Chapter 6 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

M2.7.6 Chapter 6

Line graphs

I measured my plant every day. How do I show it growing?

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 values from a line graph that shows change over time
  • Draw a line graph of a seedling's height each day

Amina grows a bean plant. Each day she measures it. She writes the height in cm.

After seven days she has seven numbers. A list of numbers is hard to see.

A line graph shows change over time in one look. It has a point for each day. A line joins the points in order.

The line along the bottom is an axis. So is the line up the side.

Draw it first

Draw Amina's line graph

  1. Step 1 shows a table with the heads day and height in cm. The heights are 2, 4, 5, 8, 10, 11, 12 for days 1, 2, 3, 4, 5, 6 and 7. Step 2 shows a line graph with the labels day and height in cm, and points for days 1, 2 and 3. Step 3 shows the whole graph for days 1, 2, 3, 4, 5, 6 and 7, with the points joined by straight lines.dayheight in cm12243548510611712

    1 Write the day and the height in a table.

  2. Step 1 shows a table with the heads day and height in cm. The heights are 2, 4, 5, 8, 10, 11, 12 for days 1, 2, 3, 4, 5, 6 and 7. Step 2 shows a line graph with the labels day and height in cm, and points for days 1, 2 and 3. Step 3 shows the whole graph for days 1, 2, 3, 4, 5, 6 and 7, with the points joined by straight lines.024681012123dayheight in cm

    2 Draw the two axes. Mark a point for days 1, 2 and 3. Join them with a ruler.

  3. Step 1 shows a table with the heads day and height in cm. The heights are 2, 4, 5, 8, 10, 11, 12 for days 1, 2, 3, 4, 5, 6 and 7. Step 2 shows a line graph with the labels day and height in cm, and points for days 1, 2 and 3. Step 3 shows the whole graph for days 1, 2, 3, 4, 5, 6 and 7, with the points joined by straight lines.0246810121234567dayheight in cm

    3 Mark every day. Join the points in order. The line shows the plant growing.

Here is the finished graph. Let us read it.

A line graph of Amina's bean plant. The labels are day and height in cm. The points for days 1, 2, 3, 4, 5, 6 and 7 are at 2, 4, 5, 8, 10, 11, 12 cm, joined by straight lines.0246810121234567dayheight in cm
Each point is one measurement. The line climbs as the plant grows.

To read day 4, find 4 along the bottom. Go up to the point. Then look across to the side.

Worked example

How tall was the plant on day 4?

  1. Find 4 along the bottom.
  2. Go up to the point above 4.
  3. Look across to the side. The point is at 8.

Answer: 8 cm

Now find the day the line climbs the most. It is the steepest part of the line.

Worked example

How much did the plant grow from day 3 to day 4?

  1. Read day 3. It is 5 cm.
  2. Read day 4. It is 8 cm.
  3. Take away. 8 − 5 = 3.
  4. No other day grows 3 cm. This is the steepest part.

Answer: 3 cm

Amina did not measure between the days. How tall was the plant halfway between day 4 and day 5? The line can tell you.

A point is a real measurement. The line between two points is an estimate. An estimate is a good guess, close to the real answer.

Worked example

How tall was the plant halfway between day 4 and day 5?

  1. Day 4 is 8 cm. Day 5 is 10 cm.
  2. Find the middle of the line between the two points.
  3. The middle is halfway between 8 and 10. It is 9.

Answer: About 9 cm. This is an estimate.

The plant may not grow in a straight line. So 9 cm is not a measurement. It is a good guess.

See it three ways

With things

Cut a paper strip as tall as the plant each day. Stand the strips side by side.

As a picture

A bar chart of the plant. The label says height in cm, days 1 to 7. The bars are labelled 1, 2, 3, 4, 5, 6 and 7 and are 2, 4, 5, 8, 10, 11 and 12 cm tall.0246810121234567height in cm, days 1 to 7

In symbols

Day 1 is 2 cm. Day 7 is 12 cm. 12 − 2 = 10. In 6 days the plant grew 10 cm.

