Barnacle Estimation – Math on the Jetty

LESSON PLAN # ___1___ ClassDay/Time___8-9___

Technology Lesson? Yes No (circle one)

Name(s): Rachel Carroll

Title of lesson: Barnacle Estimation

Date of lesson: March 24, 2006

Length of lesson: 50-60 min

Description of the class:

Name of course: Geometry

Grade level: 9-10

Honors or regular: regular

Source of the lesson:

Ideas from UTeach teacher/past students.

TEKS addressed:

Geometry TEKS

b.1. (A) The student develops an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems.

e. (1) The student extends measurement concepts to find area, perimeter, and volume in problem situations. Following are performance descriptions.

e.3. (A) The student uses congruence transformations to make conjectures and justify properties of geometric figures.

f. (2) The student uses ratios to solve problems involving similar figures.

I. Overview

The students are going to be presented with a situation in which they must come up not only with a solution, but then they will work with the solution to find a numerical answer in the end. They will use skills that are required everyday out in the working world. The situation will not give specific directions of how to come up with an answer but will require that the students do so themselves. There will not be a right/wrong answer format and the students might be a little confused but will see that can still be correct.

II. Performance or learner outcomes

Students will be able to:

Determine how to estimate the number of barnacles in the Jetty

Determine methods for random sampling

Calculate the total population from their samples

Estimate how many small and large fish are in the jetty area

III. Resources, materials and supplies needed

6 grids

6 transect lines

measuring tape

paper/pencil

6 calculators

6 clip boards

IV. Supplementary materials, handouts. (Also address any safety issues

Concerning equipment used)

None

V. Safety Issues

Be careful on the jetty. If the students are going to get on the rocks they need to do so on their hands and feet so that they won’t slip.

VI. Accommodations for learners with special needs (ELLs, Special Ed, 504, G&T)

If there are any special ed. students they might need special attention since the jetty can be a dangerous area with no barrier between the students and the water. For ELLs, a separate vocabulary list and synopsis would need to be designed so that they have an understanding of the project. However, they would do well on the math since numbers are universal. For GT students, let them do the same as everyone else and if they get finished first then ask them to think of two more ways to sample the barnacle population that are different from their first type of sampling.

Five-E Organization

Teacher Does Probing Questions Student Does

Engage: Looking at what might live in the jetty. Approx. Time__5__mins	How many organisms live in this jetty? How many small ones are there and how may large ones are there?	The topic of what is small/large might arise.
Evaluation(Decision Point Assessment):	This will be a discussion time and I’ll make sure there are several students discussing, not just one or two.	Students will offer their general thoughts on what animals are present in the jetty and the teacher will evaluate if the answers are accurate and correct any misconceptions.

Explore: Separate the students into 3 groups of equal size. Present this problem: The government needs to know how many barnacles are in this Jetty (North and South sides) because they provide funding for the maintenance of the area due to the barnacle population. The payment is $100 for each 1 million barnacles. However there is no way to count each and every barnacle, so they have hired 3 companies to do the research for them. Approx. Time__10__mins	How can you determine how many barnacles are in this Jetty? How will you count them in the most effective way? Give a couple examples of how to not count (understanding random sampling ideals). How could you count the barnacles only using this grid that we know is XXX long by XXX wide? Remember there is not just one right answer.	Students may not understand the problem at first, but giving them time with their groups they should figure it out. Help out with the group(s) that is taking samples in an incorrect fashion or those that don’t fully understand the problem.
Evaluation(Decision Point Assessment):	Go to each group individually and after they have a plan of attack for how to count the barnacles, set them loose to begin counting.	Help the groups that do not know how they should count the barnacles, but lead them to a solution…don’t give them an answer.

Explain: Counting the barnacles. The students will have some time to do some random sampling of barnacles on the rocks and record their results. Make sure all the students are participating. Come back and share the results. Let each group explain their process and give their results. Approx. Time__30__mins	The teacher will be observing here and watching the groups, so questions asked will be to the individuals. Why is this the best way to sample the barnacles? What could you do to make it more accurate? Which method do you think was the best? Vote by raising your hands for group A, B, or C. How much money would the government be paying us? Remember they were to pay $100 for every 1 million barnacles. What were some problems that you had? Who else had this problem? What could you have changed to make it work better?	The students may try to count too few or too many barnacles. They may stay in one area of the jetty instead of moving around. Any method that may not give the students the best answer can be discussed when they come back to reflect on all their answers.
Evaluation(Decision Point Assessment)	Go to each group and listen in on their discussions and observe their techniques for counting the barnacles.	Each group has come up with a method for measuring, has taken samples along the jetty, and has arrived at an answer.

Extend / Elaborate: Powers of 10 Talk about the food chain. Approx. Time__10__mins	Using your estimate of how many barnacles there are in this jetty, how many small fish, large fish do you think there are? Are these numbers the same, are they close or far away from each other? Why is this?	Students will probably not understand the powers of 10 yet in the food chain but will probably get the general estimation that there are fewer of a species when you go up in the food chain.
Evaluation(Decision Point Assessment):	Are the students participating in the discussion and are their estimates in an acceptable range?	If the students don’t understand then relate this to their eating habits and then talk about the food chain. Then have them relate it to the aquatic food chain.

Evaluate: Overview of the project. Hypothesize how the students could recreate this for another species. Approx. Time__5__mins

Would you rather have the government determine how much they pay by the number of barnacles, small fish, or large fish in the jetty area? Which would be easier to count? Which could get you a better estimation of the total population?

Hopefully students will ask if the government is paying only for each set of 1 million or if there is a different measure for the fish. If they don’t then ask probing questions.