Chapter 2 of 7

All 7 chapters
  1. 1Tally and frequency tables, readunderstood
  2. 2Pictograms with a key, readunderstood
  3. 3Bar charts, readunderstood
  4. 4Tables with rows and columns, readunderstood
  5. 5Sorting diagrams, readunderstood
  6. 6Line graphs, readunderstood
  7. 7Your own survey, readunderstood

M2.7.2 Chapter 2

Pictograms with a key

The chart has a half circle in it. What does half a circle count?

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

  • Read a pictogram where one picture stands for 2 or 5
  • Draw a pictogram with a key, using half pictures where needed

Tariq counts the pets in his street. There are cats, dogs and hens.

A pictogram shows counts with small pictures. One picture can stand for more than one pet.

The key says what one picture is worth. Read the key first.

Draw it first

Draw a pictogram of the pets

  1. A pictogram of pets in Tariq's street with the rows cat, dog and hen. The key is each symbol = 2. The cat row has 3 circles. The dog row has 4 circles and half a circle. The hen row has 2 circles.catdogheneach= 2

    1 Write the key. One circle stands for 2 pets.

  2. A pictogram of pets in Tariq's street with the rows cat, dog and hen. The key is each symbol = 2. The cat row has 3 circles. The dog row has 4 circles and half a circle. The hen row has 2 circles.catdogheneach= 2

    2 Cats: 6 pets. 6 ÷ 2 = 3, so draw 3 circles.

  3. A pictogram of pets in Tariq's street with the rows cat, dog and hen. The key is each symbol = 2. The cat row has 3 circles. The dog row has 4 circles and half a circle. The hen row has 2 circles.catdogheneach= 2

    3 Dogs: 9 pets. Draw 4 circles for 8. Draw half a circle for 1 more.

  4. A pictogram of pets in Tariq's street with the rows cat, dog and hen. The key is each symbol = 2. The cat row has 3 circles. The dog row has 4 circles and half a circle. The hen row has 2 circles.catdogheneach= 2

    4 Hens: 4 pets. 4 ÷ 2 = 2, so draw 2 circles.

A half circle is half of the key. The key is 2, so half a circle is 1.

Worked example

How many dogs are there? The dog row has 4 circles and half a circle.

  1. Read the key. Each circle is 2.
  2. Four circles: 4 × 2 = 8.
  3. Half a circle is half of 2. That is 1.
  4. 8 + 1 = 9.

Answer: 9 dogs

The key can change. Here are two charts. Each has 3 stars.

Two pictograms with 3 stars each. The first row is Ana with the key each symbol = 2. The second row is Joseph with the key each symbol = 5.Anaeach= 2Josepheach= 5
Same 3 stars. In the top chart they are 6. In the bottom chart they are 15.

Now four friends and the books they read. Each star is 5 books.

A pictogram of books read. The rows are Amina with 3 stars, Ravi with 4 stars, Mei with 2 stars and Kofi with 5 stars. each symbol = 5AminaRaviMeiKofieach= 5
Count in fives to read a row: 5, 10, 15, 20, 25.

Worked example

How many books did Ravi read? His row has 4 stars.

  1. Read the key. Each star is 5 books.
  2. Count in fives, one for each star: 5, 10, 15, 20.
  3. Ravi read 20 books.

Answer: 20 books

See it three ways

With things

Put 9 beans in a line. Make pairs. Each pair is one circle. One bean has no partner.

As a picture

Nine beans in a row. Under them is a pictogram row labelled beans, with 4 circles and half a circle. The key is each symbol = 2.beanseach= 2

In symbols

9 = 2 + 2 + 2 + 2 + 1. That is 4 circles and half a circle.

Try it

Draw a pictogram of things in your home

You need: things to count in your home, such as cups, plates and spoons, a pencil and paper.

  1. Count your cups, your plates and your spoons. Write each number.
  2. Choose a key. Let one circle stand for 2.
  3. Draw one circle for every 2. If one is left over, draw half a circle.
  4. Write the key under your chart.

What you will see: An odd number ends with a half circle. Count your circles in twos, then add 1 for the half. You get your number back.

If you cannot try it, this is what happens.
A pictogram of things in a home. The rows are cups with 3 circles, plates with 4 circles and spoons with 2 circles and half a circle. each symbol = 2cupsplatesspoonseach= 2

A wrong idea many people have

Every picture in a pictogram stands for 1.

Why it feels right: You count one picture as one thing when you count objects.

The test that breaks it: A row has 3 circles. The key says each circle is 2. Put out 6 beans. Make pairs. You get 3 pairs, so 3 circles. The row is 6, not 3.

What is true: Read the key. Each picture is worth the number in the key.

Key words

pictogram
a chart that uses small pictures to show counts.
key
the note that says what one picture is worth.

Back to your guess

The answer is A: It counts 1, because each whole circle is 2.

The key says what one whole picture is worth. Here it is 2. A half picture is half of that, so it is 1.

Check yourself

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

  1. Seeds were planted and some sprouted. How many maize seeds sprouted?

    A pictogram of seeds that sprouted. The rows are bean, maize and pea. The key is each symbol = 2.beanmaizepeaeach= 2
    See the answer

    5

    Maize has 2 whole squares and half a square. 2 × 2 = 4. Half of 2 is 1. 4 + 1 = 5.

  2. Each star is 5 books. How many books did Ana read?

    A pictogram with one row, Ana, with 4 stars. each symbol = 5Anaeach= 5
    Tap your answer.

    1. Not this one. You counted the stars. Read the key: each star is 5, not 1. Try another.

    2. Yes, that is right. Four stars, each worth 5. Count in fives: 5, 10, 15, 20.

    3. Not this one. You added 4 and 5. Each star is worth 5, so multiply. 4 × 5 = 20. Try another.

    See the answer

    20

    Four stars, each worth 5. Count in fives: 5, 10, 15, 20.

