Minds On
Collecting data
A community centre was hosting an event for students. Each student will get their choice of a pizza slice (pepperoni or cheese) and their choice of drink (water, apple juice, or orange juice).
How many different choices do students have for pizza and drink combinations? (One would be pepperoni and water.)
What data is needed so the event planner knows what to order?
How could we collect the data needed and give it to the event planner?
Throughout this learning activity, you can record your thoughts digitally, orally, or in print.
Action
Diagrams
We could use a Carroll diagram to display the pizza choices and collect the data.
| Food Choices | |||
|---|---|---|---|
| Pizza | Drink | ||
| Water | Apple juice | Orange juice | |
| Pepperoni | |||
| Cheese | |||
Tree Diagram
A tree diagram shows all possible outcomes when there are two or more choices.
A tree diagram:
- has a title
- each branch (line from the choice) represents a path
When constructing a tree diagram:
- Make a branch (a line out) for from each new choice and connect it to the next event.
- The branches (nodes) are connected.
Tree diagrams are used when there are different choices like in the community event.
Use the tree diagram to help make a list of all the combinations of choices for students. The list has been started. Record your list using a method of your choice.
- cheese slice and water
- cheese slice and apple juice
Press ‘Answer’ to reveal the possible combinations.
There are six possible combinations.
- cheese slice and water
- cheese slice and apple juice
- cheese slice and orange juice
- pepperoni slice and water
- pepperoni slice and apple juice
- pepperoni slice and orange juice
Routes to the waterfall
Two friends are going hiking.
At the park, there are three trails leading from the parking lot to the first lookout point. There are three trails from the lookout point to the waterfall. Friend A says there are six trails to choose from. Friend B thinks there are more choices.
Which friend is correct?
How many different routes are there from the parking lot to the waterfall?
What are the two attributes you are using for your tree diagram?
Use a tree diagram to support your thinking. Record your thinking using a method of your choice.
Press ‘Answer’ to reveal the the solution.
The two attributes are the trails from the parking lot and the trails from the lookout point.
There are nine different routes to the waterfall from the parking lot.
Consolidation
Let’s make a greeting card
The table has two categories labelled favourite materials and favourite tools. The table lists the favourite materials as art paper, Bristol board and construction paper. The table lists the favourite tools as markers, crayons, watercolour paint and coloured pencils. For the category of art paper, the favourite tools are markers with 19 tally marks; crayons with four tally marks, watercolour paint with four tally marks, and coloured pencils with four tally marks. For the category of Bristol board, the favourite tools are markers with five tally marks, crayons with three tally marks, watercolour paint with five tally marks, and coloured pencils with four tally marks. For the category of construction paper, the favourite tools ae markers with four tally marks, crayons with two tally marks, watercolour paint with zero tally marks and coloured pencils with three tally marks.
Learners were making greeting cards. They wanted to know which materials and tools they like to use. Here is the data they collected.
| Favourite Materials | |||
|---|---|---|---|
| Favourite tools | Art paper | Bristol board | Construction paper |
| Markers | |||
| Crayons | |||
| Watercolour paint | |||
| Coloured pencils | |||
The learners wanted to create a tree diagram to show all the possible combinations.
Use the information in the two-way table to create a tree diagram.
A tree diagram with possible combinations from the data collected for making a greeting card. Attribute 1 or tools: markers, crayons, watercolour paint, and coloured pencils. For the first tool (markers), it has 3 branches for attribute two, or materials. These materials are art paper, bristol board, and construction paper. The combinations of tools and materials are left blank. The final section is the total number of students for each tool and their favourite material, which is left blank.
Complete Tree Diagram in your notebook or using the following fillable and printable document.
Press the ‘Activity’ button to access the Tree Diagram.
Diagram questions
- How is a tree diagram different from other graphic organizers like a Venn diagram and Carroll diagrams?
- What types of situations and data does a tree diagram work well for?
Reflection
How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.
I feel…
Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.
Press ‘Discover More’ to extend your skills.
Discover MoreExamine the following tree diagram.
Do you think this is the most appropriate way to represent the data? Why or why not? How might you represent the data in another way?
Record your ideas digitally, orally, or in print.