# PRIMARY 4 THIRD TERM LESSON NOTES MATHEMATICS

WEEK 1

TOPIC: ESTIMATING LENGTH AND COMPARING MEASUREMENT

SUBTOPIC: ADDITION AND SUBTRACTION OF LENGTH

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Estimate distance in kilo meter and meters.
2. Add lengths to kilo meters and meters
3. Solve quantitative aptitude problems on length.

CONTENT

ESTIMATING LENGTH AND COMPARING MEASUREMENT

Good morning, class! Today, we’re going to dive deeper into the concept of estimation and also learn about converting measurements from meters to kilometers and vice versa.

Estimation is a valuable skill that allows us to make educated guesses or approximations rather than providing exact figures. It’s important because it helps us quickly assess and understand quantities without having to measure or calculate precisely.

When we estimate, we aim to provide an answer that is accurate or at least very close to the actual value. It’s essential to practice estimation regularly so that we can become better at estimating short lengths in centimeters, for example. By practicing estimation, we can quickly assess and understand quantities in our daily lives.

Now, let’s move on to converting measurements from meters to kilometers and vice versa. We will use an example to understand this concept better.

Imagine Nasif, who lives in a village. He walks to school, which is approximately half a kilometer away. We know that:

1 kilometer (km) is equal to 1000 meters (m).

So if Nasif walks half a kilometer, we need to determine how many meters that is. To do this, we multiply the distance in kilometers by 1000:

0.5 km * 1000 = 500 meters.

Therefore, Nasif walks 500 meters to school.

When we talk about long distances, we usually use kilometers as the unit of measurement. Examples of long distances that are measured in kilometers include the length of rivers, the distance between cities, or the length of a railway track.

Remember, estimating is a useful skill that allows us to make educated guesses. Practicing estimation regularly will help us become better at it. Additionally, understanding how to convert measurements from meters to kilometers and vice versa is important for dealing with longer distances.

I hope you found today’s lesson helpful and enjoyable. If you have any questions, please feel free to ask!

Examples

Study these examples of converting kilometres to metres.

Example 1:  2 km to metres

=2×100

=2000 meters

Example 2: 4 km 250 m to meters

= (4×1000m)+250m

=4000m+250m

=4250m

Example 3:4.758m

4.758×1000

=4758m

Exercise 2

Convert the following to meters.

• 8 km
• 9 km
• 10 km
• 7 km 615 m
• 6 km 400m
• 1 km 625 m
• 2 km 19 m
• 15 km 215 m
• 3 km 100 m
• 8 km 23 m

B .Convert the following to meters.

• 716 km
• 5.782 km
• 2.139 km
• 8.791 km
• 920 km
• 7.1 km
• 5.4 km
• 9.7 km
• 9 km
• 4.7 km

Examples

Study these examples of converting kilometres to metres.

Example 1:  2 km to metres

=2×100

=2000 meters

Example 2: 4 km 250 m to meters

= (4×1000m)+250m

=4000m+250m

=4250m

Example 3:4.758m

4.758×1000

=4758m

Exercise 2

Convert the following to meters.

• 8 km
• 9 km
• 10 km
• 7 km 615 m
• 6 km 400m
• 1 km 625 m
• 2 km 19 m
• 15 km 215 m
• 3 km 100 m
• 8 km 23 m

B .Convert the following to meters.

• 716 km
• 5.782 km
• 2.139 km
• 8.791 km
• 920 km
• 1 km
• 4 km
• 7 km
• 9 km
• 4.7 km

To change from metres to kilometres you divide by 1000.

Examples

1.Convert 1586 m to kilometre

1586 ÷ 1000

1586 km = 1.586 km =

1 km 586 m

2.Convert 678 m to kilometres

678 ÷ 1000

678.0 km = 0.678 km = 0 km 678 m

Exercise 3

Express in kilometres. Remember the position of the decimal point.

• 1345 m
• 250 m
• 3755 m
• 448 m
• 566 m
• 6495 m
• 7899 m
• 8675 m
• 94 m
• 1095 m

Convert the following to kilometres and metres.

1.9600 metres 2.8800 metres 3.4525 metres 4.3333 metres 5.1750 metres 6.6112 m 7.7009 m 8.2010 m 9.3165 m10. 1038 m

A                                                                        B

C                                                                        D

Line AB is 13 centimetres long while, line CD is 9 centimetres long.

We write AB = 13 cm

CD = 9 cm

The total length of two lines is: 13 cm + 9 cm = 22cm

The difference in their length is: 13 cm −9 cm = 4 cm

We write these as:

AB + CD = 13 cm + 9 cm = 22 cm and AB −CD = 13 cm −9 cm = 4 cm

ADDITION OF LENGTHS IN KILOMETERS AND METERS

7KM+3KM=

645+ 24m=

1.A swimming pool is 120 metres long. Michael swims 6 laps. What distance did he Cover in 6 laps?

2.The average weekly distance travelled by a marketer is 320 kilometres. How far does he travel in a year?

3.A limousines car is 800.5 cm long. Calculate its length in metres.

4.An oil pipe is to be made 16.8 m long. It is made into three equal sections.16.8m

a)How long is each section?

b)How long would each section be if it were split into seven equal sections?

5.a)Find one half of a ball of string measuring 21.2 m long.

b)Find one quarter of the same ball of string.

6.Kalu is walking to his friends house which is 10.5 kilometres away. He walks one-third of the distance and then takes a rest.

a)How far did he walk before taking a rest?

b)How far has he still to walk?

WEEK 2

TOPIC: WEIGHT

SUBTOPIC: ADDITION AND SUBTRACTION OF WEIGHT

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Solve problems on weights of objects
2. Solve problems on the multiplication of weights in kg and gram
3. Weigh some objects in their classroom environment.

CONTENT

Lesson 1: How to Solve Problems on Weights of Objects

Hello, grade 4 pupils! Today, we’re going to learn how to solve problems on the weights of objects. Weight is a measure of how heavy something is. In mathematics, we use different units to measure weight, such as grams (g) and kilograms (kg). Let’s dive into it with some examples:

Example 1:
John has a bag of apples. The bag weighs 2 kilograms. If John adds 500 grams of apples to the bag, what will be the total weight of the bag?

Solution:
To solve this problem, we need to add the weight of the bag (in kilograms) with the weight of the apples (in grams). First, we convert 500 grams to kilograms by dividing it by 1000 since there are 1000 grams in 1 kilogram.
500 grams = 500/1000 = 0.5 kilograms

Now, we can add the weight of the bag and the weight of the apples:
2 kilograms + 0.5 kilograms = 2.5 kilograms

So, the total weight of the bag with the apples is 2.5 kilograms.

Example 2:
Sara has a pencil case that weighs 800 grams. Her friend gives her another pencil case weighing 350 grams. What is the total weight of the two pencil cases?

Solution:
To find the total weight, we add the weights of the two pencil cases together:
800 grams + 350 grams = 1150 grams

However, we can also express the total weight in kilograms by dividing the sum by 1000:
1150 grams = 1150/1000 = 1.15 kilograms

Therefore, the total weight of the two pencil cases is 1.15 kilograms.

Lesson 2: How to Solve Problems on Multiplication of Weights in kg and gram

Now, let’s move on to solving problems involving the multiplication of weights in kilograms and grams. We can use multiplication to find the total weight when we have a certain weight and a certain number of objects. Let’s look at an example:

Example 1:
A box of chocolates weighs 250 grams. If there are 4 boxes, what is the total weight of the chocolates?

