Chapter 2 of 8

All 8 chapters
  1. 1Fair shares: equal parts, readunderstood
  2. 2One part: halves, quarters, thirds, fifths, readunderstood
  3. 3More than one part, readunderstood
  4. 4Fractions of a group, readunderstood
  5. 5The number line, past 1, readunderstood
  6. 6Same amount, different names, readunderstood
  7. 7Which is bigger, readunderstood
  8. 8Adding and taking away parts, readunderstood

M2.4.2 Chapter 2

One part: halves, quarters, thirds, fifths

Eight is more than four. So is 1/8 more than 1/4?

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

  • Name one equal part as a half, quarter, third or fifth
  • Say what the bottom number of a fraction tells you
  • Tell which of two parts is smaller, such as 1/8 and 1/4

Last time you cut a whole into equal parts. Now we give one of those parts a name.

Draw it first

Name one part of a strip

  1. A strip that is one whole. Fold lines cut it into 4 equal parts. One part is shaded and labelled one quarter, 1/4.one whole

    1 Draw a long strip. The whole strip is one whole.

  2. A strip that is one whole. Fold lines cut it into 4 equal parts. One part is shaded and labelled one quarter, 1/4.one whole

    2 Cut it into 4 equal parts. Fold it twice to be sure.

  3. A strip that is one whole. Fold lines cut it into 4 equal parts. One part is shaded and labelled one quarter, 1/4.one whole14one quarter

    3 Shade one part. It is one quarter of the strip, and we write 1/4.

The 4 on the bottom is the bottom number. It tells how many equal parts the whole is cut into.

The 1 on top says we take one part. 1/4 is a fraction. A fraction is a number for part of a whole.

Some people say fourth, not quarter. Both names mean one of 4 equal parts.

Cut a whole into 2 equal parts. One part is one half, 1/2. Cut it into 8 equal parts. One part is one eighth, 1/8.

Three circles of the same size. The first is cut into 2 equal parts with one shaded, labelled half. The second is cut into 4 equal parts with one shaded, labelled quarter. The third is cut into 8 equal parts with one shaded, labelled eighth.halfquartereighth
One part of each circle is shaded.

Thirds and fifths are clearer on a bar. A circle is hard to cut into 3 or 5 equal parts. Cut a bar into 3 equal parts. Each part is a third, 1/3.

Cut a bar into 5 equal parts. Each part is a fifth, 1/5.

Two bars of the same length. The top bar is cut into 3 equal parts with one shaded, labelled one third. The bottom bar is cut into 5 equal parts with one shaded, labelled one fifth.one thirdone fifth
The two bars are the same length.

Now look at the bottom numbers. 8 is more than 4. But one eighth is a smaller part than one quarter.

Why? The more parts you cut, the smaller each part is.

Five bars of the same length. They are cut into 2, 3, 4, 5 and 8 equal parts. One part is shaded in each bar. The more parts, the smaller the shaded part.12121313131414141415151515151818181818181818
Going down, the bottom number grows and the shaded part shrinks.

So 1/8 is smaller than 1/4. And 1/4 is smaller than 1/2.

See it three ways

With things

Fold a paper into 4 equal parts. Open it. Colour one part.

As a picture

A circle cut into 4 equal parts. One part is shaded.

In symbols

1 part of 4 equal parts is 1/4.

Try it

Fold and look at one part

You need: a sheet of paper, or an old page, a pencil.

  1. Fold the paper in half. Open it. You have 2 equal parts. Look at one part.
  2. Fold it in half, then in half again. Open it. You have 4 equal parts.
  3. Fold it in half 3 times. Open it. You have 8 equal parts.
  4. Colour one part each time. Compare how big each part is.

What you will see: The more times you fold, the more parts you get. Each part is smaller. One eighth is the smallest part.

If you cannot try it, this is what happens.
Three bars of the same length. The first is cut into 2 equal parts, labelled half. The second is cut into 4 equal parts, labelled quarter. The third is cut into 8 equal parts, labelled eighth. One part is shaded in each.halfquartereighth

A wrong idea many people have

The bigger the bottom number, the bigger the part.

Why it feels right: Bigger numbers usually mean more. 8 is more than 4.

The test that breaks it: Take two breads of the same size. Cut one into 4 equal parts. Cut the other into 8. Pick one part from each. Which part is bigger?

What is true: The bottom number counts the parts. More parts means smaller parts. So 1/8 is smaller than 1/4.

Key words

bottom number
the number under the line. It tells how many equal parts the whole is cut into.
quarter
one of 4 equal parts of a whole. It is written 1/4. Also called a fourth.
third
one of 3 equal parts of a whole. It is written 1/3.
fifth
one of 5 equal parts of a whole. It is written 1/5.

Back to your guess

The answer is B: No. One eighth is a smaller part than one quarter.

The bottom number counts the equal parts. More parts means each part is smaller. So 1/8 is smaller than 1/4.

Check yourself

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

  1. Which bar has 1/4 shaded?

    Bar A is cut into 4 equal parts with one shaded. Bar B is cut into 3 equal parts with one shaded.AB
    Tap your answer.

    1. Yes, that is right. Bar A has 4 equal parts and one is shaded. That is 1/4.

    2. Not this one. Count the equal parts. Bar B has 3 parts, so one part is a third, 1/3. Try another.

    See the answer

    Bar A

    Bar A has 4 equal parts and one is shaded. That is 1/4.

    • If you chose B: Count the equal parts. Bar B has 3 parts, so one part is a third, 1/3.

