General
- P5: Mathematics File Uploaded 31/07/22, 11:26
- P5: Mathematics TG File Uploaded 1/08/22, 18:29
- P5 MATH TG ( Adapted ) File Uploaded 2/11/22, 08:28
- END UNIT 1 ASSIGNMENTOpened: Saturday, 27 May 2023, 12:00 PMDue: Monday, 29 May 2023, 12:00 AM
UNIT 7:Solving problems involving measurements of length, capacity and mass
7.1 Revision problems on length, capacity and mass
Revision work 7
1. Complete the conversions.
(a) Length
From table;
• 1 dm = 100 mm
• 1 km = ___ mm
• 1 hm = ___ m
• 1 dam = ___ m
• 1 m = ___ cm• 1 m = ___ mm
(b) Capacity
From table;
• 1 l = 1 000 ml
• 1 hl = ___ l
• 1 dal = ___ l
• 1 l = ___ dl
• 1 l = ___ cl
(c) Mass
From table;
• 1 g = 10 dg
• 1 kg = ___ hg
• 1 dag = ___ g
• 1 kg = ___ mg
• 1 g = ___ mg
(d)
From table;
1 t = ___ kg
2. Convert the following into centimetres. Explain your steps.
(a) 30 mm (b) 60 mm (c) 0.7 km
3. Convert the following measurements into millimetres.
(a) 40 cm (b) 2.4 cm (c) 0.85 m (d) 0.5 km
4. Convert the following measurements into metres.
(a) 260 cm (b) 4 000 cm (c) 6 km (d) 60 cm
5. Convert the following measurements into kilometres.
(a) 600 cm (b) 360 000 mm (c) 800 m (d) 14 000 cm
6. Convert the following measurements into decimetres. Explain the
steps followed.
(a) 600 cm (b) 4 000 mm (c) 120 dam
(d) 6 dam (e) 2 km
7. Convert the following measurements into decametres and present
your findings.
(a) 1 000 000 mm (b) 10 000 cm
(c) 200 m (d) 20 km
8. Convert the following into hectometres. Discuss your steps.
(a) 3 000 dam (b) 12 000 cm (c) 1 000 m (d) 10 dm
9. Change the following into litres. Present your answers.
(a) 30 dl (b) 105 dl (c) 1 050 ml (d) 2 500 ml
10. Write the following weights in tonnes.
(a) 3 450 kg (b) 2 050 kg (c) 170 000 kg
11. (a) Subtract 2 m 6 dm 4 cm from 9 m. Give answer in dm.
(b) A person’s stride is 90 cm. How many strides can she take in a
distance of 27 dam to her school? Explain your steps to answer.
12. Work out the following. Discuss your answers.
(a) 4.5 kg + 13.6 dag = ____ kg
(b) 4 hl – 20 dal = ___ litres(c) 2 dam 3 m × 5 = ___ hm
7.2 Number of intervals between objects on an open line
Activity 7.1
(a) Measure the length of the major paths that are in the school
compound. For example:
(i) The path from the school gate to the staff room.
(ii) The path from the staff room to the P5 classroom.
(iii) The path from the P5 classroom to the assembly grounds.
(b) Make a 0.9 m stick. Use it to mark fixed distances from one point
to another. Fixed distances are called intervals. Make markings by
standing along the lines at intervals of 0.9 m. Look at the figurebelow.
(i) How many of you stood along the line?
(ii) How many intervals are there? Present your finding.(iii) What other ways could you stand along the line?
Tip: Look at an open line below:
• 4 m is the interval.
• Distance = 4 m × 4 = 16 m
• Number of intervals = 4 or (5 – 1)• Number of trees = 5 or (4 + 1)
• 5 m is the interval.
• Distance = 5 m × 3 = 15 m
• Number of intervals = 3• Number of trees = 3
• 5 m is the interval
• Distance = 5 m × 3 = 15 m
• Number of intervals = 3• Number of trees = 2
Example 7.1
A man’s stride is 10 dm long. He walks a distance of 10 dam. How many
strides does he take to cover the distance
Solution
Change 10 dam to dm.
From the conversion table, 100 dm = 1 dam
Thus, 10 dam = 10 × 100 dm = 1 000 dm
Now, Interval = Stride’s length = 10 dm. Distance = 1 000 dm or 10 dam.So we calculate the number of strides:
Practice Activity 7.1
1. A road is 2 km long. Trees were planted 2 m apart along one side of
the road. An interval of 2 m was left at one end without a tree due toan existing shop. How many trees were planted along the road?
