Scaling Our School

Purpose

In this unit we look at estimating the length and height of buildings at your school. We then compare these estimates with the actual heights or lengths. Students will then build scale models selecting appropriate scales using ratio to translate the "real" dimensions into the dimensions for the scale model.

Specific Learning Outcomes
  • calculate measurements for simple scale models
  • determine measures of height indirectly
  • make reasonable estimates of the height and length of a building
  • measure length accurately to produce simple scale models
Description of Mathematics

Estimation is an important aspect at the beginning of this unit. Students will estimate the height and length of buildings within their school grounds and then use indirect methods of measurement to determine the actual height. Measurements of length will be determined by accurate use of tape measures.

The conversion of the actual measurements of height and length involve real world ratio thinking and maybe difficult for some students.

Required Resource Materials
Measuring equipment: 30 cm rulers, metre rulers, tape measures

Photos of buildings in the school grounds

Construction materials: cardboard, scissors, tape, pens, paint

Activity

Getting Started

  1. Explain to the students that this week they will be involved in making a scale model of their school for display in the administration area (or similar). Photos of the school buildings will be required. These can either be taken by the teacher or students.
  2. The students will use photographs of school buildings to estimate the height and length of these buildings. The students are to choose one school building which they will work with for the week. These buildings will be made into a scale model for display in the school administration area. Explain to the students that they are going to estimate the length and height of the buildings. Discuss with the students some benchmarks that they could use to help them make a meaningful estimate eg. 100m is the length of a standard rugby field – goal post to goal post or 2m is the height of a door frame. Record the estimates of the school buildings in a table.
  3. Discuss the students’ estimates of the height and length of their building and how they arrived at these estimates. What is the height of the tallest building? The shortest? What is the length of the longest building? The shortest?
  4. Discuss the effect of perspective on the estimates. Structures in the foreground look larger than those at a distance. The students may need to use other visual clues to counter this effect (eg. vehicles, trees, people).
  5. Discuss how the actual length and height of the buildings can be measured. The length can be measured using a metre ruler or a tape measure. Elicit some ideas from the students as to how they might measure the height indirectly (they can’t climb the buildings!). Some ways they can measure the height include:
    • One student holds up a metre stick beside the building. Other students walk away form the building until a referent such as a paper clip, or their thumb held at arm’s length, appears to be as long as the metre stick. Using the referent students count the number of paper clips, or thumbs high the building is, then convert this to metres.
    • Take a photo of a metre stick (or other known measure) being held upright beside the building. Use the metre stick as a referent to find the height of the building.
    • Measure the shadow cast by a metre stick. Then measure the building’s shadow at the same time of day. Use the measurements to draw a scale model on grid paper. Read the height of the building from the drawing.
  6. Get students to use as many methods as appropriate to measure the actual height of their building. Put the actual length and height into the table.
    How close were the estimates?
    Was there a large difference between the estimated height or length of your structure and the actual measurement?
    Why?

Exploring

  1. Explain that to make a scale model of the school, the model of each building will need to be in proportion. The scale used by each group will need to be the same.
  2. Using the table of actual heights ask:
    What scale can we use for our models that will work for these heights and lengths? Write the ideas in a modelling book for future reference.
  3. Discuss how the scale can be recorded. Ideas could include:
    • As a ratio – 40:1 or similar
    • As a comparison – two centimetres equals one metre
    • Using a graphic – scaling.
    What are the benefits of these methods of recording a scale?
    Which method is the best?
  4. For each scale suggested ask:
    How tall will the tallest building be?
    How tall will the shortest building be?
    How long will the longest building be?
    Which buildings will this scale work for?
    How large will the whole school be?
  5. After a consensus has been reached about which scale is the most appropriate to use, discuss with the students how they will complete their scale model.
    What materials will they need?
    What problems did you think about?
    Who has some ideas for solutions?
    Does anyone have ideas about how to show the inside of a building?
  6. Before the students start to make their scale models discuss the importance of everyone using the same scale for their building. Check that all groups have an accurate scale-version height for their building.
    How did you work out the scale height?
    How can you check that you have the right scale height?
  7. Students will need to develop scale drawings (blueprint) of their building including width, depth and height. Discuss features such as doors, windows and other features of their buildings.
    How tall are doors?
    How wide?
    How tall will they be on your model?
    How wide?
    What about windows?
  8. Students could use Google Sketchup as a tool for constructing their blueprints.
  9. Once the blueprint has been completed get the students to reflect on their drawings. Are the proportions correct? Will your building fit with the other buildings in the school model?
  10. The students, in groups, then construct their school building.

Sharing

  1. Allow the students to share and reflect on the scale models.
    What did you notice about the scale models?
    What do you like best about the models?
    What would you change if you were going to do them over again?
    What things did you change your mind about when you were making your model?
  2. Assemble all of the scale models into a complete scale model of the school. Include playing fields, paths etc.

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