Grade 6 Workbook — Chapter 16: The Data Cycle and Circle Graphs

SOL 6.PS.1 · Companion to Textbook Chapter 16

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/.

PAGE 1 — Chapter opener

Chapter 16 · The Data Cycle and Circle Graphs

Standard 6.PS.1

In this chapter you will:

• Formulate questions that require collecting data
• Collect or acquire data and judge whether a sample represents a population
• Organize and represent data using circle graphs
• Analyze circle graphs and draw conclusions
• Compare circle graphs with bar graphs, pictographs, and line plots

Words to know: data cycle · statistical question · population · sample · representative sample · circle graph · sector · pictograph · line plot (dot plot)

Tool note: you will need a protractor for pages 10 and 11. A spreadsheet may be used for the technology version.

PAGE 2 — The four phases

16.1 The Data Cycle

FIGURE: fig1-data-cycle.png (full width) [Four-phase circular flow diagram: formulate questions; collect or acquire data; organize and represent data; analyze data and communicate results.]

Write the four phases in order.

Name the phase for each action.

PAGE 3 — One project, four phases

The Cycle in Action

A class wants to help the cafeteria plan the menu. Complete the table.

Explain. Why is the data cycle drawn as a circle instead of a straight line?

Challenge. The class finishes its graph, and a teacher asks, "Do seventh graders agree?" Which phase does the class return to, and what must they do next?

PAGE 4 — Exit ticket 16.1

Exit Ticket · Lesson 16.1

Name: ________________________ Date: ____________

1. Name the four phases of the data cycle in order.

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2. Which phase includes choosing between a survey and an experiment? ______________

3. A student draws a circle graph of class data. Which phase is that? ______________

4. Explain why analyzing data comes after representing it.

PAGE 5 — Good questions

16.2 Formulating Good Questions

A statistical question is answered with data that vary from person to person or thing to thing.

Circle S for statistical or N for not statistical.

A question fits a circle graph when:

1. The responses are ____________________, not measurements.
2. Each person is counted ____________ time(s).
3. The categories cover ____________________.

Rewrite each question so it fits a circle graph.

"What sports do you like?" → _______________________________________________

"What music do you like?" → _______________________________________________

PAGE 6 — Exit ticket 16.2

Exit Ticket · Lesson 16.2

Name: ________________________ Date: ____________

1. Is "How many siblings do sixth graders have?" a statistical question? Explain.

2. Name one requirement a question must meet before its data can go in a circle graph.

3. Rewrite "What music do you like?" so it fits a circle graph.

4. Why does "circle all that apply" ruin a circle graph?

PAGE 7 — Collecting data

16.3 Collecting Data

Match each question to the best method: observation, measurement, survey, or experiment.

FIGURE: fig2-population-sample.png (half width) [Large rectangle labeled "Population: all 300 sixth graders" filled with student icons; a shaded oval inside labeled "Sample: 60 students" enclosing a scattered subset.]

Fill in.

The ____________________ is the entire group you want to describe.

The ____________________ is the part of that group you actually collect data from.

A school has 500 students. A club surveys 50 of them.

Population: _______________ Sample: _______________

PAGE 8 — Is this sample fair?

Representative or Biased?

Write R for representative or B for biased, then give a reason.

Fix the question. Rewrite so it is neutral: "Wouldn't you rather have longer recess than more art class?"

Name three factors that help make a sample representative.

1. _______________________ 2. _______________________ 3. _______________________

PAGE 9 — Exit ticket 16.3

Exit Ticket · Lesson 16.3

Name: ________________________ Date: ____________

1. A club surveys 30 of the 500 students in a school. Population: ____________ Sample: ____________

2. Which method would you use to find the favorite movie genre of sixth graders? ____________

3. Give one reason a sample of 5 students is weak for a grade of 250.

4. What makes a sample representative of a population?

PAGE 10 — Mid-chapter check

Mid-Chapter Check · Lessons 16.1–16.3

Name: ________________________ Date: ____________

1. Name the four phases of the data cycle in order.

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2. Write S or N: "What is the favorite lunch of students in our class?" ______

3. Name the collection method: standing at the door and recording how each student arrives. ______________

4. A school has 240 seventh graders and a class surveys 40. Population: ______ Sample: ______

5. Give one reason surveying only the chess club is biased for a question about the whole grade.

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6. Rewrite so each student is counted once: "Which after-school clubs do you like?"

