At a glance. One lesson of about 60 minutes. Students build a line graph point by point, read steepness as rate of change, read between points and make a limited prediction.
Calculator: no calculator. Nothing here needs one. Every reading is a halving or a small subtraction.
What students will learn
Know
- Time goes on the horizontal axis and the measured quantity on the vertical axis.
- A steeper segment means faster change.
- Between plotted points a value can be read; beyond them it is a prediction.
Understand
- Points are joined because a measured quantity exists between the readings.
- The further a prediction goes past the data, the less reliable it is.
- A line graph suits a continuous quantity over time, not separate categories.
Do
- Read a value and a change from a line graph.
- Compare rates by steepness.
- Predict from a steady rate, and say how far to trust it.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: reading values, changes and rates (questions 1 to 6).
- Criterion B. Investigating patterns: the plotting figure. Ask students to describe how the weekly rise changes, and to predict the next rise before plotting it.
- Criterion C. Communicating: justifying a prediction and saying how far to trust it, in a full sentence (question 8 and the what-if).
- Criterion D. Applying mathematics in real-life contexts: plant growth, rivers, candles and pools (the hook and questions 2 to 6).
The one thing to do with the figure
Ask for a prediction before the first slide. “After week 5, will the line keep getting steeper, flatten off, or turn down?” Take a show of hands, then plot to week 8.
In the second figure ask for the reading at week 6.5 before moving the marker. Then switch on the prediction and ask how sure they are of week 10 compared with week 9.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook and the first figure on building the line. |
| 10 min | Key idea; the second figure on reading between and predicting. |
| 10 min | Worked example on the water tank; students finish the faded snail example in pairs. |
| 5 min | Question 1, the check. If many choose A, go back to the first figure. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 19; 25%; continuous. |
|---|---|
| Worked example | 10 litres; 23 litres; about 44 litres. |
| Faded example | Minutes 5 to 10 (18 cm). |
| 1. Which data suits a line graph | B. A, C and D are categories; only B is a measurement over time. |
| 2. Change between two points | 12. 21 − 9. |
| 3. Read between two points | 14. (18 + 10) ÷ 2. |
| 4. Reading steepness | A. B misreads the flat part; C and D ignore the rise. |
| 5. Rate from two readings | 4. 16 ÷ 4. |
| 6. Predict from a steady rate | 65. 45 + 4 × 5. |
| 7. Where two lines meet | 3. Both 13 cm. |
| 8. Limits of prediction | B. A, C and D give reasons that are not about how far beyond the data the guess goes. |
| 9. Setting up a line graph | B. A swaps the axes; C treats heights as categories; D picks the wrong chart. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A, C or D in question 1 | Chose a category set because it was a list of values. | Ask: is there a value between two of the items? If not, no line. |
| 15, 21 or 2 in question 2 | Used the wrong start, gave the reading, or took one month. | Ask them to circle the two readings the question names. |
| 18, 10 or 28 in question 3 | Gave an endpoint, or added the two heights. | Ask what is halfway between two numbers, then add and halve. |
| B, C or D in question 4 | Misread which parts of the line are steep. | Work out the change in each period before choosing. |
| 16 or 3.2 in question 5 | Gave the total growth, or divided by the week number. | Count the gaps between weeks, not the week names. |
| 50, 75 or 135 in question 6 | Added one minute, added the readings, or multiplied. | Draw the line with a table of minute and litres and extend it one step at a time. |
| 13, 4 or 2 in question 7 | Gave the height, the last week, or the week before. | Write both heights for each week side by side. |
| A, C or D in question 8 | Confused extending with an impossible task, or a multiple. | Ask what the data says about week 20 or 40. |
| A, C or D in question 9 | Swapped the axes or treated heights as categories. | Ask what is between week 2 and week 3. |
Questions worth asking
- What does a flat part of a line graph tell you? No change over that time. Listen for “it stayed the same”.
- Why can you read between points on a line graph but not on a bar chart? A measured quantity exists between readings; categories have no between.
- Can you read a value between two months on a graph of monthly rainfall? No. The line shows the trend only; a month has one total and nothing in between. Listen for “it is a total for the whole month”.
- Which prediction would you trust more: next week or week 20? Next week: it is close to the data. Listen for “further away, less sure”.
- How can two lines on one graph show who is growing faster? The steeper line is faster. Listen for steepness, not height.
Differentiation
A way in for anyone stuck
- Give a graph already plotted and ask only for the rise in each period before any prediction.
- Use whole-number halves only: read midpoints between numbers that add to an even sum.
- Mark the weeks on the axis and let students lay a ruler across to read.
Stretch
- Question 6, then: when will the pool hold 100 litres? (At minute 16: 45 + 11 × 5 = 100.)
- Find a real quantity that would make a straight-line prediction fail within a month, and say why.
Students learning in English as an additional language
“Steep” means going up or down quickly, like a steep hill. “Predict” means to say what will happen next. Say “between” with two hands apart and “beyond” with one hand pointing away.
| Word | Plain meaning | Example |
|---|---|---|
| line graph | a graph that joins points to show change over time | the height of a plant by week |
| axis | a line with a scale along one side of a graph | the horizontal axis shows weeks |
| steep | rising or falling quickly | the line is steepest from week 2 to week 4 |
| rate of change | how much a quantity changes in one unit of time | 4 cm per week |
| predict | say what will happen beyond the data | 52 cm at week 9 |
| trend | the general direction the data is going | rising, then levelling off |
Sentence starters for explaining aloud or in writing:
- Between … and … the value rose by …, which is … per …
- I read … at … because it is halfway between … and …
- I would trust this prediction … because …
Two things not to say
“Just extend the line.” Extending is a guess; say how far and why.
“The highest point is the best.” On a line graph, steepness shows speed of change, not good or bad.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- ReadA graph passes through 6 at 1 hour and 14 at 3 hours. What is the reading at 2 hours, if it is straight?
10. - RiseA plant is 15 cm at week 2 and 27 cm at week 5. How much did it rise?
12 cm.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- ContextA kettle's temperature is 20 at 0 minutes and 80 at 3 minutes, heating steadily. What is it at 2 minutes?
60. It rises 20 per minute. - Earlier work (Unit 2, lesson 6)A reading goes from 50 to 65. What is the percentage increase?
30%.
3Challenge
Reasoning, generalising and working backwards.
- ReasoningA line passes through (1, 4) and (5, 12). It is steady. Predict the value at 8.
18. It rises 2 per unit, and 12 + 3 × 2 = 18. - Spot the faultA line graph joins the numbers of students in four clubs. What is wrong?
The clubs are categories: nothing lies between them, so a bar chart is correct.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
Both figures work with the keyboard (tab to a slider, then the arrow keys) and by touch. Under each one, “Show me the steps” gives the same states in words.
No device? Plot the nine readings on squared paper and use a ruler for the halfway reads.