Grade by Grade
D. Data · Data and Probability

Data Detectives: Asking Questions and Making Decisions

D1.5 A1About 40 minutes
Learning goals
  • I can ask and answer questions about data in bar graphs, line plots, and Venn and Carroll diagrams.
  • I can compare data using words like more, fewer, and how many in all.
  • I can draw a conclusion from data.
  • I can make a decision and give a convincing reason using numbers from the data.

Words to know

analyse
To look carefully at data to find out what it tells us.
conclusion
Something you figure out is true by looking at the data.
convincing argument
A reason that makes others agree with you, because it uses facts and numbers from the data.
informed decision
A choice you make after looking at the data.

Let's get started!

A detective looks at clues to solve a mystery. A data detective looks at data to answer questions and make good choices!

Today you will analyse data. That means you look closely, ask questions, figure out what the data tells you, and use it to make a decision.

Three kinds of questions

Data detectives ask three kinds of questions:

  1. Read it: What does the graph say? How many votes did the farm get?
  2. Compare it: How do the groups compare? How many more? How many fewer? How many in all? Which is the most?
  3. Think beyond it: What does it mean? What should we do? Where should we go on our trip?
Where Should We Go on Our Field Trip?012345678910Science ctr.FarmSugar bushPlaceNumber of votesSource: vote in Mr. Diaz's Grade 2 class
Bar graph of field trip votes: science centre 9, farm 6, sugar bush (a maple syrup farm) 7.
Worked example

Analysing a bar graph

Mr. Diaz's class voted on a field trip. Look at the bar graph. Ask and answer some questions. Then make a decision.

  1. Read it: How many votes did the sugar bush get? The bar reaches 7.
  2. Compare it: How many more votes did the science centre get than the farm? 9 − 6 = 3 more.
  3. Compare it: How many children voted in all? 9 + 6 + 7 = 22.
  4. Think beyond it: Which place got the most votes? The science centre (9). It is the mode.
  5. Decision: The class should go to the science centre.
  6. Convincing argument: "We should go to the science centre because it got 9 votes. That is 2 more than the sugar bush and 3 more than the farm. More children chose it than any other place."

Go to the science centre, because it got the most votes (9 out of 22).

Make it convincing

A convincing argument uses numbers from the data and the word because.

  • Not very convincing: "The science centre, because it's fun."
  • Convincing: "The science centre, because it got 9 votes, more than any other place."

Analysing a Venn diagram

Ms. Kaur wants to set up activity centres for free time. She asked 18 children, "Do you like reading? Do you like drawing?"

Likes readingLikes drawing5 kids6 kids4 kids3 kids
Venn diagram: 5 like only reading, 6 like both, 4 like only drawing, 3 like neither.
Worked example

What does the Venn diagram tell us?

Use the Venn diagram. How many children like drawing? Should Ms. Kaur set up a reading centre, a drawing centre, or both?

  1. Read it: 6 children are in the middle. They like reading and drawing.
  2. Compare it: Likes drawing: 4 + 6 = 10. Likes reading: 5 + 6 = 11.
  3. Compare it: Only 3 children like neither. 18 − 3 = 15 children like at least one of them.
  4. Think beyond it: Lots of children like each activity, and the numbers are close (11 and 10).
  5. Decision: Set up both centres. The 3 children who like neither could suggest another centre, like building blocks.

10 children like drawing. Set up both centres, because 11 like reading and 10 like drawing.

Analysing a line plot

Mr. Diaz's class asked: "How many books did you read in March?"

Books We Read in March01XX2XXX3XXXXX4XXXX5XX6XNumber of books read
Line plot: books read in March. Source: survey of Mr. Diaz's class.
Worked example

What does the line plot tell us?

Use the line plot. Answer the questions and draw a conclusion.

  1. Read it: How many children read 4 books? 4 Xs, so 4 children.
  2. Compare it: What is the mode? The tallest stack is above 3. Most often, children read 3 books.
  3. Compare it: How many children read 3 or more books? 5 + 4 + 2 + 1 = 12. How many read fewer than 3? 2 + 3 = 5.
  4. Count everyone: 2 + 3 + 5 + 4 + 2 + 1 = 17 children.
  5. Conclusion: Most of the class (12 out of 17) read 3 or more books. Nobody read 0 books.