Bars show each day on its own. A line graph joins the days. You see the change from one day to the next.

Try it

Grow a seed and graph it

You need: a bean or maize seed, or any plant near you, a cup, a cloth and water, a ruler, or a paper strip marked in cm, paper and a pencil.

Be safe: Do not eat the seed or the shoot. Wash your hands afterwards.

  1. Put the seed on a damp cloth in a cup. Keep the cloth damp.
  2. Each day, measure the shoot. Use a ruler or a paper strip.
  3. Write the day and the height in cm. Do this for six days.
  4. Draw two axes. Put the days along the bottom and cm up the side.
  5. Mark a point for each day. Join the points in order with a ruler.

What you will see: The line climbs. The steeper the line, the faster the shoot grew that day.

If you cannot try it, this is what happens.
A line graph of a maize shoot. The labels are day and height in cm. The points for days 1, 2, 3, 4, 5 and 6 are at 0, 1, 3, 6, 8, 10 cm, joined by straight lines. The line climbs.0246810123456dayheight in cm

Here is a line graph of favourite fruits. It looks neat. But it is wrong.

A wrong line graph. The labels are fruit and votes. The points for mango, guava, lime and plum are joined by a line that goes down and then up. The fruits are not in any order.0246810mangoguavalimeplumfruitvotes
Do not draw this. A line between two fruits means nothing.

A wrong idea many people have

Any chart can have a line joining its points.

Why it feels right: A line looks neat. Many graphs in books have lines.

The test that breaks it: Write the four fruits in a new order. Draw the line again. The votes are the same, but the line has a new shape. Days cannot swap like that. Day 3 always comes after day 2.

What is true: Join points only when they go in an order, such as days. For fruits, use a bar chart.

Key words

line graph
a graph that joins points in order to show change over time.
axis
a line along the bottom or up the side of a graph.
estimate
a good guess that is close to the real answer.

Back to your guess

The answer is B: Put a point for each day and join them in order.

A line graph shows change over time. The points go in order of day. The line shows the plant growing.

Check yourself

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

  1. Use Amina's graph. How tall was the plant on day 6?

    A line graph of Amina's bean plant. The labels are day and height in cm. The points for days 1, 2, 3, 4, 5, 6 and 7 are at 2, 4, 5, 8, 10, 11, 12 cm, joined by straight lines.0246810121234567dayheight in cm
    See the answer

    11 cm

    Find 6 along the bottom. Go up to the point. Look across to the side. It is at 11.

  2. Use Amina's graph. How much did the plant grow from day 1 to day 7?

    See the answer

    10 cm

    Day 7 is 12 cm. Day 1 is 2 cm. 12 − 2 = 10.

  3. Which one needs a line graph?

    Tap your answer.

    1. Not this one. This counts choices. No time passes. A bar chart fits better. Go to M2.7.3. Try another.

    2. Yes, that is right. The water changes as the hours pass. A line graph shows change over time.

    3. Not this one. These are kinds, not times. Tally them and use a bar chart. Go to M2.7.3. Try another.

    See the answer

    The depth of water in a rain bucket each hour

    The water changes as the hours pass. A line graph shows change over time.

    • If you chose A: This counts choices. No time passes. A bar chart fits better. Go to M2.7.3.
    • If you chose C: These are kinds, not times. Tally them and use a bar chart. Go to M2.7.3.

  4. Use Amina's graph. Estimate the plant's height halfway between day 1 and day 2.

    See the answer

    About 3 cm

    Day 1 is 2 cm. Day 2 is 4 cm. Halfway between 2 and 4 is 3. It is an estimate.

  5. Kofi measures the water in a rain bucket each hour. After hour 1 it is 2 cm. After hour 2 it is 4 cm. After hour 3 it is 7 cm. After hour 4 it is 8 cm. Draw a line graph. How much did the water rise from hour 2 to hour 3?

    See the answer

    3 cm. Mark 2, 4, 7 and 8 over hours 1 to 4. Join the points.

    After hour 2 it is 4 cm. After hour 3 it is 7 cm. 7 − 4 = 3.

