a.m
Kali 9:00 a.m

Assessment
1. The table below shows the arrival and departure time of a bus. The bus
was travelling from Koja to Mioto through Lewa.
Use the table to answer the following questions:
(a) Where was the bus at 1115 h?
(b) At what time did the bus leave Lewa?
(c) When did the bus arrive at Mioto
town arrival Depature
Koja 0935
Lewa 1115h 1205
mioto 1655h

2.6 MONEY
• Prepare simple budget in different situations,
• Determine buying and selling prices of different items in the
community,
• Work out profit from sales of different items in the community,
• Calculate loss realized from sales of different items in the community,
• Identify types of taxes in different situations,
• Appreciate use of money in real life situations

PRICE LIST
Group activity
In groups of five
1.Write ten items commonly bought from a shop.
2. Discuss and write the price of each item.
3. Record the items and their prices in a table as shown.
4. Discuss the table and share with other groups
Note
A list showing the items and their prices is called a price list.
item price

Below is an example of a price list Price (sh)
Example
Furaha bought a packet of milk, a loaf of bread and two exercise books. Use the
price list to find how much he paid for the items.
item price
A match box
A ruler
A rubber
500 ml packet of milk
A packet of yoghurt
A loaf of bread
2 kg packet of wheat flour
2 kg packet of maize flour
kg of rice
Exercise book 46 pages
5
30
20
50
100
60
140
120
150
80

solution
A packet of milk sh 50
A loaf of bread sh 60
Two exercise books sh 160
Total sh 270

ASSESSMENT
Use the PRIVIOUS price list given to answer the following questions.
1. Write the price of each of the following items:
(A) A packet of yoghurt
(B) an exercise book
(C) A rubber
(D) 2 kg packet of wheat flour
2. What is the cost of a packet of yoghurt and one kilogram of rice?
3. Kwendo bought a 2 kg packet of wheat flour, a 2 kg packet of maize flour and a ruler.
How much did he pau for the items altogether?
4. Twili bought three rubbers, 5 match boxes and two exercise books. How much did he pay
altogether?
5. Noor bought 2 packets of yoghurt, two loaves of bread and kilogram of rice. How much
money did he spend on the items?

Factors to consider when preparing a simple
budget Group
Activity 2
What would you consider when preparing a simple budqet fora
birthday party?
In groups of five:
1 Write down the things that you consider when making abudget for
your birthday party.
Discuss and share with other groups

Note
Some of the factors to consider when preparing a simple budget are:
Availability of money.
2. Source of money.
3. Cost of items required.
4. Financial goals.
5. Spending habits.
6. Balancing between income and expenses.

Assessment
• 1. Your class plans to visit a children's home near your school. List
four things you will consider as you prepare a budget for the day.
• 2. Your family plans to visit an elderly woman near your home. List
three things you will consider as you prepare a budget for the day.

Preparing a simple budget
Group Activity
You have sh 2000 to spend on a birthday party. Prepare a budget.
In groups of four:
1.Identify the number of people to be invited and the venue.
2. Identify the items to be bought.
3. Estimate the cost per item.
4. Find the estimated total cost.
5. Balance the amount available and expenses.
6. Discuss your budget and share with other groups

Assessment
Prepare a budget for each of the following situations:
1. A breakfast for three people to cost sh 200.
2. Back to school shopping to cost sh 1200.
3. A birthday party for a friend. The number of people to be invited is
15 and the amount of money available is sh 2000

Profit and loss
Identifying profit and loss
Group Activity
In groups of five:
1.Consider the following situations:
(i) Kaikai bought a calf for sh 10 000. Later in the day, he sold the calf
for sh 12 000
(ii) Chiro bought a dress for sh 800. She later sold if for sh 750.
2. Compare the buying price and the selling price of the calf.
3. Compare the buying price and the selling price of the dress

Note
1.When the selling price is more than the buying price, profits made.
2.When the selling price is less than the buying price, loss is made.
Example
A businessman bought a bundle of maize flour for sh 1200.He later sold
it for sh 1300. Did he make a profit or a loss?

• Solution
• Buying price is sh 1200
• Selling price is sh 1300
• The selling price is more than the buying price. Therefore, he made a
profit.
• A trader bought a tray of eggs for sh 280. She later sold the tray of
eggs for sh 270. Did she make a profit or a loss?
• Solution
• Buying price is sh 280 Selling price is sh 270 The selling price is less
than the buying price. Therefore, she made a loss.

