Ratio of Buildings to Playground

Task Description

Studentsare given an aerial photograph of their school and explore ways to calculate the ratio of buildings to playground on the school site.

Length of Task

60 minutes

Materials

  • Aerial photograph of school, rulers, graph paper, trundle wheels, measuring tapes, scissors, calculators.

Using the Activity

Introductory

The teacherdisplays a large aerial photograph of the school site on the board. The teacher draws around various features of the school andasks the students to estimate the size. For example, ‘What is the area of the school? Our classroom? The school buildings? The oval? The playgrounds?’ etc. The teacher asks the students to brainstorm ways they might calculate these areas. The methods are recorded on the board.

Main Activity

The students form small groups and are givenan aerial map of the school. The teacher asks the groups to compare how much of the school site is covered by buildings to playground (or non-building area) and estimate theratio. Each group’s estimate is recorded. The groups formulate a strategy for calculating the ratio and trial this strategy.

Possible approaches undertaken for this task are:

  • The students calculate the area of the entire school site. They cut the aerial map into a jigsaw of buildings and playground. The buildings are clustered together to form one block. The area of the block of buildings is calculated and deducted from the total area of the school. The playground is calculated as the remaining part of the school. The areas of the buildings and playground are compared to form the two terms of the ratio.
  • The students use trundle wheels and measure the perimeter of the school and buildings to calculate the area of each item. They add the building areas together and subtract the total from the overall school area to find the area of the playgrounds.
  • Students wanting to add a scale to the aerial view of the map mayselect one building on the map, measured the length of one side of the building and compared this to the length on the map representation. They are able to determine what1cm on the map represents (e.g. 3.75m in the case of the trial). With this information the students are able to provide accurate figures for the area of all buildings and the playground. The students can subtract the buildings from the school site to calculate the playground area. The ratio isproduced from these two terms.
  • Some students may calculate all the areas of the buildings and all the parts of the playground from the aerial map to form the terms of the ratio.
  • Some students may draw a grid over the top of the aerial map and count up the squares that contain the buildings and playground. They calculate the ratio using the number of squares for each term.

Reflection

The teacher draws the students together to share their approaches and responses to the problem.The teacher encourages students to simplify their ratio if possible. The students and teacher explore the different responses to determine an estimated ratio of the buildings to playground (e.g. 1:4).The teacher invites the students to represent the ratio inequivalent representations of fractions, percentages and decimals.

Key Mathematical Concepts

  • Calculating ratios through comparison of area.
  • Representation of simple ratios as percentages, fractions and decimals.

Prerequisite Knowledge

  • Understanding of simple ratios and their representation as fractions, decimals and percentages.
  • Calculate the area of a rectangle.

Links to VELS

Dimension / Standard
Number (Level 4) / Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, 3/4 = 9/12 = 0.75 = 75% =3 : 4 = 6 : 8).
Working Mathematically (Level 4) / Students use the mathematical structure of problems to choose strategies for solutions. They explain their reasoning and procedures and interpret solutions. They create new problems based on familiar problem structures.

Assessment

To be working at Level 4, students should be able to:

  • Use ratio to compare the relationship between quantities.
  • Find equivalent representations of a ratio inpercentages, fractions and decimals.

Extension Suggestions

For students who would benefit from additional challenges:

  • Students complete the Design Your Own School Task.

Teacher Adviceand Feedback

The teachers trialling this task were pleasantly surprised by the range of strategies employed by the class. While some strategies were less efficient and accurate than others the overall result was pleasing.

The aerial view of most metropolitan schools can be found on the Google Mapswebsite.

It was unnecessary for the students to measure any part of the school with the trundle wheel to determine the ratio between the buildings and playground. It would be recommended for students who are keen to determine the area of the school to use a map with a scale or create a scale based on measuringonly one side of a building and comparing this to the wall represented on the map.

Potential Student Difficulties

Some students become overwhelmed withthe multiple calculations carried out for the area of the buildings. These students might be encouraged to draw a grid over the aerial map and count the number of blocks covering the building and playground. The task might be further simplified by asking students to explore the ratio of one building (e.g. a portable classroom)to the school oval.

References/ Acknowledgements

Thank you to the teachers and students from Lloyd Street PS, for providing valuable feedback on the use of this activity.


Viewing the aerial map

The teacher displays the aerial map of the school from Google Maps and highlights different areas that are the playground.

Student work samples

Example 1: Working at Level 4

These students are creating a jigsaw through cutting out each if the buildings on the map and clustering the pieces into one block for ease of calculation.

Example 2: Working at Level 4

This student is drawing a grid over the aerial view of the school. The group will count the squares filled with buildings compared to the squares filled with playground to create the ratio.

Example 3: Working at Level 4

This group is calculating the area of each building to determine the overall area of the buildings. They will subtract the area of the buildings from the area of the school site to determine the area of the playground. These two figures are the ratio terms.

This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the TTML Project Leader.