Year 6 Mathematics · AC9M6ST02

Evaluating Statistically Informed Arguments

Check data sources, samples, displays, summaries and claims

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Learning goalsSay it simply

Learning goal

Students inspect question wording, sample selection, missing context, graph scale, selected statistics and causal language before deciding how strongly data support a claim.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: analyse statistically informed arguments presented in traditional and digital media; discuss and critique how data are represented and used to support claims
Key conceptTeach from the board

Audit a media statistics claim

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

1Claim‘9 in 10 prefer Brand A’
2SourceWho conducted and funded it?
3SampleHow many, selected how, from where?
4QuestionWas wording leading?
5DisplayAre scales and categories complete?
6StatisticCount, percentage, mean, mode?
7ConclusionWhat is actually supported?

A numerical statement can be accurate yet misleading if the sample, denominator, comparison or omitted categories are unclear.

Identify common representation tactics

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

tacticrisktruncated axisexaggerates visual differencesmall voluntary sampleselection biaspercentage without denominatorhides sample sizeaverage without distributionhides spread or extremesassociation phrased as causeoverstates evidence

Critique the argument, not the people. State what additional information would allow a stronger judgement.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6ST02 - Evaluating Statistically Informed Arguments
Example 1

1 Claim ‘9 in 10 prefer Brand A’

Example 2

tactic risk truncated axis exaggerates visual difference small voluntary sample selection bias percentage without denominator hides sample size average without distribution hides spread or extremes association phrased as cause overstates evidence

Example 3

: investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey

Example 4

: evaluating reports and secondary data relating to the distribution and use of non-renewable resources around the world

Curriculum examplesCopied content

AC9M6ST02: identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions

  • E1: investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
  • E2: evaluating reports and secondary data relating to the distribution and use of non-renewable resources around the world
  • E3: identifying potentially misleading data representations in the media; for example, graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made and pie charts in which the whole pie does not represent the entire population about which the claims are made
  • E4: investigating both traditional and digital media relating to First Nations Australians, identifying and critiquing statistically informed arguments

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Ask who/whom/how many.
  • Check denominator.
  • Spot truncated axis.
  • Question causal language.
  • Request missing evidence.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Any percentage treated as strong evidenceCheck denominator and sample.
Graph style trusted without valuesRead axes and labels.
Mean considered typical automaticallyInspect distribution and outliers.
Correlation described as causeCausal claims need stronger design and reasoning.
Curriculum alignmentStart here

Learning goal

Students inspect question wording, sample selection, missing context, graph scale, selected statistics and causal language before deciding how strongly data support a claim.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: analyse statistically informed arguments presented in traditional and digital media; discuss and critique how data are represented and used to support claims
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