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CCSS 6.SP.A & 6.SP.B

Unit 8 HyperDoc — Statistics

Data Lab: build a plot, then read the mean, median, mode, and range. Follow the 5 steps from top to bottom.

Neft Teacher · Grade 6 Mathematics

Learning Target

I can recognize a statistical question and explain why it has variability. (6.SP.A.1)
I can find the mean, median, mode, and range of a data set. (6.SP.B.5)
I can interpret data displays (dot plots, histograms) and describe shape, center, and spread. (6.SP.A.2, 6.SP.B.4)
I can explain when the mean or median better describes a data set. (6.SP.A.3)

📐 Standards: 6.SP.A.1–3 · 6.SP.B.4–5 ⏱ Estimated time: 55 minutes 📦 Materials: pencil, this HyperDoc, optional dot-plot handout 👥 Format: individual or pair work

Teacher Notes (not for student display)

Pacing

Engage — 5 min: collect real sleep data from the class (show of hands); chart range on board.
Explore — 10 min: 3D Data Lab game + 3 min debrief on what measure changed most.
Explain — 8 min: work through the table example whole-class; students copy steps.
Apply — 5 min self-check + 15 min graded NTKit questions.
Reflect — 7 min individual writing; collect as PDF deliverable.

Grouping

Pair students for Explore; individual for Apply and Reflect.
For small groups: have students compare mean vs. median answers before checking.

Differentiation — Support

Provide a step-by-step "How to find the mean" reference card.
Allow calculator use for mean computation.
Reduce Apply to Q1–Q4 for students who need scaffolding.

Differentiation — Challenge

Ask: "If you add one very large number to a data set, which measures change? By how much?"
Extension: introduce Mean Absolute Deviation (MAD) as a measure of spread.
Have students create their own statistical question, collect data from the class, and compute all four measures.

ESOL / Language Supports

Post bilingual vocabulary: media/mean, mediana/median, moda/mode, rango/range, pregunta estadística/statistical question.
Use the sorted data table as a visual organizer — point to each step.
Accept numeric answers without full sentences for emerging English learners.
Sentence frames for reflection: "The median is better when … because …"

Step 1 · Engage

A Question Worth Measuring

Your class asks: "How many hours do we sleep each night?" Some students sleep 6 hours. Some sleep 10. The answers are different each time. That makes it a statistical question — it has many answers that vary.

Do this: Think of one question about your class that would get many different answers. You will write it in Step 5.

Non-statistical example: "How old am I?" — only one answer. Statistical example: "How old are the students in my class?" — many different answers.

Step 2 · Explore

Play and Explore

Do this: Open the 3D game in a new tab. Build the plot and find the measures. Then come back here.

Play: Data Lab (3D) Stack blocks, read the measures Math Hub All units and tools Graphic Novels Read the math story

After playing: which measure (mean, median, mode, range) changed the most when you added a very large value? Remember this for the reflection.

Step 3 · Explain

The Words You Need

Mean — the average. Add all numbers, then divide by how many.

Median — the middle number when sorted small to big.

Mode — the number that shows up most.

Range — biggest number minus smallest number.

Statistical question — a question with answers that vary (not just one answer).

Distribution — the shape of data: symmetric (even), skewed (pulled to one side), or clustered.

Worked example. Hours of sleep: 6, 8, 8, 7, 6

First sort them: 6, 6, 7, 8, 8

Measure	How	Answer
Mean	(6+6+7+8+8) ÷ 5 = 35 ÷ 5	7
Median	middle of 6, 6, 7, 8, 8	7
Mode	6 and 8 each appear twice	6 and 8
Range	8 − 6	2

Key idea: When there is an outlier (a very large or very small number), the mean gets pulled toward it. The median is usually a better description of "typical" in that case.

Rubric

How Your Work Is Scored

Level	Score	What this looks like
4 — Exceeds	6/6	All 6 graded questions correct AND both reflection responses are detailed with real-world examples. Self-check completed before graded section.
3 — Meets	5–6/6	At least 5 graded questions correct. Both reflections answered in complete sentences. Minor arithmetic error in mean or range.
2 — Approaching	3–4/6	Some correct answers; confuses mean with median, or does not sort before finding median. At least one reflection attempted.
1 — Beginning	0–2/6	Fewer than 3 correct; does not demonstrate understanding of center vs. spread. Reflections missing or incomplete.

Step 5 · Reflect

Think About It

Write in complete sentences. Use math vocabulary from Step 3.

1. Write one statistical question about your class. Explain why it is statistical (why the answers would vary).

2. When is the median a better choice than the mean? Give a real-world example using numbers.

Deliverable: When you finish, press Save as PDF below and upload it to your class folder. Your reflection responses and score will be included in the document.

Your reflections are saved in your PDF and DOC downloads below.

Teacher Resource

Answer Key

Show / Hide Answer Key (Teacher Only)

#	Question	Correct Answer	Standard	Explanation
Self-Check A	Statistical question?	B — how many books per month	6.SP.A.1	Answers vary from student to student.
Self-Check B	Mean of 2, 4, 6, 8, 10	6	6.SP.B.5	(2+4+6+8+10) ÷ 5 = 30 ÷ 5 = 6.
Self-Check C	Outlier effect	Mean	6.SP.A.3	The mean includes all values; one large outlier pulls it significantly.
Q1	Statistical question?	B — height of students	6.SP.A.1	Each student has a different height, so answers vary.
Q2	Mean of 4, 8, 6, 2	5	6.SP.B.5	(4+8+6+2) ÷ 4 = 20 ÷ 4 = 5.
Q3	Median of 3, 9, 5, 1, 7	5	6.SP.B.5	Sorted: 1, 3, 5, 7, 9 — middle value is 5.
Q4	Mode of 2, 5, 2, 8, 2, 5	2	6.SP.B.5	2 appears 3 times; 5 appears 2 times. Mode = 2.
Q5	Range of 10, 4, 7, 2, 9	8	6.SP.B.5	10 − 2 = 8.
Q6	Outlier in dot plot	B — the mean	6.SP.A.3	The mean is pulled toward 4; mode (1) and median (1) stay the same.

Finish

Name, Score, and Save

Type your name above. Check answers in Step 4. Then Save as PDF or DOC to turn in.