At a glance. One lesson of about 60 minutes. Direction, form and strength, outliers named separately, and the difference between strength and steepness.
Calculator: no calculator. No calculator is needed: the arithmetic is small differences and ratios.
What students will learn
Know
- Direction: positive, negative or none.
- Form: linear or non-linear.
- Strength: how closely the dots follow the pattern.
- An outlier is a dot far from the pattern.
Understand
- Strength is not steepness.
- No linear correlation is not the same as no relationship.
Do
- Describe a scatter graph with direction, form and strength.
- Compare the strength of two graphs.
- Name an outlier separately.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: direction, form and strength vocabulary (questions 1 to 6).
- Criterion B. Investigating patterns: students vary spread and shape and record what changes and what does not.
- Criterion C. Communicating: a description uses all three words and names any outlier.
- Criterion D. Applying mathematics in real-life contexts: puppies, shoe length and height.
The one thing to do with the figure
Choose Rises with spread 4, then Falls with spread 1, and ask which is stronger. Most students pick the second: the steepness of the pattern is the same, only the spread differs.
Then press No link and slide the spread: nothing changes. Ask why.
A possible order
| 5 min | Warm-up, then answers. |
|---|---|
| 8 min | Hook: three words, guess. |
| 12 min | The figure; say the words before reading them. |
| 12 min | Worked examples; shoe length 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 | Negative; the independent variable; 16. |
|---|---|
| Worked examples | Puppies: positive, linear, strong, one outlier. Graph A is stronger. |
| Faded example | Positive, linear, moderate. |
| 1. Describing a pattern | B. A reads the direction wrongly; C ignores the spread. |
| 2. Total rise | 34. |
| 3. Distance from a trend | 5. |
| 4. Comparing spread | 3. |
| 5. Curved patterns | B. A and C describe only half of the arch as if it were the whole pattern. |
| 6. Share inside a band | 75 per cent. |
| 7. Highest possible dot | 48. |
| 8. Strength is not steepness | C. A confuses steepness with strength; B treats a positive direction as stronger. |
| 9. A full description | A. B lets two dots cancel the pattern; C gets the direction wrong. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| A or C in question 1 | Reads the direction wrongly or ignores the spread. | Ask: which word is about the shape and which is about the width? |
| 52, 4 or 15 in question 2 | Reads one y value, or the change in x. | Underline the first and last y values. |
| 66 or 15 in question 3 | Reports the line's value, or forgets the constant. | Work out the line's value on its own line first. |
| 6, 12 or 27 in question 4 | Subtracts, adds or multiplies instead of dividing. | Ask what 'how many times as wide' means. |
| 25 or 15 in question 6 | Reports the outside share or the count. | Ask: how many are inside, then what percentage of 20? |
| A or B in question 8 | Confuses steepness, or a positive direction, with strength. | Draw both graphs and ask which dots are closer to their line. |
Questions worth asking
- What changes when the spread goes up, and what stays the same? Listen for “direction and form stay, strength falls”.
- Why does No link ignore the spread? Listen for “there is no pattern to spread out from”.
- Is the curve a weak correlation? Listen for “no: it is a strong relationship that is not linear”.
Differentiation
A way in for anyone stuck
- Give a three-column table with the words direction, form and strength and a sentence frame for each.
- Provide four printed graphs to sort into strong, moderate and weak before using the figure.
- Show a ruler laid along the dots to judge how close they are.
Stretch
- Sketch a graph with a strong correlation and a very small gradient, and one with a weak correlation and a large gradient.
- Can a graph have a strong non-linear relationship and no linear correlation? Sketch one.
Students learning in English as an additional language
Pair “strong” with a sketch of tight dots and “weak” with a sketch of a loose cloud.
| Word | Plain meaning | Example |
|---|---|---|
| correlation | a link between two variables seen in a scatter graph | positive, linear, strong |
| linear | following a straight line | dots in a band |
| strength | how closely the dots follow the pattern | strong or weak |
| outlier | a dot that sits far from the pattern | one dot far below the band |
| non-linear | following a curve, not a straight line | an arch |
Sentence starters for explaining aloud or in writing:
- The direction is …, the form is … and the strength is …
- The dots are close to / far from the line, so the correlation is …
- There is an outlier at …
Two things not to say
“A steep line means a strong correlation.” Strength is about closeness.
“The dots are not in a line, so there is no relationship.” A curve is a relationship.
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.
- DescribeThe dots fall in a narrow band. Describe the correlation.
Negative, linear, strong. - CompareDots within 5 units of a line and dots within 20 units of the same line. Which is stronger and by how many times as narrow a band?
The first; 4 times as narrow.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- Percentage25 dots, 3 outliers. What percentage are inside the band?
88 per cent. - TrendLine y = 5x + 40; a dot at x = 6 has y = 66. How far from the line is it, and on which side?
The line gives 70, so the dot is 4 below it.
3Challenge
Reasoning, generalizing and working backwards.
- ReasoningA graph is steep but the dots are widely scattered. Is the correlation strong?
No, it is weak: strength is closeness to the line, not steepness. - From Lesson 1Which variable goes on the x axis: hours of revision or test mark?
Hours of revision.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
The buttons and slider work with the keyboard and by touch; “Show me the steps” describes five states in words.
On paper: six pre-drawn graphs with different spreads to sort.