MATHEMATICS SECOND TERM E LESSON NOTE FOR BASIC SIX

TABLE OF CONTENT

Week Topic

1. Revision

2. Money

3. Length

4. Perimeter

5. Area (Trapezium)

6. Volume (Prisms, cube and spheres)

7. Capacity

8. Weight

9. Time

Class:- Basic 6

Subject:- Mathematics

Week:- 2

Topic: Money ( Rates, Taxes, Shares and dividends)

Behavioral objective:- At the end of the lesson the pu.pils should be able to:-1.
Solve problems on taxes and Rates on population and economic Consequences.

2. Solve problem on buying and Selling of shares and dividends.

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6
Building Background /connection to prior knowledge : Students are familiar
with the uses of money

Content

MONEY

Rate – means what the government Provides for her people.

Example:- Agege Local government charges N5.50 monthly for the user: Find
The total rent collected monthly From

(A). 50 stalls (B) 160 stalls

Solution:-

(A). Monthly rate collected for N50

Stalls is 𝑁5.50×50 𝑁275.00

Taxes: This is the money that Government uses to build schools, Hospitals,
roads etc

Example:- Tax deducted from the taxable Income of an employee is 35K on

Every N1. Find the tax paid if the Taxable income is N4,500

Solution:-

= (4,500×35)K = 1,575.00K = 1,575.00

Shares: The amount needed is Divided into units and each unit is

Called a share.

Example:- A metal manufacturing company Sells some of its 40K share to the
Public who are ready to buy in Multiples of 200.

(i). What is the cost of 800 shares?

(ii). How many shares can I buy With N1, 250?

Solution

Cost of one share = 40K

Cost of 800 Share = 40×800 = N( 40×800)= N32,000

(ii). 40K can buy only one share: N1,250 will buy 1250×200 40 1 = 1250×5

= N6,250 shares

Dividends:- This is the amount Made from the goods sold at the End of the year.
The profit is called Dividend.

Example: A share holder has 200 shares in a Company. How much is his
Dividend if dividend are given at 5 1/2K per share.

Solution

Dividend on 1 share = 5 1/2

Dividend on 200 shares = 11/ 2 × 200/ 10 = N1100

Evaluation:-

1. An executive lady earns two million naira per annum.

(a) Work out her income tax b) Work out her monthly tax

2. At the Marina Car Park, Ώ400 naira is charged to park a jeep and Ώ250 to park
a car. How much will the Car Park Authority collect for parking 250 cars and 360
jeeps in a day?

3. The IKEDC charge for a company is Ώ48275 VAT inclusive. If 10% was charged
as VAT, how much was that?

4. Find the rent collected by Local Government Authority from 276 stalls at the
rate of Ώ5600 per stall.
Class:- Basic 6

Subject:- Mathematics

Week:- 3

Topic: Length

Behavioral objective:- At the end of the lesson the pupils should be able to:-1.
Recognise and convert the units of length

2. Apply pythagoras’ rule to find the unknown length of a given right-angled

triangle

3. Identify pythagorean triples

4. Find the heights and distances of objects

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students are familiar

with the various ways of measuring length.

Content:-

LENGTH

The standard unit of length are:

– millimetres (mm) – metres (m)

– centimetres (cm) – kilometres (km)

10 millimetres (mm) = 1 centimetre (cm) 1000 millimetres = 1 metre

100 centimetres = 1 metre (m) 1000 metres = 1 kilometre (km)

Examples

1. 10mm = 1cm ∴ 18cm = 18 × 10mm = 180mm ∴

2. 1000m = 1km 1.08km = 1.08 × 1000m = 1080m

Examples

1. 10mm = 1cm ∴ 280mm = 280 ÷ 10cm = 28cm

2. 100cm = 1m ∴ 185cm = 185 ÷ 100m = 1.85m

Pythagoras theorem
Study the diagrams below

Triangles ABC, LMN and XYZ are right-angled triangles.

Bˆ, Mˆ and Yˆ are right angles (i.e. 90º) The side facing (opposite) each right
angle is the longest side. This side is called the hypotenuse. That is, AC, LN and
XZ are the hypotenuses of triangles ABC,
LMN and XYZ respectively.

ABC is a right-angled triangle with Bˆ = 90º

AB = 3cm, BC = 4cm and AC = 5cm

Area of red square = 3cm × 3cm = 9cm2

Area of blue square = 4cm × 4cm = 16cm2

Area of red square + Area of blue square 9cm2 + 16cm2 = 25cm2

Area of black square = 5cm × 5cm = 25cm2

From the calculation, you will see that the area of the black square equals the
sum of the areas of both the red square and blue square.

