Science notes, unit 6

Measurement

Textbook Science Year 3 (DLP), pages 79–94

What this chapter covers

You can name the units for area (cm², m², km²) and volume (mℓ, ℓ, cm³, m³) (6.1.1)
You can measure the area of a flat, regular shape with 1 cm × 1 cm paper squares (6.1.2)
You can estimate the area of an odd-shaped surface using graph paper (6.1.3)
You can find the volume of a hollow box by filling it with 1 cm³ cubes (6.1.4)
You can read the volume of a liquid with your eyes level with the meniscus (6.1.5)
You can find the volume of a stone using the water displacement method (6.1.6)
You can explain why measuring carefully stops us from wasting things (6.1.7)

6.1Area and volume

A big fish pond can hold more fish than a small one. How do we know which one is bigger? We measure it! In this unit you will measure area and volume.

What is area?

Area is the size of a place or a flat surface.

A football field has a big area. Your exercise book has a small area. We write area with a square unit. Look at the little "2" at the top: cm² is said "square centimetre".

Booksquare centimetre (cm²)

Matsquare metre (m²)

Sabahsquare kilometre (km²)

Pictures: Science Year 3 (DLP) textbook, p. 80.

Small things use small units. Big places use big units. A leaf is measured in cm², a badminton court in m², and a very big lake in km².

Measuring the area of a regular surface

A regular surface has straight sides, like a card, a tile or a book cover. We can fill it with paper squares. Each square is 1 cm long and 1 cm wide. One square has an area of 1 cm².

A 3 cm by 2 cm card filled with six numbered 1 cm squares — Six paper squares fill this card. So its area is 6 cm². (Textbook p. 81)

How to do it

Paste 1 cm × 1 cm paper squares on the card. Leave no gaps.
Count the squares.
The number of squares is the area in cm².

A name card needs 4 rows of 5 paper squares. What is its area?

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4 rows of 5 squares = 20 squares, so the area is 20 cm².

Estimating the area of an irregular surface

An irregular surface has a wavy or odd shape, like a leaf, a starfish or a puddle. Paper squares will not fit nicely. So we estimate the area. To estimate means to find a number that is close, not exact.

We use graph paper. Graph paper is paper filled with small squares. On our graph paper each square is 1 cm × 1 cm.

A leaf traced on graph paper, then the squares inside it ticked — Kina traces the leaf, then ticks the squares inside it. (Textbook p. 84)

How to do it

Put the object on graph paper. Draw around it.
Tick (✓) every full square.
Tick every square that is half full or more.
Do not tick squares that are less than half full.
Count the ticks. That is the area in cm².

An odd-shaped pond on 1 cm squares with 17 squares ticked — Aiman drew his kampung pond on graph paper. He ticked 17 squares, so the pond's area is about 17 cm².

Do not tick tiny bits at the edge! A square that is only a little bit covered is not counted.

Name two things at the beach with an irregular surface.

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Any two: a starfish, a leaf, a seashell, a puddle.

What is volume?

Volume is the amount of space that can be filled with a solid, a liquid or a gas.

A school bus can carry more pupils than a van. The bus is bigger, so its volume is bigger.

Carton of milkmillilitre (mℓ)

Bottle of waterlitre (ℓ)

Water tankcubic metre (m³)

Pictures: Science Year 3 (DLP) textbook, p. 85.

Solids such as boxes use cubic centimetre (cm³). Look at the little "3" at the top: it means "cubic".

Did you know? 1 mℓ of water fills exactly 1 cm³. A small packet of drink at the school canteen holds about 200 mℓ. A big bottle of cooking oil at the pasar holds about 1 ℓ, which is 1000 mℓ!

Measuring the volume of a hollow box

A hollow box is empty inside. We fill it with small cubes. Each cube is 1 cm long, 1 cm wide and 1 cm high. One cube has a volume of 1 cm³.

A 2 cm box and the eight 1 cm cubes that fill it

Left picture: textbook p. 86.

The box needs 8 cubes to fill it. So its volume is 8 cm³.

Puan Lina needs 90 cubes of 1 cm³ to fill a box. What is the volume of the box?

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90 cm³ (one cube = 1 cm³).

Measuring the volume of a liquid

We use a measuring cylinder or a beaker. A measuring cylinder is a tall glass tube with a scale on it.

Water in a thin tube is not flat on top. It curves down in the middle. This curve is called the meniscus.

The curved surface of a liquid at the 200 mark, labelled meniscus — The meniscus is the curve on the top of the liquid. (Textbook p. 89)

Three pupils reading a measuring cylinder from above, below and at eye level — Lim reads 210 mℓ, Langgi reads 190 mℓ and Aishah reads 200 mℓ. Only Aishah is right. (Textbook p. 89)

Put the cylinder on a flat table. Bend down so your eyes are level with the bottom of the meniscus. Then read the scale.

If your eyes are too high, the reading is too big. If your eyes are too low, the reading is too small.

Volume of an irregular solid

A stone, a key or a padlock has an odd shape. We cannot fill it with cubes. We use the water displacement method. "Displace" means "push away". The stone pushes the water up. The water that moves up has the same volume as the stone.

Measuring cylinder with 20 ml of water, then 30 ml after a stone on a thread is put in — Method 1: use a measuring cylinder. (Textbook p. 91)

Method 1: measuring cylinder

Pour some water into a measuring cylinder. Read it. This is the initial volume (start): 20 mℓ.
Tie the stone with thread. Lower it slowly into the water.
Read the water level again. This is the final volume (end): 30 mℓ.
Volume of stone = final volume − initial volume = 30 − 20 = 10 cm³.

A eureka can full of water; a stone pushes water out of the spout into a measuring cylinder — Method 2: use a eureka can. The water that flows out has the same volume as the stone. (Textbook p. 91)

Did you know? A eureka can is a can with a spout. "Eureka" means "I found it!" A clever man in old Greece shouted it when he saw the water rise in his bath.

The water starts at 40 mℓ. After Ah Meng puts in a key, it is at 45 mℓ. What is the volume of the key?

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45 − 40 = 5 cm³.

Why measuring is important

Measuring helps us not waste things. Lim's father wants new tiles for his floor. He measures the area of the floor first. Then he buys just enough tiles. If he does not measure, he may buy too many (waste money) or too few (not enough tiles).

Mak measures 2 cups of rice for nasi lemak. She cooks just enough, so no rice is thrown away.

Summary

What	Units	How we measure
Area of a regular surface	cm², m², km²	Fill with 1 cm × 1 cm paper squares and count
Area of an irregular surface	cm²	Draw around it on graph paper; count full and half-or-more squares
Volume of a hollow box	cm³, m³	Fill with 1 cm³ cubes and count
Volume of a liquid	mℓ, ℓ	Measuring cylinder; eyes level with the meniscus
Volume of an irregular solid	cm³	Water displacement: final volume − initial volume

Measuring carefully helps us to avoid wastage.