Learning ratios and proportions through scale drawings.

Laskey, Erwin                           Eugene Field School
1503 Lita                               508-4030
Deerfield Il. 60015
459-9898

Objectives:

To understand that a ratio is a comparison between two numbers. 

To understand that a proportion is an equivalent relation between two 
ratios.

To understand that scale drawings are ratios.

Given the ratios, the children will be able to make a scale drawing of 
the classroom.

Apparatus Needed:

1/4" and 1/2" graph paper
yardsticks
a variety of large wall maps

Recommended Strategy:

Introduction:

     Write the word scale and discuss different types of scales 
including those used for weight, temperature, and maps.  Allow the 
children to come up with as many ideas as possible and write them on 
the board.  Tell the children that you will be discussing scales on a 
map and that scales are ratios.  To explain ratios, draw a set of 3 
triangles and 4 squares.  Explain that this is a ratio of three 
triangles to four squares which can be written as 3 to 4, 3:4, or 3/4.  
Give other examples of ratios then use the map as the final example.  
Discuss the map ratio which is the scale of the map.  Ask how the ratio 
affects the size of the map.  What would happen if the ratio were 
different?  Try to show maps with other ratios. 

Activity:

     Divide the children into teams so that each team has a surface 
area to measure including the floor and the walls but not the ceiling.  
Each team must have two dimensions and be able to change the dimensions 
of the room in order to draw it on the 1/4" graph paper scale.  It 
might be wise to demonstrate this before the teams begin working.  When 
each team has completed, have them cut out their surface leaving 1/2" 
edges around all sides except that which is adjacent to the ceiling.  
Tape the walls and floors together creating a room model.  The children 
might want to do furniture to scale given enough time.  You might also 
include blackboards, bulletin boards, and wall outlets.   Have the 
children repeat this procedure with 1/2" graph paper.  Compare the 
difference between the two models and discuss the idea of proportion.  
Carrying the activity one step further convert the measurements of the 
room to metric and do the activity on centimeter paper. 

Extended activities:

     Using the different models, discuss volume of the room and whether 
or not the metric would be the same as or different from the standard 
measure.  Use salt or sand to do volume measurements. 

     Have the children make an enlargement of a candy wrapper showing           
that a scale drawing can help to enlarge as well as make smaller.  
Divide the candy wrapper into 1/4" grids and then divide a large piece 
of white art paper into 3/4" or 1" grids.  Have the children fill in 
one grid at a time using colored markers the same way it is done on the 
wrapper.  Do the details first then the larger areas that might be all 
the same color.  An M & M box is a good example of an easy object to 
work on. 
     
     Spaces, a book located in the SMILE math library, has another set 
of activities similar to the room scale drawing.  It includes 2 cm 
graph paper and an activity to design a scale model veterinarian's 
office with an equipment list and their measurements.  It's meant to be 
Xeroxed.   (NOTE: As of 8/2000 Spaces by Peter Parnall was still 
available from amazon.com - ISBN 1562943367)