Teacher’s guide: dice sums & variability

DARJIX · Grade 6 statistics & probability · Two fair six-sided dice (sums 2–12) · darjix.com/dice-game/

Purpose

Students experience variability in data: each roll can produce a different sum. The tool supports recognizing a statistical question, watching a distribution emerge, and connecting center, spread, and shape to the plots and summary numbers.

Time & materials

About 20–40 minutes, depending on depth of discussion.
One device per pair is enough; a projector lets you discuss one shared dataset.

Standards touchpoints (CCSS)

6.SP.A.1 — Contrast “What is my sum on this roll?” (one answer after rolling) with the class question: “What sums do we get when we keep rolling?” The second anticipates variability.
6.SP.A.2–A.3 — Use the plots to name shape (mound near 7, tails toward 2 and 12), center (mean / average, median), and spread (range, MAD, IQR).
6.SP.B.4 — Compare the same data on the number line, dot plot, and histogram.
6.SP.B.5 — Relate n (number of observations—here, rolls), measures of center, and measures of variability to the context: sums of two dice, fair rolls.

Before students work

Clarify that each recorded value is the sum of the two dice, not the pair of faces separately.
Ask for a quick prediction: Which sums will be easiest to get? Rarest? (Do not require correctness—elicit reasoning.)

Suggested flow

Roll manually until there are enough points to see a pattern (or use Add 10 rolls / Add 100 rolls to build data faster).
Read Summary statistics aloud; ask students which numbers changed the most after a big batch of rolls.
Hover rows in the table to open the Definitions panel—have students explain the formulas in their own words.
Switch among Number line, Dot plot, and Histogram; ask which display best answers a partner’s question about frequency, shape, or outliers.
Use Clear to reset and compare a “small sample” run to a “large sample” run (stability of mean; smoother shape).

Discussion prompts

Why is 7 in the middle of the distribution for fair dice? (Combinations—optional extension.)
When would the mean and median nearly match? When might they differ? (This symmetric context: usually close.)
What does a larger range or MAD tell you about a class’s rolls versus another class’s?
How does adding 100 rolls change the shape compared to only 10 rolls?

Using the definitions column

Encourage keyboard users to tab through summary rows. The right-hand panel restates ideas in student-friendly language and shows arithmetic for the current dataset—useful after a whole-class bulk roll.

Accessibility & classroom tips

Reduced-motion settings shorten roll animation.
For very large counts, dots shrink and may split into columns so stacks stay on screen—emphasize that taller still means more observations (more rolls) for that sum.

Offline extension

Have pairs record physical dice sums on paper, then enter only totals into discussion—or compare the computer’s long run to a short physical experiment.