Return to Mathematics IndexLearning ratios and proportions through scale drawings.

Laskey, Erwin Eugene Field School

508-4030

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 mapsRecommended Strategy:Introduction: Write the wordscaleand 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 areratios. 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. (As of 8/2000,Spacesby Peter Parnall is available from

Amazon.com for $21.90 - ISBN 1562943367 - info added by Roy Coleman 8/2000)