Solution:
To find the total weight, we need to multiply the weight of one box by the number of boxes:
250 grams * 4 = 1000 grams

Again, we can express the total weight in kilograms by dividing the product by 1000:
1000 grams = 1000/1000 = 1 kilogram

So, the total weight of the chocolates is 1 kilogram.

Lesson 3: Weighing Objects in the Classroom Environment

To understand weights better, it’s important to practice by weighing objects in your classroom environment. You can use a weighing scale or balance to measure the weights. Here are a few objects you can weigh:

1. Books: Pick different books from your classroom library and weigh them. Compare their weights and see which one is heavier or lighter.

2. Stationery: Weigh objects like pencils, erasers, and sharpeners. Arrange them in order from lightest to heaviest.

3. Classroom supplies: Weigh objects like notebooks, markers, and scissors. Make a list of their weights and compare them.

Remember to record the weights in grams or kilograms, depending on the scale you’re using.

That’s it for today’s lesson, grade 4 pupils! I hope you now have a better understanding of how to solve problems on weights of objects and how to multiply weights. Practice weighing objects in your classroom environment to reinforce your learning. Good luck!

The standard unit of weight is the gram

Remember: 1 000 grams = 1 kilogram

i.e. 1 000 g = 1 kg

The gram is the unit of weight,

and is used to measure very small masses.

1. 500 grams is equal to __________ kilogram.
a) 0.005
b) 0.05
c) 0.5
d) 5

2. The weight of a bag is 3 kilograms and 200 grams. In grams, it can also be written as __________ grams.
a) 3,200
b) 2,300
c) 3,020
d) 3,002

3. The weight of an object is 1 kilogram and 500 grams. In grams, it can also be written as __________ grams.
a) 1,500
b) 1,005
c) 1,050
d) 1,501

4. Mary has a bag of sugar weighing 750 grams. If she adds 250 grams more, the total weight of the bag becomes __________ grams.
a) 1,000
b) 500
c) 750
d) 1,250

5. Convert 2 kilograms to grams: __________ grams.
a) 200
b) 20
c) 2,000
d) 2

6. The weight of a book is 850 grams. Express it in kilograms as __________ kilograms.
a) 8.5
b) 0.085
c) 0.0850
d) 85

7. A box of crayons weighs 300 grams. If there are 5 boxes, the total weight of the crayons is __________ grams.
a) 150
b) 600
c) 3,000
d) 1,500

8. Convert 4,500 grams to kilograms: __________ kilograms.
a) 4
b) 45
c) 4.5
d) 450

9. The weight of a bag is 1 kilogram and 250 grams. In grams, it can also be written as __________ grams.
a) 125
b) 1,025
c) 1,250
d) 1,500

10. If each pencil weighs 20 grams and there are 6 pencils, the total weight of the pencils is __________ grams.
a) 26
b) 120
c) 1200
d) 200

11. Convert 3.5 kilograms to grams: __________ grams.
a) 350
b) 35
c) 3,500
d) 0.035

12. The weight of a toy car is 150 grams. Express it in kilograms as __________ kilograms.
a) 1.5
b) 0.015
c) 0.15
d) 15

13. A packet of candies weighs 750 grams. If there are 3 packets, the total weight of the candies is __________ grams.
a) 2,500
b) 225
c) 750
d) 1,500

14. Convert 5,000 grams to kilograms: __________ kilograms.
a) 5
b) 500
c) 5.0
d) 0.

Converting kilogram and grams

To convert kilograms to grams, multiply by 1 000.

Examples

1. Convert to grams.
2. 9 kg  2. 1.5 kg  3. 0.048 kg

Solution

1. 9 kg = 9 ×1 000 g = 9 000g
2. 1.5 kg = 1.5 ×1 000 g = 1 500g
3. 0.048 kg = 0.048 ×1 000 g = 48g

B.

Convert to grams.

1.2kg 350g 2.3kg 75kg 3.5kg 8g

Solution

1. 2kg 350g= 2 ×1000g + 350g

=2000+350g

=2350g

1. 3kg 75g= 3 ×1000g + 75g

= 3000g + 75g

= 3075g

1. 5kg 8g= 5×1000g+8g

=5000g+ 8g

=5008g

Lesson 1: Word Problems Involving Addition and Subtraction in Weight

Hello, grade 4 pupils! Today, we’ll be solving word problems involving addition and subtraction in weight. These types of problems help us understand how to combine or take away weights. Let’s go through some examples:

Example 1:
Mary has a bag of apples that weighs 1.5 kilograms. She buys another bag of apples weighing 750 grams. What is the total weight of the apples Mary has?

Solution:
To find the total weight, we need to add the weight of the first bag (1.5 kilograms) with the weight of the second bag (750 grams). However, we need to convert grams to kilograms first:
750 grams = 750/1000 = 0.75 kilograms

Now, we can add the weights:
1.5 kilograms + 0.75 kilograms = 2.25 kilograms

So, the total weight of the apples Mary has is 2.25 kilograms.

Example 2:
John has a box of chocolates that weighs 2.7 kilograms. He eats 500 grams of chocolates from the box. What is the weight of the box after John eats the chocolates?

Solution:
To find the weight of the box after John eats the chocolates, we need to subtract the weight of the chocolates (500 grams) from the initial weight of the box (2.7 kilograms). Let’s convert grams to kilograms:
500 grams = 500/1000 = 0.5 kilograms

Now, we can subtract the weights:
2.7 kilograms – 0.5 kilograms = 2.2 kilograms

So, the weight of the box after John eats the chocolates is 2.2 kilograms.

Lesson 2: Word Problems Involving Multiplication and Division in Weight

Now, let’s move on to solving word problems involving multiplication and division in weight. These problems help us understand how to find weights when we know the weight of one object or the weight per unit. Let’s explore some examples:

Example 1:
A bag of rice weighs 2 kilograms. How much would 4 bags of rice weigh?

Solution:
To find the total weight of 4 bags of rice, we need to multiply the weight of one bag (2 kilograms) by the number of bags (4):
2 kilograms * 4 = 8 kilograms

So, 4 bags of rice would weigh 8 kilograms.

Example 2:
A packet of candies weighs 250 grams. How many packets can be made from 1 kilogram of candies?

Solution:
To find the number of packets that can be made, we need to divide the total weight of candies (1 kilogram) by the weight of one packet (250 grams). However, we need to convert kilograms to grams first:
1 kilogram = 1,000 grams

Now, we can divide the weights:
1,000 grams ÷ 250 grams = 4 packets

So, 1 kilogram of candies can make 4 packets.

Remember, practice is key to improving your problem-solving skills in weight-related word problems. Keep practicing, and you’ll become an expert in no time!

That’s it for today’s lesson, grade 4 pupils! I hope you now have a better understanding of solving word problems involving addition, subtraction, multiplication, and division in weight. Keep up the great work!

Exercise 1

1.

Convert each of the following to grams.

• 4kg
• 1.25kg
• 5.504kg
• 0.75kg
• 2kg 121g
• 31\2kg
• 1kg 567g
• 71\ 10kg

ADDITION OF WEIGHT IN KILOGRAMS AND GRAMS

Here 6kg 940g has been added ton 2kg 705g.