The class reads a lot! 12 of 17 children read 3 or more books in March.

Is the data enough?

Sometimes data cannot answer a question. The book line plot tells us how many books, but not which books or if they were long or short. A good data detective says, "The data doesn't tell us that. We would need to collect more data."

Just for fun

Data detectives don't really need a magnifying glass 🔍 to read a bar graph… but it does make you look very clever while you do it!

Listening to others

Data detectives share their thinking and listen to others. If a friend makes a different decision, ask, "What number in the data made you think that?" You might both have good reasons! Being respectful while you disagree is part of doing math.

Hands-on activity

Data detective at home

  1. Look at a graph your family made in a past lesson, or make a new one. (Example: ask everyone at home "What should we have for dinner on Friday: tacos, pasta or soup?")
  2. Write 3 questions: one Read it, one Compare it, and one Think beyond it.
  3. Answer your questions.
  4. Make a decision and give a convincing argument with numbers and the word because.
  5. Look for graphs in a newspaper, flyer, or kids' magazine. What questions can you ask about them?

Your turn

1

Use the field trip graph. How many votes did the farm get?

2

Use the field trip graph. How many fewer votes did the farm get than the sugar bush?

3

Use the Venn diagram. How many children like reading?

4

Use the Venn diagram. How many children like only drawing (not reading)?

5

Use the line plot. How many children read exactly 2 books?

6

Use the line plot. How many children read 5 or 6 books?

7

Write a convincing argument for this decision: "Our class should buy more hockey sticks." The data: hockey 12 votes, soccer 5 votes, basketball 3 votes.

More practice: warm-up

1

What does analyse mean?

2

Use the field trip graph. Which place got the fewest votes?

3

Use the Venn diagram. How many children like neither reading nor drawing?

4

Use the line plot. How many children read 0 books?

5

Which word helps make a convincing argument: because or maybe?

More practice: on your own

1

Use the field trip graph. If the 6 farm voters all switched to the sugar bush, which place would win?

2

Use the Venn diagram. How many children were asked? Show how you know.

3

Use the line plot. Did more children read fewer than 3 books, or more than 3 books?

4

A Carroll diagram shows: wears glasses and likes winter 3; wears glasses and does not like winter 1; no glasses and likes winter 9; no glasses and does not like winter 5. How many children like winter?

5

Same Carroll diagram. Can you tell from this data why children like winter?

Challenge

1

Use the line plot. Mr. Diaz wants everyone to read at least 3 books next month. How many children need to read more than they did in March? Explain.

2

Two classes voted on a class pet. Class A: fish 10, hamster 8. Class B: fish 4, hamster 9. The two classes will share one pet. Which pet should they get? Give a convincing argument.

3

Pia says, "Most children in the Venn diagram like drawing more than reading." Is she right? Explain.

Check your understanding

Quiz

1.

Field trip votes: science centre 9, farm 6, sugar bush 7. How many children voted?

2.

Which is the most convincing argument for the science centre?

3.

Venn diagram: reading only 5, both 6, drawing only 4, neither 3. How many like drawing?

4.

In the book line plot, how many children read 3 or more books?

5.

Which question is a think beyond it question?

6.

A graph shows how many children like each fruit. Which question can the graph not answer?

For parents and teachers

What your child is learning: to analyse data in bar graphs, line plots and logic diagrams (Venn and Carroll) by asking and answering questions, comparing amounts, drawing conclusions, and making informed decisions backed by convincing arguments (Ontario expectation D1.5). Explaining thinking and listening respectfully to others' reasoning are part of the social-emotional learning and mathematical processes in Strand A.

Common difficulties:

  • Answering from opinion instead of the data. Ask, "What number in the graph tells you that?"
  • Mixing up how many more (subtract) with how many in all (add).
  • In Venn diagrams, forgetting to count the middle.
  • Thinking data can answer any question. Praise your child for noticing when the data can't tell us something.

At home: use data for real family decisions: vote on a weekend outing or a dinner, graph the votes, and have your child announce the decision with a reason that uses because and a number.