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PAGE 11 — Building a circle graph

16.4 Making a Circle Graph

FIGURE: fig3-circle-graph-fruit.png (half width) [Circle graph "Favorite Fruit, 20 Students": Apple 126 degrees 35%, Banana 90 degrees 25%, Orange 72 degrees 20%, Grape 72 degrees 20%.]

$$\text{percent} = \frac{\text{count}}{\text{total}} \qquad \text{angle} = \frac{\text{count}}{\text{total}} \times 360°$$

Twenty students say how they get to school. Complete the table.

Check: percents add to ______ and angles add to ______.

PAGE 12 — Draw it

Draw the Graph

FIGURE: fig4-circle-graph-steps.png (full width) [Three-panel protractor step diagram: draw circle and one radius; measure the first central angle; finished labeled circle graph.]

Fifty students vote for an elective. Complete the table, then draw the circle graph in the space below.

BLANK CIRCLE: 3 in diameter, center marked, one radius drawn straight up

Find the missing percent. A circle graph shows $45\%$, $20\%$, $15\%$, and one more sector. Missing: ______

Find the error. A student reports sectors of $40\%$, $30\%$, $20\%$, and $15\%$. What is wrong?

PAGE 13 — Exit ticket 16.4

Exit Ticket · Lesson 16.4

Name: ________________________ Date: ____________

1. Four out of 20 students chose grapes. Percent: ______ Angle: ______

2. Five out of 25 students walk to school. Percent: ______

3. A circle graph shows $35\%$, $25\%$, and $25\%$. Missing percent: ______

4. Explain how to turn a count out of a total into a central angle.

PAGE 14 — Reading a circle graph

16.5 Analyzing Circle Graphs

FIGURE: fig5-circle-graph-transportation.png (half width) [Circle graph "How 200 Sixth Graders Get to School": Bus 45% at 162 degrees, Car 25% at 90 degrees, Walk 20% at 72 degrees, Bike 10% at 36 degrees.]

$$\text{count} = \text{percent} \times \text{total}$$

Complete the table for the 200 students.

Answer.

Most common method: ______________ Least common: ______________

Students who walk or bike: ______ How many more ride the bus than ride in a car? ______

PAGE 15 — Observation or conclusion?

Observations and Conclusions

Write O for observation or C for conclusion.

Ana's $40 allowance: savings $50\%$, snacks $25\%$, gifts $15\%$, games $10\%$.

Savings: $______ Snacks: $______ Gifts and games together: $______

How much more goes to savings than to snacks? $______

Think. School A: $50\%$ of 20 students chose soccer. School B: $25\%$ of 200 students chose soccer. Which school has more soccer fans, and why?

PAGE 16 — Exit ticket 16.5

Exit Ticket · Lesson 16.5

Name: ________________________ Date: ____________

Graph: "60 Minutes of Homework" — math $40\%$, reading $25\%$, science $20\%$, other $15\%$.

1. Largest share of time: ______________

2. Minutes on reading: ______

3. Minutes on science and other combined: ______

4. Write one conclusion this graph supports, and name the observation behind it.

PAGE 17 — Four ways to show the same data

16.6 Choosing the Best Representation

FIGURE: fig6-four-representations.png (full width) [Four panels of the same favorite-sport data: circle graph with sectors 144, 90, 72, 54 degrees; bar graph with bars 8, 5, 4, 3; pictograph with key 1 figure = 2 students; line plot of number of siblings for 20 students.]

Twenty students named one favorite sport: soccer 8, basketball 5, baseball 4, swimming 3. Complete the table.

Match the question to the best graph.

PAGE 18 — Justify your choice

Justify It

Sentence frame: "A ____________ is best, because the question asks ____________, and this graph shows ____________."

Use the frame for each question.

