Bridge Building on Lake Champlain

Transcription

1 Bridge Building on Lake Champlain Bridges are made of trusses. Examples of Warren Trusses are shown below: 1 Truss: 5 meters long 2 Trusses: 10 meters long 3 Trusses: 15 meters long A new bridge is being built across the Lake Champlain Islands. The bridge will be 1 kilometer long. Task Part 1: If the engineers build the bridge using Warren Trusses, how many trusses will need to be built? Task Part 2: How many beams ( ) will this new bridge require? TM Bridge Building on Lake Champlain - Page 1 -

2 Grade Level 3 5 Bridge Building on Lake Champlain Bridges are made of trusses. Examples of Warren Trusses are shown below: 1 Truss: 5 meters long 2 Trusses: 10 meters long 3 Trusses: 15 meters long A new bridge is being built across the Lake Champlain Islands. The bridge will be 1 kilometer long. Task Part 1: If the engineers build the bridge using Warren Trusses, how many trusses will need to be built? Task Part 2: How many beams ( ) will this new bridge require? Context This task can be used during a unit on measurement but is most appropriately given during a unit on patterns, functions, and algebra. What This Task Accomplishes To successfully complete this task, students need to be able to create and extend patterns, and then to generalize patterns. The teacher can assess which students are able to apply this higher level thinking skill. This task also assesses students ability to convert kilometers to meters. - Page 2-

3 What the Student Will Do Most students will make a data chart in which to record the information presented in the task. Students will identify, then develop a rule for the pattern. Then students will realize that in order to go across the lake, they need 1,000 meters of trusses. They need to divide 1,000 by 5 to get the necessary 200 trusses needed. They will use the rule in the table to find the number of beams required in 200 trusses. Time Required for Task This task takes 1 or 2 forty five minute class periods. Interdisciplinary Links This task obviously links well to the study of bridges. A study of rivers and lakes would work as well. There are many different types of trusses that students can be introduced to, each having its own pattern. A book entitled Building Toothpick Bridges by Jeanne Pollard has other ideas for teaching about bridges, and shows the different types of trusses. Teaching Tips To personalize this task, you may want to substitute a lake or river near you. Before giving this task to students, they need to have many opportunities to identify visual patterns and to make function tables or in out machines. The book Algebra Thinking, First Experiences, by Creative Publications has many activities for introducing this concept to students. This task can be adapted for students who have special needs by making the number of trusses needed a smaller number. For students who need more of a challenge, you could ask them to compare and contrast the number of beams needed for bridges with different types of trusses. Suggested Materials Most students will require paper, pencils and calculators. Some students may want to build trusses to continue to the pattern, and toothpicks are great tools for doing this. - Page 3-

4 Possible Solutions 200 trusses are needed (200 trusses x 5 meters = 1000 meters = 1 kilometer) Benchmark Descriptors Novice The novice solution will be mostly incorrect. The student will not be able to find a correct pattern, nor will the novice know what to do with the measurement aspect of the task. Little or no math language will be used, and representations will be limited to rudimentary drawings that do not mimic the mathematical situation presented in the task. Apprentice The apprentice will achieve a partially correct solution. The apprentice will either not be able to find a pattern or will not know how to determine the number of trusses needed. The apprentice will use accurate math language, but it will be sparse. A diagram or table will be used, but it will lack labels and accuracy in terms of consistency. Practitioner The practitioner will achieve a correct solution. The practitioner will find a pattern and will be able to generalize it to the number of trusses needed. The practitioner will correctly determine the number of trusses needed and then the number of beams needed to cross the lake. The practitioner will use accurate and appropriate math language throughout. Tables and diagrams used will be accurate, labeled, and will communicate clearly. Expert The expert will achieve a correct solution for all parts of the problem. The expert s solution will be clearly communicated, and all work will be documented. The expert will use algebraic notation to describe the generalized pattern. The expert will also make mathematically relevant comments and observations about her/his solution. - Page 4-

5 Author Carol Amico McNair, who teaches grade 6 at the Camels Hump Middle School in Richmond, Vermont, wrote this task. The task was piloted in Carol Amos grade 4 classroom located in Sutton, Vermont. - Page 5-

6 Novice The student creates a chart that is accurate to the solution. The student uses an incorrect pattern that will never lead to a correct solution. It is unclear why the student stops at 34 trusses. - Page 6-

7 Apprentice The student creates a table as an attempt to solve the problem. It is unclear what the student is trying to do here. The student s approach would take a long time to carry out to a correct solution. The student s work is correct as far as it goes. - Page 7-

8 Practitioner The student creates a table and finds a rule that leads to a solution. A correct answer is achieved. Accurate math language is used. The student explains his/her approach. - Page 8-

9 Expert The student shows his/her approach. The student creates an accurate and appropriate table. A correct answer is achieved. - Page 9-

10 Expert (cont.) The student explains his/her reasoning. - Page 10-

11 Expert (cont.) Accurate and appropriate notations are used. The student generalizes the solution to any number of trusses. - Page 11-