"Design and build a model birdhouse from a single sheet of 8.5" x 11" sheet of paper." This open ended activity seems simple at first but will require careful planning and attention to detail for students to be successful.
You might start off this activity by showing a photo of an actual birdhouse and asking students to brainstorm the features of a good birdhouse. A website like this one might be a good guide.
Next you can talk about the expectations for their model birdhouse design:
Students should then be asked to create a design. The design should minimize wasted paper (i.e. use as much of the page as possible) and be easy to assemble (i.e. minimize the number of pieces you have to cut out and assemble). You can then show students an example of a finished design.
Step 1 - Students should brainstorm some possible designs (at least two) on a piece of looseleaf
Step 2 - Ask students to pick their favourite idea and share it with the teacher
Step 3 - Once the teacher approves their design, students are given a piece of card stock. They can then lay out their design with a ruler
Step 4 - When finished, students will measure and record all dimensions for their model. Students then calculate the surface area and volume of their design
Step 5 - The final step is to cut out and assemble their birdhouse model!
Here is a Google slides document that could be used to introduce the activity to students and make the expectations clear.
Math at Work 10 Activity: One teacher modified this activity by giving students a selection of designs to choose from instead of designing their own (here are links to pdf template 1 and template 2). Students then did all of the measurements and computations and had to determine costs for shingles on the roof, siding for the walls and paint for the interior. Here is a handout similar to the one she used.
Extensions: If you were to take your model and use it to build an actual birdhouse from wood, what would have to change? By what scale factor would you have to increase the size? How would building with 3/4" thick wood (instead of flat paper) change the size of the pieces needed? What supplies would you need and how much would it cost to build?
Mathematics 9 - G01 Students will be expected to determine the surface area of composite 3-D objects to solve problems
Mathematics 10 - M03 Students will be expected to solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including right cones, right cylinders, right prisms, right pyramids, and spheres.
Mathematic at Work 10 - M04 Students will be expected to solve problems that involve SI and imperial area measurements of regular, composite, and irregular 2-D shapes and 3-D objects, including decimal and fractional measurements, and verify the solutions.
Mathematics Essentials 12 - 2.4 Sketch and construct a model which will enable a student to show others some mathematics involved in a career interest