  6. From an earlier chapter

    Use the bar chart. How many more children chose mango than lime?

    A bar chart of favourite fruit. The bars are mango, guava, lime and plum. Mango has 15 votes. Guava has 10. Lime has 5. Plum has 20.05101520mangoguavalimeplumvotes
    See the answer

    10

    Mango has 15. Lime has 5. 15 − 5 = 10.

  7. Kofi measures rain in a bucket. How deep is the water after hour 5?

    A line graph of rain in a bucket. The labels are hour and depth in cm. The points for hours 1, 2, 3, 4, 5 and 6 are at 2, 4, 6, 6, 10, 12 cm, joined by straight lines.024681012123456hourdepth in cm
    Tap your answer.

    1. Yes, that is right. Find 5 along the bottom. Go up to the point. Look across to the side. It is at 10.

    2. Not this one. That is the hour. Go up from 5 to the point. Then read the side. Try another.

    3. Not this one. That is the point for hour 6, the last one. Hour 5 is one point before it. Try another.

    See the answer

    10 cm

    Find 5 along the bottom. Go up to the point. Look across to the side. It is at 10.

    • If you chose B: That is the hour. Go up from 5 to the point. Then read the side.
    • If you chose C: That is the point for hour 6, the last one. Hour 5 is one point before it.

  8. Use the same graph. About how deep is the water halfway between hours 4 and 5?

    A line graph of rain in a bucket. The labels are hour and depth in cm. The points for hours 1, 2, 3, 4, 5 and 6 are at 2, 4, 6, 6, 10, 12 cm, joined by straight lines.024681012123456hourdepth in cm
    Tap your answer.

    1. Not this one. That is the depth at hour 4. The line climbs after it, so the water was deeper. Try another.

    2. Not this one. That is the depth at hour 5. Halfway comes before the end of the climb. Try another.

    3. Yes, that is right. Hour 4 is 6 cm. Hour 5 is 10 cm. Halfway between 6 and 10 is 8. It is an estimate.

    See the answer

    About 8 cm

    Hour 4 is 6 cm. Hour 5 is 10 cm. Halfway between 6 and 10 is 8. It is an estimate.

    • If you chose A: That is the depth at hour 4. The line climbs after it, so the water was deeper.
    • If you chose B: That is the depth at hour 5. Halfway comes before the end of the climb.

  9. Ravi measures a shoot each day. He draws a line graph. Where do the days go?

    Tap your answer.

    1. Not this one. The heights go up the side, in cm. The days go along the bottom. Try another.

    2. Yes, that is right. Time goes along the bottom, from the first day to the last. The heights go up the side.

    3. Not this one. The days must be in order. Day 3 comes after day 2. Mixed days give a wrong line. Try another.

    See the answer

    Along the bottom, in order.

    Time goes along the bottom, from the first day to the last. The heights go up the side.

    • If you chose A: The heights go up the side, in cm. The days go along the bottom.
    • If you chose C: The days must be in order. Day 3 comes after day 2. Mixed days give a wrong line.

  10. On day 3 Ravi's shoot is 3 cm. On day 4 it is 6 cm. Where is the point for day 4?

    Tap your answer.

    1. Yes, that is right. Find day 4 along the bottom. The height is 6 cm. Go up to 6 on the side and mark the point.

    2. Not this one. You swapped the two axes. The day goes along the bottom. The height goes up the side. Try another.

    3. Not this one. You used the day number for the height too. The height on day 4 is 6 cm. Try another.

    See the answer

    Above 4 along the bottom, level with 6 on the side.

    Find day 4 along the bottom. The height is 6 cm. Go up to 6 on the side and mark the point.

    • If you chose B: You swapped the two axes. The day goes along the bottom. The height goes up the side.
    • If you chose C: You used the day number for the height too. The height on day 4 is 6 cm.

Keep it

Copy this into your exercise book.

A line graph shows change over time. Put a point for each day and join them in order. A point is a measurement. The line between points is an estimate. Do not join fruits or games.

Draw: Draw two axes. Put days along the bottom and height up the side. Mark three days and join them.

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.