At a glance. One lesson of about 60 minutes. Pairs of values, independent and dependent variables, choosing a scale, a broken axis, and the direction of the dots.
Calculator: no calculator. No calculator is needed: the arithmetic is subtraction and division by small whole numbers.
What students will learn
Know
- Bivariate data are pairs of values.
- The independent variable goes on the x axis and the dependent variable on the y axis.
- A scatter graph has one dot per pair; its direction is positive, negative or none.
Understand
- A pattern can be easier to see in a graph than in a table.
- A negative direction describes the shape of the dots, not whether the result is good or bad.
Do
- Name the variables and say which is independent.
- Choose a scale and plot pairs.
- Describe the direction of a scatter graph.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: variable roles and plotting pairs (questions 1 to 5).
- Criterion B. Investigating patterns: students predict the pattern before the last dots appear and test the prediction.
- Criterion C. Communicating: axes labelled with name and unit, and a broken axis flagged.
- Criterion D. Applying mathematics in real-life contexts: sleep and reaction time, car prices (questions 7 and 9).
The one thing to do with the figure
Stop at three dots and ask for a prediction. Three dots can say something or nothing; ask students to commit, then add the rest and compare.
Ask which value is the lowest so far and what that means for a reaction: a lower time is a quicker reaction. This is the hinge of the exit ticket.
A possible order
| 5 min | Warm-up, then answers. |
|---|---|
| 8 min | Hook: sleep and reactions; write a guess. |
| 12 min | The figure; stop at three dots to predict. |
| 12 min | Worked examples; bus repair bills in pairs. |
| 5 min | Question 1, the check. |
| 13 min | Your turn, Levels 1 to 3. |
| 5 min | Exit ticket, question 9. |
The answers
| Warm-up | 3 across and 5 up; 7; the values sit between 240 and 380, so 0 would waste space. |
|---|---|
| Worked examples | Temperature is independent; the direction is negative. Axes 10 to 30 and 0 to 100. |
| Faded example | Age independent; the repair bill rises, so positive. |
| 1. Choosing the x axis | A. B reverses the roles; C ignores the convention. |
| 2. Counting dots | 10. |
| 3. Reading a pair | 22 minutes. |
| 4. Average change | 20. |
| 5. Scale on an axis | 2 cm. |
| 6. Predicting a direction | B. A and C both rise together. |
| 7. Direction with an exception | 1. |
| 8. Reading a negative trend | 100, at x = 5. |
| 9. Reading a negative direction | B. A reverses the pattern; C names the direction by the good news instead of the shape. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| 12 or 22 in question 2 | Counts pupils or single values instead of complete pairs. | Ask: can you plot a dot with only one coordinate? |
| 40, 7 or 26 in question 3 | Adds, or uses the wrong pair or the wrong variable. | Underline the pair for each pupil first. |
| 60 or 10 in question 4 | Total fall, or fall for one unit of x. | Ask how many steps of 2 there are. |
| 4 or 40 in question 5 | Misreads the scale. | Write 'ms per cm' and work it out first. |
| 0 or 5 in question 7 | Thinks a trend means every move, or counts the wrong direction. | Ask: does one dot above the trend change the direction? |
| Choosing A in question 9 | Confuses the dots' direction with the good-news direction. | Say what the fall in reaction time means. |
Questions worth asking
- Which variable might explain the other, and how can you tell? Listen for “one happens first or is the thing we can choose or measure beforehand”.
- Why does the y axis start at 240? Listen for “all the values are between 240 and 380, and a broken axis saves space; we must say so”.
- Does the graph prove that sleep makes you quicker? Not yet: plant this for Lesson 6.
Differentiation
A way in for anyone stuck
- Give a table with columns headed x and y and a pre-drawn pair of axes with the scale filled in.
- Let students plot the ten pairs on paper before using the slider.
- Use a sentence frame: As x goes up, y goes …, so the direction is …
Stretch
- Find two variables in your own life that you would expect to have a negative direction, and draw the rough graph.
- Could two variables have a direction that changes part of the way along? Sketch one.
Students learning in English as an additional language
Pair each term with a quick sketch: a rising set of dots, a falling set, and a cloud.
| Word | Plain meaning | Example |
|---|---|---|
| bivariate data | pairs of values, two measurements for each person or thing | hours of sleep and reaction time for ten pupils |
| independent variable | the variable that might explain the change; plotted on the x axis | hours of sleep |
| dependent variable | the variable that responds; plotted on the y axis | reaction time |
| scatter graph | a graph with one dot for each pair of values | ten dots for ten pupils |
| direction | whether the dots rise (positive) or fall (negative) from left to right | negative |
Sentence starters for explaining aloud or in writing:
- The independent variable is … because …
- As x goes up, y goes …, so the direction is …
- The axis starts at … because the values are between … and …
Two things not to say
“Negative means it is bad.” Negative describes the shape of the dots.
“Just join the dots.” A scatter graph shows a pattern; it is not a line graph.
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.
- VariablesName the independent variable: the height of a plant after 4 weeks of different amounts of water.
The amount of water. - CountNine pupils give two numbers each, and one number is missing for one pupil. How many dots?
8.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- DirectionPairs: (1, 40), (2, 35), (3, 36), (4, 28). Direction?
Negative: 40 falls to 28 overall. - ScaleA y axis covers 0 to 500 in 10 cm. How many cm for 125 units?
2.5 cm.
3Challenge
Reasoning, generalizing and working backwards.
- ReasoningGive one pair of variables with a positive direction and one with a negative direction.
Answers vary, such as height and arm span; age of a car and its price. - From Year 7Find the mean of 12, 15, 21 and 24.
18.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
The slider works with the keyboard and by touch; “Show me the steps” describes four states in words.
On paper: ten stickers or counters on a pre-drawn grid reproduce the figure.