Chapter 4 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

M2.7.4 Chapter 4

Tables with rows and columns

The bus timetable is full of numbers. How do I find the one I need?

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 table with rows and columns
  • Fill in a two way table from a list
  • Read a bus timetable and find how long a trip takes

A table packs many facts into a small space. Here are 8 children.

Each child lives in East or West. Each child walks or takes the bus.

A list of 8 children with the headings Name, Village and Way. Amina East walk, Ravi West bus, Mei East walk, Kofi West walk, Ana East bus, Tariq West bus, Joseph East bus, Lucía West bus.NameVillageWayAminaEastwalkRaviWestbusMeiEastwalkKofiWestwalkAnaEastbusTariqWestbusJosephEastbusLucíaWestbus
A list. We want to know how many children are in each group.

A row goes across the page. A column goes down the page.

A two way table sorts each child two ways at once. Here it is village and way.

Each child goes in one cell only. A cell is where a row and a column meet.

Draw it first

Fill in a two way table

  1. A two way table with the headings Way, East, West and Total. The rows are walk, bus and Total. walk has 2 for East, 1 for West and 3 in total. bus has 2 for East, 3 for West and 5 in total. The last row has 4, 4 and 8.WayEastWestTotalwalkbusTotal

    1 Draw the table. The rows are the ways. The columns are the villages.

  2. A two way table with the headings Way, East, West and Total. The rows are walk, bus and Total. walk has 2 for East, 1 for West and 3 in total. bus has 2 for East, 3 for West and 5 in total. The last row has 4, 4 and 8.WayEastWestTotalwalk21busTotal

    2 Go down the list. Put each child in one cell. Walkers: 2 from East, 1 from West.

  3. A two way table with the headings Way, East, West and Total. The rows are walk, bus and Total. walk has 2 for East, 1 for West and 3 in total. bus has 2 for East, 3 for West and 5 in total. The last row has 4, 4 and 8.WayEastWestTotalwalk21bus23Total

    3 Now the bus riders: 2 from East and 3 from West.

  4. A two way table with the headings Way, East, West and Total. The rows are walk, bus and Total. walk has 2 for East, 1 for West and 3 in total. bus has 2 for East, 3 for West and 5 in total. The last row has 4, 4 and 8.WayEastWestTotalwalk213bus235Total448

    4 Add each row and each column. The corner total is 8, the number of children.

To read a table, find the row. Then find the column. Read the cell where they meet.

A two way table with the headings Way, East, West and Total. The rows are walk, bus and Total. walk has 2 for East, 1 for West and 3 in total. bus has 2 for East, 3 for West and 5 in total. The last row has 4, 4 and 8.WayEastWestTotalwalk213bus235Total448
The shaded cell is in the bus row and the West column. 3 West children take the bus.

Worked example

How many West children walk?

  1. Find the row for walk.
  2. Find the column for West.
  3. They meet at 1.

Answer: 1 child

Worked example

How many children take the bus?

  1. Look at the bus row.
  2. 2 from East and 3 from West.
  3. 2 + 3 = 5. The total column says 5 too.

Answer: 5 children

A timetable is a table of times. Each row is a stop. Each column is a bus.

It uses 24 hour time. 09:45 is 45 minutes past 9 in the morning.

The hours go on after noon. 13:10 is 10 past 1 in the afternoon.

A bus timetable with the headings Stop, Bus 1, Bus 2 and Bus 3. Market 08:45, 09:45, 13:10. School 09:20, 10:20, 13:45. Clinic 09:40, 10:40, 14:05. River 10:05, 11:05, 14:30.StopBus 1Bus 2Bus 3Market08:4509:4513:10School09:2010:2013:45Clinic09:4010:4014:05River10:0511:0514:30
Read down a column to follow one bus. Read along a row to see one stop.

Bus 2 leaves Market at 09:45. It reaches School at 10:20.

Two clock faces. The first shows 09:45. The second shows 10:20.12345678910111209:4512345678910111210:20
The start and the end of the trip.

