Reading a graph

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

• Slides Download Copy address for Prepare Present from the browser, or export to PowerPoint or PDF.
• Worksheet Download Copy address for Prepare Print the student copy; the Teacher edition has the answers.

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.

Timing

Predict and Run 8 min · Investigate 12 min · Modify 12 min · Practise and Make 13 min

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

1. Predict: take a show of hands. Ask a student who chose 'At 24 hours the temperature is 15 °C' which axis they read first.
2. Run: ask students to say each reading in a sentence with units before moving the cursor.
3. 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.
4. Modify: before the fuel graph, ask: which axis is the 26 on?
5. Make: compare two students' graphs. Both fall every two hours. How do they differ?

When students get stuck

Answers to the checks

1. what does a point say?: A graph shows temperature (°C) up the side and time (h) along the bottom. One point on it is $(15, 24)$. What does that point say?
   At 15 hours the temperature is 24 °C. The first number is read along the bottom axis (Time), the second up the side (Temperature), just as when you plotted points. (At 24 hours the temperature is 15 °C swaps the axes.)
2. move the cursor: Move the cursor $R$ to 15 hours. Was your prediction right?
   
3. Temperature: What is the temperature at 9 hours?
   14
   At 9 h the line is at 14 °C, so the point is (9, 14).
4. The highest point: At what time (in hours) is the temperature highest?
   15
   The highest point is (15, 24): the temperature is highest at 15 h.
5. Find the mistake: Priya reads the temperature at 6 hours from the graph. Click the line where she goes wrong.
   line 4
   Line 4: the line is at 9 when the time is 6, and 9 is read up the side, so it is the temperature. At 6 hours the temperature is 9 °C. Priya swapped the two numbers.
6. Fuel: A car's fuel tank: fuel (L) against distance (km). Move $R$ to where 26 litres are left. How far has it gone?
   
   The line is at 26 L when the distance is 200 km: the point is (200, 26).
7. A flat line: What happens to the plant's height from week 3 to week 6?
   It stays the same (a flat line)
   The line is flat from week 3 to week 6: the height is 14 cm each time, so it does not change.
8. Below zero: What is the lowest temperature on the night graph, in °C?
   -6
   The lowest point is (8, −6): at 8 hours the temperature is −6 °C.
9. The time: What is the temperature at 21 hours?
   16
   At 21 h the line is at 16 °C: the point is (21, 16).
10. The fuel: How much fuel is left after 300 km, in litres?
    14
    At 300 km the line is at 14 L: the point is (300, 14).
11. Which sentence?: A graph of cost ($) against time (hours) has the point $(4, 30)$. Which sentence is true?
    4 hours cost $30
    The first number is the time (4 hours) and the second is the cost ($30).
12. Review: Review: find $y = 4x + 1$ when $x = 3$.
    13
    y = 4 × 3 + 1 = 12 + 1 = 13.
13. tell a story with a graph: 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.
    
    Start at 100 and end at 20, lower each time, such as 100, 80, 60, 40, 20 (a steady fall) or 100, 70, 50, 30, 20.

Solutions

One possible solution for each task. Other correct programs are fine.

other graphs › Fuel

Open task: any program that does what the step asks.

other graphs › A flat line

Open task: any program that does what the step asks.

other graphs › Below zero

Open task: any program that does what the step asks.

tell a story with a graph

Open task: any program that does what the step asks.

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.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 7 student in Australia. Help me understand ONE idea only, from the lesson "Reading a graph".

The idea: Reading and interpreting graphs of real data: I can Students read values from graphs of authentic data and describe what the graph shows in context.

What understanding looks like:
- Reads specific values from a graph accurately.
- Describes trends (increasing, decreasing, constant, periodic) in contextual terms.
- Does not interpret a graph in isolation from its axes labels and units.

Mistakes students often make here:
- A student gives the time when asked for the temperature, or the reverse (Priya's mistake).
- A student cannot find a value between gridlines.
- A student reads a negative value as positive.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Reading a graph".

Exit ticket

A graph of height (cm) against age (years) has the point (12, 150). What does it say?

At 12 years the height is 150 cm.

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.

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.