This is called the Pythagoras theorem. In this right-angled triangle ABC,

pythagoras’ theorem tells you that area Y (black) = area R (red) + area B (blue)

Pythagoras’ theorem

In any right-angled triangle, the area of the square on the hypotenuse side is
equal to the sum of the areas of the squares on the other two sides

Application of Pythagoras’ theorem to calculate the missing side of a right-

angled triangle

Pythagoras’ theorem is usually written using the lengths of the sides of the
triangle.

In this right-angled triangle ABC,

Pythagoras’ theorem tells you that

b2 = a2 + c2

The square of the hypotenuse side is

equal to the sum of the squares of the other

two sides.

This rule is used to find an unknown side of a right-angled triangle when the
other two sides are given.

Example

1. Study how the length of the side marked y is found.

Hypotenuse = 13cm

∴ 132 = y2 + 52

∴ 169 = y2 + 25

169 – 25 = y2

√144 = y2

∴ y2 = 144

y = 144 = 12cm

Evaluation:-

2. Find the length of the hypotenuse of a right-angled triangle if the lengths of

the other two sides are 12cm and 16cm respectively.

3. A right-angled triangle has its hypotenuse as 10cm and one other side as 8cm.
Calculate the length of the third side
Class:- Basic 6

Subject:- Mathematics

Week:- 4

Topic: Perimeter (Regular & Irregular Shapes)

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. Review work done on perimeters of plane shapes

2. identify rectangles that have same area but different perimeters

3. find the perimeters of compound shapes

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students are familiar

with the measurement of length and height from the previous lesson

Content

Perimeter

Perimeter means the sum of lengths of all the sides of a plane shape. It also
means the distance round a shape, field or plot.

Formulae
 .

Perimeter of irregular shapes/compound shapes

Evaluation:-

1. The perimeter of a rectangle is 78cm. Find the length if the breadth is 15cm.

2. A rectangle and square have the same areas but different perimeters. If the
side of the square is 8cm and the breadth of the rectangle is 2cm, find:

( a) the length of the rectangle. (b) the perimeters of the square and the
rectangle.
Class:- Basic 6

Subject:- Mathematics

Week:- 5

Topic: Area (Trapezium)

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. Define and draw a trapezium

2. Measure the area of a trapezium

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students are familiar

with the ways of measurement

Content

Trapezium

A trapezium is a rectangular shape joined with either a triangle at one end or a

triangle each at two ends.

ABCD is a rectangle. BCE is a triangle.

∴ ABCD + BCF = ABED.

ABED is known as a trapezium,

that is a rectangle plus a triangle as shown in Fig 1

ABC is a triangle. EDF is also a triangle. BEDC is a rectangle.

Thus ABC + BEDC + EDF = trapezium ABEF

Hence trapezium ABEF = a rectangle + 2 triangles as shown in Fig 2

Examples

Study these methods to find the area of parallelogram ABED in Fig 1 above given
that AB = 10cm, CE = 7cm and AD = 4cm.

Method 1

Area of rectangle ABCD = length × breadth= 10cm × 4cm = 40cm2.

Area of triangle BCD = 1/2 base height 2 × = 1 7cm 4 cm 2× × = 14cm2

Area of trapezium ABED = area of rectangle ABCD + area of triangle BCE = 40cm2
+ 14cm2 = 54cm2

Method 2

Draw a line from B to D.

Trapezium ABED = Triangle ABD + Triangle BED ∴ Area of ABED = Area of ABD +
Area of BED Note: Area of trapezium ABED. = 1 4 cm (10 cm + 17 cm) 2 × = 1 BC
(AB + DE) 2 × × = 1 height (sum of the parallel sides) 2 × × = 1 base height 2 base
height 2 1 × × = 1 AB AD + 2 DE BC 2 1 × × = 1 10 cm 4 cm + 2 (10 cm + 7 cm) 4 cm

= 1 4 cm (10 cm + 17 cm) 2 = 1 4cm + 27 cm = 54cm2

Examples

Study these methods to find the area of trapezium ABEF, shown in fig 2 above.

