Hut building

Achievement objectives

GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.

GM4-2: Convert between metric units, using whole numbers and commonly used decimals.

GM4-6: Relate three-dimensional models to two-dimensional representations, and vice versa.

Description of mathematics

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.

Required materials

See Materials that come with this resource to download:

• Hut building activity (.pdf)

Activity

A hut is to be built with a single-pitch roof. The plans below show the main structure of the hut, but it needs a chimney to be added with the following specifications:

• The top of the chimney must be 500 mm above the top of the roof.
• The chimney will be attached to the centre of the outside of the south wall.
• The base of the chimney is to be 1m wide by 50 cm deep.

Draw the chimney on the plans.

Note: Each of the squares on the paper is 5 mm x 5 mm.

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 support to understand the meaning of the scale 1:200 and how the various 2-dimensional drawings relate to one another.)
• What are the important conditions for the location of the chimney? Where will the chimney be in each drawing? Which part of the chimney will be visible?
• Does this look or sound like a problem I have worked on before? (Students should relate the task to drawings of other objects, such as cube structures.)
• What information has been given?
• Is there anything missing? (The location of the chimney on each view requires inference from the conditions provided and the view diagrams.)
• What will the solution look like? (The chimney will be visible in each view, including the perspective drawing.) 

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 do I need to know to get started?
• Can I build a 3-dimensional model of the hut to help me? What materials would be helpful? (Modelling clay or plasticine.)
• What strategies can I use to get started? (Starting with one view first, then progressing to the others, is a useful strategy.)
• Which view should I try to get right first? Why choose that view?

Take action

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

• Have I worked in a systematic, step-by-step way? Have I got the scale correct and used the 5mm squares to make the chimney the correct size?
• How can I check that the drawings I have made are correct? Should I compare my drawings to those of other students? How can I check my drawings using the model I made?
• How could I make sure that I haven’t missed anything?
• Does my solution make sense? Does it match my visual image of the hut?
• Does my solution answer the question? Is the chimney visible on all drawings? Should it be?

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 the solution? 
• Is my drawing clear for someone else to follow?
• How would I convince someone else that I am correct? (The model might be useful.)
• What have I learned about solving problems like this?
• What could I try differently next time?
• Is there some mathematics that I need to learn from this task?