Ottawa Architecture. Ottawa Architecture. 1 of 9. Copyright 2007, Exemplars, Inc. All rights reserved.

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1 One of the things that most impressed me about Ottawa, Canada, was the architecture. The buildings were beautiful and had unique designs. One of the buildings that most impressed me was the Pavilion of the Arts at the University of Ottawa, where we will be staying. I made a sketch of a design that ran along the building. If this design were to be considered as 1 section, and it was 30 feet long, how many of each shape of stone would be required to surround a building with a perimeter of 300 yards? 1 of 9

2 Suggested Grade Span 8 Task One of the things that most impressed me about Ottawa, Canada, was the architecture. The buildings were beautiful and had unique designs. One of the buildings that most impressed me was the Pavilion of the Arts at the University of Ottawa, where we will be staying. I made a sketch of a design that ran along the building. If this design were to be considered as 1 section, and it was 30 feet long, how many of each shape of stone would be required to surround a building with a perimeter of 300 yards? Alternative Versions of Task More Accessible Version One of the things that most impressed me about Ottawa, Canada, was the architecture. The buildings were beautiful and had unique designs. One of the buildings that most impressed me was the Pavilion of the Arts at the University of Ottawa, where we will be staying. I made a sketch of a design that ran along the building. If this design were to be considered as 1 section, and it was 30 feet long, how many of these sections of stone would be required to surround a building with a perimeter of 500 yards? of 9

3 More Challenging Version The original version, and If the section shown is 8 feet long, determine the area of each face shown. Support your conclusions mathematically. Context This task was given to students who recently completed a unit on functions and algebra. The class is also planning an end-of-the-year trip to Ottawa as part of a Canadian studies unit. What This Task Accomplishes This task allows me to see which students are still able to create and use function tables to solve tasks. It also allows the teacher to see who can visualize how the pattern continues. It also provides the opportunity for students to practice measurement conversion. What the Student Will Do Most students start by sketching the next section of the building. Some students ask for another copy of the task so they can cut out the original drawing and tape it on to see how the next section fits. Next, students make a function table. They then determine that 30 sections of the building are needed and solve for 1,, 3, 30, n sections in their function table. Time Required for Task One 5-minute period. Interdisciplinary Links Our sixth-grade classes study Canada and go on an end-of-the-year overnight trip to Ottawa. The architecture in Ottawa really is beautiful. While there, I will ask students to find another building that has a repeating pattern, sketch the pattern and bring the sketches to math and social studies classes for future investigations upon our return. Teaching Tips 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 to be successful with this problem. The book Algebra Thinking, First Experiences, copyright 1990, Creative Publications, has many activities for introducing this concept to students. A good warm-up to this problem is "Bridge Building on Lake Champlain," a 3 5 task featured on this CD. 3 of 9

4 Suggested Materials Crayons or colored pencils Extra copies of the pattern Possible Solutions An added unit should look like this: When added, it should look like this: Sections 1 3 n 30 A 8 n+ B 8 n+ C 8 n+ D 3 n+1 31 E 1 3 n 30 F n 0 G n 0 H 1 3 n 30 of 9 I n 0

5 More Accessible Version Solution 30 feet 3 feet in a yard = 10 yards = 50 More Challenging Version Solution A = 9 square feet B = square feet C = square feet D = 1 square feet E = 1 square feet F = square feet G =.5 square feet H = 1 square feet I = square feet Task-Specific Assessment Notes 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. Apprentice The Apprentice will achieve a partially correct solution. The Apprentice will either not be able to find a pattern or not know how to connect each section. The Apprentice will use accurate math language, but it may be sparse. A diagram or table will be used, but it will lack labels and accuracy. Practitioner The Practitioner will achieve a correct solution. The Practitioner will find rules to solve the task and will be able to apply them to the number of sections needed. The Practitioner will use accurate and appropriate math language throughout. Tables and diagrams used will be accurate and labeled and will clearly communicate the student s solution. 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 patterns. The Expert will also make mathematically relevant comments and observations about her/his solution or demonstrate understanding of how the rules can be generalized either by applying them to more than one other case or by explaining their derivation. 5 of 9

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