Describing a relationship
Describe how one measurement changes as the other increases, one section of the graph at a time: it increases, decreases or stays constant.
A graph tells a story about how two things change together. Telling that story in words, section by section, is how scientists and journalists use graphs.
A graph does not just give values. It shows how one measurement changes as the other changes. Look at one section at a time, and ask: as the time goes on, does the other measurement increase, decrease, or stay constant (not change)? 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.
Which story?
What is measured up the side? What would the line do if the cyclist stopped?
Follow the ride
Move the cursor a step at a time. For each section, say what the distance from home does as time goes on.
Move the cursor along the whole ride, to 4 hours. Was your prediction right?
Use the board. This ticks when you get there.
Describing sections
Here is how to describe a graph, one section at a time.
- Take one section at a time and compare its start and end. The distance increases.
- The distance does not change. It is constant.
- The distance decreases.
- Put the sections in order. Say it: "As time increases, the distance from home increases, then stays constant, then decreases."
Read Omar's working one line at a time. What is the line really showing?
Omar describes the ride from 3 to 5 hours. Click the line where his reasoning goes wrong.
Other stories
Each task loads a new graph. Describe the sections before you answer.
Need a hint?
The water stops rising when the line goes flat. When does it start to go down?
Water in a bath (L) against time (min). Move to the moment the water starts to go down.
Use the board. This ticks when you get there.
Describe and match
Review: what is the temperature at 20 minutes, in °C?
Draw a bath
Drag each point up or down. Then describe your graph in a sentence.
Stretch: draw a bath that fills quickly at first, then slowly.
Need a hint?
The bath starts empty: what is the water at 0 minutes?
Another hint
A flat part means two points at the same height.
Draw this story: a bath is empty at 0 minutes. It fills until 4 minutes, stays the same from 4 to 6 minutes, then empties and is empty again at 10 minutes.
Use the board. This ticks when you get there.
For teachers
Students describe how one measurement changes as the other increases, section by section, and tell the story a graph shows without reading it as a picture (AC9M7A04, node 2). About 45 minutes.
Open the teacher guide: answers, solutions, slides and a worksheet.
Students will be able to
- I can describe a section of a graph as increasing, decreasing or constant.
- I can tell the story of a graph in order, with the measurements named.
- I can draw a graph that matches a story.
Before class
Do the Run, Modify (bath) and Make boards yourself first. In Make, the points move up and down only, so students choose each value and the times stay fixed.
The data are plausible examples, not real measurements. The new move is describing a section by comparing its start and end: as time increases, the other measurement increases, decreases or stays constant.
The common slip is reading the graph as a picture of the journey, so that a line going down means a hill. Omar's working addresses it. A flat section is a constant measurement while time still passes: the cyclist is stopped, not going slowly.
The cooling drink adds a decrease that slows down: the line is always going down but gets less steep.
Running the lesson
- Predict: take a show of hands. Ask a student who chose the hill story what the vertical axis measures.
- Run: ask students to narrate the ride aloud as you move the cursor.
- Investigate: model the worked example live: section by section, start value, end value, then the word.
- Modify: after the cooling drink, ask: does the temperature ever go up? How does the drop in the first 10 minutes compare with the last 10?
- Make: compare two students' baths: where is the flat part, and how do you know?
When students get stuck
- A student says the line going down means the cyclist is going downhill (Omar's mistake). Ask: What does the vertical axis measure? What would the line do if the road were flat but the cyclist rode home? Fix: Rewrite with the axis name: the distance from home is getting smaller.
- A student says a flat line means no time has passed, or no movement is happening at all. Ask: What is going along the bottom axis? Does it keep going? Fix: Time keeps going. A flat line means the other measurement is not changing.
- A student describes only the start and end of the whole graph. Ask: What happens in the middle? Fix: Split the graph into sections where the direction changes, and describe each one.
Stretch and support
Stretch: Draw a graph of the depth of water in a bath where the water fills quickly, then slowly, then the plug is pulled. Describe it in a sentence.
Support: Give the sentence frame: As time increases, the ___ increases / decreases / stays constant. Mark where each section starts and ends on a printed graph.
Where it leads
Next: the straight line gets a rule. The gradient (how steep) and the intercept (where it starts) name what these graphs have been showing.
Where it leads in class: describing graphs in science (speed, temperature, growth) and in geography.
What each step is for
- which story?: Committing to a story for a line that rises, flattens and falls exposes reading the graph as a picture of hills instead of as distance changing with time.
- follow the ride: Moving the cursor section by section shows what the distance does while the time goes on, and that a flat line still has time passing.
- describing sections: Describe each section by comparing its start and end: the measurement increases, decreases or is constant as time increases; a line going down does not mean going downhill.
- other stories: One change at a time: a story with a turning point, two graphs on one set of axes, and a measurement that decreases at a slowing rate.
- describe and match: Describing and matching on new graphs, with one reading question mixed in so students must decide whether a question asks for a value or a description; the review is reading a value from the last lesson.
- draw a bath: Making a graph from a story reverses describing: students choose each value to fit the words, and must keep the flat part flat.
- Describe a section of a graph as increasing, decreasing or constant.
- Tell the story of a graph in order, with the measurements named.
- Draw a graph that matches a story.