Solution:

Kg       g

6       940

+2       705= 8kg    1645  Change 1645 to kg and grams

8kg    1645g=8kg +1kg+645g

=9kg  645g

245+416g=661g

Exercise 1

1.2kg 371g and 5kg 258g     2.13kg 107g and 8kg 887      3.51g 47g and 36kg 69g       4.53.7kg and 34.85kg          .5.  989g and 7kg 918g         6.26kg 55g and 3kg 69g        7.0.758kg and 0.587kg

SUBTRACTION OF WEIGHT IN KILOGRAMS AND GRAMS

Examples

1. Subtract 2kg   715g from 7kg     875g

Solution: 7kg 875g- 2kg   715g=5kg     124g

1. Subtract 13kg 76gfrom 37kg 161g

Solution:37kg  161g-7kg  875g=24kg  85g

Exercise

Subtract the following.

1.11kg 45g from 16kg 200g      2.5kg 140g from 9kg 345g       3.17.5kg from 20.3kg      4.1.881kg from 2kg

5.0.385kg from 1kg             6.3kg 48g from 5kg

Word problems involving addition and subtraction

Example

Mrs. Adoh has 567.5kg of beans in her shop. She sold 273.75kg. What weight of beans does she have left?kg

Weight of beans in the shop   =    567.50

Weight of beans sold                = –273.75

Weight of beans left                 =   293.75

Exercise

Solve the following word problems.

1. The weight of a bucket filled with water is 7.25kg. If the weight of the bucket is 1.75kg,

What is the weight of the water?

2 Take away 15.38kg from 73.4kg.

1. Take away 2.145kg from 2.645kg.
2. What is 5kg minus 3.257kg.

5.Comfort bought 15kg 250g of yam flour. She used 12kg 800g for a feast. What quantity of flour does she have left?

6.Adeoye weighs 2.235kg less than Bolaji. If Bolaji weighs 84.0kg, find Adeoye’s weight.

7.Sola weighs 63kg 725g and Sulaiman’s weight is 67kg 10g. Find their difference in weight.

8 Khadija weighs 29.5kg and Ngozi weighs 31.05kg. Find their difference in weight.

9.The weight of two bags containing yam flour and cassava flour is 9kg 25g. If one of the bags weighs 6kg 70g, what is the weight of the other?

10.The weight of three books is 3.54kg. Two of them weigh 2.6kg. Find the weight of the third book.

Multiplication of weight in kilograms and grams

Study these examples of multiplying weights.

Examples

1.Multiply 3kg 325g by 5

2.8kg 50g ×6

Solution: Note 1000g = 1kg

1. Kg      g

3        325

×   5              =15kg       1625g.

Change 1625g t0 1g 625g

15kg + 1g + 625g

=16kg   625g

1. kg     g

8    50

×       6     = 48kg     300g

Solve the following.

1.30kg 170g ×9         2.12kg 56g ×4    3.52kg 80g ×15       4.31kg 855g ×12

Division of weight in kilograms and grams

Study these examples of dividing weights.

Examples

1. Divide 33 kg 720 g by 6   2. 25 kg 376 g ÷ 8    3. 23.049 kg ÷ 9

•  5 kg       620 g

6       33 kg      720 g

30 kg/       +3 000 g/

3 kg          3 720 g

– 36/

120

–120/

00

Thus 33 kg 720 g ÷ 6 = 5 kg 620 g

1.   3 kg     172 g

8    25 kg    376 g

24 kg     +1 000 g/

1 kg        1 376 g

– 8̅̅̅̅̅̅/

57

– 56/

16

– 16\00

Thus 25 kg 376 g ÷ 8 = 3 kg 172 g

2.561 kg/

9       23.049 kg

– 18/

50

– 45/

54

– 54/

09

– 09/

00

Thus 23.049 kg ÷ 9 = 2.561 kg

Exercise

1. Divide 12 kg 260 g by 4   2. Divide 5 kg 200 g by 4   3. Divide 6 kg 360 g by 5
2. Divide 10 kg 260 g by 6   5. Divide 7 kg 263 g by 3   6. Divide 15 kg 366 g by 6
3. Divide 10 kg 989 g by 9   8. 41.976 kg ÷ 4                 9. 17.152 kg ÷ 8
4. 21.315 kg ÷ 5

Unit 7

Word problems involving multiplication and division

Examples

1. A bag of cement weighs 50 kg. What is the total weight of 4 bags of cement?

Solution

kg

50

× 4

200 kg

The total weight of 4 bags of cement is 200 kg.

1. Five women share 14.5 kg of maize equally. How much will each get?

Solution

2.9 kg/

5   14.5 kg

– 10/

45

– 45/

00

” Each woman will get 2.9 kg of maize

Sure! Here are 15 fill-in-the-blank questions with options for the topics of word problems involving addition and subtraction in weight, and word problems involving multiplication and division in weight:

1. John weighs 35 kilograms. If he gains 7 kilograms, his new weight will be __________ kilograms.
a) 42
b) 28
c) 35
d) 52

2. A box of books weighs 15 kilograms. If two books are removed from the box, and each book weighs 1.5 kilograms, the new weight of the box will be __________ kilograms.
a) 13
b) 16
c) 18
d) 12

3. Sara has a bag of flour that weighs 2.5 kilograms. She uses 800 grams of flour for baking. The weight of the remaining flour is __________ kilograms.
a) 1.7
b) 1.8
c) 1.2
d) 1.7

4. A carton of juice weighs 800 grams. If each serving size is 200 grams, the number of servings in the carton is __________.
a) 4
b) 8
c) 16
d) 12

5. A basket of fruits weighs 2 kilograms. If the weight of the basket is 500 grams, the weight of the fruits alone is __________ kilograms.
a) 2.5
b) 1.5
c) 3
d) 2

6. Mary has a bag of apples weighing 1.2 kilograms. If she adds 300 grams of apples to the bag, the new weight of the bag will be __________ kilograms.
a) 1.5
b) 1.7
c) 1.8
d) 1.3

7. A box of chocolates weighs 500 grams. If Sarah eats 150 grams of chocolates, the weight of the chocolates left in the box is __________ grams.
a) 350
b) 300
c) 450
d) 650

8. The weight of a watermelon is 6 kilograms. If 2 kilograms are cut and eaten, the weight of the remaining watermelon is __________ kilograms.
a) 8
b) 4
c) 6
d) 2

9. A box of crayons weighs 300 grams. If each crayon weighs 25 grams, the number of crayons in the box is __________.
a) 8
b) 10
c) 12
d) 14

10. David weighs 42 kilograms. If he loses 10 kilograms, his new weight will be __________ kilograms.
a) 52
b) 32
c) 42
d) 22

11. A bag of rice weighs 5 kilograms. If each serving size is 250 grams, the number of servings in the bag is __________.
a) 20
b) 25
c) 30
d) 35

12. A crate of oranges weighs 10 kilograms. If 3 kilograms of oranges are removed from the crate, the weight of the remaining oranges is __________ kilograms.
a) 6
b) 7
c) 8
d) 9

Exercise

1. Four cartons of soft drinks weigh 15 kg 316 g. How much will one carton weigh?
2. Find the total weight of 8 tins of paint if each weighs 1.75 kg.
3. A pair of shoes weighs 875 g. Find the weight of 12 similar pairs of shoes.
4. A sachet of gari weighs 255 g. Find the weight of 15 similar sachets of gari.
5. Eight women are to share 35 kg 232 g of rice equally among themselves. How much does each woman get?
1. A man carried 5 bags of sand from one place to another. Each bag weighs 24.75 kg.Find the total weight of sand carried by the man.
1. Find the weight of 14 concrete blocks if each weighs 14 kg.
2. 1 kg 449 g of powdered milk is shared among 9 pupils. How much will each receive?
3. Multiply 5 kg 37 g by 8.
4. Divide 123 kg 750 g by 18.