1. What share of the class chose each field trip?

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2. How many more students chose the museum than the zoo?

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3. How many minutes each of 20 students read, showing every value?

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Explain. Name one thing a bar graph shows that a circle graph does not, and one thing a circle graph shows that a bar graph does not.

PAGE 19 — Exit ticket 16.6

Exit Ticket · Lesson 16.6

Name: ________________________ Date: ____________

1. Which graph best shows each category as a share of the whole? ______________

2. Which graph best shows exact counts on a numbered scale? ______________

3. With a key of 1 symbol = 2 students, how many symbols show 7 students? ______

4. Why is a line plot, not a circle graph, right for the number of siblings each student has?

PAGE 20 — Chapter 16 review, part 1

Chapter 16 Review

Part A · Formulating questions

1. Circle the statistical questions: a) How many pets does Mr. Lee own? b) How many pets do sixth graders own? c) What is the favorite season of students in our class? d) What time does school start?

2. Rewrite "What sports do you like?" for a circle graph: _______________________________________________

3. Why should the question say "choose exactly one"? _______________________________________________

4. Write a statistical question about your grade that fits a circle graph, and list four choices.

   Question: _______________________________________________

   Choices: ____________, ____________, ____________, ____________

Part B · Collecting data and samples

5. Best method: a) classroom temperature each hour ____________ b) favorite music genre ____________ c) students wearing sneakers Monday ____________ d) plants under a lamp or window ____________

6. School of 500, club surveys 50. Population: ______ Sample: ______

7. Two reasons the basketball-tryouts survey is biased:

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8. Three factors that make a sample representative: ____________, ____________, ____________

Part C · Making circle graphs

9. 25 students: pizza 10, sandwich 5, salad 5, pasta 5. Percents: ______, ______, ______, ______ Total: ______

10. 10 students: dog 4, cat 3, fish 2, bird 1. Angles: ______, ______, ______, ______ Total: ______

11. Sectors $40\%$, $25\%$, $20\%$, and one more. Missing percent: ______ Angle: ______

12. Why is a survey of 20 students easier to graph by hand than a survey of 17 students?

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PAGE 21 — Chapter 16 review, part 2

Chapter 16 Review (continued)

Part D · Analyzing circle graphs

Graph: "Favorite Season, 200 Students" — summer $40\%$, fall $25\%$, winter $20\%$, spring $15\%$.

13. Chose summer: ______

14. Chose winter or spring: ______

15. How many more chose summer than fall? ______

16. One observation: _______________________________________________

    One conclusion: _______________________________________________

Part E · Comparing representations

17. Best representation: a) share of class per field trip ____________ b) how many more chose museum than zoo ____________ c) minutes read by each of 20 students ____________

18. Key of 1 symbol = 5 students. Symbols for 20: ______ for 15: ______ for 10: ______

19. One thing a bar graph shows that a circle graph does not: _______________________________________________

    One thing a circle graph shows that a bar graph does not: _______________________________________________

Part F · Application and reasoning

20. 20 students: orange 8, apple 6, grape 4, other 2.

Conclusion: _______________________________________________

21. A student surveys 6 friends and reports that $50\%$ of the whole grade prefers tacos. Name two problems and how to fix them.

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22. Walk through the four phases for "Which after-school club should the school add?" One sentence each.

    Formulate: _______________________________________________

    Collect: _______________________________________________

    Organize: _______________________________________________

    Analyze and communicate: _______________________________________________

23. Two circle graphs each show a $50\%$ soccer sector, one from 20 students and one from 200. Why are these not the same number of students?

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Canva production notes

• Page size: 8.5 × 11 in, 0.75 in margins
• Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
• Blank circle: page 12 needs a 3 in circle with a marked center and one vertical radius; leave 3 in of clear space beneath for the student's labeled graph
• Figure widths: fig1-data-cycle.png, fig4-circle-graph-steps.png, and fig6-four-representations.png full width; circle graphs at half width beside their tables
• Tables: keep each row on one line so Canva text boxes do not reflow
• Protractor: pages 11–12 assume students have a protractor; note this on the teacher copy