Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Interpret the slope and intercept of a line of best fit
Statistics and probability
CCSS 8.SP.A.3England: KS3 Statistics
Objective and success criteria
Students will: Interpret the slope and intercept of a line of best fit.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Make predictions with a line of best fit; Interpret rate of change and initial value in context
Leads to: the next skill in this area.
Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Make predictions with a line of best fit; Interpret rate of change and initial value in context). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- The line of best fit for test score (y) against hours of practice (x) is y = 6x + 26. Predict the score after 8 hours. → 74Prompt: Substitute the x-value into the equation.
- A savings jar has 37 coins and 2 coins are added each week. In y = mx + b, what is m? → 2Prompt: m is the rate of change: how much per unit of time.
- A line of best fit is y = 2x + 3. For which x does it predict y = 17? → 7Prompt: Set the equation equal to the y-value.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Interpret the slope and intercept of a line of best fit. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: For plants, the line of best fit of height in cm (y) against age in weeks (x) is y = 5x + 20. What does 5 mean?
- Step 1: Slope 5: about 5 cm more for each extra week.
- Answer: Plants grow about 5 cm per week
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- For plants, the line of best fit of height in cm (y) against age in weeks (x) is y = 9x + 59. What does 9 mean? (Plants are 9 cm tall at the start / Plants grow 59 cm per week / Plants grow about 9 cm per week / Plants grow for 9 weeks) → Plants grow about 9 cm per weekPrompt: The slope is the change in y for each 1 increase in x.
- The line of best fit for the cost of a taxi ride (y, in currency units) against distance (x, in km) is y = 2x + 12. What does 12 represent? (The longest possible trip / The cost per km / The predicted cost for a 0 km trip (the starting charge) / The cost of a 12 km trip) → The predicted cost for a 0 km trip (the starting charge)Prompt: The intercept is the value of y when x = 0.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- The line of best fit for the cost of a taxi ride (y, in currency units) against distance (x, in km) is y = 1x + 16. What does 16 represent? (The cost of a 16 km trip / The predicted cost for a 0 km trip (the starting charge) / The cost per km / The longest possible trip) → The predicted cost for a 0 km trip (the starting charge)Prompt: The intercept is the value of y when x = 0.
- For plants, the line of best fit of height in cm (y) against age in weeks (x) is y = 5x + 56. What does 5 mean? (Plants grow 56 cm per week / Plants grow for 5 weeks / Plants are 5 cm tall at the start / Plants grow about 5 cm per week) → Plants grow about 5 cm per weekPrompt: The slope is the change in y for each 1 increase in x.
Watch out for
- Forgetting to put data in order before finding the median.
- Reading a bar's height wrongly when the scale goes up in 2s or 5s.
Support and stretch
Support
- Review first: Make predictions with a line of best fit.
- Use concrete materials: squared paper for charts.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder