The Skate Ramp Project: The Pythagorean Theorem

1. The Skate Ramp Project:The Pythagorean Theorem Your Name:_______________ In-Class Worksheets

2. Ref #1 3D Plan

3. Ref #2  two side views  the base view  the back view  the ramp 3D Plan (disassembled)     

4. Worksheet #1 Team-Up You need to collaborate with your peers to do this activity. Therefore, the first task for you is to team up a group of three. Each person should take responsibility for a certain task to get it done in a given time. The below table will help you to divide up the tasks among the members of your group, as well as to schedule your work. Self-Evaluation for Collaboration (Rubric #4) *Note: Those who are in charge of presentation should keep taking reflection notes or daily journal throughout the project periods so as to present how your team has been going about the project. See the Powerpoint templates provided.

5. Worksheet #2 You are here!!  The side views • The triangle below is a side view for your ramp, where you need two of them. You need to calculate the lengths of three sides; AB, AC, and BC. This pattern plays an important role in the shape of your ramp as well as the function of it. Here are some tips for you design. You must show your calculations for BC. • The scale of your ramp model is 1:10 throughout the design. That is, if you want to make a real ramp that is 1m high, your ramp model should be 0.1m (or 10cm) high. • The angle between A and C should not exceed 30º. • You need to use the Pythagorean theorem for this pattern. Identify the right angle and the hypotenuse on the triangle. Length Calculations: 1) : ______________ cm 2) : ______________ cm 3) : ______________ cm Show all calculations to the right. B hypotenuse  C A

6. Worksheet #3 You are here!!  The base view • The rectangle below is the base view of your ramp. You need to calculate the length of two sides; AB and AC. Here are some tips for your design. • The scale of your ramp is 1:10, as stated earlier. • You should remember that the length of each side is closely related to that of the other patterns. Lengths: 1) : ______________ cm 2) : ______________ cm D C  A B

7. Worksheet #4 Lengths: 1) : ______________ cm 2) : ______________ cm Lengths of wood sticks:________cm Show all calculations to the right. You are here!!  The back view • The rectangle below is the back view of your ramp, which needs trusses all the way around to hold up the ramp as indicated below with patterned lines. The width of wood sticks is 13mm (1/2 inch). Calculate the length of wood truss you need for this pattern. Here are some tips for your design. • The scale of your ramp is 1:10, as stated earlier. • You should remember that the length of each side is closely related to that of the other patterns. Top D C  B A

8. Worksheet #5 You are here!!  The ramp • The rectangle below is a pattern of the ramp, which needs trusses to sustain just like the back view. However, you need to put X-trusses on it as shown below. Therefore, you need to calculate the lengths of the two sides (AB and AC) as well as the length of two identical diagonals (AD or BC). Calculate the length of the wood truss that you need for the diagonals. Here are some tips for your design. • The scale of your ramp is 1:10, as stated earlier. • You need to use the Pythagorean theorem for this pattern. • You should remember that the length of each side is closely related to that of the other patterns. Length Calculations: 1) : ______________ cm 2) : ______________ cm 3) : ______________ cm Lengths of wood sticks:________cm Show all calculations to the right. C D hypotenuse A B

9. Worksheet #6 All Calculations 1. Fill in all the calculations for your ramp model.  Side views: 1) : ______________ cm 2) : ______________ cm 3) : ______________ cm  Base: 1) : ______________ cm 2) : ______________ cm  The ramp: 1) : ______________ cm 2) : ______________ cm 3) : ______________ cm  Back view: 1) : ______________ cm 2) : ______________ cm 2. Which lengths are consistent with which? And why?

10. Worksheet #7 Verifying Your Design with GSP Now, you have all the dimensions needed for your ramp model at hand. However, it is better to verify your calculations before you cut the pieces of cardboards to build the model. In this activity, you are asked to verify your design and calculations by using Geometer Sketchpad(GSP). Draw five plans (2 side views, a base view, a back view, and a ramp) according to the calculations that you wrote in the worksheets (WS #2 through #6) and see if GSP is able to do so. If not, your design needs to be corrected. Fill out the table below and redo calculations where necessary. Remember you need to hand in GSP-generated plans as well as this worksheet by Day 3.

11. Worksheet #8 Constructions Now, it’s fun time! All the members of your team need to participate in building a ramp model based on your design. You might need to go back and forth between your design and construction many times as you construct a model. Build a ramp model using tapes, staples, wood sticks, etc. Remember you have two sides where needed truss(es) to sustain the ramp (See the transparent model that the teacher provided). If you want to put more trusses on any other sides, which is optional, you will get some bonus points. You may also decorate your ramp to make it cool! Please take a look at the evaluation rubric for this activity (Rubric#5). After construction, fill out the table provided below as reflection and hand it in.