Assessment
1. Philip bought a bicycle for sh 8000.she sold it for 7000 find the loss
he made
2. Atrader bought a jacket for sh 2300.He later sold it for sh 1900
3. Nandia bought a carpet for sh 7 000. She later sold if for sh 10 000.
4. Timau bought a goat for sh 4 700. He later sold if for sh 6 000.
5. Laura bought a bunch of bananas for sh 400. She later sold if for sh
360

Profit
Group Activity
Atieno bought a piece of cloth for sh I 700. She later sold it for sh 2 300. Find
the profit
In pairs:
1. Write the buying price.
2. Write the selling price.
3. Work out the profit.
4. Discuss your answer with other groups
Note
Profit = Selling price - buying price

Example
A shopkeeper bought an iron sheet for sh 1100.He sold it for sh 1400.
What was the profit?
Solution
Selling price is sh 1400
Buying price is sh 1100
Profit = Selling price - buying price
Profit = sh 1400 - sh 1100
= sh 300
profit was sh 300

Assessment
1. Moses bought a book for sh 2 700. He later sold it for sh 3 300. What was
the profit?
2. A trader bought a motorbike for sh 50 000. He sold it for sh 56 000.
Calculate the profit..
3. A shopkeeper bought seeds for sh 10 000. How much would he have sold
the seeds to make a sh 2 000 profit?
4. Peter bought a sheep for sh 6 500. He later sold it for sh 8 500 the
following day. What was the profit?
5. Kevina bought a packet of sweets for sh 380. She later sold the sweets for
sh 470. What was her profit?
6. Elizabeth bought a packet of face masks for sh 450. He later sold the
masks for sh 550. What was the profit?

LOSS
Group Activity
Omondi bought a TV set for sh 3I 500. He later sold the TV set for sh 28 000.
What was the loss?
In pairs, answer the following questions:
1.What was the buying price?
2.What was the selling price?
3. What was the loss?
Note
Loss = Buying Price - Selling Price

Example 4
Kim bought a bicycle for sh 8000 for sale.He later sold the bicycle for sh
7 850. What was the loss?
Solution
Buying price sh 8 000
Selling price sh 7 850Loss
= Buying Price - Selling Price
= sh 8 000 - sh 7 850
= sh 150

Assessment
1. Sarah bought a dress for ksh80 and sold it for ksh60. What was her loss?
2. John purchased a bike for ksh300 and sold it for ksh250. What was his loss?
3. A bookstore bought 100 copies of a book for ksh10 each and sold them for ksh8 each. What was the total
loss?
4. A company bought a piece of equipment for ksh5,000 and sold it after a year for ksh4,200. What was the
loss?
5. Tom bought shares in a company for ksh50 each. He sold them later for ksh45 each. What was his loss per
share?
6. A grocery store bought 200 kilograms of apples for ksh2.50 per kilogram. Due to spoilage, they had to sell
them at ksh2 per kilogram. What was the total loss?
7. Emma bought a smartphone for ksh600 and sold it for ksh500. What was her loss?
8. A car dealership purchased a used car for ksh12,000 and later sold it for ksh10,000. What was the loss on
the transaction?
9. A farmer bought a herd of cattle for ksh15,000 and sold them for ksh12,000. What was the loss incurred?
10. A restaurant bought seafood for ksh800 and had to discard it due to spoilage. What was the loss on the
seafood?

Types of taxes
Group Activity
In groups of five discuss the following:
1. What is tax?
2. Name types of taxes.
3. Who collects tax on behalf of the government?
Discuss your results and share with other groups.
Note
(i) Tax is the amount of money paid to the government by the citizen to enable it to
offer services.
(ii) Some types of taxes are income tax, value added tax (VAT),excise duty, excise tax
and stamp duty.
(iii) Kenya Revenue Authority is entrusted by the qovernmentto collect taxes.

Income tax
Group Activity
In groups of five, answer the questions:.
What is income tax?
Who pays income tax
How is income tax calculated?
Discuss in your groups and share.
Note
Income tax is a direct tax that is imposed on income got from business,
employment, rent, dividends and interests.

Assessment
1 What is income tax?
2 Write four sources of income tax
3 Name four services provided by the government aftercollecting
income tax

VAT
Group Activity
In groups of five,
discuss the following
1. What is VAT ?
2. Identify items that can be used directly without being processed or in
processed form.
3. Name five manufactured goods Discuss your results and share with other
groups.
Note
When goods are processed or manufactured, their value is increased. Such
products are charged a tax called Value Added Tax (VAT).
For example, potatoes are used to manufacture crisps and maize is turned to
maize flour.

Assessment
1. What does the abbreviation VAT stand for?
2. What is VAT?
3. Who pays VAT?
4. Name four processed items where VAT is charged.

STRAND 2 MESURMENT.pptx grade 6 cbc for learners

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