Use Data and Probability to Test a Claim

Success criteria

• I support a claim with specific numbers from the data.
• I use a tree diagram to count compound outcomes and calculate a probability.
• I use that probability to determine an expected outcome over repeated trials.
• I distinguish “supports” from “proves.”
• I name at least one limitation and critique a misleading representation.

Learn and explain

Suppose a paper-plane design flew past a target line in 9 of 12 trials. That is 75% of these trials. The result supports the claim “this design often passed the line in our test.” It does not prove that it always works, that it beats every design, or that wind had no effect.

Use this reasoning chain:

1. Claim: precise and answerable.
2. Evidence: numbers or observations that actually address it.
3. Reasoning: why those numbers matter.
4. Limitation: what the sample or method cannot establish.

Compound chance with a tree diagram

First flip a fair coin, then spin a fair three-colour spinner. Follow every branch to a complete leaf in this tree diagram:

• Heads
  • Heads → red
  • Heads → blue
  • Heads → green
• Tails
  • Tails → red
  • Tails → blue
  • Tails → green

There are 6 equally likely paths. 2 end in red, so the probability of red is 2/6 = 1/3. Over 24 repetitions, the expected number of red outcomes is 8. Expected does not mean guaranteed; it describes the long-run share predicted by the model.

Independent practice

Unfamiliar transfer — graph detective

Two products score 90 and 100. A graph starting at 90 uses its full plotting height for their 10-point difference; a graph starting at 0 uses only one tenth of that height for the same difference. The truncated axis therefore magnifies the visible difference by a factor of 10.

Collect or reuse one small authentic dataset. Make a graph by hand, write one supported claim, and name one limitation. Then create a two-stage chance experiment, draw its complete tree, calculate one event probability, and compare the expected count with a short run of real trials.

Delayed check

One to two weeks later, inspect an unfamiliar graph from a newspaper, school notice, or advertisement. Record its source, claim, evidence, scale, and one question you would ask before believing it. Also reconstruct a two-stage tree from a verbal chance description and check that no paths are missing.

Evidence path

Save the final graph, raw data, supported claim, limitation, and revision note to jeremy/portfolio/math/unit-6/lesson-18-data-claim/.

Next step

• Repair: if claim and evidence do not match, narrow the claim until the numbers address it.
• Continue: if tree probability and data critique are independent, complete the Unit 6 delayed check and year comparison.
• Stretch: compare an experimental frequency with the tree model and explain why a short run can differ.