Method 1

Area of trapezium ABEF = Area of triangle ABC + Area of rectangle BEBC + area
of triangle EDF = 1 base height + length breadth + 2 base height = 1 7 cm 4cm +
10 cm 4 cm + 2 4 cm 4 cm

= 14cm2 + 40cm2 + 8cm2 = 62cm

Method 2
Area of ABEF = 1 height sum of the parallel sides) 2 × × (= 1 BC (BE + AF) 2 × ×= 1
4 cm (10 cm + 21 cm) 2 × ×= 1 4 cm 31 cmv= 62cm2

In general the area of a trapezium =

1/2(a + b)h

Where a and b are parallel lines and h is the perpendicular height.

Evaluation:-

1. A trapezium has an area of 126cm2. If the sum of the parallel sides is 28cm,
what is the height of the trapezium?

Class:- Basic 6
Subject:- Mathematics

Week:- 6.

Topic: Volume (Prisms, cube and spheres)

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. Identify different types of prism

2. Find the volume of prism

3. Calculate the volume of cube

4. Calculate the volume of spheres

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students are familiar

with a ludo dice and Maggie which are examples of cube

Content

VOLUME

A prism is a solid with a uniform cross section. The cross section is congruent
and can be a square, rectangle, circle, triangle, etc. The cross section is cut
parallel to the solid.

The end of the cross section is also called the base, which comprises of the
length and width. The side that is vertical when the end is sitting on the

ground is called the height.

The volume of a prism is the area of its end or cross section times the height.

Volume of prism = Area of end or cross section × height.

Volume of a cube

The end is a square, but all the sides are equal. Volume of a cube = Area of the
square × height

Volume of a cuboid

The end could either be a square or a rectangle.

Volume of a cuboid = Area of the square or rectangle × height.

Volume of a cylinder

The end is a circle. Volume of a cuboid = Area of the circle × the height of the
cylinder. Volume of a sphere

Evaluation:-

Calculate the volume of each of these spheres.

1. Radius 5cm 2. Radius 3cm 3. Radius 6cm

4. Radius 10cm 5. Diameter 16cm 6. Diameter 8cm

7. Calculate the volume of a water melon whose radius is 10.5.

8. Find the volume of a football whose radius is 26cm.

9. The shot put has a radius of 8cm. Calculate its volume.

10. Find the volume of a sphere whose diameter is 14cm.

11. Calculate the volume of a sphere whose diameter is 56cm

Class:- Basic 6

Subject:- Mathematics
Week:- 7

Topic: Capacity

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. Do some conversions involving units of capacity

2. Identify the relationship between capacity and volume

3. Carry out basic operations on capacity

4. Solve word problems on capacity

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students understand the

fact that every object has capacity

Content

The volume of an object is the space occupied by the object.

The capacity of an object is the amount of substance (either liquid or solid) it

can hold or contain.

Table on capacity

10 millilitres (PƐ ) = 1 centilitre (FƐ )

10 centilitres (FƐ) = 1 decilitre (GƐ )

10 decilitres (GƐ ) = 1 litre (Ɛ)

From the table above, it can be deduced that

10 × 10 × 10PƐ = 1000PƐ = 1 litre.

Table on volume

.10mm × 10mm × 10mm = 1cm × 1cm × 1cm ∴ 1000mm3 = 1cm3

10cm × 10cm × 10cm = 1dm × 1dm × 1dm ∴ 1000cm3 = 1dm3

10dm × 10dm × 10dm = 1m × 1m × 1m. ∴ 1000dm3 = 1m3

Note: A cube with sides of 10cm contains 1 litre of a liquid.

Volume of the cube = 10cm × 10cm × 10cm = 1000cm3

Cahapacity of the cube = 1litre

Hence 1000cm3 = 1litre = 1000PƐ ∴ 1cm3 = 1PƐ

Table of cubic measures

Basic operation on capacity

Evaluation:-
1. The flow of water into a cistern is 27.5 litres every second. How much water
flows into the cistern in one hour?

2. Milk arrives at a Super Mart in a container which holds 97.2 litres and is used
to fill 6 milk bottles all of equal volume. How much milk will one bottle hold?

3. A cow provides 5.6 litres of milk every day. How much milk would 25 cows,
each producing the same quantity of milk, produce in 9 days?

4. If a litre of paint weighs 895 grams, find the weight of 17 litres of paint in
kilograms.

5. A petrol tanker supplies a filling station 22500NƐ of fuel. How many cars with
a tank capacity of 25 litres are needed to empty the petrol tank?

6. A dairy served 2211 customers with milk. 780 of them had 1 litre every day of
the week except 2 litres on Sunday, 806 had a 12 litre every day of the week
except 1 litre on Sunday and the rest had 2 litres every day of the week. How
much milk was sold in a week?

