How Clean is the Water in Your Town?

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

(1)(C) The student uses numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.

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

§111.32. Algebra I

(3) (B) Given situations, the student looks for patterns and represents generalizations algebraically.

I. Overview

The overall concept of “Arrow Worms, Copepods, and Diatoms…Oh My!” is for the students to understand ratios in nature, specifically what the ratio of diatoms to copepods to arrow worms is at the Port Aransas coast, and how ratios in food webs are good to know for organisms as they adapt to their environment. I feel this concept is important to know because it demonstrates a real life application of mathematics in nature, and helps to explain why we can only sustain so much life in a certain area. We will see that nature is a delicate balance, and disruptions in that balance can be catastrophic. This will be extended to the students’ “How Clean is the Water in Your Town?” project because it will be a introduction to ratios and proportions that the students will need to know in order to explore and demonstrate the ratios and proportions needed to sustain the human population in their town. Furthermore, the students will need to pick the water purification technique they feel is best, and demonstrate the efficiency of their technique based on the proportions and ratios of clean water the technique makes.

II. Performance or learner outcomes

Students will be able to:

a.) Collect data on the number of species in a particular sample

b.) Formulate ratios between three species of phytoplankton

c.) Theorize why the ratio is what it is, and why does it exist

d.) Apply this knowledge to other species in nature

III. Resources, materials and supplies needed

1.) Copies for all students of attached worksheets

2.) Visuals of arrow worms, copepods, and diatoms (on cardboard and laminated)

3.) Students should bring pencils/pens

4.) 10 Photos of 10 sections of a sample of plankton taken earlier by teacher for each group of students.

5.) If possible, a pond/stream/puddle on school grounds the students could look at.

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

Concerning equipment used)

All materials are listed above. As far as safety goes, we will be a big group of high school students and 1 teacher in a classroom of 20 or so students. Safety rules are those set by the teacher/school for the classroom and should be followed. All students should treat each other with respect. The materials, i.e. the microscopes and slides, should also be treated with care and respect.

Five-E Organization

Teacher Does Probing Questions Student Does

Engage:

Learning Experience(s)

Welcome students to class. Give the students an overview of what we are going to be doing/learning today, what they will be doing, and hopefully what they will discover. Assign groups of 4 to 5 students, as well as roles within each group. Give out ratio handouts, slides, and discovery microscopes. Also address safety issues when working with the equipment. The students will be expected to behave accordingly and help each other out. The materials are to be treated with care and respect, and returned exactly the way they were received. Get the students into groups and pass out materials.

Critical questions that will establish prior knowledge and create a need to know

What is a ratio? How do we represent ratios?

What do we as humans eat? What do animals eat? What is this idea called? What is at the bottom?

What about fish and organisms in the water? Do they have food chains/food pyramids?

What do you think is at the bottom? At the top?

What exactly is phytoplankton? Zooplankton?

What do you think you are going to discover?

Expected Student

Responses/Misconceptions

Ratios are ways of representing relations between 2 things.

As humans, we eat meat, other animals, fruit, vegetables, etc. The food chain is what keeps the balance in nature. All organisms need nourishment to survive. Plants are usually at the bottom.

All organisms feed on another organism to survive.

Plankton are microscopic organisms that float freely with oceanic currents and in other bodies of water. Plankton is made up of tiny plants (called phytoplankton) and tiny animals (called zooplankton).

Explore:

Learning Experience(s)

I will show them photographs (the cardboard ones) of what they will be looking for. Each group will come up and collect the materials. Each group will look at 10 different photographs of 10 different sections of a sample of plankton taken by the teacher at an earlier date. I was told by Mike from UMSCI that the microscope onboard Katy is able to take pictures of the screen, so I intend to take 10 for each group of students I’ll have, and print them out. Each photo should be a different section. The students will look at the pictures and count how many diatoms, copepods, and arrow worms they find on each view. The worksheet then goes on to have them make ratios of each species, and build a food pyramid. Diatoms (plants) should be at the bottom, then copepods, and then arrow worms. I will be walking around and assisting groups as need be.

Critical questions that will allow you to decide whether students understand or are able to carry out the assigned task (formative)

What species are we looking for again?

How do we make a ratio?

Which organism do you think is phytoplankton?

Which are zooplankton?

Any questions?

Expected Student

Responses/Misconceptions

Students are looking for diatoms, copepods, and arrow worms. They are more than welcome to describe and record any other organisms they find to look up later.

We make ratios by reducing the number of 2 things to the least possible multiple of one to the other.

