Students work with scale in a number of mathematics courses in Nova Scotia. In the Mathematics Essentials 12 course, they work with scale in conjunction with reading blueprints. This scale activity uses the blueprints for an iconic Canadian airplane, the DHC-3 Otter. I started the lesson with some estimation.
I didn't let students know the name of the airplane to start with so that they don't just Google the name of the airplane and find out the actual length. Instead they use clues from the photo to make an estimate. Some references might include the size of the dock or ramp, the height of the wing, or the size of the windows or door. We use a routine I learned from Estimation180 to ask for an estimate they know is too low, an estimate they know is too high and then a just right estimate. After everyone had made and estimate, I showed them an image from a blueprint and asked them if they'd like to revise their estimate using some additional information.
On the blueprint, they can see a scale drawn above the plane. Students use this information to either confirm or adjust their estimate. We can then use the scale to measure the image to find out the actual length of the plane (about 41 ft). After this opening activity, I showed them a picture of a 1/48 scale plastic model and ask them to tell me what the size of the finished model is knowing the size of the actual plane and the scale factor.
The opening estimation allowed students a chance to think about scale. Next I handed out the blueprints for the plane. Our task was to use the blue prints to help create a 1/10th scale drawing of the top view of the plane using painters tape on the floor.
Students worked in small groups to recorded their measurements and calculate the measurements for the scale drawing. Once they were finished each group was provided with some painters tape and measuring tapes in order to make their scale drawing on the floor. It could be nice to have one group do their drawing on the wall, then it could stay up as a reference to their work with scale. We also talked about writing their measurements on the painters tape as they put it down.
Variations and Extensions
Students who finish quickly can continue to add additional details such as the pontoons. This activity could also be done with larger groups creating a life size drawing of this plan using sidewalk chalk outside (weather permitting).
Mathematics Essentials 12 - 3.1 Calculate the dimensions of actual objects using blueprints with various scales
Mathematics 11 - M02 Solve problems that involve scale diagrams, using proportional reasoning
Mathematic at Work 11 - G02 Students will be expected to solve problems that involve scale; and G04 Students will be expected to draw and describe exploded views, component parts and scale diagrams of simple 3‑D objects.
Mathematics Essentials 11 - E4 create 2-D scale diagrams and 3-D scale models
Mathematics 9 - G03 Students will be expected to draw and interpret scale diagrams of 2-D shapes.