Minutes stop at 60. Count to the next hour first. Then count on.

Worked example

Bus 2 leaves Market at 09:45 and reaches School at 10:20. How long is the trip?

  1. 09:45 to 10:00 is 15 minutes.
  2. 10:00 to 10:20 is 20 minutes.
  3. 15 + 20 = 35.

Answer: 35 minutes

See it three ways

With things

Put out 35 beans, one for each minute. Move 15 to one side. They are the minutes up to 10:00. The other 20 come after it.

As a picture

Thirty five beans in rows of 10. The first 15 are filled in. They are the minutes from 09:45 to 10:00. The other 20 are the minutes from 10:00 to 10:20.

In symbols

15 + 20 = 35. The trip takes 35 minutes.

Try it

Make a two way table with beans and stones

You need: about 12 beans and stones, some big and some small, a pencil and paper.

  1. Gather the beans and stones. Count them.
  2. Draw a table. The rows are beans and stones. The columns are big and small.
  3. Sort the things. Put each one in one cell. Write the counts.
  4. Add each row and each column. Add the totals in the corner.

What you will see: The corner total is the number of things you began with. Each thing sits in one cell only.

If you cannot try it, this is what happens.
A two way table with the headings Kind, Big, Small and Total. beans 3, 4, 7. stones 2, 3, 5. Total 5, 7, 12.KindBigSmallTotalbeans347stones235Total5712

A wrong idea many people have

A child who walks and lives in East goes in two cells.

Why it feels right: The child has two facts, so you may write the child twice.

The test that breaks it: Count the children on the list. There are 8. Add up all the cells in your table. A sum above 8 means a child went in two cells.

What is true: Each child makes one mark, in one cell. The cells add up to the number of children.

Key words

row
a line of cells going across a table.
column
a line of cells going down a table.
timetable
a table of times.

Back to your guess

The answer is B: Find the row and the column. Read the cell where they meet.

Every cell sits in one row and one column. Find both, then read the cell where they meet.

Check yourself

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

  1. What time does Bus 2 reach Clinic?

    A bus timetable with the headings Stop, Bus 1, Bus 2 and Bus 3. Market 08:45, 09:45, 13:10. School 09:20, 10:20, 13:45. Clinic 09:40, 10:40, 14:05. River 10:05, 11:05, 14:30.StopBus 1Bus 2Bus 3Market08:4509:4513:10School09:2010:2013:45Clinic09:4010:4014:05River10:0511:0514:30
    See the answer

    10:40

    Find the Clinic row. Find the Bus 2 column. They meet at 10:40.

  2. Bus 1 leaves School at 09:20 and reaches River at 10:05. How long is the trip?

    Two clock faces. The first shows 09:20. The second shows 10:05.12345678910111209:2012345678910111210:05
    Tap your answer.

    1. Yes, that is right. 09:20 to 10:00 is 40 minutes. 10:00 to 10:05 is 5 minutes. 40 + 5 = 45.

    2. Not this one. You took 05 from 20. Minutes stop at 60. Count to the hour first: 09:20 to 10:00, then on. Try another.

    3. Not this one. You took 0920 from 1005 as plain numbers. An hour has 60 minutes, not 100. Try another.

    See the answer

    45 minutes

    09:20 to 10:00 is 40 minutes. 10:00 to 10:05 is 5 minutes. 40 + 5 = 45.

    • If you chose B: You took 05 from 20. Minutes stop at 60. Count to the hour first: 09:20 to 10:00, then on.
    • If you chose C: You took 0920 from 1005 as plain numbers. An hour has 60 minutes, not 100.

  3. Bus 3 leaves Market at 13:10. It reaches Clinic at 14:05. How long is the trip?

    See the answer

    55 minutes

    13:10 to 14:00 is 50 minutes. 14:00 to 14:05 is 5 minutes. 50 + 5 = 55.

