MEASUREMENTS OF LENGTH, MASS AND VOLUME
Measurements of length What is length?
Length is the distance between two points.
Types of measuring tools of length
There are two types
- Non-standard tools
- Standard tools
Non-standard tools for measuring length
The use of non–standard measuring tools of length depends on the type of objects being measured.
For example, the length of a chalkboard or table can be measured using non–standard tools such as handspan, stick, rope or footsteps.
Non-standard tools like a handspan do not give exact measurements because the obtained length will depend on the size of the person’s handspan.
The following picture shows a pupil measuring the length of a table by handspan
Activity 1: Measuring the length of a classroom
(a) Measure the length of the classroom using footstep.
(b) Record the length of the classroom.
(c) Ask your friend to measure and record the length of the classroom using similar tool used in task 1.
(d) Compare the measurements you obtained and that of your friend.
(e) Explain about the similarities or differences of the obtained measurements.
Standard tools used for measuring length
Standard tools for measuring length provide exact results which are acceptable worldwide.
Examples of Standard tools used for measuring length
- tape measure,
- ruler
- metre stick
These tools give measurements in metric units.
The common metric units of length include
- Millimetres (mm)
- centimetres (cm)
- metres (m)
- kilometres (km).
The following picture shows some of the standard tools for measuring length.
Ruler
Tape measures
Activity 2: Measuring length of different objects
1. Identify any four objects in your environment whose lengths can be measured by using nonstandard and standard tools.
2. Choose one object then measure its length using both non–standard and standard tools.
3. Record its length using both non–standard and standard tools. How comparable are they?
Activity 3: Measuring the length of an exercise book
- Measure the length of your exercise book in centimetres using a ruler.
- Record the length measured in task 1.
- Repeat task 1 by using a tape measure.
- Record the length measured in task 3.
- Compare the measurements obtained in task 3 and 4.
- Explain your observation from task 5?
Measuring length in centimetres and millimetres
Measurements in centimetres and millimetres are used more often when object are measured by using a ruler.
One centimeter is equal to ten millimetres ( 1cm = 10 mm) The smallest measurement unit of a ruler is the millimetre.
Example 1
What is the length of the piece of cloth in the following picture?
Answer
The length of the piece of cloth is 5 cm.
Example 2
What is the length of the piece of wood in the following picture?
Answer
The length of the piece of wood is 3 cm and 5 mm.
Exercise 1
1. Measure the length of each object in cm and mm from the following list.
- Table
- Desk
- Pencil
4. Exercise book 5. Ruler 6. Mathematics book
7. Eraser 8. Mathematical set kit
Measuring length in metres
One metre is equal to one hundred centimetres, (1 m = 100 cm.)
The given picture shows a ruler which is 100 centimetres or 1 metre long.
Activity 4: Measuring length of different objects
1. Measure the length of each object in metres from the following list.
2. Record the length of each object.
3. Which object has the largest length? Write its value.
Measuring length in kilometres
The length of a long distance can be measured in kilometres.
One kilometre is equal to one thousand metres. This relationship can be written as 1 km = 1000 m.
Exercise 2
1. Which measurement unit among cm, m and km is appropriate for measuring the following?
(a) your height
(b) distance from your class to the school toilet
(c) distance from your school to home
(d) length of a piece of chalk
2. Amina measured the length of a chalkboard using a ruler. John measured the length of the same chalkboard using his handspan. Who obtained the most correct measurement? Give reasons for your answer.
3. The distance from one school to a nearby dispensary is 800 m. The distance from the same school to a nearby market is one kilometre. Which one is far from the school between the dispensary and the market?
4. What is the length of the pencil in the following picture.
Measurements of mass
Mass is a measure of the amount of matter in an object.
The tools for measuring mass are divided into two types, non–standard tools and standard tools.
Non- standard tools for measuring mass
Non–standard tools for measuring the mass gives a rough estimate of the amount measured. Some of the tools used include spoons, cups, boxes, sacks and buckets. The following picture shows two buckets that contain rice.
Which bucket has more rice? Explain your answer?
STANDARD TOOLS FOR MEASURING MASS
Standard tools used for measuring the masses are called weighing balances.
Examples of weighing balances
UNITS FOR MEASURING MASS
The basic units used for measuring mass are gram (g) and kilogram (kg).
A gram is a smaller measurement unit than a kilogram.
The unit of gram is usually used for items whose mass is less than one kilogram. For heavier items, the unit of kilogram is used.
The relationship between gram (g) and kilogram (kg).
kilogram (kg) = 1000 grams (g). 0.5kg = 500 grams (g). kg = 250 gram (g)
Activity 5: Measuring mass of items in grams and kilograms
- In your environment, identify items whose masses can be measured.
- Select two items and measure their masses.
- Measure about 750 g of the first item, then about 1 kg of the second.
- From the measurements taken, which item is heavier? Give reasons.
Exercise 3
1. Measure the mass of the following items:
(a) An empty bottle of soda
(b) Exercise book
(c) Mathematical set
2. From the masses of items you have measured in Question 1:
(a) Which item is the lightest?