Diatoms are phytoplankton, and copepods and arrow worms are zooplankton.

Explain:

Learning Experience(s)

The students will regroup, and present what they have found. They should see that more or less, they had a ratio of 10 between each species. The more or less may be because they should have to multiply by a factor in order to get the 1:10 ratio. Students should also as a whole theorize as to why the ratio is 10%, how much is lost when going to another level in the food pyramid, and where does that 90% goes. Why is knowing this ratio important for organisms as they adapt to their environment?

Critical questions that will allow you to help students clarify their understanding and introduce information related to concepts to be learned

What are the ratios you came up with?

Which organism, then do you think is at the bottom of or food chain/pyramid? Why?

Which organism is at the top? Why?

Why is knowing this ratio important for organisms as they adapt to a new environment? Suppose that a tsunami wiped out all the diatoms, what would happen to the copepods? What if the tsunami only wiped out the copepods, what would the arrow worms eat, and what would happen to the population of each species?

Expected Student

Responses/Misconceptions

The ratios follow a 1:10 pattern, and therefore, diatoms are at the bottom, then copepods, and finally the big monsters are the arrow worms. This shows us that diatoms are plants or phytoplankton, and copepods and arrow worms are animals or zooplankton.

This is good to know so organisms can be aware of how much food is available to them. If a tsunami wiped out all the diatoms, the copepods would have nothing to eat, die out, and then the arrow worms would have nothing to eat, and then the arrow worms would die out… A terrible domino effect.

If the tsunami only killed all the copepods, the arrow worms would have only the diatoms to feed on, and probably would grow in population with the abundance of diatoms in relation to arrow worms.

Extend / Elaborate:

Learning Experience(s)

We saw that our food pyramid of diatoms, to copepods, to arrow worms is based on this ratio of 1:10. Further research shows that this ratio is common to other food pyramids.

If possible, we will go to our school pond and collect a sample of water. The students can make ratios of what they see in the water. For example, the ratio of leaves to sticks or bugs. They will be able to combine their data as a class set of data and theorize as to why there are more bugs or more sticks or more leaves. For instance, if it’s Fall, there will probably be more leaves in the water. If it’s Spring, probably more bugs. How do ratios connect to proportions? How does this connect to our project on water quality? Hopefully the students will explain that they will have to connect this to their “How Clean is the Water in Your Town?” project when they make ratios and proportions of amount of water needed per person per town. Furthermore, they will have to make ratios when deciding which water cleaning technique is the best based on how much water per person it cleans.

If there is no pond/lake/ stream/puddle outside that we can go to, the students can work on ratio problems and hypothesize how much water they drink in a given day. They can make a ratio of amount of water per student in the class. We will cover proportions in the next 2 days, as well as research how much water is needed per person/per household and extrapolate how much water is needed for their town.

All these ratios can be done on the back of their Arrow worm/Copepod/Diatom worksheet.

Critical questions that will allow you to decide whether students can extend conceptual connections in new situations

What do you see in our water? Why is that stuff there? What ratios can you make?

How do ratios connect to proportions?

How is this related to our project?

How much food is needed for 1 billion people then if each person ate 1 pound of food a day?

Furthermore, this means that 90% of what is available is not being used for nourishment. Where does this all go to?

Expected Student

Responses/Misconceptions

The students will tell me what they see, what ratios they want to make, and will make then.

Proportions are a statement of equality between two ratios. For example, four quantities a, b, c, and d, are said to be in proportion if a/b = c/d.

The students hopefully will see that they need to make ratios and proportions in order to determine how much water they need to survive as a person and town.

If we had 1 billion people to feed, we would need 10 billion pounds of meat and 100 billion pounds of plants!

90 % is lost in bio waste, energy consumption, natural disasters etc… there are many contributing factors. The point is that we need to have that much in order to sustain the population we have.

Evaluate:

Lesson Objective(s)

Learned (WRAP –UP at end) -> Summarize

Overall, we saw that more or less, our 3 species in the plankton of the Gulf of Mexico has a delicate balance when it comes to sustaining life.

Students will summarize what they discovered and ask any last questions or concerns they have. Comments are welcomed, and students can write these down on the back of their worksheets before returning them to me.

Critical questions that will allow you to decide whether students understood main lesson objectives

Based on your observations, if we ate 10 pounds of food a day, how much would we gain?

Any last minute questions or concerns or comments?

Thank you all for your attention and participation today.

Expected Student

Responses/Misconceptions

We’d probably gain about a pound.