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Honeycombs are a network of hexagons that bees create for their hives. They are a wonderful natural shape because they use material efficiently for the amount of area they create, and they are strong.
Manufacturers use honeycomb structures made of aluminum or plastic to provide strong, lightweight cores for everything from aircraft walls to whiteboards.
You are an engineer working for Plasticore, a manufacturer of honeycomb core products. You and your team have been asked to design round banquet tables with honeycomb cores, so you need to learn more about honeycombs.
1.
Let’s see how a honeycomb shape can
be built starting with one hexagon:
We add new hexagons outside all around the
as we start to build our hive:
Stage 0: Stage 1:
How many new hexagons did we add? _____
How many do we have all together? _______
2.
How many honeycombs do you predict will be in the next formation? __________________
Explain how you arrived at your answer.
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0

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3.
Draw the next three honeycomb formations on the grid provided.
Use different colors for each stage and label each, “Stage 2, 3, 4.”
Was your prediction in
Question 2 right or wrong?
___________
Why?
4.
Complete the table below.
Honeycomb Stage
Number of hexagons added
Total number of hexagons
Pattern for total number of hexagons
0 0 1 1
1 6 7 1 + 6 = 7
2
3
4
5
5.
Write an explicit rule to describe the number of hexagons added for each stage.
6.
Is this sequence arithmetic, geometric, or neither? Explain your answer.
7.
Write a recursive rule to describe the total number of hexagons in each stage.
8.
Is this sequence arithmetic, geometric, or neither? Explain your answer.
9.
Plasticore wants you to design round banquet tables. Your team will be responsible for designing a table with a specific diameter. The core of each table is made of an arrangement
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0

Name: Date: Page 3 of 7 of honeycomb-like structures like those you found in Problem 3. The diameter of the table increases with each stage as shown. Complete the table.
Honeycomb Application - Banquet Tables
Honeycomb Stage Diameter of the table (inches)
0
1
2
3
4
5
2
6
10
10.
Is the sequence that models the diameter of the tables arithmetic, geometric, or neither? Explain your answer.
11.
Write a recursive rule to describe the diameter of the table in each successive stage. Use the rule to predict the diameter in stage 10.
12.
Write an explicit rule for the diameter at any stage. Use the rule to predict the diameter in stage 10.
13.
Which rule was easier to use? Why?
14.
Which table size was your team asked to design? ____________
15.
How many stages will it take to create a honeycomb core for that size table? _____________
Explain how you arrived at your answer.
16.
How many honeycomb cells (hexagons) will be needed for that size table? ______________
Explain how you arrived at your answer.
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0

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17.
Each honeycomb cell costs $0.02 to manufacture, including material and labor costs. Find the cost to manufacture one honeycomb core for the table you were assigned to design. Show your work.
18.
Plasticore just got an order from the Aquaturf for 174 tables in the size you designed. What is the total cost be for the honeycomb cores? Show your work.
Project Name: ____________________________________________ Date: ______________
Team Members: ____________________________________________ (Leader/Editor)
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0

Name: Date: Page 5 of 7
____________________________________________ (Recorder/Secretary)
____________________________________________ (Checker)
____________________________________________ (Spokesperson)
Statement of Purpose:
_________________________ ________________________________________
______________________________________________________________________________
Which table size must your group design? _______________
Results (Show and/or explain the mathematics you used to get your results.) :
How many stages will it take to create a honeycomb core for your table? ____________
Explain how you arrived at your answer.
How many honeycomb cells (hexagons) will be needed for your table? ____________
Explain how you arrived at your answer.
What is the cost to manufacture one honeycomb core for your table? _________________
Show your work.
For full credit, submit one copy of this report per team, along with each of your completed packets.
Period __ Leader/Editor Recorder/Secretary Checker Spokesperson
Table
Diameter in inches
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0

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Team 1
Team 2
Team 3
Team 4
Team 5
Period __ Leader/Editor Recorder/Secretary Checker
Team 1
Team 2
Team 3
Team 4
Team 5
Team 6
Period __ Leader/Editor Recorder/Secretary Checker
Team 1
Team 2
Team 3
Team 4
Team 5
Team Members: __________________________________ (Leader/Editor)
__________________________________ (Recorder/Secretary)
Spokesperson
Spokesperson
86
70
90
106
78
Table
Diameter in inches
86
106
86
98
78
90
66
Table
Diameter in inches
74
78
94
74
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0

Name: Date: Page 7 of 7
Honeycomb
Stage
17
18
19
20
21
22
23
24
25
26
27
28
29
__________________________________ (Checker)
__________________________________ (Spokesperson/Press Secretary/Webmaster)
Statement of
Purpose
Stages of your
Honeycombs
How many
Honeycomb Cells?
Cost to
Manufacture
Excellent
(15 pts)
Clear Sentence of what group was asked to do.
Excellent
(20 pts)
Correct with unit.
Clear Explanation
Correct with unit.
Clear Explanation
Correct with unit.
Clear Explanation
Good
(10 pts)
Clear description of what group was asked to do.
Good
(15 pts)
Correct without unit. Clear
Explanation
Correct without unit. Clear
Explanation
Correct without unit. Clear
Explanation
Almost There
(5 pts)
Unclear what group was supposed to do.
Almost There
(10 pts)
Correct without unit. Explanation
Correct without unit. Explanation
Correct without unit. Explanation
Below Standard
(0 pts)
Not written
Below Standard
(5 pts)
No Explanation
No Explanation
No Explanation
Honeycombs
Added
102
108
114
120
126
132
138
144
150
156
162
168
174
Total
Honeycombs
919
1027
1141
1261
1387
1519
1657
1801
1951
2107
2269
2437
2611
Diameter
90
94
98
102
106
110
114
118
70
74
78
82
86
Cost per
Table $
18.38
20.54
22.82
25.22
27.74
30.38
33.14
36.02
39.02
42.14
45.38
48.74
52.22
Cost for 174
Tables $
3198.12
3573.96
3970.68
4388.28
4826.74
5286.12
5766.36
6267.48
6789.48
7332.36
7896.12
8480.76
9086.28
Final Score: ____________________________ /75 pts
Unit 1 Performance Task CT Algebra I Model Curriculum Version 3.0