(b) Which one is the heaviest?
3. List about 5 items that can be measured by using the standard measuring tools of mass.
4. Arrange the following masses in the descending order:
1600 g, 500 g, 25 kg, 50 kg, and 650 g.
5. Zipora says the mass of 1000 grams is heavier than that of 1 kilogram. Is Zipora collect? Explain your answer.
6. Which measurement unit between gram and kilogram is appropriate for measuring:
(i) The mass of your mathematics textbook.
(ii) A bottle filled with two litres of cooking oil.
(iii) A bags of rice.
(iv) The mass of a students.
MEASUREMENT OF VOLUMES
Volume is the amount of space occupied by an object.
It can be measured by using non–standard and standard tools.
Non-standard tools used for measuring volume
Common tools used for measuring volume include spoons, cups and buckets. The following picture shows pupils measuring the volume of water by using cups and buckets.
The pupils use cups to fill buckets of the same size with water.
Each pupil uses the same number of cups to fill the bucket. Will the volume of water in each bucket be the same? Explain your answer
Activity 6: Measuring the volume of water
- Take two empty containers of the same size.
- Counting the number of cups, fill one container with water. 3. Ask your friend to do task 2 by using the same measuring tools used in task 2.
- Record the number of cups used to fill your container and that of your friend.
- Do the number of cups used to fill the containers differ? Explain.
- Identify other three items in your environment whose volume can be measured by using this activity?
Standard tools for measuring volume
Standard tools for measuring volume give exact values. These tools include beakers, cylinders and bottles. The following picture shows some of the standard tools used for measuring volume.
UNITS FOR MEASURING VOLUME
The common units for measuring volumes of items are millilitres and litres.
Millilitre is the smaller unit than the litre.
Millilitres are usually used for items with less volume than one litre while litres are used for larger volumes. Their relationship is as follows:
1 litre (L) = 1000 millilitres (ml) 
litre = 500 ml 
of a litre = 250 (ml)
Activity 7: Measuring the volume of water 1. Take a measuring cylinder.
- Pour some water into the cylinder until it reaches halfway.
- Read the volume of water in the cylinder.
Exercise 4
1. Arrange the following volumes from the smallest to the largest; 450 ml, 40 ml, 2 L, and 4 ml.
2. Examine the following table and then answer the questions that follow:
3. Which measuring tools can be used for measuring volume?
4. Which unit measures volume?
5. List the measuring tools that measure larger volumes (d) List the measuring tools that measure smaller volumes.
6. Observe the following jugs and then write the highest amount each jug can hold.
7. A cow produces 20 litres of milk every day. How many litres of milk will it produce in three days?
8. A pupil bought a bottle of 1 litre of juice. The pupil then gave 500 ml of juice from the bottle to another pupil. How many millilitres of juice did the pupil remain with?
Summary
- The basic unit of length is metre (m).
- The basic unit of mass is kilogram (kg).
- The basic unit of volume is litre (L).
- The relationship between metre and centimetre is 1 ml = 100 cm.
- The relationship between kilograms and grams is 1 kg = 1000 g.
- The relationship between litre and millilitre is
- 1 L = 1000 ml.
Vocabulary
Length Distance between two points
Mass Measure of the amount of matter in an object
Volume Amount of space occupied by an object
Standard tools Tools which give accurate and exact measurements Non–standard tools Tools which give measurements than are not exact
REVISION EXERCISE
1. Choose correct units of measurement from list B that can be used for measuring the lengths in list A.
List A
A. The length of the teachers’ office _______
B. Length of piece of chalk ______
C. The length of the road from Dodoma to Dar es Salaam _______
List B
2. Which of the following items can be estimated to weigh one kilogram? (a) Bicycle
(b) Pineapple
(c) A piece of paper
3. In the following pictures, write the units of mass (either gram (g) or kilogram (kg)) that you can use to estimate the mass of the following items. (a) is provided as an example.
4. If two stones weighing 500 g and 250 g are used to find the mass of rice, how much does the rice weigh?
5. You are given two stones weighing 250 g and one stone weighing 500 g. How will you measure one kilogram using the given stones?
6. If you are given the following volumes: 150 ml, 400 ml, nand 500 ml, what combination of volumes will you use to measure 550 millilitres?
7. Mzee Kinene has 750 ml of cattle medicine left in a 1000 ml bottle. How much medicine does he need to fill the medicine bottle?
8. Amina bought one litre of water. If she drank 500 ml during lunch, how many millilitres of water were left?
9. Aisha was asked to measure the distance of a netball pitch. Which of the following units is more appropriate for representing this distance: cm, m or km? Give reasons for your choice.
10. Kameme’s ruler is broken so that it begins at 3 cm mark. If he wants to draw a line which is 5 cm long, at what mark of the ruler will the line end?
11. Which unit will you use to express the mass of an orange?
12. If a bag of potatoes weighs 2,000 g and a bag of rice weighs 1 kg, which bag is heavier?
13. Clare bought 500 ml of cooking oil from school. She used 250 ml, what volume of cooking oil remained?
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