Camping groups

Achievement objectives

NA3-2: Know basic multiplication and division facts.

NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.

Required materials

See Materials that come with this resource to download:

• Camping groups activity (.pdf)

Activity

A class of 24 students is planning a camping trip.

The school has tents that fit three people each and backpacks that can be shared, one between two students.

The teacher wants the class to be split into cooking groups that will be as small as possible so that everyone sharing a tent will be in the same cooking group.

Also, each pair of students sharing a backpack will need to be in the same cooking group.

How many students will be in each cooking group? Explain how you arrived at your answer.

The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.

Make sense

Introduce the problem. Allow students time to read it and discuss it in pairs or small groups.

• Do I understand the situation and the words? (Students may need to act out the scenario of sharing tents and backpacks.)
• What maths is involved in this problem?
• Does this look or sound like a problem I have worked on before?
• What will my solution look like? (The solution will be the smallest number of students in each cooking group justified by some working.)

Plan approach

Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.

• Do I have all the information I need, or do I need to find some things out?
• What strategies will be useful to solve a problem like this? Will a diagram be useful? Could I use objects to be "make-believe" students? Should I just try some numbers to see if they work?
• What maths am I likely to need? How do I know?
• What will I need to work out first? Why will that be first?
• How will I record my workings?

Take action

Allow students time to work through their strategy and find a solution to the problem.

• Am I showing my workings in a step-by-step way?
• Is my first strategy working, or do I need to try something else?
• Do I need help from others?
• Am I using the most efficient way to find my answer? What numbers and operations are most efficient?
• Have I identified any relationships? Can I describe the relationships? (Common multiples should be noticed.)
• How can I express the relationships I found using words and symbols?
• Does my solution make sense? Does it work? Explain.

Convince yourself and others

Allow students time to check their answers, and then either have them pair share with other groups or ask for volunteers to share their solution with the class.

• What is my solution? Is it clearly expressed?
• Are my workings clear for someone else to follow?
• How would I convince someone else that I am correct?
• Are my workings expressed in a mathematical way? 
• Would my strategy work in a different situation? What kind of situation?
• Is there some mathematics I need to learn to solve similar problems?
• What have I noticed that seems to work all the time in these types of problems?