Algebra One Sequences - Honeycomb Performance task

We start the school year with a short little unit on sequences. Not the usual longer approach you see in Algebra 2 or PreCalculus with sequences & series. Just dabbling in arithmetic and geometric sequences. A little bit with Fibonacci and Pascal's triangle. And maybe some "other" types (like triangular numbers). It's a nice way to start the year, looking at patterns and making sense of them.

I've had a few posts on this unit already. Some specifics on my ISN foldables and some expanded thoughts on developing the rules for arithmetic and geometric sequences.

This post is to share a little more information on how we end the unit. We do the usual test with study guide prep. But every unit in Algebra 1 in our school has a performance task. This one is called the Honeycomb Performance Task.

The Basic Task:

You are an engineer for Plasticore Corporation who makes custom tables of varying sizes for banquet halls. You have been asked to design and manufacture round banquet tables with layered honeycomb cores. Each honeycomb in the core has a height of one foot.  The size of the honeycombs do not change, as the size of the table increases the number of honeycomb layers increases.  

a)  Your team at Plasticore has been asked to build a table that measures 15 feet in diameter. Each individual honeycomb cell costs $0.25 to manufacture, including material and labor costs. What is the total cost to manufacture the honeycomb core for your table?

b)  Plasticore just got an order from the Aquaturf for 80 tables that measure 15’ in diameter. What is the total cost for the honeycomb cores used to build the 80 tables?

c)  Since The Plasticore Corporation is located in the state of Connecticut, Aquaturf has to pay 6.35% sales tax on the total cost calculated in part (b). Also Plasticore charges a shipping and handling delivery fee of 10% of the pre-tax cost.  Calculate those two extra fees and find the final total cost of the Aquaturf order of eighty 15 feet diameter honeycomb core tables.

Preparation before the task:

Before students are given the performance task we do a little preparation (yes of  course there are all the lessons of this unit but also...) with a honeycomb exploration. 

Honeycombs are a network of hexagons that bees create for their hives. They are a wonderful natural shape because they efficiently use material for the amount of area they create and they are strong. This task has you creating a network of honeycombs.

Work with your group to create the following honeycomb stages on hexagonal grid paper. You should have 5 different color pencils, markers or highlighters.  Let’s see how a honeycomb shape can be built starting with a single hexagon and building out.

PART ONE:

1A)  The center of your honeycomb is the black hexagon in the center of your grid paper.  For stage one, choose a colored pencil and color all the hexagons that touch the black hexagon.  How many hexagons did you color for stage 1?  Enter this number into the table below in the “Number of Hexagons Added” column. 

1B)  For stage two, choose a different pencil and color all the hexagons that touch a stage 1 hexagon.  You should now have two “rings” of hexagons colored.  How many hexagons did you color for stage 2?  Again, enter this number into your table in the “Number of Hexagons Added” column. 

1C)  Now choose a different color and color all the hexagons around this first layer you did. Enter this number into the table for stage 3. Continue this coloring method & recording for stages 4 & 5. 

Students then create a visual pattern with colors that they investigate using what they know about sequences. Everything is detailed in the document honeycomb patterns.

Once they've got all that (they do this in small groups and compare results, tweaking as they go). They are ready for the performance task.

We talk through the scenario. And I show them a model of a honeycomb core "table" that I made (with corrugated cardboard, an xacto knife and glue gun).

This model has an accompanying circular "cover" so they can see how the table has the core in it to stabilize and strengthen the table.

Then they are on their own to complete all the parts of this task. We do focus on the mathematical standards of "Make sense of problems and persevere in solving them", "model with mathematics" and "look for and make use of structure". Especially the perseverance piece. So there is no more classtime for this task, they are on their own and the rubric has a 4 point score for perseverance. (we've had a problem with students "not trying" so this motivates them to really use all the tools available to them and persevere!). 

All documents are found here.