Reading a graph
A point on a graph of real data pairs two measurements. Find one value on its axis, go to the line, and read across to the other axis.
Weather maps, phone battery meters and sports stats all use graphs. Before you can use one, you need to read it: which number is on which axis?
A graph of real data pairs two measurements. Each point says: when this one was measured, that one was measured. To read a graph, first check the axis labels: what is measured across, and what is measured up. The data on these graphs are examples.
- Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
- Try: Try it on the board and compare the result with your prediction.
- Investigate: Work out why it happens, one step at a time.
- Modify: Change the problem on purpose and see what happens.
- Practise: A few on your own, to check you have it.
- Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
What does a point say?
Which axis is the first number read from? What are the units of each number?
Move the cursor
Use the slider, the − and + buttons, or click on the graph. The readout names both values with their units. At 15 hours, how hot is it?
Move the cursor to 15 hours. Was your prediction right?
Use the board. This ticks when you get there.
Reading values
Here is how to read a graph, step by step.
- Check the labels first.
- Find the value you know on its own axis.
- Go up from 9 to the line.
- Read across to the other axis.
- Say it in a sentence, with the units.
Read Priya's working one line at a time. Which number came from which axis?
What is the temperature at 9 hours?
At what time (in hours) is the temperature highest?
Priya reads the temperature at 6 hours from the graph. Click the line where she goes wrong.
Other graphs
Each task loads a new graph. Read the axis labels first.
Need a hint?
Read up the side to find 26, then follow across to the line.
Need a hint?
A point below the Time axis has a negative temperature.
A car's fuel tank: fuel (L) against distance (km). Move to where 26 litres are left. How far has it gone?
Use the board. This ticks when you get there.
What is the lowest temperature on the night graph, in °C?
Read the graph
What is the temperature at 21 hours?
How much fuel is left after 300 km, in litres?
Review: find when .
Tell a story with a graph
The points move up and down only. Then answer: what does your graph say about the battery at 4 hours?
Stretch: draw a graph where the battery falls quickly at first, then slowly.
Need a hint?
The battery starts full. What is the battery at 0 hours?
Another hint
Each point must be lower than the one before it, and the last one is 20.
Mia's phone is fully charged (100%) at 0 hours. It goes down every two hours, and is at 20% after 8 hours. Drag each point up or down to draw it.
Use the board. This ticks when you get there.
For teachers
Students read values from graphs of real data, starting from either axis, and say what a point means in a sentence with units (AC9M7A04, node 1). About 45 minutes.
Open the teacher guide: answers, solutions, slides and a worksheet.
Students will be able to
- I can say what a point on a graph of real data means, with units.
- I can find a value on one axis and read the matching value from the other.
- I can tell the graph's variables from its axis labels.
Before class
Do the Run board and the Make board yourself first. The cursor reads both values off the line; students can click the graph, use the slider, or use the − and + buttons.
The data are plausible examples, not real measurements. If you have real data (a school weather station, a class experiment), swap in a graph of your own for the Investigate questions.
Students know how to plot points (the last lesson). The new move is reading a point as two measurements with units: the first from the bottom axis, the second up the side. Axis labels now carry the names and units, such as Time (h).
The Modify tasks read the other way (from the up-axis to the across-axis), meet a flat section, and meet negative values below the axis.
Running the lesson
- Predict: take a show of hands. Ask a student who chose 'At 24 hours the temperature is 15 °C' which axis they read first.
- Run: ask students to say each reading in a sentence with units before moving the cursor.
- Investigate: model the worked example live on a projected graph: say the axes, put a finger on the known value, go to the line, then across.
- Modify: before the fuel graph, ask: which axis is the 26 on?
- Make: compare two students' graphs. Both fall every two hours. How do they differ?
When students get stuck
- A student gives the time when asked for the temperature, or the reverse (Priya's mistake). Ask: What is this axis called? Is 9 measured in hours or in degrees? Fix: Write the units next to each number: 6 h and 9 °C. Then say the sentence: at 6 hours the temperature is 9 °C.
- A student cannot find a value between gridlines. Ask: Which two gridlines is the line between? Is it closer to the lower or the upper one? Fix: Count the grid squares in fives or tens, and use the cursor's readout to check.
- A student reads a negative value as positive. Ask: Is the point above or below the Time axis? Fix: Below the axis is below zero: write the minus sign.
Stretch and support
Stretch: Using the temperature graph, find two different times when the temperature is 16 °C. Why are there two?
Support: Give a printed graph with the gridlines labelled and a ruler, and read the first value together, naming the axis out loud.
Where it leads
Next: describing the whole relationship in words (it increases, decreases or stays constant) instead of one point at a time.
Where it leads in class: reading graphs in science experiments and in geography.
What each step is for
- what does a point say?: Committing to what (15, 24) means exposes swapped axes and reading the point as one number, before any graph is shown.
- move the cursor: Moving the cursor along the line shows both readings change together: the time on the bottom axis and the temperature at the line.
- reading values: Reading a graph is four moves: check the axes, find the known value on its own axis, go to the line, read across to the other axis; the units go in the answer. Swapping the axes is the common slip.
- other graphs: One change at a time: read the other way (from the up-axis to the across-axis), a flat section, and negative values below the axis.
- read the graph: Reading both ways on new graphs, mixed with a sentence-meaning question so students must decide which axis each number comes from; the review is substitution from an earlier lesson.
- tell a story with a graph: Making a graph from a story reverses reading: students choose each value to fit the words.
- Say what a point on a graph of real data means, with units.
- Find a value on one axis and read the matching value from the other.
- Tell the graph's variables from its axis labels.