Sears Tower md. 5-Task 6 Domain




Дата канвертавання28.04.2016
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Formative Instructional and Assessment Tasks




Sears Tower

5.MD.5-Task 6

Domain

Measurement and Data

Cluster

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Standard(s)

5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.



Materials

Paper and pencil

isometric dot paper



Task

This is a diagram of the Sears Tower (now called the Willis Tower) skyscraper in Chicago.

The base of the tower is a 75 x 75 meter square. If each floor is 4 meters tall, what is the volume of the Sears Tower?
TEACHER NOTE: This is a complex, many-step task. Many students will not be able to complete the entire process without making a calculation error or losing track of one of the towers. Instead of focusing on getting a right answer, focus on the student’s process for attacking and solving the problem.




Rubric

Level I

  1. Level II

Level III

Limited Performance

  • Student is unable to develop a strategy for solving the task without assistance.

  • Student demonstrates a tenuous (shaky) understanding of the concept of volume.

  • Student does not persevere with the task and needs frequent encouragement and assistance in order to solve.




  1. Not Yet Proficient

  • Student develops a strategy for solving the problem but the strategy may be inconsistent or lack understanding of part of the task.

  • Student’s strategy demonstrates an understanding of the concept of volume.

  • Student may become frustrated with the task and need encouragement to persevere in solving it.




Proficient in Performance

  • Student develops a strategy for solving the problem and carries out the strategy. There may be organization or calculation errors in carrying out the strategy.

  • Student’s strategy demonstrates a clear and strong understanding of the concept of volume.

  • Student perseveres in solving the problem.

Answer Key:

The base of each tower is 625 m2, with the exception of the red tower, which has a base of 1250m2.


To find the height, you must multiply the number of floors by 4.

Color

Height

Volume

Blue

50 x 4 = 200 m

200 x 625 = 125,000 m3

Green

66 x 4 = 264 m

264 x 625 = 165,000 m3

Gold

90 x 4 = 360 m

360 x 625 = 225,000 m3

Red

108 x 4 = 432 m

432 x 1250 = 540,000 m3

There are 2 blue towers = 250,000 m3

There are 2 green towers = 333,000 m3

There are 3 gold towers = 675,000 m3

There is 1 red tower = 540,000 m3

Total volume: 1,798,000m3






Standards for Mathematical Practice

1. Makes sense and perseveres in solving problems.

2. Reasons abstractly and quantitatively.

3. Constructs viable arguments and critiques the reasoning of others.

4. Models with mathematics.

5. Uses appropriate tools strategically.

6. Attends to precision.

7. Looks for and makes use of structure.

8. Looks for and expresses regularity in repeated reasoning.



Sears Tower
This is a diagram of the Sears Tower (now called the Willis Tower) skyscraper in Chicago.

The base of the tower is a 75 x 75 meter square. If each floor is 4 meters tall, what is the volume of the Sears Tower?




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