Name: ______Per: ______

11/28-11/29 Activity: Rectangular Pattern Challenges*

Preliminary Questions

  1. Examine Stage No. 1 and Stage No. 2. Then examine Stage No. 2 and Stage No. 3. Describe what you have to do to Stage (N-1) to create Stage N. (This problem is asking about the designs themselves, not the mathematical model.)
  1. Observe the designs looking for patterns. Use the patterns to predict Stages 0, 4, and n. Organize your information into the table below.

Stage No. / 0 / 1 / 2 / 3 / 4 / n
# of Blue
# of Red
# of Green
Total #

Thought Questions:

  1. Which color of squares is growing at the slowest rate?
  2. Which color of squares is growing at the fastest rate?
  3. On a separate sheet of graph paper, graph the 3 formulas to get a picture of the growth of all three. Graph all three formulas on one coordinate grid.
  4. How many squares of each color will be in the 8th stage of the design?
  5. Will the design use 42 blue squares in any stage? Is so, state the stage number.
  6. Will the design use 102 red squares in any stage? Is so, state the stage number.
  7. Will it ever use 830 squares in all? If so, state the stage number.
  8. What are the dimensions (length and width) of the rectangular designs for each stage including n? Show that when you multiply the length and width you get the total number of squares in each rectangular design.

Stage No. / 1 / 2 / 3 / 4 / n
Length
Width
Area

Name: ______Per: ______Grade: ______/ 60

Rectangular Pattern Challenges Project

STAPLE THIS PAGE TO THE FRONT OF YOUR FINAL PROJECT.

DIRECTIONS: On square grid paper create your own design, showing at least 3 stages. It must have at least two lines of symmetry, and it must follow a regular numerical growth pattern. On a separate sheet of paper, fill in the calculations in a table like the ones in “11/28-11/29 Activity: Rectangular Pattern Challenges”. Be prepared to exchange papers with the other students in class and figure out one another's patterns. After completing your own design and solving another student’s challenge, reflect on what you learned, what you enjoyed, what was challenging, and anything else. The self-reflection should be at least one paragraph.

DUE DATES:

  • The design is due on 11/30 (R) or 12/1 (P).
  • The completed table and additional copy of the design is due on on 12/6 (R) or 12/7 (P).
  • Students will trade challenges and solve them on 12/12 (R) or 12/13 (P).
  • Final project with self-assessment and all work is due on 12/14 (R) or 12/15 (P).

Rectangular Pattern Challenges Project Grading Rubric
16 – 20 points / 12 – 15 points / 6 – 11 points / 0 – 5 points
The design has at least 3 stages, 2 lines of symmetry, and follows a regular numerical growth pattern. Design is neat and appropriately colored. / The design is missing one of the three requirements. / The design is missing more than one of the three requirements. / No attention to requirements or late, regardless of quality.
Table is completely filled in and all calculations are evident and correct. Table is neat and appropriately labeled. / Work clear, with less than three errors uncorrected. / Work disorganized, with three to five uncorrected errors. / Many errors uncorrected. Disorganized. Or late, regardless of quality.
8 – 10 points / 6 - 7 points / 3 – 5 points / 0 – 2 points
1 challenge solved successfully, or errors discovered. All work neatly shown. / 1 challenge attempted or most errors discovered. Most work shown. / 1 challenge attempted but not much work shown. / 1 challenge barely attempted or not attempted at all.
5 points / 4 points / 3 points / 0 – 2 points
1 extra copy of your design turned in on time. Design is neat and appropriately colored. / 1 extra copy of your design turned in on time. Design is a bit messy or not colored. / 1 extra copy of your design turned in late. Design is neat and appropriately colored. / 1 extra copy of design turned in incomplete or not at all.
Self-assessment paragraph and elaboration neatly written typed. / All points covered, without elaboration. / Some points not addressed. / None

*This activity was created by Cynthia Lanius (