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## Measuring Up: Prototypes for Mathematics Assessment (1993) Mathematical Sciences Education Board (MSEB)

### Citation Manager

. "The Towers Problem." Measuring Up: Prototypes for Mathematics Assessment. Washington, DC: The National Academies Press, 1993.

 Page 134

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Measuring Up: Prototypes for Mathematics Assessment

Presenting the task: Initially the class is to work in groups of three. Each group should have a supply of Unifix® cubes of two different colors — about 40 cubes of each color. The teacher should explain that the task is to build towers of Unifix® cubes, saying something like this:

"Each tower is to be three cubes tall. You may use the cubes on your table, which include cubes of two different colors. Please build as many different towers as possible.

"Besides building the towers, please explain your work to the other students at your table, to convince them that you have not left any out, and that you have no duplicates. Please make only towers that are right-side up, like this:

and do not make any "upside down" towers, like this:

Then the teacher should pass out copies of the student sheet and read through the directions to be sure that everyone understands the task.

Student assessment activity: See the next page.

 Page 134
 Front Matter (R1-R10) Introduction (1-3) The Challenge (4-4) The Criteria (5-6) The Caveats (7-7) The Audience (8-8) The Prototypes (9-11) The Tryouts (12-12) The Format (13-13) The Protorubrics (14-15) The Standards (16-18) The Future (19-20) The Prototypes (21-22) Mystery Graphs (23-30) The Checkers Tournament (31-42) Bridges (43-52) Hexarights (53-64) Bowl-A-Fact (65-74) Point of View (75-84) The Quilt Designer (85-94) How Many Buttons? (95-100) The Taxman (101-114) Lightning Strikes Again (115-124) Comparing Grizzly Bears and Black Bears (125-132) The Towers Problem (133-140) The Hog Game (141-156) Resources (157-160) Mathematical Sciences Education Board (161-164) Credits (165-166)