  2. A bread is cut into 5 equal parts. What is one part called?

    Tap your answer.

    1. Yes, that is right. The bottom number is the number of equal parts. 5 parts gives fifths.

    2. Not this one. A fourth is one of 4 equal parts. Count again. This bread has 5. Try another.

    3. Not this one. A third is one of 3 equal parts. This bread has 5. Try another.

    See the answer

    one fifth

    The bottom number is the number of equal parts. 5 parts gives fifths.

    • If you chose B: A fourth is one of 4 equal parts. Count again. This bread has 5.
    • If you chose C: A third is one of 3 equal parts. This bread has 5.

  3. Which is the smaller part, one quarter or one eighth?

    Tap your answer.

    1. Not this one. 8 is more than 4, but that means more parts. More parts are smaller parts. Try another.

    2. Yes, that is right. Cutting a whole into 8 parts gives smaller parts than 4 parts.

    See the answer

    one eighth

    Cutting a whole into 8 parts gives smaller parts than 4 parts.

    • If you chose A: 8 is more than 4, but that means more parts. More parts are smaller parts.

  4. From an earlier chapter

    Mei cuts a flat bread into 4 pieces. The pieces are not the same size. Is one piece a quarter?

    Tap your answer.

    1. Not this one. Counting pieces is not enough. A quarter must be one of 4 equal parts. Go to M2.4.1. Try another.

    2. Yes, that is right. Quarters, halves and thirds are always equal parts. Pieces of different sizes are not.

    See the answer

    No. The parts must be equal.

    Quarters, halves and thirds are always equal parts. Pieces of different sizes are not.

    • If you chose A: Counting pieces is not enough. A quarter must be one of 4 equal parts. Go to M2.4.1.

  5. Draw a bar. Cut it into 3 equal parts. Shade one part. What is the shaded part called, and how do you write it?

    See the answer

    One third, written 1/3.

    The bar has 3 equal parts, so the bottom number is 3. You took one part, so the top is 1.

  6. Ravi cuts a bread into 5 equal parts and takes one. How does he write his part?

    Tap your answer.

    1. Not this one. The bottom number counts all 5 equal parts. It does not count the parts left over. Try another.

    2. Not this one. The top number says how many parts Ravi takes, which is 1. The bottom counts all the equal parts. Try another.

    3. Yes, that is right. The bread has 5 equal parts, so the bottom number is 5. Ravi takes 1 part, so the top is 1.

    See the answer

    1/5

    The bread has 5 equal parts, so the bottom number is 5. Ravi takes 1 part, so the top is 1.

    • If you chose A: The bottom number counts all 5 equal parts. It does not count the parts left over.
    • If you chose B: The top number says how many parts Ravi takes, which is 1. The bottom counts all the equal parts.

  7. Mei shades one part of the bar. How do you write the shaded part?

    A bar of bread cut into 4 equal parts with one part shaded. The label is a bar of bread.a bar of bread
    Tap your answer.

    1. Yes, that is right. The bar has 4 equal parts, so the bottom number is 4. One part is shaded, so the top is 1.

    2. Not this one. You counted the parts left over, which is 3. The bottom number counts all the equal parts. Try another.

    3. Not this one. You counted the lines, which is 5. Count the parts between the lines. Try another.

    See the answer

    1/4

    The bar has 4 equal parts, so the bottom number is 4. One part is shaded, so the top is 1.

    • If you chose B: You counted the parts left over, which is 3. The bottom number counts all the equal parts.
    • If you chose C: You counted the lines, which is 5. Count the parts between the lines.

  8. Three breads are the same size. Which part is smallest: 1/2, 1/4 or 1/8?

    Tap your answer.

    1. Not this one. 2 is the smallest bottom number. But fewer parts means each part is bigger. Try another.

    2. Yes, that is right. The bread cut into 8 parts has the most parts. So each part is the smallest.

    3. Not this one. Each one is 1 part. But the bottom number says how many parts. More parts means smaller parts. Try another.

    See the answer

    1/8

    The bread cut into 8 parts has the most parts. So each part is the smallest.

    • If you chose A: 2 is the smallest bottom number. But fewer parts means each part is bigger.
    • If you chose C: Each one is 1 part. But the bottom number says how many parts. More parts means smaller parts.

  9. Which bar is cut into quarters?

    Three bars, each 240 long. Bar A has 3 parts, 80, 80 and 80 long. Bar B has 4 parts, 24, 72, 72 and 72 long. Bar C has 4 parts, 60, 60, 60 and 60 long.ABC
    Tap your answer.

    1. Not this one. Bar A has 3 equal parts. That makes thirds. Count the parts, not the lines. Try another.

    2. Not this one. Bar B has 4 parts, but they are not the same size. Quarters are equal parts. Go to M2.4.1. Try another.

    3. Yes, that is right. Bar C has 4 parts of the same size. Bar B has 4 parts that are not equal.

    See the answer

    Bar C

    Bar C has 4 parts of the same size. Bar B has 4 parts that are not equal.

    • If you chose A: Bar A has 3 equal parts. That makes thirds. Count the parts, not the lines.
    • If you chose B: Bar B has 4 parts, but they are not the same size. Quarters are equal parts. Go to M2.4.1.

Keep it

Copy this into your exercise book.

The bottom number says how many equal parts. One part of 4 is 1/4. More parts means smaller parts, so 1/8 is smaller than 1/4.

Draw: Two strips of the same length. Cut one into 4 equal parts and one into 8. Shade one part in each.

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

No internet tomorrow? Save the whole book as one file (790 KB). It opens on any phone.