Exercise

1. Convert 3 kg 356 g to grams only.
2. Convert 0.84 kg to grams.
3. Convert 1 1750 kg to grams.
4. Convert 2 045 g to kilograms only.
1. Convert 3 124 g to kilograms and grams. 6. Add 5 kg 495 g to 2 kg 705 g.
2. 1.785 kg to 0.578 kg. 8. Subtract 3 kg 715 g from 7 kg 875 g.
3. What is 5 kg 297 g from 2 kg 775 g? 10. Solve 2 kg × 5.
4. 5.35 kg × 4. 12. Divide 63 kg 720 g by 6.
5. Divide 18 kg 198 g by 9. 14. Multiply 5 kg 39 g × 8.
6. The weight of 7 crates of mineral is 10.5 kg. What is the weight of one?

WEEK 3

TOPIC: TIME

SUBTOPIC: TELLING THE TIME ON THE CLOCK

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Identify the seconds, minutes, and hour on a clock
2. tell the time on a clock
3. read the calendar and recite 6o seconds make 1 minute
4. use the a.m and p.m notation for the time of the day

1. convert the unit of time

CONTENT

TIME

Telling time to hours and minutes

ToThe clock face on the left shows the hour and minutes hands.

The clock face is divided into 12 large                                                                  divisions and 60 small divisions. Between 2 large divisions there are 5 small divisions.  When the minute hand moves from 12 and back to 12 (one complete turn), it moved 60 minutes and the hour hand moves from one large number to another. This means that the hour-hand moves through 1 large division every 60 small divisions the minute hand moved. Thus: 60 minutes = 1 hour

The short form of hour is h and the short form of minutes is min.

Examples:

Exs:

EXERCISE

Draw a clock to show each of the following times

1. 8:15.      2. 4:18.       3. 3:45.       4. 1:20.     5. Twenty- five minutes to seven      6.  Thirteen minutes past six

USING THE A.M AND P.M NOTATION FOR THE TIME.

In English system the day starts at midnight and ends at the next midnight.

The day begins just after 12 o’clock at midnight. The next 12 o’clock in the day time is called midday. Then the next 12 o’clock is the next midnight.

The time from a midnight to coming midday is called antemeridian. It is written in short as a.m. We say the time between midnight and noon is called a.m.

The time between 12 o’clock of the day, i.e., midday to next midnight is known as postmeridian. It is written in short as p.m.

We say the time between midday (noon) to next midnight is called p.m.

Antemeridian (a.m.) and Postmeridian (p.m.) are Latin words which mean midnight to noon (a.m.) and noon to midnight (p.m.). We use a.m. to express the time between 12:00 midnight and 12:00 noon. We use p.m. to express the time between 12:00 noon and 12:00 midnight.

Our general clock expresses the time of both time periods by the same numbers. We affix a.m. for the time between midnight and noon and p.m. for the time between noon and midnight.

to be bed at 10 p.m. in the night and get up at 6 a.m. in the morning.

The time before 12:00 noon is expressed as a.m. and the time after 12:00 noon is expressed as p.m. When it is 12 0’clock at night, we say it is 12:00 midnight or 00:00 hour. When it is 12 o’clock during day, we say it is 12:00 noon or 12:00 hours.

Examples:

• Twenty minutes past ten in the morning is written as 10: 20
• Half past three in the afternoon is written as 3:30pm

Exercise

À. Write out these times using a.m or p.m

• The time is when the school assembly begins at 7:30
• The time when the school closes at 2:0clock
• The time when you have your dinner at 7 O’Clock
• The time when you go to bed at 9 o’clock.
1. Copy and complete the following statements. The first is done for you
• Four hours after midnight is 4 a.m
• Three hours before midnight is……………….
• Nine hours after midnight is…………….
• Five hours after midday is………………..
• Eleven hours after midday is….    ……….

Lesson 1: Identifying Seconds, Minutes, and Hours on a Clock

Hello, grade 4 pupils! Today, we will learn how to identify seconds, minutes, and hours on a clock. A clock helps us keep track of time and is divided into different units. Let’s understand each unit:

1. Seconds: Seconds are the smallest unit of time. There are 60 seconds in 1 minute. On a clock, the seconds are represented by the moving hand, which completes a full revolution in 60 seconds.

2. Minutes: Minutes are the next unit of time. There are 60 minutes in 1 hour. On a clock, the minutes are represented by the longer hand, which moves gradually around the clock’s face.

3. Hours: Hours are the largest unit of time on a clock. There are 12 hours on a clock face. The hours are indicated by the shortest hand, which points to the current hour.

Example:
Let’s say the clock’s short hand is pointing to the number 4, the long hand is pointing to the number 9, and the second hand is at the 12 o’clock position. This tells us that it is 4 hours, 9 minutes, and 0 seconds.

Lesson 2: Telling the Time on a Clock

Now, let’s learn how to tell the time on a clock. By reading the positions of the clock hands, we can determine the current time. Let’s go through an example:

Example:
On a clock, the short hand points to the number 3, the long hand points to the number 8, and the second hand is at the 12 o’clock position. This means it is 3 hours, 8 minutes, and 0 seconds.

Lesson 3: Reading the Calendar and Reciting 60 Seconds Make 1 Minute

To understand time better, we need to be familiar with the calendar and the relationship between seconds and minutes. The calendar helps us keep track of days, weeks, months, and years. We can also learn about special events and holidays on the calendar.

Additionally, it’s important to remember that 60 seconds make 1 minute. This means that for every 60 seconds that pass, the minute hand on a clock moves forward by one unit.

Lesson 4: Using the A.M. and P.M. Notation for the Time of the Day and Unit Conversion

When talking about time, we often use the notation of a.m. and p.m. to indicate whether it is morning or afternoon/evening. “A.M.” stands for ante meridiem (before noon), while “P.M.” stands for post meridiem (after noon).

Moreover, we can also convert units of time. For example, there are 60 minutes in 1 hour, 24 hours in 1 day, 7 days in 1 week, and 12 months in 1 year. By understanding these conversions, we can calculate and compare different units of time.

It’s important to practice reading the clock, understanding the calendar, and using the appropriate notation for the time of day. Regular practice will help you become more comfortable with these concepts.

That’s it for today’s lesson, grade 4 pupils! I hope you now have a better understanding of identifying seconds, minutes, and hours on a clock, telling the time, reading the calendar, using a.m. and p.m. notation, and converting units of time. Keep practicing, and you’ll become a time-telling expert!

CONVERSION OF UNIT OF TIME

Examples:

1. Convert 310 seconds to minutes and seconds

Solution:

60 seconds = 1 minutes

310 seconds =310÷60 minutes

= 310/60

= 5 minutes 1 seconds

1. Convert 16 mins 43 seconds

Solution:.

60seconds = 1 minutes

16 minutes= 16× 60 seconds

= 160×6s

=960s

16mins 43s= 960s+43s

= 1003 seconds

…Consider the following examples on units of time:

1. Convert the following:

(i) 7 days 6 hours into hours.

(ii) 6 hours 40 minutes into minutes.

(iii) 4 minutes 25 seconds into seconds.

