Chapter 4 of 8

All 8 chapters
  1. 1Centimetres and metres, readunderstood
  2. 2Millimetres and kilometres, readunderstood
  3. 3Tenths and the decimal point, readunderstood
  4. 4Grams and kilograms, readunderstood
  5. 5Millilitres and litres, readunderstood
  6. 6Telling the time, readunderstood
  7. 7How long it takes, readunderstood
  8. 8Perimeter and area, readunderstood

M2.6.4 Chapter 4

Grams and kilograms

Is a big thing always heavier than a small thing?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Weigh things on a scale in grams and kilograms
  • Read a scale where the marks go up in 100 g
  • Change 2 kg 300 g into 2 300 g

We can weigh things on a scale. For light things we use the gram. We write g.

For heavier things we use the kilogram. We write kg.

1 000 g make 1 kg. The water in a 1 litre bottle weighs about 1 kg.

Look at this scale. The numbers on it are kilograms.

Draw it first

Read a scale

  1. A scale from 0 to 3 kg. Step 2 adds a small mark for every 100 g. Step 3 adds an arrow just after the 2, with the label 2 kg 300 g.0123kg

    1 The numbers on this scale are kilograms.

  2. A scale from 0 to 3 kg. Step 2 adds a small mark for every 100 g. Step 3 adds an arrow just after the 2, with the label 2 kg 300 g.0123kg

    2 Between two numbers there are 10 marks. Each mark is 100 g.

  3. A scale from 0 to 3 kg. Step 2 adds a small mark for every 100 g. Step 3 adds an arrow just after the 2, with the label 2 kg 300 g.0123kg2 kg 300 g

    3 The arrow is 3 marks past 2. That is 2 kg 300 g.

To read a scale, find the last number the arrow passed.

Then count the small marks after it. Each one is 100 g.

Worked example

Write 2 kg 300 g in grams.

  1. 1 kg is 1 000 g. So 2 kg is 2 000 g.
  2. 2 kg 300 g is 2 000 g and 300 g more.
  3. 2 000 + 300 = 2 300.

Answer: 2 300 g

See it three ways

With things

The water in a 1 litre bottle weighs about 1 kg. That is 1 000 g.

As a picture

A bar cut into 10 equal parts. Each part is 100 g. The label under it says 1 kg = 10 × 100 g.1 kg = 10 × 100 g

In symbols

10 × 100 g = 1 000 g = 1 kg. So 2 kg 300 g = 2 300 g.

A balance shows which of two things is heavier.

Try it

Make a balance

You need: a stick or a coat hanger, string, two bags the same, a stone as big as your fist, and dry leaves.

Be safe: Hang the balance low. Keep your feet and face away from the stone. Wash your hands after you touch leaves or soil.

  1. Tie a string to the middle of the stick. Hang it from a hook.
  2. Slide the string until the stick hangs level.
  3. Hang a bag from each end, the same distance from the middle.
  4. Put the stone in one bag. Fill the other bag with dry leaves.
  5. Watch which side goes down.

What you will see: The stone side goes down. The small stone is heavier than the bag of leaves.

If you cannot try it, this is what happens.
A home made balance. A stick hangs by a string from its middle. A small bag with a stone hangs from the left end, which is lower. A big bag of leaves hangs from the right end, which is higher. The labels are stone and leaves.stoneleaves

A wrong idea many people have

A bigger thing is always heavier.

Why it feels right: Big rocks and big boxes are often heavy.

The test that breaks it: Fill a bag with dry leaves. Put a stone as big as your fist in the other bag. The leaves take far more room. The stone side goes down.

What is true: Size is not weight. A bag of dry leaves is big but light. A small stone is heavy. Weigh them to find out.

Key words

gram
a small amount of weight. We write g.
kilogram
1 000 g. We write kg.
balance
two bags on a stick. The lower side is heavier.

Back to your guess

The answer is B: No. A small thing can be heavier than a big thing.

No. A small stone can be heavier than a big bag of leaves. The leaves still weigh something, only less. Size alone does not tell you.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. What does the arrow show?

    A scale from 0 to 3 kg with a mark for every 100 g. An arrow points at the fourth small mark after the 1.0123kg
    Tap your answer.

    1. Not this one. You counted 4 marks, but each mark is 100 g. So 4 marks are 400 g. Try another.

    2. Yes, that is right. The arrow passed 1 kg. It is 4 marks further. 4 × 100 g = 400 g.

    3. Not this one. You counted only the marks. First read the last number the arrow passed. That is 1 kg. Try another.

    See the answer

    1 kg 400 g

    The arrow passed 1 kg. It is 4 marks further. 4 × 100 g = 400 g.

