High School Mathematics Problems from Alaska

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Predicting Plant Coverage

Beth Sukraw

Standards: Estimation and Computation, Statistics and Probability

Performance Standards: A3.3.1, A3.3.2, A3.3.3, A3.3.4, A3.3.5, A3.3.6, A3.4.1, A3.4.5, A3.4.6, A6.3.1, A6.4.1

Concepts: Estimating, Organizing Data, Predicting, Computing in Percents, Decimals, and Setting up and Solving proportions.

Carnegie Chapter: Analyzing Data and Making Predictions, Connecting Situations to Equations.

Overview: During the summer, our local biologists are out in the field studying plants using a similar one meter by one meter square plot sample. If possible, call your local botanist and go out into the field or have him/her bring in past records and tools used to record plant coverage in your area. This is a great unit to include local native language for plants. The estimation skills of the guest speakers you bring to class should be emphasized.

Let’s explore a plant prediction situation. In one square kilometer you randomly picked one square meter to record as an example of the surrounding vegetation. You and your research team did this for several sites. You will use this chart to make predictions and answer questions. For each problem, show all your work and write your answers in complete sentences.

The following is the square metric chart you recorded. You constructed a key to show the vegetation. If the square has the letter mentioned, it is over 50% of that plant in that 10 cm by 10 cm square.

Key:

 S Sedge M Moss C Cranberry L Lichen O Other

 M M M L L L L L L L M M L L L M L L L L M L L L L M L L L M M L M C M O S L L M M M M C C L L L M M M M M M M M O C C C M M M C S M M M M M M M M C C L L L L L M M M M M M L L L L C C M M M L L L M M

1. Make a first prediction of the percentage of each type of plant in the square meter. Use no computations. At a glance, what percentage of each type of plant do you see?

____% Sedge

____% Moss

____% Cranberry

____% Lichen

____% Other

1. Find the actual recorded percentages for each type of plant in the square meter.

 Plant Type Tally Frequency Percentage Actual Percentage Estimate from question #1 Difference |Estimate- Actual| Sedge Moss Cranberry Lichen Other

1. Suppose the square meter is a good sampling of the square kilometer it came from. Find how much of the area in the square is covered by each type of plant.

Example: If 10% of the square meter is covered by sedges, then

 .10 x ----------- = ----------- 1 m2 1 km2 x = 10,000 m2 or .01 km2
 Keep in mind that, 1 km = 1,000 m

 Plant Type Coverage Area in Square km Sedge Moss Cranberry Lichen Other

1. What is the total area (cm2) covered by cranberries in
1. 1,000 square centimeters?

2. 2,000 square centimeters?

3. 100 square centimeters?

1. Write an equation describing the total area covered by cranberries.

1. Construct a graph for the cranberry coverage area. Label the axes and indicate the scale.

1. What if the square meter randomly picked as an example of the surrounding vegetation was a poor example? Explain possible errors and implications.

1. How could a sampling area be picked to better exemplify the surrounding area other than randomly?

1. The following table shows the percentage results of 10 more one-meter square samples. Use this data to estimate the overall area covered by each plant in the square kilometer. Round to the nearest tenth of a percent.
 C S M L O 1 22% 7% 31% 34% 6% 2 21% 1% 36% 38% 4% 3 21% 3% 21% 46% 9% 4 28% 14% 31% 24% 3% 5 20% 11% 48% 9% 12% 6 14% 15% 35% 29% 7% 7 5% 4% 53% 33% 5% 8 19% 9% 41% 25% 6% 9 28% 9% 39% 13% 11% 10 17% 6% 46% 29% 2%

____% Sedge

____% Moss

____% Cranberry

____% Lichen

____% Other

1. Explain any changes that occurred from your group’s estimate to the combined averages.

1. Create a bar graph to illustrate the estimated area covered by each plant in the square kilometer. Label your axes, create an appropriate scale and give a title to your graph.

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Handbook for Culturally Responsive Science Curriculum by Sidney Stephens
Excerpt: "The information and insights contained in this document will be of interest to anyone involved in bringing local knowledge to bear in school curriculum. Drawing upon the efforts of many people over a period of several years, Sidney Stephens has managed to distill and synthesize the critical ingredients for making the teaching of science relevant and meaningful in culturally adaptable ways."

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