Solution:

(i) 1 day = 24 hours

Therefore, 7 days 6 hours    = (7 x 24) hours + 6 hours

= 168 hours + 6 hours

= 174 hours

(ii) 1 hour = 60 minutes

Therefore, 6 hours + 40 minutes    = (6 x 60) minutes + 40 minutes

= (360 + 40) minutes

= 400 minutes

(iii) 1 minute = 60 seconds

Therefore, 4 minutes 25 seconds   = (4 x 60) seconds + 25 seconds

= (240 + 25) seconds

= 265 seconds

Exercise

1. Convert each of the following to seconds

6mins

10mins

12mins

2mins 8s

1. Convert each of the following to minutes

360s

1080s

1800s

1020s

1. There are __________ seconds in 1 minute.
a) 60
b) 10
c) 30
d) 100

2. The long hand on a clock represents __________.
a) seconds
b) minutes
c) hours
d) days

3. The short hand on a clock indicates the __________.
a) seconds
b) minutes
c) hours
d) days

4. There are __________ minutes in 1 hour.
a) 10
b) 100
c) 60
d) 30

5. In the morning, we use the notation __________.
a) A.M.
b) P.M.
c) B.C.
d) C.E.

6. The hour hand on a clock points to the current __________.
a) seconds
b) minutes
c) hours
d) days

7. If it is 3:45 p.m., how many minutes have passed since noon?
a) 45
b) 60
c) 15
d) 30

8. The calendar helps us keep track of __________.
a) time of the day
b) seconds
c) months and years
d) hours

9. There are __________ hours in 1 day.
a) 7
b) 12
c) 60
d) 24

10. If it is 9:30 a.m., how many minutes have passed since midnight?
a) 90
b) 60
c) 30
d) 45

11. In the evening, we use the notation __________.
a) A.M.
b) P.M.
c) B.C.
d) C.E.

12. How many seconds are there in 1 hour?
a) 60
b) 600
c) 3600
d) 10

13. To tell the time on a clock, we need to look at the positions of the __________.
a) seconds and minutes hands
b) minutes and hours hands
c) seconds and hours hands
d) minutes hand only

14. If it is 7:20 a.m., how many minutes have passed since midnight?
a) 200
b) 60
c) 20
d) 120

15. When we say it is 12:00 p.m., we mean it is __________.
a) midnight
b) noon
c) morning
d) evening

WEEK 4

TOPIC: Angles

SUBTOPIC: properties of a square and rectangle

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. State the properties of a square
2. State the properties of a rectangle
3. Find the area of a rectangle using the formula
4. Calculate areas involving square meters and hectares.

1. Develop interest in finding shapes in their environment.

CONTENT

Properties of a square

1. The diagonals of a square bisect each other and meet at 90°
2. The diagonals of a square bisect its angles.
3. Opposite sides of a square are both parallel and equal in length.
4. All four angles of a square are equal. …
5. All four sides of a square are equal.
6. The diagonals of a square are equal.

Properties of a rectangle

1.Opposite sides are equal.

2.All angles in a rectangle is 90 degrees.

3.Diagonals are equal and they bisect each other.They are also congruent.

4.Perimeter of a rectangle is 2(l+b) where l is length and b is breadth.

5.Area of rectangle is l*b.

6.Square of length of diagonal is the sum of squares of length and breadth.

AREA OF RECTANGLE AND SQUARE

To find the area by counting squares could take a long time especially if you have to find the area of a large surface There is a formula to calculate the area of a rectangle or a square.

Properties of a Square:

1. All sides of a square are equal in length.
2. Opposite sides of a square are parallel.
3. All angles in a square are right angles (90 degrees).
4. Diagonals of a square are equal in length and bisect each other at right angles.
5. The perimeter of a square is four times the length of its side.
6. The area of a square is given by the formula A = side^2, where A represents the area and side represents the length of one side.

Properties of a Rectangle:

1. Opposite sides of a rectangle are equal in length.
2. Opposite sides of a rectangle are parallel.
3. All angles in a rectangle are right angles (90 degrees).
4. Diagonals of a rectangle are equal in length and bisect each other.
5. The perimeter of a rectangle is twice the sum of its length and width.
6. The area of a rectangle is given by the formula A = length × width, where A represents the area, length represents the length of the longer side (also known as the length of the rectangle), and width represents the length of the shorter side (also known as the width of the rectangle).

Finding the Area of a Rectangle Using the Formula:

To calculate the area of a rectangle, you can use the formula A = length × width. Simply multiply the length of the rectangle by its width to find the area. Make sure both measurements are in the same unit (e.g., meters, centimeters, etc.) before performing the multiplication.

Calculating Areas Involving Square Meters and Hectares:

Square meters (m²) and hectares (ha) are commonly used units for measuring areas. To calculate areas in these units, you need to know the conversion factors:

1 hectare (ha) = 10,000 square meters (m²)
1 square meter (m²) = 0.0001 hectare (ha)

To convert an area given in square meters to hectares, divide the area by 10,000. To convert an area given in hectares to square meters, multiply the area by 10,000.

Developing Interest in Finding Shapes in the Environment:

Encourage students to develop an interest in finding shapes in their environment by providing real-life examples and engaging activities. Some ideas include:

1. Taking students on a shape hunt around the school or neighborhood, where they can identify and name different shapes they come across.
2. Assigning students to find and photograph shapes in their daily surroundings, such as shapes in buildings, signs, or natural objects.
3. Organizing a “shape of the week” challenge, where students have to find and share examples of a specific shape they encounter during the week.
4. Incorporating hands-on activities where students use materials like clay, blocks, or straws to construct and explore various shapes.
5. Introducing books, videos, or online resources that showcase the beauty and importance of shapes in art, architecture, and nature.

By making shape recognition interactive and relevant to their daily lives, students can develop a keen eye for shapes and a deeper understanding of their presence in the world around them.

Example:

The formulary for calculating the area of a rectangle is A = L×B

Length = 8cm

Area= 8cm×6cm

= 48cm²

A= L× L

L= 8cm

B= 8cm

A= 8cm×8cm

A= 64cm2

Length= 3ft

Area: L xB

A= 3 x 5ft.

A= 15ft.

Length= 7mm

Area= LxB

A= 7mm x7mm

A=49mm.

Class work

Calculate the area of the following:

1.   Rectangle 9cm by 3cm.
2. Rectangle 4cm by 7cm.
3. Rectangle 10cm by 2cm
4.   Rectangle 9cm by 1cm.
5.   Rectangle 2cm by 5cm.
6. Rectangle 9cm by 2cm

Calculate the area of the following:

1. Square side 5cm.
2. Square side 3cm.
3.   Square side 6cm.
4. Square side 4cm.
5.   Square side 8cm.
6.  Square side 7cm

Examples

Given either the length or breadth of a rectangle, you simply divide the given area by

either the breadth or the length.

4 cm

Area = 12 cm2

Area = 12 cm2 Length = 4 cm

= 3 cm

Area = 21 cm2 3 cm

Area = 21 cm2 Breadth = 3 cm

∃ Length = 21/3

= 7 cm

Exercise 3

Calculate the length or breadth required for each of the following rectangle where the units

for length and breadth are in centimetres.

1. Area = 48, Length = 6     2. Area = 12, Breadth = 2    3. Area = 36, Breadth = 6
2. Area = 20, Breadth = 4    5. Area = 100, Length = 10  6. Area = 11, Breadth 7. Area = 120, Length = 10  8. Area = 21, Length 4     9. Area = 72, Length 12
3. Area = 80, Breadth 8

To find the side of a square when only the area is given, simply work out the square

root of the area.

Side of a square = Area

Exercise 4

Calculate the sides of each of the squares.

