Which Snack Wins?
Twenty bags of crackers, one label claiming 'about 20 per bag' — and one suspicious bag holding 35. Students ask a genuinely statistical question, plot the distribution, meet median, mean, IQR, and the outlier that drags the mean — then choose which summary honestly answers the label's claim.
Common Core standards covered
- 6.SP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
- 6.SP.A.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
- 6.SP.A.3Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
- 6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 6.SP.B.5Summarize numerical data sets in relation to their context.
- 6.SP.B.5.aSummarize numerical data sets in relation to their context, such as by reporting the number of observations.
- 6.SP.B.5.bSummarize numerical data sets in relation to their context, such as by describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- 6.SP.B.5.cSummarize numerical data sets in relation to their context, such as by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.B.5.dSummarize numerical data sets in relation to their context, such as by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Recognize statistical questions, describe distributions by center, spread, and shape, display data in dot plots and box plots, and summarize data sets in context — choosing measures of center and variability to match the distribution's shape.
Student target: “I can recognize statistical questions, display a distribution, compute median, mean, and IQR, and choose which center-and-spread pair to report based on the shape.”
Success criteria: I can tell statistical questions (variability expected) from lookup questions. · I can build a dot plot and describe center, spread, and shape. · I can compute median, mean, quartiles, and IQR from ordered data. · I can choose median/IQR or mean/MAD by shape, and justify the choice.
Essential question
A label says 'about 20 crackers per bag.' Twenty bags disagree with each other — so what single number, if any, answers honestly, and what must ride along with it?
Learning target: I can recognize statistical questions, display a distribution, compute median, mean, and IQR, and choose which center-and-spread pair to report based on the shape.
Success criteria
- I can tell statistical questions (variability expected) from lookup questions.
- I can build a dot plot and describe center, spread, and shape.
- I can compute median, mean, quartiles, and IQR from ordered data.
- I can choose median/IQR or mean/MAD by shape, and justify the choice.
Why this matters
6.SP is statistics' constitution: A.1 defines which questions the discipline even owns (variability expected), A.2-3 split center from spread as different jobs, B.4 gives the pictures, and B.5 demands the full contextual summary — including d's mature judgment that SHAPE picks the summary. The outlier bag makes that judgment real: mean 21.8 flatters the label; median 21 with IQR 2.5 tells the truth. Grade 7's Growing Contest and every data claim students will ever read stand on this.
Students should already be able to
- Dot plots — informal.
- Mean as fair share.
- Ordering and dividing data lists.
Vocabulary to define explicitly
- Statistical question
One that anticipates variability in the answers — the standard's own test.
Example: 'How many crackers per bag in this brand?' — bags vary; the question expects it.
Not an example: 'How many crackers are in my bag?' — one count, no variability. Look it up.
🔒 3 more terms with examples and non-examples — Distribution (center, spread, shape), Median & IQR, Mean and its weakness — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- The question sort.
- Landmark computations during club work.
- The cross-examination.
Summative — the graded evidence: The exit ticket (sort, measures, choice), scored with the four-criterion rubric.
The task students work on
The consumer club tests the label 'about 20 crackers per bag.' THE QUESTION SORT: which of four candidate questions are statistical? THE DATA: twenty bags counted — 18, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, and one bag of 35 (a family-size mislabel that snuck in). THE PLOTS: dot plot, then the five-number box. THE NUMBERS: median, mean, Q1, Q3, IQR. THE RULING: does 'about 20' hold — and which center honestly speaks for these bags: the 21.8 mean or the 21 median?
Club report — the five-part summary (B.5's own outline).
| Part | Finding |
|---|---|
| a. How many observations | |
| b. Attribute and units | |
| c. Center and spread | |
| d. Shape and deviations | |
| Ruling on the label |
Anticipated student strategies
The question test defines the enterprise, landmarks give the numbers, and the sensitivity experiment converts 'choose by shape' from rule to reason.
- Variability test for questions. The student asks 'would honest answers differ?' to sort statistical from lookup questions.
A.1's own criterion — share first; it defines the whole discipline in one test.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
The test posted: a statistical question EXPECTS its answers to vary. My-bag and my-age are lookups; the brand and the school anticipate spread — statistics owns those. (The school question is the standard's own example.)
Listen for: Rephrase it across many bags — variability enters, statistics applies. The question's scope, not its topic, decides.
Center vs spread named as different JOBS (A.3): one number for 'typical,' one for 'how much they vary.' Shape described: clustered, one striking deviation (B.5.c's language).
- Median and quartiles are positions in the ORDERED list.
- IQR measures the middle half — extremes can't vote.
Listen for: The 35-bag — a single far value shifts the balance point but can't budge the middle position. The plot showed it before the numbers did.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “'How many crackers in my bag' is statistical — it's about data.” One bag, one count, no expected variability — a lookup. Widen it to many bags and statistics wakes up. The test is anticipated VARIABILITY, not the topic.
- “The mean is always the best center.” — the teacher response is in the full lesson.
- “Spread means the range.” — the teacher response is in the full lesson.
- “Outliers should be deleted.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 4 independent.
- I doOrder the twenty counts, then find the median, Q1, Q3, and IQR.
🔒 5 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- Statistical or not: 'How many pets do students in our grade have?' Reason required.
🔒 2 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Sort questions: statistical or not. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Dot-plot the twenty bags; describe center, spread, shape. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Compute median, mean, quartiles, and IQR. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Rule on the label — choosing measures by shape. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Ordered-list scaffolds carry the quartiles; extend with the outlier-removed comparison and the box plot.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: One full five-part summary (count, attribute, center, spread, shape/deviations) with the center chosen by shape and defended.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.