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Grade 8 · Mathematics · 30 minutes

Unit 3 · Geometry and bivariate evidence · Lesson 3 of 3

Scatter Plots and Plant-Growth Models

Fit a simple line to paired measurements without claiming a causal result.

Mr. S Teaches · Original starter mini-lesson · MS8-MATH-06

Learning objective

Plot paired data, describe association and interpret a line’s slope in context.

Before you begin

  • Coordinate plotting
  • Linear models

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

bivariate data
Paired measurements of two variables.
association
A pattern in how two variables vary together.
outlier
A point separated from the main pattern.
residual
The difference between an observed value and a model’s prediction.

Understand the concept

A scatter plot keeps paired measurements together. A line may summarize a roughly linear pattern, but it need not pass through every point. Slope describes modeled change in the output per input unit. Association alone does not establish that one variable causes the other; other growing conditions could differ.

Teach it step by step

  1. Plot fictional pairs of weekly light-hours and plant growth in cm: (2,3),(4,5),(6,6),(8,9),(10,11).
  2. Describe the upward association and compare the points with the trial line y = x + 1.
  3. Calculate the model’s prediction at 6 light-hours and compare with the observed growth.
  4. Add a point (8,2) and discuss whether it would be unusual relative to the pattern.
  5. Write a conclusion using “associated with” and propose a controlled comparison needed for a causal claim.

Make the thinking visible

Worked example or model response

The trial line predicts 7 cm at 6 light-hours, while the observed value is 6 cm, a residual of −1 cm. Its slope means one additional light-hour is associated with 1 cm more modeled growth. The +1 intercept is a model parameter, not proof of growth without light.

Guided practice

For pairs (1,8),(2,6),(3,5),(4,3), sketch the scatter plot and test y = −1.5x + 9. Predict the output at x = 2.

Independent practice

1. Use y = 2x + 3 to predict y when x = 5. If the observation is 12, find the residual. 2. Explain why a study finding taller plants with more light does not by itself rule out different soil or water conditions.

Quick assessment

Would swapping only one x-coordinate between data pairs preserve the original scatter plot? Explain.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: Negative association; the trial model predicts 6 at x = 2, matching the given observation.
  2. Independent 1: Prediction 13; residual 12−13 = −1. 2: Light may be associated with growth while other conditions also influence it; control or account for those variables.
  3. Quick check: No. Re-pairing one coordinate changes which measurements belong together and alters the evidence.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use labeled coordinate cards and plot one pair at a time before describing the overall pattern.

Extension challenge

Compare the trial line with y = 0.9x + 1.5 and judge fit by several vertical differences, not one point.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

8.SP.A.1

Common Core · Grade 8

Construct a scatter plot and describe association and an unusual point.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

8.SP.A.2

Common Core · Grade 8

Informally judge how a line fits paired quantitative data.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

8.SP.A.3

Common Core · Grade 8

Use a linear model to predict and interpret slope in context.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.