    • If you chose A: You counted the stars. Read the key: each star is 5, not 1.
    • If you chose C: You added 4 and 5. Each star is worth 5, so multiply. 4 × 5 = 20.

  3. How many more books did Kofi read than Mei?

    A pictogram of books read. The rows are Amina with 3 stars, Ravi with 4 stars, Mei with 2 stars and Kofi with 5 stars. each symbol = 5AminaRaviMeiKofieach= 5
    See the answer

    15

    Kofi has 5 stars, which is 25. Mei has 2 stars, which is 10. 25 − 10 = 15.

  4. Each circle is 10. A row has 3 circles and half a circle. How many is that?

    A pictogram with one row, Joseph, with 3 circles and half a circle. each symbol = 10Josepheach= 10
    See the answer

    35

    Three circles: 3 × 10 = 30. Half of 10 is 5. 30 + 5 = 35.

  5. Draw a pictogram with a key of 2. Bananas 8, oranges 6, mangoes 5. How many circles in each row?

    See the answer

    Bananas: 4 circles. Oranges: 3 circles. Mangoes: 2 circles and half a circle.

    Divide each count by 2. 8 ÷ 2 = 4 and 6 ÷ 2 = 3. For 5, 2 circles make 4. Draw half a circle for the 1 left.

  6. From an earlier chapter

    The tally for banana is 3 gates and 4 strokes. What is the frequency?

    See the answer

    19

    Count the gates in fives: 5, 10, 15. Then add the 4 strokes. 15 + 4 = 19.

  7. How many cups does Hana have?

    A pictogram of cups. Hana has 3 squares and half a square. Diego has 2 squares. each symbol = 2HanaDiegoeach= 2
    Tap your answer.

    1. Yes, that is right. Hana has 3 whole squares and a half square. 3 × 2 = 6, and half of 2 is 1. 6 + 1 = 7.

    2. Not this one. You counted each picture as 1. Each square is worth 2. Half a square is worth 1. Try another.

    3. Not this one. You counted the half square as a whole one. Half a square is half of 2, which is 1. Try another.

    See the answer

    7

    Hana has 3 whole squares and a half square. 3 × 2 = 6, and half of 2 is 1. 6 + 1 = 7.

    • If you chose B: You counted each picture as 1. Each square is worth 2. Half a square is worth 1.
    • If you chose C: You counted the half square as a whole one. Half a square is half of 2, which is 1.

  8. Sipho has 11 stones. Each circle is 2 stones. What should his row show?

    A pictogram with one row, Sipho, with no symbols yet. each symbol = 2Siphoeach= 2
    Tap your answer.

    1. Yes, that is right. 11 ÷ 2 is 5, with 1 left over. Draw 5 circles for 10 stones. Add half a circle for the 1 left.

    2. Not this one. 6 circles show 12 stones, and Sipho has 11. The last symbol is only half a circle. Try another.

    3. Not this one. That counts each circle as 1 stone. Each circle is 2 stones, so you need fewer circles. Try another.

    4. Not this one. 5 circles show 10 stones. One stone is left over, so add half a circle. Try another.

    See the answer

    5 circles and half a circle

    11 ÷ 2 is 5, with 1 left over. Draw 5 circles for 10 stones. Add half a circle for the 1 left.

    • If you chose B: 6 circles show 12 stones, and Sipho has 11. The last symbol is only half a circle.
    • If you chose C: That counts each circle as 1 stone. Each circle is 2 stones, so you need fewer circles.
    • If you chose D: 5 circles show 10 stones. One stone is left over, so add half a circle.

  9. Leila and Diego collected shells. Who has more shells?

    Two pictograms of shells. The first row is Leila, with the key each symbol = 2. The second row is Diego, with the key each symbol = 5.Leilaeach= 2Diegoeach= 5
    Tap your answer.

    1. Not this one. You can tell. Use each key. 4 × 2 = 8 for Leila, and 3 × 5 = 15 for Diego. Try another.

    2. Not this one. You counted the symbols. Their worth is different in each chart, so read each key first. Try another.

    3. Yes, that is right. Leila has 4 symbols of 2. 4 × 2 = 8. Diego has 3 symbols of 5. 3 × 5 = 15. 15 is more than 8.

    See the answer

    Diego has more.

    Leila has 4 symbols of 2. 4 × 2 = 8. Diego has 3 symbols of 5. 3 × 5 = 15. 15 is more than 8.

    • If you chose A: You can tell. Use each key. 4 × 2 = 8 for Leila, and 3 × 5 = 15 for Diego.
    • If you chose B: You counted the symbols. Their worth is different in each chart, so read each key first.

  10. Tariq counted his stones. His row has 2 squares and a half square. What is the half square worth?

    A pictogram with one row, Tariq, with 2 whole squares and a half square. each symbol = 10Tariqeach= 10
    Tap your answer.

    1. Not this one. That is a whole square. A half square is half of the key. Try another.

    2. Yes, that is right. A half square is half of the key. Half of 10 is 5.

    3. Not this one. Half a symbol is 1 only when the key is 2. Here the key is 10, so find half of 10. Try another.

    See the answer

    5

    A half square is half of the key. Half of 10 is 5.

    • If you chose A: That is a whole square. A half square is half of the key.
    • If you chose C: Half a symbol is 1 only when the key is 2. Here the key is 10, so find half of 10.

Keep it

Copy this into your exercise book.

Read the key first. It says what one picture is worth. Count the pictures, then multiply by the key. A half picture is half the key.

Draw: A pictogram with three rows and a key of 2. Add one half circle.

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 (828 KB). It opens on any phone.