1. Area = 100 cm2 2. Area = 49 cm2 3. Area = 64 cm2 4. Area = 144 cm2
2. Area = 36 m2 6. Area = 81 m2 7. Area = 25 m2 8. Area = 16 m2
3. Area = 169 m2 10. Area = 4 cm2

SQUARE OF A METER AND HECTARE

The square metre is too small to measure very large areas such as states, countries, etc.

The area of Nigeria in square metres is 923 768 000 000 m2

The number of digits are reduced when we use acre and it is reduced further when

we use hectare.

The acre is 4 000 m2 and it is more convenient for measuring fields but the most

common units are the hectare and square kilometre.

1 acre = 4 000 m2 1 hectare = 2 1/2acres = 10 000 m2

1 square kilometre = 1 000 000 m2 = 100 hectares

Exercise 1

Write down the area of Nigeria in

1. acres
2. hectares
3. square kilometres

Convert these to acres.

1. 7 hectares 5. 18 hectares 6. 53 hectares
2. 9.6 hectares 8. 14 hectares 9. 30.7 hectares
3. 82.1 hectares 11. 14.27 hectares 12. 35.84 hectares
4. Convert these to acres.
5. 12 000 m2  2. 8 000 m2  3. 16 000 m2  4. 24 000 m2  5. 36 000 m2  6. 60 000 m2  7. 14 000 m2 8. 10 000 m2  9. 6 000 m2  10. 7 500 m2

Remember 1 acre = 4 000 m2

Exercise 2

Convert these to hectares.

Remember 1 hectare is 2 12a cres.

1. 600 acres 2. 200 acres 3. 450 acres 4. 129 acre 5. 285 acres 6. 2 036 acres 7. 1 963.2 acres 8. 3 001.8 acres  9. 20 000 m2   10. 80 000 m2   11. 36 000 m2   12. 49 000 m2 13. 24 600 m2 14. 51 200 m2   15. 17 650 m2  16. 90 160 m2 17. 74 380 m2   18. 66 210 m2

Exercise 3

1. Find the breadth of one hectare of farmland with
2. a) Length – 500 m b) Length – 1 000 m
3. Find the length of one acre of a poultry farm with
5. A land speculator bought 10 hectares of land and mapped out 200 plots for sale. What

was the area of each plot?

1. Calculate the area of 10 of the plots in question 3
2. The area of the Federal Capital Territory, Abuja is about 925 000 km2. Convert this to metre2.

Exercise 4

Word problems

1. The area of a town is 14 400 square metres. Find the width if the length is 300 metres.
2. Find the area of a rectangle 24 cm long and 9 cm wide.
3. A tray is 18 cm wide and 28 cm long. What is the area of the surface of the tray?
4. Kitchen tiles are 30 by 20 cm. What is the area of each tile.
5. How many kitchen tiles are needed to cover one side of my kitchen wall measuring 300 cm by 200 cm.
1. A floor is rectangular in shape and it measures 4.5 m by 4 m. What is the area? 225
1. A rectangle has length 25 cm and breadth 18 cm. If a diagonal is drawn to form two triangles, find the area of one triangle.
1. How many squares of 2 cm side can be cut from a square 10 cm side.
2. Find the area of a plot of land 40 m long and 18 m wide.
3. An oil company is drilling oil in a rectangular plot measuring 28 kilometres by 37 kilometres. What is the area of the plot? Answer in km2.

WEEK 5

TOPIC: Capacity

SUBTOPIC:  Capacity addition and subtraction of liters

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Recapitulate the standard measurements of some liquid
2. Convert liters to centiliters
4. Subtract liters correctly

CONTENT

CAPACITY ADDITION AND SUBTRACTION IN LITERS

Capacity is the measure of the amount of liquid in a container. The standard unit of

measuring capacity is the litre ( l

Small amount of liquid is measured in millilitre (ml) while large amount is measured in litres.

Table of capacity measure

10 milliliters ( ml) = 1 centiliter ( cl) 10 centilitres = 1 decilitre (dl)

10 deciliters = 1 litre (l) 10 litre = 1 decilitre (dl)

10 decilitres = hectolitre (hl)  10 hectolitres = 1 kilolitre (kl)

Note that

1 000ml  = 1 litre ( l ) 100 cl = 1 litre 1 000 l = 1 kilolitre (kl)

When converting a smaller capacity measure to a higher one, note the following:

1. a) From ml to cl, divide by 10 b) From cl to l, divide by 100
2. c) From ml to l, divide by 1 000 d) From l to kl, divide by 1 000

Examples

1. Convert 4 000ml to l =4000/1000l=4l
2. Convert 600cl to l = 600/100=6l

100 􀆐􀀃= 6 􀆐

Exercise 1

Express the following in litres L

1. 2 000ML 2. 1 200CL 3. 650cl 4. 800cl 5. 5 000ml
2. 20 000ml 7. 900ml 8. 14 000ml 9. 700ml 10. 10 500ml

When converting higher capacity measure to a smaller capacity, note the following:

1. a) From cl to ml, multiply by 10 b) From l to cl, multiply by 100
2. c) From l to ml,, multiply by 1 000 d) From kl to l, multiply by 1 000

Examples

1. Convert 6 litres to cl

1 l􀆐 = 100 cl􀆐

6 􀆐 = 100 × 6 = 600 cl􀆐

1. Convert 5.5 l to ml

1l  = 1 000 ml􀆐

5.5 􀆐 = 5.5 × 1 000 ml􀆐 = 5 500ml􀁐􀆐

Exercise 2

1. Convert the following to 􀁆􀆐
2. 7 cl􀁆􀆐 2. 6.5 l􀆐􀀃 3. 10 l􀆐 4. 8.5 l􀆐􀀃 5. 12l􀆐
3. Convert the following to ml
4. 2 l􀆐􀀃 2. 10 cl􀆐 3. 1.5 l􀆐􀀃 4. 3 cl􀆐 5. 4 l􀆐
5. Convert the following to 􀆐
6. 1.5 kl􀁎􀆐 2. 3kl 􀁎􀆐 3. 4.3 kl􀁎􀆐 4. 0.8kl 􀁎􀆐 5. 0.26kl 􀁎􀆐
7. 1.2 kl􀁎􀆐 7. 0.3 kl􀁎􀆐 8. 0.15 kl􀁎􀆐 9. 1.04 kl􀁎􀆐 10. 3.13kl 􀁎􀆐

Examples

1. 2.38 l􀆐 + 1.65 l􀆐

= 2 · 38 􀆐+ 1 · 65 =4 · 03 l􀆐

1. 46.35l 􀆐 – 29.l6 l􀆐

= 46 · 35 􀆐– 29 · 16 = 17 · 19 l

Exercise

Copy and complete the following.

1. 4 · 3 + 2 · 4l

2.7 · 9+ 8 · 6l

1. 14 · 3+ 9 · 8l
2. 8 · 42+ 3 · 25l
3. 5. 12 · 86+ 4 · 91
4. 15 · 63+ 14 · 78
5. 3 · 175+ 18 · 134
6. 13 · 217+ 19 · 893
7. 27 · 398+ 24 · 923
8. 34 · 654+ 27 · 678
9. 49 · 415+ 50 · 687
10. 5 · 6− 2 · 4l
11. 9 · 2− 5 · 4l
12. 11 · 8− 6 · 9
13. 7 · 43− 2 · 19l
14. 20 · 24− 8 · 77l
15. 32 · 03− 18 · 15l
16. 32 · 714− 16 · 250l
17. 46 · 038− 15 · 71l
18. 53 · 412− 26 · 891l
19. 60 · 105− 42 · 314l
20. 76 · 964+ 9 · 087
21. 795 · 22+ 900 · 11l
22. 900 · 85+ 25 · 22
23. 18.23 􀆐 + 19.47 􀆐 26. 26.08 􀆐 + 34.971 􀆐􀀃 27. 41.376 􀆐 + 39.8 􀆐
24. 30.317 􀆐 – 12.888 􀆐􀀃 29. 46.053 􀆐 – 18.94 􀆐 30. 61.7 􀆐 – 45.632 􀆐

WEEK  6

TOPIC: Capacity

SUBTOPIC:  Capacity multiplication and division of liters

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Multiply in liter by whole
2. Divide in liter by whole
3. Appreciate liter as the unit of capacity

CONTENT

Multiplication and division involving litres

Multiplication

Example

Four cars each have 18.5 litres of petrol put in them. How much petrol is this?