2. A path is 5 dam long. Trees are to be planted at intervals of 5 dm on
both sides. How many trees are needed?
3. Electric poles are fixed along one side of 16 km section of road. This
was to light the road. The poles are placed 10 m apart from each other.
How many poles are fixed? Discuss why it is important to light the
road.
4. A farmer planted crops in straight lines. In each line, an interval gap
was left without crop for easy movement at both ends. There are 10
lines. Each line is 20 m. The interval for plants in each line is 0.5 m.
(a) How many plants are in each line? Justify your answer.
(b) How many plants are in 10 lines? Discuss your answer.
5. A farmer planted 20 trees along a terrace of his land. The trees were
planted at intervals of 2 m. What is the length of the terrace planted
with trees? Present your findings. Why is it important to plant trees
along terraces?
6. 21 vegetables were planted along a straight line in a garden. The
vegetables were planted at fixed intervals. The line was 30 m long. Work
out the length of the interval, then explain your answer. Why should
we have a kitchen garden?
7. A section of a road is 3 km long. Flowers were planted 200 cm apart
alongside the road. There were two rows of flowers on each side of the
road. How many flowers were planted along the road? Discuss youranswers.
7.3 Finding the number of intervals on a closed line
Activity 7.3
– Measure a 1 metre long stick.
– Make a square and a rectangle on the ground using measured stick.Let their perimeters be 12 m.
– Starting at one corner, fix small stones at equal intervals of 1 m.
(i) How many small stones have you used?
(ii) How many intervals are there?
– Tell the daily life situation relating to the activity.– Discuss your findings.
Tip: Look at these figures:
On every closed line or field;
• Number of intervals = number of poles.
• Number of intervals × interval length = distance of closed field
line.
Look at the example below.
Example 7.2
The length of a rectangular piece of land is 48 m by 12 m. Poles were
fixed at intervals of 2 m to fence it.
(a) What is the distance round the land?
(b) How many poles were used to fence the land?
Solution
(a) Distance round the land = perimeter
= 48 m + 12 m + 48 m + 12 m= 120 m
Practice Activity 7.2
1. In a town, a square plot has sides of 50 m. Poles were fixed to fence it
at intervals of 2 m. How many poles were used? Where can you fence
and why?
2. A circular fish pond has a circumference of 154 m. Poles are to be fixed
at intervals of 3.5 m. How many poles are required to fence around the
entire pond? Tell the importance of rearing fish.
3. A rectangular tank was built to store water. The tank had a length
of 125 m and a width of 100 m. It was fenced using 150 poles fixed at
equal intervals. Calculate the length of each interval.
4. The fence distance round an animal park is 4.2 km. 210 trees are
planted along the park fence at equal intervals. Calculate the length of
each interval in metres. Explain your answer. Why do we fence round
the animal park?
5. A farmer fenced her cassava farm using 50 poles. The poles were
spaced at equal intervals of 2.5 m. Calculate the distance round her
farm in decametres. Discuss your answer. Explain the importance of
cassava.
6. In a certain town, trees were planted round it. The trees were equally
spaced at intervals of 6 m. The distance round the town was 402 m.Find the number of trees round the town. What have you observed?
Revision Activity 7
1. Name the types of lines below. Why?
2. Convert:
(i) 25 dm = ___ hm (ii) 300 mm = ___ dam
(iii) 3.45 t = ___ kg (iv) 30 dl = ___ l
3. In an athletic competition, an athlete ran a distance of 80 dam. The
length of her stride was 80 cm. How many strides did she take?
4. While walking along the road, I counted 91 trees in a straight line.
The trees were equally spaced at intervals of 8 m. Find the distance
of the road planted with trees. Explain your answer.
5. 41 poles were put up to fence one side of a field. The length of the
side was 12 dam. Find the interval between the poles in metres.6. Look at the piece of land below.
It was to be fenced using posts at intervals of 3 m. How many posts
were to be used? Present your work. What materials do you need for
fencing?
7. In an open field, 7 trees were planted to prevent soil erosion. The
interval between the trees was 5 m. Calculate the distance of field
that was planted. Why should we prevent soil erosion?
8. 75 trees were planted around a field. They were equally spaced at
intervals of 4 m. Calculate the distance of the field that was planted.Justify and present your answer.
Word list
Length Capacity Mass Interval
Open line Closed line Distance
Task
Do the following.
(i) Read each word aloud to your friend.
(ii) Write the meaning of each of the words above. Discuss with your friend.(iii) Write sentences using each of the words above. Read with your friend.