Chapter 1 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

M2.7.1 Chapter 1

Tally and frequency tables

My friends all shout their answers at once. How do I keep 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

  • Record data in a tally and frequency table
  • Find totals and differences from a frequency table

Amina asks 20 friends which fruit they like best. The answers come fast.

She draws a mark for each answer. A mark you draw to count is a tally.

Four strokes go down. The fifth stroke crosses them. That is one gate of five.

Draw it first

Tally the favourite fruit

  1. A tally chart with the headings Fruit, Tally and Frequency. mango has 8 strokes, banana 5, orange 4 and apple 3. The frequency column shows 8, 5, 4 and 3.Fruitmangobananaorangeapple

    1 Write the fruits down the page. Leave room for the marks.

  2. A tally chart with the headings Fruit, Tally and Frequency. mango has 8 strokes, banana 5, orange 4 and apple 3. The frequency column shows 8, 5, 4 and 3.FruitTallymangobananaorangeapple

    2 Draw one stroke for each answer. Make every fifth stroke cross four.

  3. A tally chart with the headings Fruit, Tally and Frequency. mango has 8 strokes, banana 5, orange 4 and apple 3. The frequency column shows 8, 5, 4 and 3.FruitTallyFrequencymango8banana5orange4apple3

    3 Count each row. Write the number in the frequency column.

The number of times something happens is its frequency. Mango has a frequency of 8.

Count a tally in fives. Count the gates first, then the single strokes.

Four tallies, each with its number. 4 is four strokes. 5 is one gate. 8 is one gate and three strokes. 13 is two gates and three strokes.45813
Each gate is 5. The strokes after the last gate are single ones.

Here is a longer tally. Count it in fives.

A tally made of three full gates of five and two single strokes.

Worked example

How many are in this tally? It has 3 gates and 2 strokes.

  1. Count the gates in fives: 5, 10, 15.
  2. Now count the strokes: 16, 17.
  3. The tally is 17.

Answer: 17

A table with a frequency for each thing is a frequency table. Add the frequencies to get the total.

A frequency table with the headings Fruit and Frequency. mango 8, banana 5, orange 4, apple 3. Total 20.FruitFrequencymango8banana5orange4apple3Total20
The total is the number of friends Amina asked.

Worked example

How many friends did Amina ask?

  1. Add all the frequencies.
  2. 8 + 5 + 4 + 3 = 20.
  3. She asked 20 friends.

Answer: 20 friends

Worked example

How many more friends chose mango than orange?

  1. Find the two frequencies. Mango is 8. Orange is 4.
  2. Take the smaller from the bigger. 8 − 4 = 4.

Answer: 4 more friends

See it three ways

With things

Put out 7 beans, one for each answer. Lay them in a line.

As a picture

Seven beans in a row, with a tally of 7 under them. The tally is one gate and two strokes.

In symbols

One gate is 5. Two more strokes make 7. 5 + 2 = 7. The frequency is 7.

Try it

Tally the vowels in a line of writing

You need: a line of writing from a book or a sign, a pencil and paper.

  1. Write a, e, i, o and u down the page. Leave room beside each.
  2. Go along your line. For each vowel, draw a stroke in its row.
  3. Cross the fifth stroke in a row. Then start a new gate.
  4. Write the frequency at the end of each row.

What you will see: The five frequencies add up to all the vowels in your line. Count the vowels again to check.

If you cannot try it, this is what happens.
A tally for the line Ravi and Joseph carry water to the house. a has 4, e has 4, i has 1, o has 3 and u has 1. The line gives total 13.Ravi and Joseph carrywater to the housea4e4i1o3u1total 13

A wrong idea many people have

The crossing stroke does not count. A gate is only 4.

Why it feels right: The cross comes last. It looks like a line that ties the strokes.

The test that breaks it: Tally five friends, one stroke for each. After four friends there are four strokes. The fifth friend still needs a mark. That mark is the cross.

What is true: The crossing stroke is the fifth answer. A gate is 5.

Key words

tally
a mark you draw to count one thing. Every fifth mark crosses four.
frequency
the number of times something happens.
total
all the numbers added together.

Back to your guess

The answer is B: Draw a stroke for each answer, and cross every fifth stroke.

Draw one stroke for each answer. Cross the fifth stroke, so each gate is 5. Groups of five are quick to count and hard to get wrong.

Check yourself

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

  1. Count the tally. How many is it?

    A tally made of full gates of five and a few single strokes.
    See the answer

    13

    There are 2 gates. 5, 10. Then 3 single strokes. 11, 12, 13.

  2. Which tally shows 6?

    Three tallies labelled A, B and C. Each is made of gates of five and single strokes.ABC
    Tap your answer.

    1. Not this one. A is one gate. A gate is 5. The cross is the fifth stroke, not a sixth. Try another.

    2. Yes, that is right. B is one gate and one single stroke. 5 + 1 = 6.

    3. Not this one. C is a gate and two strokes. That is 5 + 2 = 7. Try another.

    See the answer

    Tally B

    B is one gate and one single stroke. 5 + 1 = 6.

