Andrew's Caravan

Purpose

The purpose of this activity is to engage students in solving a problem using measurements that are not in a compatible format.

Achievement Objectives
GM4-2: Convert between metric units, using whole numbers and commonly used decimals.
Description of Mathematics

This activity assumes the students have experience in the following areas:

  • Working with metric units for length.
  • Identifying parts of a circle.
  • Finding lengths and areas in composite shapes.

The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.

The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.

Activity

 

Andrew wants to store his caravan in a shed with clearance of 2.25 m to get into the shed.

The caravan body is 1.85 m high and is on wheels of diameter, 40 cm. He is going to fit a dome ceiling window in the roof of the caravan.

What is the maximum height the dome could be, so that he can still use the shed for storage? 
 


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 in pairs or small groups.

  • Do I understand the situation and the words? (Students may need support to understand the meaning of diameter, caravan body and dome.)
  • Can you visualise the measurements on the picture of the caravan? Estimate how high the shed doorway is.
  • What will my solution look like? (The solution will be the height of the dome so the caravan can still fit into the shed.)
  • Do I have all the information I need to get started?

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.

  • What else do I need to know to get started?
  • How will I record my working so I can cope with all the information?
  • Can I express all the measurements in the same unit? Why will that help?
  • What tools (digital or physical) could help my investigation? Will using a ruler or tape measure help me understand the real sizes of the caravan and shed?

Take action

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

  • Have I shown my workings in a clear way using a diagram?
  • Do my calculations seem correct? Do they match any estimates I made?
  • Does my solution seem reasonable?
  • Is there another possible way to solve this problem?

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.

  • Is my working clear for someone else to follow?
  • How would I convince someone else I am correct?
  • How might Andrew use the advice my solution gives him?
  • Would my answer work in a different situation?
  • What have I learned about using units of length?
  • Which ideas or tools worked well in my investigation?

Examples of work

Work sample 1

  • The student calculates correctly to solve the problem, within the context given, with guidance.

Click on the image to enlarge it. Click again to close. 

Work sample 2

The student calculates correctly to solve the problem, within the context given.

Click on the image to enlarge it. Click again to close. 

Attachments

Printed from https://nzmaths.co.nz/resource/andrew-s-caravan at 9:37pm on the 29th March 2024