    • If you chose A: You counted 4 marks, but each mark is 100 g. So 4 marks are 400 g.
    • If you chose C: You counted only the marks. First read the last number the arrow passed. That is 1 kg.

  2. Change 4 kg 50 g into grams.

    Tap your answer.

    1. Not this one. You put 4 and 50 side by side. 4 kg is 4 000 g, not 400 g. Try another.

    2. Not this one. You wrote 50 g as 500 g. 4 000 + 50 is 4 050. Try another.

    3. Yes, that is right. 4 kg is 4 000 g. 4 000 + 50 = 4 050.

    See the answer

    4 050 g

    4 kg is 4 000 g. 4 000 + 50 = 4 050.

    • If you chose A: You put 4 and 50 side by side. 4 kg is 4 000 g, not 400 g.
    • If you chose B: You wrote 50 g as 500 g. 4 000 + 50 is 4 050.

  3. Change 5 000 g into kilograms.

    See the answer

    5 kg

    1 000 g make 1 kg. 5 000 ÷ 1 000 = 5.

  4. Tariq says a big pillow must be heavier than a small stone. Is he right?

    Tap your answer.

    1. Not this one. Size is not weight. A big pillow is full of air, so it can be light. Try another.

    2. Yes, that is right. A pillow is big but light. A stone is small but heavy. A balance shows which is heavier.

    3. Not this one. Every thing has weight, soft things too. A pillow is light, but a scale shows some weight. Try another.

    See the answer

    No. A bigger thing is not always heavier.

    A pillow is big but light. A stone is small but heavy. A balance shows which is heavier.

    • If you chose A: Size is not weight. A big pillow is full of air, so it can be light.
    • If you chose C: Every thing has weight, soft things too. A pillow is light, but a scale shows some weight.

  5. From an earlier chapter

    Write 3 m 70 cm in metres, with a decimal point.

    See the answer

    3.7 m

    70 cm is 7 lots of 10 cm. That is 7 tenths. So 3 m 70 cm is 3.7 m.

  6. The arrow is 5 marks past 2 kg. Each mark is 100 g. Write the weight in grams.

    See the answer

    2 500 g

    2 kg is 2 000 g. 5 marks are 5 × 100 = 500 g. 2 000 + 500 = 2 500.

  7. What weight does the arrow show?

    A scale from 0 to 3 kg with a mark for every 100 g. An arrow points at the seventh small mark after the 2.0123kg
    Tap your answer.

    1. Yes, that is right. The arrow passed 2 kg. It is 7 marks further. 7 × 100 g = 700 g.

    2. Not this one. You started at 3 kg. The arrow has not reached 3 yet. Start at 2, the last number it passed. Count 7 marks on. Try another.

    3. Not this one. Each mark is 100 g, not 10 g. So 7 marks are 700 g. Try another.

    See the answer

    2 kg 700 g

    The arrow passed 2 kg. It is 7 marks further. 7 × 100 g = 700 g.

    • If you chose B: You started at 3 kg. The arrow has not reached 3 yet. Start at 2, the last number it passed. Count 7 marks on.
    • If you chose C: Each mark is 100 g, not 10 g. So 7 marks are 700 g.

  8. The arrow points at 3 kg. How many grams is that?

    A scale from 0 to 3 kg with a mark for every 100 g. An arrow points at the 3.0123kg
    Tap your answer.

    1. Yes, that is right. 1 kg is 1 000 g. So 3 kg is 3 × 1 000 = 3 000 g.

    2. Not this one. You used 100 g for 1 kg. 1 kg is 1 000 g. So 3 kg is 3 000 g. Try another.

    3. Not this one. You kept the same number. But 1 kg is 1 000 g. So 3 kg is 3 lots of 1 000 g. Try another.

    See the answer

    3 000 g

    1 kg is 1 000 g. So 3 kg is 3 × 1 000 = 3 000 g.

    • If you chose B: You used 100 g for 1 kg. 1 kg is 1 000 g. So 3 kg is 3 000 g.
    • If you chose C: You kept the same number. But 1 kg is 1 000 g. So 3 kg is 3 lots of 1 000 g.

Keep it

Copy this into your exercise book.

1 000 g make 1 kg. 2 kg 300 g is 2 300 g. On a scale, count 100 g marks from the last number. Big is not always heavy.

Draw: A scale from 0 to 3 kg. Draw an arrow 3 marks past 2. Write 2 kg 300 g.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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