    • If you chose A: A is one gate. A gate is 5. The cross is the fifth stroke, not a sixth.
    • If you chose C: C is a gate and two strokes. That is 5 + 2 = 7.

  3. Tariq saw these animals on a walk. How many animals did he see in all?

    A table with the headings Animal and Seen. hen 9, goat 6, dog 4, cat 3.AnimalSeenhen9goat6dog4cat3
    See the answer

    22

    Add all the frequencies. 9 + 6 + 4 + 3 = 22.

  4. How many more hens than dogs did Tariq see?

    A table with the headings Animal and Seen. hen 9, goat 6, dog 4, cat 3.AnimalSeenhen9goat6dog4cat3
    See the answer

    5

    Hens are 9 and dogs are 4. Take 4 from 9. 9 − 4 = 5.

  5. Ten friends choose a colour. First five: red, blue, red, red, green. Next five: blue, red, green, red, blue. Make a frequency table.

    See the answer

    red 5, blue 3, green 2. The total is 10.

    Count each colour. Red comes 5 times, blue 3 times and green 2 times. 5 + 3 + 2 = 10, the number of friends.

  6. Priya made a tally of the birds she saw. How many birds is that?

    A tally made of 3 full gates of five and 1 single stroke.
    Tap your answer.

    1. Not this one. You may have counted each gate as 4. The cross is the fifth stroke, so a gate is 5. Try another.

    2. Not this one. You may have counted each gate as 1. A gate holds 5 strokes, so count in fives. Try another.

    3. Yes, that is right. There are 3 gates. Count in fives: 5, 10, 15. One more stroke makes 16.

    See the answer

    16

    There are 3 gates. Count in fives: 5, 10, 15. One more stroke makes 16.

    • If you chose A: You may have counted each gate as 4. The cross is the fifth stroke, so a gate is 5.
    • If you chose B: You may have counted each gate as 1. A gate holds 5 strokes, so count in fives.

  7. Yusuf asked friends which sport they like best. How many friends did he ask?

    A frequency table with the headings Sport and Frequency. football 7, running 5, swimming 3.SportFrequencyfootball7running5swimming3
    Tap your answer.

    1. Yes, that is right. Add all the frequencies. 7 + 5 + 3 = 15. Each friend gave one answer.

    2. Not this one. That is the biggest frequency, for football. To find all the friends, add every frequency. Try another.

    3. Not this one. That counts the rows. Each friend made one answer, so add the frequencies. Try another.

    See the answer

    15

    Add all the frequencies. 7 + 5 + 3 = 15. Each friend gave one answer.

    • If you chose B: That is the biggest frequency, for football. To find all the friends, add every frequency.
    • If you chose C: That counts the rows. Each friend made one answer, so add the frequencies.

  8. Joseph tallies how friends get to school. He has 4 strokes for bus. Another friend says bus. What does he draw?

    A tally with the label bus and four straight strokes.bus
    Tap your answer.

    1. Not this one. That friend would not be counted. The cross is the fifth stroke, so a gate is 5. Try another.

    2. Yes, that is right. The fifth stroke crosses the four. Now the gate shows 5 friends, and it is quick to count.

    3. Not this one. Single strokes are slow to count. Cross the four, so the gate shows 5 at a glance. Try another.

    See the answer

    A fifth stroke across the four.

    The fifth stroke crosses the four. Now the gate shows 5 friends, and it is quick to count.

    • If you chose A: That friend would not be counted. The cross is the fifth stroke, so a gate is 5.
    • If you chose C: Single strokes are slow to count. Cross the four, so the gate shows 5 at a glance.

  9. Hana asked 20 friends which pet they like best. The total is 20. How many friends chose bird?

    A frequency table with the headings Pet and Frequency. cat 9, dog 6, fish 2, bird has no number yet. Total 20.PetFrequencycat9dog6fish2birdTotal20
    Tap your answer.

    1. Not this one. That is the total for all four pets. Bird is only one row of the table. Try another.

    2. Not this one. 17 is what cat, dog and fish make together: 9 + 6 + 2. Bird is what is left of 20. Try another.

    3. Yes, that is right. Cat, dog and fish make 9 + 6 + 2 = 17. The total is 20. 20 − 17 = 3 chose bird.

    See the answer

    3

    Cat, dog and fish make 9 + 6 + 2 = 17. The total is 20. 20 − 17 = 3 chose bird.

    • If you chose A: That is the total for all four pets. Bird is only one row of the table.
    • If you chose B: 17 is what cat, dog and fish make together: 9 + 6 + 2. Bird is what is left of 20.

Keep it

Copy this into your exercise book.

Draw one stroke for each answer. Cross the fifth stroke. The number in each row is its frequency. Add the frequencies to get the total.

Draw: A tally chart with three rows. Write the frequency for each row, and the total.

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.