  4. Fill in a two way table for these 7 pets. The rows are cat and dog. The columns are black and white.

    A list of 7 pets with the headings Pet and Colour. cat black, dog white, cat white, dog black, dog white, cat white, dog white.PetColourcatblackdogwhitecatwhitedogblackdogwhitecatwhitedogwhite
    See the answer

    cat: 1 black, 2 white. dog: 1 black, 3 white. The total is 7.

    Put each pet in one cell. Count each cell. 1 + 2 + 1 + 3 = 7, the number of pets.

  5. A table for 8 children has cells that add up to 11. What went wrong?

    Tap your answer.

    1. Yes, that is right. The cells should add up to 8. A sum of 11 means 3 extra marks, from children counted twice.

    2. Not this one. Missing children would make the sum smaller than 8, not bigger. Try another.

    3. Not this one. More rows do not fix the sum. Each child goes in one cell only. Try another.

    See the answer

    Some children went in two cells.

    The cells should add up to 8. A sum of 11 means 3 extra marks, from children counted twice.

    • If you chose B: Missing children would make the sum smaller than 8, not bigger.
    • If you chose C: More rows do not fix the sum. Each child goes in one cell only.

  6. From an earlier chapter

    This chart is for a big school. It shows children who walk. How many more walk from East than from West?

    A bar chart of children who walk, with the label walkers. The bars are East and West. East reaches 15 and West reaches 5.05101520EastWestwalkers
    See the answer

    10

    East reaches 15. West reaches 5. 15 − 5 = 10.

  7. What time does Bus 3 reach School?

    A bus timetable with the headings Stop, Bus 1, Bus 2 and Bus 3. School 09:20, 10:20, 13:45. Clinic 09:40, 10:40, 14:05.StopBus 1Bus 2Bus 3School09:2010:2013:45Clinic09:4010:4014:05
    Tap your answer.

    1. Not this one. That is the School row, but the Bus 1 column. Bus 3 is the last column. Try another.

    2. Not this one. That is the Bus 3 column, but the Clinic row. Find the School row. Try another.

    3. Yes, that is right. Find the School row. Find the Bus 3 column. They meet at 13:45.

    See the answer

    13:45

    Find the School row. Find the Bus 3 column. They meet at 13:45.

    • If you chose A: That is the School row, but the Bus 1 column. Bus 3 is the last column.
    • If you chose B: That is the Bus 3 column, but the Clinic row. Find the School row.

  8. What does the shaded box count?

    A two way table with the headings Way, East and West. walk has 2 for East and 1 for West. bus has 2 for East and 3 for West. One box is shaded.WayEastWestwalk21bus23
    Tap your answer.

    1. Not this one. That is the bus row. The shaded box is in the walk row. Try another.

    2. Yes, that is right. The shaded box is in the walk row and the East column. It counts children who walk and live in East.

    3. Not this one. That is the West column. The shaded box is in the East column. Try another.

    See the answer

    Children who walk and live in East.

    The shaded box is in the walk row and the East column. It counts children who walk and live in East.

    • If you chose A: That is the bus row. The shaded box is in the walk row.
    • If you chose C: That is the West column. The shaded box is in the East column.

  9. A child lives in West and takes the bus. Which box does the child go in?

    Tap your answer.

    1. Not this one. Each child makes one mark, in one box. The bus row and the West column meet in a single box. Try another.

    2. Not this one. That box is for bus riders from East. This child lives in West. Try another.

    3. Yes, that is right. The way is bus, so use the bus row. The village is West, so use the West column. Mark the box where they meet.

    See the answer

    The box where the bus row meets the West column.

    The way is bus, so use the bus row. The village is West, so use the West column. Mark the box where they meet.

    • If you chose A: Each child makes one mark, in one box. The bus row and the West column meet in a single box.
    • If you chose B: That box is for bus riders from East. This child lives in West.

Keep it

Copy this into your exercise book.

Read a table by its row and its column. The answer is in the cell where they meet. Each count goes in one cell. For a trip, count to the next hour, then on.

Draw: A two way table with 2 rows and 2 columns. Add the totals.

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.