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D. Data · Data and Probability

Data and Probability: Unit Review

A1 D1.1 D1.2 D1.3 D1.4 D1.5 D2.1 D2.2About 40 minutes
Learning goals
  • I can sort data by two and three attributes using Venn, Carroll and tree diagrams.
  • I can collect data and organize it in a frequency table.
  • I can read and make pictographs and bar graphs where one picture or space stands for more than one.
  • I can find the mean and mode and explain what they tell me.
  • I can use data and likelihood to make predictions and decisions.

Words to know

attribute
A feature you can sort by, like size or pattern.
frequency table
A table that shows how many times each category or number happens.
key
Tells how many each picture in a pictograph stands for.
scale
The numbers up the side of a bar graph. They start at 0 and go up by equal amounts.
mean
The fair share when the data is evened out.
mode
The value that appears most often.
likelihood
How likely something is to happen: impossible, unlikely, equally likely, likely or certain.

Let's review!

In this unit you became a Grade 3 data detective. You sorted by three attributes, collected data in frequency tables, made pictographs and bar graphs with keys and scales, found the mean and mode, analysed data to make decisions, and used likelihood words to make predictions. This review has a few questions from every lesson. Try each one, then press Show answer to check.

1. Aska question2. Collecttallies, interviews3. Organizetable or graph4. Analysemean, mode, compare5. Decideor predictDatadetective
The steps a data detective follows. After you decide or predict, you often think of a new question, and the cycle starts again.
LargeRoundlarge roundsmall squareWhere does each button go?
Use this Venn diagram for the first question below. Ask of each button: Is it large? Is it round?

Sorting by Two and Three Attributes: Venn, Carroll and Tree Diagrams

1

Venn diagram with the circles Large and Round. Where does a large round button go? Where does a small square button go?

2

A tree diagram sorts toys by big or small, then soft or hard, then old or new. How many end branches does it have?

3

Lost-and-found: which items are plain hats? (A striped small hat, B plain large hat, E striped large hat, G plain small hat, I striped small hat)

Collecting Data: Questions, Tallies and Frequency Tables

1

Is how many minutes you read last night qualitative or quantitative data?

2

Make a frequency table: maple, oak, maple, birch, maple, oak, spruce, maple.

3

Counting the cars that pass your house is an interview, an observation or an experiment?

Pictographs Where One Picture Stands for Many

1

Key: ● = 2 children. A row has 4 circles and a half circle. How many children?

2

Key: ● = 10 cans. How do you show 35 cans?

3

Key: 📚 = 5 books. How many 📚 show 30 books?

Bar Graphs with Scales

1

A scale counts by 2s. A bar ends halfway between 10 and 12. What number?

2

Your data is 20, 50, 35, 15. Which scale would you use?

3

What is wrong with the scale 0, 5, 10, 20, 25?

Mean and Mode: What Is Typical?

1

Find the mean of 4, 8, 6.

2

Find the mode of 2, 7, 2, 5, 7, 1.

3

Find the mean and mode of 3, 3, 3, 7.

4

What does the mean tell us?

Data Detectives: Analysing Data and Making Decisions

1

Two bar graphs show the same data. One has a scale up to 20 and one up to 100. Why do the bars look different?

2

Votes for a class game: tag 8, four square 5, soccer 11. Make a convincing argument for which game to play.

3

In the game votes, how many people voted in all?

Impossible, Unlikely, Equally Likely, Likely, Certain

1

A spinner has 4 equal parts: 1 green, 3 blue. How likely is blue? Green? Yellow?

2

A bag has 4 green blocks and 4 yellow blocks. Compare picking green and picking yellow.

3

You win if you pick yellow. Bag A: 1 yellow, 7 green. Bag B: 6 yellow, 2 green. Which bag do you choose?

Will Another Group Have the Same Mean and Mode?

1

Grade 3 children's mean number of teeth lost is 5. Predict the mean for a group of Kindergarten children. Why?

2

Five children in Room 4 counted the letters in their first names: 6, 4, 5, 4, 6. Find the mean and the mode.

3

Your prediction about another class's mode didn't come true. What does that mean?

Just for fun

Knock, knock.

Who's there?

Tally.

Tally who?

Tally me your favourite snack, and I'll add a mark to my chart!

How to use this review

  • Do the review in two or three short sittings. Each section matches one lesson.
  • Let your child use tools: cubes or LEGO for levelling, paper and a ruler for graphs, a homemade spinner.
  • After each answer, ask "How do you know?" Explaining with numbers from the data matters as much as the answer.
  • Note which section had mistakes, then revisit that lesson's examples and practice.
Check your understanding

Quiz

1.

Venn diagram with the circles Hats and Striped: where does a plain hat go?

2.

A tree diagram sorts by 3 attributes, each with 2 choices. How many end branches?

3.

Which question gives qualitative data?

4.

Key: ● = 10 cans. A row has 2 circles and a half circle. How many cans?

5.

A bar graph's scale counts by 10s. A bar ends halfway between 40 and 50. What number?

6.

What is the mean of 3, 5, 10?

7.

What is the mode of 6, 2, 6, 9, 2, 6?

8.

Two graphs of the same data look different. What should you check first?

9.

A spinner has 3 equal parts: 2 yellow and 1 blue. Spinning yellow is...

10.

Two Grade 3 classes in the same town are asked their favourite winter activity. Will they have the same mode?

For parents and teachers

What this review covers: the whole Data and Probability unit: sorting by two and three attributes (D1.1), collecting data and frequency tables (D1.2), pictographs and bar graphs with many-to-one correspondence (D1.3), mean and mode (D1.4), analysing data and graphs with different scales (D1.5), likelihood words (D2.1), and predicting the mean and mode for different populations (D2.2), with social-emotional learning and process skills (A1) throughout.

Which lesson to revisit:

  • Items in the wrong part of a Venn diagram, or getting lost in a tree diagram: go back to Sorting by Two and Three Attributes.
  • Mixing up qualitative and quantitative data, or frequencies that don't add up to the total: go back to Collecting Data.
  • Counting pictures instead of using the key, or trouble with half pictures: go back to Pictographs Where One Picture Stands for Many.
  • Reading grid lines instead of the scale, or uneven scales: go back to Bar Graphs with Scales.
  • Confusing mean and mode, or sharing by the wrong number: go back to Mean and Mode.
  • Judging graphs by bar heights, or arguments with no numbers: go back to Data Detectives.
  • Calling a likely event certain, or ignoring part sizes on spinners: go back to Impossible, Unlikely, Equally Likely, Likely, Certain.
  • Saying another group will definitely have the same mode: go back to Will Another Group Have the Same Mean and Mode?

Quiz guide: questions 1 and 2 are sorting; 3 is collecting data; 4 is pictographs; 5 is bar graphs; 6 and 7 are mean and mode; 8 is analysing; 9 is likelihood; 10 is predicting for another population.

How to help: redo one example from the lesson with real objects, then try a similar question. Praise explanations that use because and a number from the data.