Gold Seal Lesson:
Multilink Think

Copernicus Education Gateway

Subject:

Mathematics

Grade:

5-8

ICLE Standards:

Patterns and Functions: Describe, extend, analyze, and create a wide variety of patterns.

Geometry: Represent and solve problems using geometric models.

Performance Task:

Mike used wood squares to make various size frames. The three smallest frames he made are shown below.

Each frame has one more squares on a side than the previous frame.
If n represents the number of wooden squares on each side of the frame and n is an integer equal to or greater than three, write a function, T 1 , describing the total number of wooden squares needed to make a frame with n wooden blocks on each side. You may want to build a few more frames using multilink cubes. Make a table showing T 1 for all values of n from n = 3 to n = 10.

Joanne used wood squares to make the frames shown below. The three smallest frames are shown. The longer side of each frame has 2 more squares than the previous frame. If n represents the number of squares in the longest side of the frame, write a function, T 2 , describing the total number of wooden squares needed to make a frame with n wooden blocks on the longer side where n is an even number greater than or equal to 4 and the number of squares on the shorter side follows the pattern shown in Joanne's frames. Make
a table showing T 2 for all values of n from n=4 to n=18.

Write a brief paragraph comparing and contrasting the two functions T 1 and T 2 .

Knowledge / Skills:

Apply transformation concepts to understand and create congruent and similar figures.  (m49)

Know how to express a linear function (e.g., y = 1/3x+5) using the functional notation f(x) = 1/3x+5, and determine the ordered pairs.  (m64)

Understand and use a variety of organizational formats such as compare/contrast, inductive/deductive, most important to least important, and least important to most important.  (ela50)

Use expository writing skills in subjects other than English language arts.  (ela58)

Rubric:

4 Points  =  The student independently completes the task. He/she demonstrates the ability to analyze and continue a pattern. The student demonstrates knowledge of functions, is able to write the two functions from the given geometric patterns, and is able to construct the tables for each function. The student clearly compares and contrasts the two functions.

3 Points  =  The student needs some assistance to complete the task. He/she has difficulty analyzing and continuing the given geometric patterns. The student demonstrates only a partial knowledge of functions. Although he/she needs some help to write the functions, he/she is able to construct tables from the written functions.

2 Points  =  Even with assistance, the student is unable to complete the task correctly. He/she has much difficulty with analyzing and continuing the geometric patterns, but with considerable help is able to complete this part of the task. The student has only a vague knowledge of functions and is unable to write the correct function describing each pattern. He/she attempts to construct tables from the written functions, but makes several errors. The comparing and contrasting of the two functions is meaningless.

1 Point  =  The student does not successfully complete any part of the task. He/she is unable to analyze and continue the geometric patterns. Hence, the student is unable to do any remaining parts of the task.

Keywords:

ALGEBRA
FUNCTIONS
PARABOLA GEOMETRY
GEOMETRIC SHAPES
COMPARE/CONTRAST
EXPOSITION STATISTICS
TABLES

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [X] - 6 [X] - 7 [X] - 8 [X] - 9 [] - 10 [] - 11 [] - 12 []

ICLE Application:

D

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