Learning ratios and proportions through scale drawings.

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 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. (As of 8/2000, Spaces by Peter Parnall is available from
Amazon.com for \$21.90 - ISBN 1562943367 - info added by Roy Coleman 8/2000)