18 · 5 􀆐

× 4

74 · 0 􀆐

􀆐

Exercise 1

Copy and complete the following.

1. 􀆐

8 · 3l

× 2

.2. 􀆐

7 · 1l

× 8

1. 􀆐

4 · 7l

× 3

1. 􀆐

5 · 9l

× 4

1. 􀆐

3 · 2l

× 9

1. 􀆐

9 · 4l

× 7

1. 5.6 l× 5. 8. 6.2 l× 6      9. 8.0l × 8    10. 1.7l × 9
2. 15 · 6 l

× 2

1. 27 · 9 l

× 8

1. 36 · 3 l􀆐

× 7

1. 47 · 9 l􀆐

× 6

1. 54 · 8l􀆐

× 9

1. 68 · 4 l

× 3

1. 43.6 􀆐 × 7 18. 52.2 􀆐 × 9 19. 39.9 􀆐 × 6 20. 20.7 􀆐 × 8

Division

Example

Three customers bought 5.7 litres of palm oil and then

shared it equally among themselves. How many litres did

each customer get?

5.7l ÷ 3 = 1.9 􀆐 5.7 /3 = 1.9 􀆐

1.9 􀆐

3 √5.7

Each customer got 1.9 litres.

Exercise 2

Work these out using the method in the example.

1. 4.8 l ÷ 4.    2. 8.4 l ÷ 6 3. 7.2l  ÷ 9.   4. 8.0  ÷ 5
2. 91.6/2􀆐 6. 74.7 /3. 7. 41.6/8􀆐 8. 53.6 /4
3. 3√ 17.1l  10. 7 √37.8l 􀆐 11. 9 √66.6l 􀆐 12. 5√ 89.5l 􀆐
4. Divide 63.7 l􀆐􀀃by 7 14. Divide 83.2 􀆐 by 8

Examples

Word problems on capacity

1. 1. A drum contains 12.58 litres of water, another drum contains 15.71 litres of water.

How much water will the two drums hold?

One drum contains = 12 . 58l 􀆐

Another drum contains = 15 . 71l 􀆐

Both drums hold = 28 . 29l􀆐

231

1. A basin contains 30 litres of water. Bisi used 8.29 litres to wash. How much water is left in

the basin.

A basin contains 30 litres of water = 30 · 00 􀆐

+ 8 · 29

21 · 71 􀆐

used 8.29 litres

Amount of water left 30 – 8.29 litres

1. A car tank holds 40 litres of fuel. How many litres can three such cars hold?

One car 40 litres

Three cars 40 × 3 litres = 120 litres

1. 36 litres of milk was given to 4 pupils to share. How much milk will each pupil get?

No of litres to share = 36 litres 9 litres

4√ 36

36

No of pupils to share it = 4

One pupil will get = 36 ÷ 4

Exercise 3

Word problems

1. 3.6l of water is poured into a bucket that already contains 2.9 􀆐 of water. How much

water is now in the bucket?

1. A tank is full and it contains 30 􀆐 of petrol. 12.72 􀆐 of this is used. How much petrol is left

in the tank?

1. Five friends shared 4 􀆐 of fanta equally. How many litres did each receive?
2. A station has only 92.4 litres of petrol left. This is shared equally by six customers.

How many litres of petrol will each customer receive?

1. A trader sells 43 bottles of oil a day. Each bottle contains 0.6 litres of oil. How many

litres did she sell?

1. Thirty-six children took 1.2 litres of water each with them on a journey. What was the

total capacity of water taken?

1. A car uses 8.76 litres out of the 30.92 􀆐 of petrol in the tank. What capacity of petrol is

left in the tank?

1. A tanker emptied its water into two containers of 3 260 litres and 2 846 litres

respectively. What is the capacity of the tank?

1. A bucket of water contain 7.2 litres of water when full. Equal amount is given to

four goats. What capacity of water will each goat drink?

1. A driver bought 36.82 litres of petrol when traveling to Benin. On his way back he

bought 48.45 􀆐. What is the total capacity of petrol bought?

WEEK  7

TOPIC: Plane shape

SUBTOPIC:   Symmetrical plane shape.

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. State the meaning of symmetry
2. Identify Symmetrical plane shape
3. Locate line of symmetry of plane figures at school and home.
4. Identify right angle,acute and obtuse andle in a plane shape.
5. Distinguish between horizontal and vertical.

CONTENT

symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide. For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first. There can also be symmetry in one object, such as a face

.

SYMMETRICAL PLANE SHAPE

Right angle, acute angle and obtuse angle

RIGHT ANGLE

Acute angle

Obtuse angle

Exercise

The secondary cardinal points

Between North and East, the direction is called North East (NE)

Between South and East, the direction is called South East (SE)

Between South and West, the direction is called South West (SW)

Between North and West, the direction is called North West (NW)

Thus; NE, SE, SW and NW are called the secondary cardinal points.

Exercise

1. From the North direction, record the direction the compass pointer turns through in a

clockwise direction:

1. 11/2

right angles = South East (SE) 2. 1/2

right angle = _______________

1. 2 right angles = _______________ 4. 3 right angles = _______________
2. 21/2

right angles = _______________ 6. 31/2

right angles = _______________

1. How many right angles are turned through by facing:
2. North and turn clockwise to face South?
3. West and turn clockwise to face North East?
4. South and turn clockwise to face North East?
5. North and turn anti clockwise to face East?
6. North and turn anti clockwise to face South East?

Copy and complete this table.

Name of shape Number of lines of symmetry

1. a) Trapezium
2. b) Kite
3. c) Parallelogram
4. d) Rhombus
5. e) Equilateral triangle
6. f) Right-angled triangle
7. g) Isosceles triangles
8. h) Circle

Copy and complete.

1. a) A plane shape with all its four sides equal is a
2. b) An equilateral triangle has ____________ equal sides.
3. c) An isosceles triangle has ____________ line of symmetry.
4. d) A rhombus has ____________ lines of symmetry.
5. e) A rectangle has ____________ lines of symmetry.
6. f) A square has ____________ lines of symmetry.
7. g) A kite has ____________ line of symmetry.
8. h) A parallelogram has ____________ line of symmetry.
9. i) A circle has ____________ lines of symmetry.

Draw each of the following shapes and show their line(s) of symmetry.

1. Isosceles trapezium 14. Square 15. Rhombus 16. Rectangle

Unit 3 Properties of parallelogram, rhombus, kite and trapezium

1. Properties of parallelogram

Parallelogram is described as a rectangle pushed over

1. A parallelogram has four sides.
3. Opposite sides are equal.
4. Two opposite sides are parallel.
5. Angles are not right angles.
6. Opposite angles are equal.
7. Diagonals are not equal but bisect each other.
8. No line of symmetry.