7. A water tank can contain 4500 litres of water when full. If it has a daily
leakage of 1.2 litres, how many litres will be left in the tank after 2 weeks?

8. The pharmacist pours syrup in 230PƐ bottles. If she has 92 litres to pour into
the 230PƐ bottles, how many bottles will she pour into?

9. The gas station attendant paid the sum of Ώ192725.00 to the cashier by
midday. If gas is sold for Ώ65 per litre, how much gas did she sell?

10. Rosy bought 30 litres of lemonade for a breakfast fellowship. How many
mugs of lemonade can she pour if each mug holds 300 millilitres?

Class:- Basic 6

Subject:- Mathematics
Week:- 8

Topic: Weight

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. do conversion involving unit of weight

2. do basic operations on weight

3. solve word problems involving weight.

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students are familiar

with various ways of measuring weight

Content

Weight

Conversion involving unit of weight

1000 grams (g) = 1 kilogram (kg) 1000 kilograms = 1 tonne (t)

1 tonne = 1000 × 1000 grams = 1000 000 g

Basic operation on Weight

Evaluation:-

Change these to grams.

1. 23 kg 2. 105 kg 3. 29.2 kg 4. 17.06 kg 5. 12 kg 6. 14 kg 7. 18 kg 8. 1100kg

Change these to tonnes.

9. 7000 kg 10. 19046 kg 11. 312345 kg 12. 896 kg 13. 500 kg 14. 250 kg 15. 125 kg
16. 10 kg

Change these to kilograms.

17. 11000 g 18. 27726 g 19. 400 g 20. 250 g 21. 16 tonnes 22. 73 tonnes 23. 8.9
tonnes 24. 0.67 tonnes

How many quarter-kilogram packets of sugar can be packed from each of the
amounts of sugar listed below?

25. 50 kg 26. 32 kg 27. 20250 kg 28. 110 kg 29. 18 tonne 30. 0.4 tonne 31.12
tonne 32. 1 tonne

Word problems on weight

Exercise

1. A shopkeeper sold 478 kg 400 g of rice in January and 762 kg 710 g of rice in
February. How much rice did he sell in January and February?

2. Adisa is 5.5 kg heavier than Chukwu, who weighs 26.4 kg. What is Adisa’s
weight?

3. Give your answer to 4 in grams and kilograms.

4. A sack of groundnuts weighs 22 kg 200 g. The sack alone weighs 6 kg 450 g.

What is the weight of the groundnuts?

5. The heaviest boy in Seyi’s class weighs 39.6 kg. The lightest boy weighs 27.9
kg. What is the difference between the weights of the heaviest boy and the
lightest boy in Seyi’s class?
6. From a five hundred kilogram of butter, a trader sells ten lots of twenty
kilograms and six lots of two kilograms five hundred grams. How much butter is
left?

7. A lorry carried seven baskets of kolanuts. Two of the baskets weighed 21

kilograms 90 grams and 26 kilograms 400 grams. Each of the other five baskets
weighed 20 kilograms 350 grams. Find the total weight of all the baskets of
kolanuts.

8. An empty box weighing 0.75 kilogram is filled with twenty-four packets of

rice, each weighing 0.56 kilogram. What is the total weight of the box?

9. A piece of brick weighs 2.25 kilograms. What is the weight of twelve pieces of
such bricks?

10. Eight tins of milk weigh 17.6 kilograms. What is the weight of ten tins of
milk?

Class:- Basic 6
Subject:- Mathematics

Week:- 9

Topic: Time

Behavioral objective:- At the end of the lesson the pupils should be able to:-

1. Tell the time on a 24-hour clock

2. Read time tables on journeys

3. Calculate average speed

4. Calculate athletic time.

Instructional material/Reference material:- Learn Africa Mathematics UBE

edition for primary school book 6

Building Background /connection to prior knowledge : Students are familiar

with wall clock and wrist watches which are object that tells time

Content

Time

24 hours clock

Bus, railway, ship and airline timetables use the 24-hour clock to state the times
of departure and arrival of journeys.

Remember: The 24-hour clock numbers hours from 00 to 24, that is, for a whole
day from midnight to midnight. When 24-hour clock times are written with four
figures, the first two figures represent hours and the last two figures represent
minutes past the hour. A point usually separates the hours from the minutes,
e.g.

1. 7.25 am is written as 07.25

2. 7.25 pm is written as 19.25

You have to add on 12 hours if it is pm or after. That is why 7.25 pm is 19.25.

