"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
How much does it cost to mail a package in Canada? What factors determine the cost of postage? If you have ever put a box in the mail at a Canada Post location, you'll notice the mail person do several things. First they put the box on a scale, then they measure the dimensions of the box with a measuring tape. Finally, they read the postal code for the destination and input it all into their computer. Then they'll tell you the price to mail it.
Getting students to measure items with a variety of measurement tools is great practice to get familiar with metric and imperial measurement systems as well as becoming familiar with common measurement units. Sometimes this practice is just measuring lines on a worksheet or measuring objects around the classroom (paperclips, pencils, desks, etc.). This can seem a bit trivial. I was hunting for measurement with a purpose and thought of the measurements that postal employees do. It turns out, you can find the rate for mailing a package by using a page on Canada Post's website.
The students seemed to enjoy the activity and got some purposeful practice using metric and imperial measurements.
Mathematics Essentials 12 - 1.6 Identify, use, and convert among and between SI units and Imperial units to measure and solve measurement problems
Mathematics 10 - M01 Students will be expected to solve problems that involve linear measurement, using SI and imperial units of measure, estimation strategies, and measurement strategies.
Mathematic at Work 10 - M03 Students will be expected to solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.
Mathematics Essentials 10 - D3 estimate distances in metric units and in imperial units by applying personal referents.
Over the Christmas holiday, the number of LEGO bricks in my house increased significantly. My son received LEGO sets as gifts from numerous grandparents, aunts and uncles. I was a LEGO fan when I was a child and now I have an excuse to play with them again as an adult. We've had lots of fun recently building sets and designing our own creations. At some point I became inspired to create a scale model of our home.
Planning and Building
I started this small project by building a test model to try out the proportions and to see what kinds of bricks I would need. The sizes of the door and window established the overall size. I continued revising the structure it until it looked right and then started collecting the bricks I needed.
Building this model reminded me of working on an OpenMiddle.com math problem. In an "open middle" problem, there is a one starting point and one solution but many different paths to get to the solution. With LEGO, there are many different ways to create, revise and improve your model. There are lots of different building techniques that will all result in a well designed scale model.
After I created my initial rough model I did some reading up on LEGO scale. It turns out that it is a fairly complex topic that lots of different people have investigated. I found the Brick Architect web site to be very helpful. For "classic minifigure" scale a ratio of 1:42 can be used. One major difficulty in discussing scale is that the proportions of a LEGO minifigure are not even close to the proportions of an actual person. A LEGO minifigure is about 4 cm tall and 1.6 cm wide. An average male human is about 175 cm tall and 40 cm wide... about half as wide as a minifigure would be at that height. Another challenge is converting units. The architectural drawings of my house are in feet, which I converted to metric (cm), then a scale factor is applied and finally the metric units are converted into LEGO bricks. I found an awesome tool that does this all for you, the LEGO Unit Converter.
I used a lot of estimation to determine how many bricks of each type I would need. LEGO bricks are not cheap so you don't want to order more than you need (Check out Jon Orr's activity involving cost, Is LEGO Gender Biased?). I purchased the bricks I needed on BrickLink.com, a large online LEGO marketplace. BrickLink provides a detailed price guide for every brick available which makes it really easy to know if you're getting a good deal or not.
I needed lots of 45 degree angle slope bricks for the roof of my house. These price stats let me know what a reasonable price is to pay for new or used bricks of this type. It is amazing to see how many bricks are sold on this site. I think that the stats from this site could make for an interesting grade 12 math research project.
The Finished Project
Constructing Rectangular and Triangular Prisms
Determining the surface area of a prism can get a bit stale. Textbooks contain lots of pictures of various right rectangular and triangular prisms. These prisms are carefully labeled with the exact information that a student needs. Students are given the task of inserting these numbers into a formula and doing some basic calculations. These types of problems often don't require much thought. I've recently had the pleasure of working in some junior high classrooms. We were looking for a more hands-on and thought provoking activity for surface area. We were also looking for an activity in which students could be creative. This is what we came up with.
Students, working in pairs, are given either a yellow or blue piece of coverstock. Students with a yellow piece are asked to design and draw the net of a right rectangular prism. Students with a blue piece are asked to design and draw the net of a right triangular prism. Students can draw whatever size or shape prism they wish as long as it covers the majority of the paper (at least half). Students use a ruler to carefully draw and measure the net. They measure and label the length and width of each face and calculate the area of each face on the net they have drawn. Once students have accurately drawn their nets and labeled the area of each side, a teacher will review their work. If it is an accurate net, the teacher will give the students a pair of scissors to cut it out. Make sure students do their calculations inside the net so that it is not lost when they cut it out. Once cut out, students can fold and tape their prism.
Students found this activity to be more challenging than they expected. Several had to start over after realizing that the prism they started wouldn't fit on the page or their net wouldn't fold into a proper prism. You could extend this activity by having students tape their nets inside out (with the calculations on the inside) and then challenging them to order the prisms from least surface area to greatest surface area.
Why I Like This Task
Double the Surface Area
Nova Scotia Mathematics Curriculum Outcomes
Grade 8 M02 - Students will be expected to draw and construct nets for 3-D objects.
Grade 8 M03 - Students will be expected to determine the surface area of right rectangular prisms, right triangular prisms, and right cylinders to solve problems.
Grade 9 G01 - Students will be expected to determine the surface area of composite 3-D objects to solve problems
Math at Work 11 M01 - Students will be expected to solve problems that involve SI and imperial units in surface area measurements and verify the solutions.