1. Properties of a rhombus

A rhombus is described as a square pushed over.

1. A rhombus has four sides.
3. All four sides are equal.
4. Two opposite sides are parallel.
5. Diagonals not equal but bisect each other.
6. Angles not right angles.
7. Opposite angles are equal.
8. Two lines of symmetry.

. Properties of a kite

1. A kite has four sides.
3. Two sides next to each other are equal.
4. No sides is parallel.
5. It has one line of symmetry.

Exercise

1. Write down two properties of
2. a) rhombus b) kite
3. All the properties of the parallelogram and rhombus are the same except in two

properties. Mention the two properties that are different.

1. How would you describe a quadrilateral? Give 2 examples.
2. Draw and name four plane shapes.
3. Using dotted lines show the line or lines of symmetry in each shape.
4. a) When do we say an object is symmetrical?
5. b) Give two examples of symmetrical objects.
6. Draw four letters of the alphabet with their lines of symmetry.
7. List the ones with no lines of symmetry. Only 5
8. How many lines of symmetry does
9. a) an equilateral triangle have?
10. b) an isosceles triangle have?

Week 8

TOPIC: Shapes

SUBTOPIC:   3 dimensional shapes

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Distinguish between open and close shapes
2. State the properties of close shapes
3. Appreciate the presence and use 3 dimensional shapes in Homes.
4. Identify right angle,acute and obtuse andle in a plane shape.
5. Distinguish between horizontal and vertical.

CONTENT

Cube

A cube has 8 vertices

A cube has 12 equal edges

A cube has 6 equal faces

Cuboid

A cuboid has 8 vertices

A cuboid has 12 unequal edges

A cuboid has 6 unequal faces

)

Cylinder

A cylinder has one curved face

It has two flat faces

It has no vertex

Sphere

A sphere has one curved face only.

Curved face

It has no edge and no vertex.

Cone

A cone has 1 vertex

A cone has 1 curved face

A cone has 1 flat face (i.e. a closed cone)

A cone has 1 edge

Exercise

Object                Number of vertices    Number of edges      Number of faces

1. Maggi cube
2. Die
3. Concrete block
4. Tin of milk
5. Football
6. Sugar cube
7. Ice-cream cone
8. Box
9. Class-room

Exercise 1

Study the pictures above and on page 251 along with other solid objects around the class

and classify them into open and closed objects.

Observations

1. Open object do not have a cover at the top. The inside of an open object can be seen,

because it has no cover or top face.

1. The inside of a close object cannot be seen because of the cover or top face.

Study this table carefully

Open object                             Closed object

Cube No of vertices          8                                           8

No of edges                     12                                         12

No of faces                        5                                          6

Cuboid No of vertices        8                                          8

No of edges                      12                                        12

No of faces                        5                                           6

Cylinder No of curved faces 1                                        1

No of flat faces                      1                                       2

No of vertices                        0                                       0

Note:

1. Tubes, pipes, straws are special cylinders with no flat face. They are known as hollow

cylinders. The two ends are open.

1. A sphere is always a closed objects.

Exercise 2

Copy and complete this table, stating whether the following solids are open or closed objects.

Name of shape     Open            Closed

Bucket

Cup

Refrigerator

Ice-cream cone

Ludo die

Cube of sugar

Tin of milk

Tin of Milo

Tin of tomato

1. Copy and complete the table drawn below.

Number of faces     Number of edges       Number of vertices

closed cube

closed cuboid

open cube

open cuboid

closed cylinder

open cylinder

sphere

cone

1. Copy and complete the following.
2. A three-dimensional shape having equal faces _____________.
3. A cuboid has _____________ unequal faces.
4. The face of a cuboid is a _____________.
5. A cylinder has _____________ flat circular faces.
6. A cone has _____________ edge.
7. An open shoe box has _____________ faces

Week 9&10

TOPIC: Pictogram and mode

SUBTOPIC:  Bar gragh and mode

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to:

1. Represent data on a pictogram.
2. Determine the mode from the pictogram
3. Read and interpret bar graph
4. Determine the mode from bar gragh
5. Appreciate the presence of most common events/data in daily activities.

CONTENT

1. Number of red colored boxes sold by William, a shopkeeper, in six days of a week. See the picture graph or pictograph to answer the questions.

Examples of Pictographs

Information gathered from the above table:(i) Number of red boxes sold:

Monday – 4, Tuesday – 2, Wednesday – 3, Thursday – 5, Friday – 8, Saturday – 1

Therefore, sale during the week = 23

(ii) Lowest sale – on Saturday, only 1 box was sold.

Maximum sale on Friday is 8 boxes were sold.

1. Number of illiterate children of 5 small towns, Melrose, Marengo, Midway, Parral and Rushville. See the picture graph or pictograph to answer the questions.

Information gathered from the above table:

(i) Number of illiterate children of different small towns:

Melrose – 5, Marengo – 4, Midway – 7, Parral – 3 and Rushville – 2

(ii) Total number of illiterate = 21

1. Information about 300 children of a school who come to school by different modes of transportation.

Pictographs Face

→ 1 face represents 10 children

See the picture graph or pictograph to answer the questions.

Picture Graph or Pictograph

36SaveInformation gathered from the above table:

(i) Number of students going to school by different modes of transportation:

Auto-rickshaw = 6 × 10 = 60, Car = 4 × 10 = 40, Bicycle = 7 × 10 = 70, Bus = 10 × 10 = 100, On foot = 3 × 10 = 30

(ii) Total number = 60 + 40 + 70 + 100 + 30 = 300

A BAR GRAPH

A bar graph (bar chart) is presented in rectangular form

having horizontal and vertical axes as shown opposite:

Examples

Table: Favorite Type of Movie

Comedy Action Romance Drama SciFi

4 5 6 1 4

We can show that on a bar graph like this:

Favorite Type of Movie

It is a really good way to show relative sizes: we can see which types of movie are most liked, and which are least liked, at a glance.

We can use bar graphs to show the relative sizes of many things, such as what type of car people have, how many customers a shop has on different days and so on.

Example: Nicest Fruit

A survey of 145 people asked them “Which is the nicest fruit?”:

Fruit: Apple Orange Banana Kiwifruit Blueberry Grapes

People: 35 30 10 25 40 5

And here is the bar graph:

bar graph for fruit

That group of people think Blueberries are the nicest.

Bar Graphs can also be Horizontal, like this:

bar graph horizontal

In a recent test, this many students got these grades:

Students: 4 12 10 2

And here is the bar graph:

Exercise 1.

1. Umoh and Rashid were recordin g the types of vehicle passing their school gate during

lunch break and produced the table below.

Type of vehicle        Bicycle      Motorbike    Car      Lorry

Number                          4             10              25         16

Draw a bar chart to show the information.

1. The table below shows the rainfall recorded in one week

Day                               Sun       Mon    Tue     Wed     Thur    Fri    Sat

Rainfall per week (mm) 40           35       20       30         25     15    15

Draw a bar graph to show the information.

257

1. The number of litres of kerosene consumed by housewives in a group of 55 houses are

shown in the table.

Number of litres              1    2    3      4     5     6

Number of houses          11  16  12     5     8      3

Draw a bar graph to show the information.

1. The table below shows the responses of pupil’s opinions about the quality of school

lunches.

Opinion                  Very good       Good     Okay      Poor     Very poor

Number of Pupils            2                12          20         10            8

Draw a bar graph to show the information\

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