When it gets to midnight, the 24-hour clock changes from 13.59 to 00.00

Reading timetables of journeys (Flights and trains)

Train time-table

Passenger train schedule

The following passenger train services are currently running across the country.

O Lagos – Ilorin (Tuesdays, Fridays & Saturdays)

– Departs Iddo 09.00 hrs

– Arrives Ilorin 18:34 hrs of same day.

O Ilorin – Lagos (Wednesdays, Saturdays & Sundays)

– Departs Ilorin 11.00 hrs of Wednesday

– Arrives Lagos 20.59 hrs of same day

– Departs Ilorin 09.00 hrs on Saturdays and Sundays

– Arrives Lagos 20.59 hrs.

O Lagos – Kano (Every Friday)

– Departs Iddo 12.00 hrs

– Arrives Kano 17.01 hrs on Saturday

O Kano – Lagos (Every Monday)

– Departs Kano 09-00 hrs

– Arrives Lagos 14.24 hrs on Tuesday

O Offa – Kano (Every Tuesday)

– Departs Offa 22.00 hrs

– Arrives Kano 18.05 hrs on Wednesday

O Kano – Offa (Every Friday)

– Departs Kano 08.30 hrs

– Arrives 05.35 hrs on Saturday

O Minna – Kaduna – Minna (Every Sunday, Monday & Tuesday)

O Nguru – Kano (Every Tuesday and Friday)

O Kaduna Inter-city [Commuter service] (Mondays – Saturdays)

O Lagos Inter-city [Commuter service] (Mondays – Saturdays)

Average speed

Speed is often measured in kilometres per hour. This

is written for short as km/h. To find the average
speed, you divide distance by time taken. That is:
Average speed = Distance covered/ Time Taken

Examples

Study how the following word problems have been solved.

1. An aeroplane flies 2800km in 5 hours. What is its average speed?

Average speed = Distance covered/Time Taken

2800/ 5 = 560km/h

When you are asked to find the time covered, you use the formula

Distance covered/ Average Speed∴ In the previous example you did 2800/ 560 =
10/ 2 = 5 hrs

To find the distance covered, you do average speed multiplied by time.

That is 560 × 5 = 2800km

2. Abel walked a distance of 90metres in 1minute. Find his walking speed in

km/h.

Speed = Distance/Time = 9÷1 000km ÷ 1\ 60 h = 90/ 1 000 × 60km/h = 5410

km/h = 5.4km/h

Athletic time

Short periods of time are recorded in seconds (s) or fractions of a

second. Athletic time is recorded in seconds but using 1minute plus for

long distant races.

For this purpose a stop watch us

used to give accurate timing.

The minute shown on this stopwatch is between 0 and 1. The second is 14.2. An
electric timer is needed if a measurement to two decimal places is required
(1/100s).We measure short periods of time in seconds. There are 60seconds in

1 minute. A stopwatch or seconds pendulum can be used to record short

periods of time, such as in races, debates, quiz competitions and mental sums.

Group activity

Use the stopwatch to time these events.

1. How long does it take your partner to blink her eyes?

2. How long does it take your partner to walk from one end of theclassroom to
the other?

3. How long does it take to write a sentence? (Choose the same sentence.)

4. How long does it take to boil water in an electric kettle?

5. How long does it take to boil a cup of water on a stove?

6. How long does it take to warm a plate of rice in a microwave oven?

7. How long does it take to defrost a frozen chicken?

Evaluation:-

1. A motorist left his home at 10.00 am to travel to a city of distance 260km. He

reckoned he could average 80km/h. At what time would he arrive at the city?

2. Express a speed of 60metres per second in kilometres per hour correct to 1

decimal place.

3. A motor car travels at 60km/h. At this speed how far will it travel in:

a) 1min b) 10min c) 3/4h?

4. The distance between Ibadan to Ilesha is 120 kilometres. A passenger lorry

left Ilesha for Ibadan at 6 a.m and arrived back in Ilesha at 12 noon. It stopped
at Ile-Ife for 30minutes, at Gbongan for 1 hour and at Ibadan for 11/2 hours.
Find the time spent traveling, not including stopping time. With this time find
the average speed for the journey. (Remember to exclude stopping time.)

5. How many minutes are there between each start and finish time.

Start. Finish Start Finish

a) 20.20 → 23.40 b) 23.25 → 01.10

6. A flight that was scheduled to take off at 22.55 was delayed for 25 minutes.
What time did it finally take off?