Learning Experience: 4



Probable Cause

Activity Overview

In this module, students explore (review) probabilities (percentages) by drawing weather strips representing rainy and clear days from a container. The module is designed such that the class is divided into groups of 3-4 students. Each group reports their results to the class at the end of the lab.

Student Learning Objectives

The student:

1. Works cooperatively in groups.

2. Understands the concept of probability.

3. Completes a data table and constructs a graph using the data.

4. Relates the probability experiment to the weather forecast.

5. Communicates valid conclusions.

6. Identifies how percentages are used in a weather forecast.

Teaching Summary

Step 1

Journal/Bell Work - if appropriate

Step 2

Review / Introduce Probabilities - Optional

Step 3

Probable Cause Experiment

Collect Data

Graph Data

Calculate Probabilities

Step 4

Class Discussion - Group Reports to Class

Step 5

Assessment / Homework

Materials

For the teacher

Weather Forecast

Prepare one of the following

1. A pre-recorded weather forecast from the local weather station,

2. A weather forecast with a percent chance of rain on it from the local newspaper or Internet,

3. The NOAA forecast map provided on the next page. Note the map foreshadows weather symbols and information to be discussed in latter modules. Modify the percent chance of rain in the journal / bell work question to match the forecast you select.

For the students

Probable Cause lab experiment write-up

A container (small paper bags work well as the containers) is necessary for each student group. Each container represents rainfall forecast probabilities. Weather strips and container labels are available at the end of this learning module. It is suggested that the weather strips be printed out on card stock or laminated. The following containers and forecast probabilities are necessary. For larger classes, duplicate containers as necessary to provide one container per group.

Container 1 - 20% chance of rain - 2 rain strips and 8 clear strips

Container 2 - 40% chance of rain - 4 rain strips and 6 clear strips

Container 3 - 80% chance of rain - 8 rain strips and 1 clear strip

National Standards

Module provides integrated approach to address science, math, reading and geography national standards. See Teacher Guide for specific standards addressed for grades 5-8.

Texas Essential Knowledge and Skills (TEKS)

Module provides integrated approach to address science, math, reading, and geography standards. See Teacher Guide for specific standards addressed for grades sixth, seventh, and eighth.

Weather Folklore

Clear moon, frost soon.

Possible scientific basis, taken from Weather Proverbs True or False? “If the atmosphere is clear, the surface of the earth will cool rapidly as heat is radiated away at night. There is no “blanket” of clouds to keep the heat that the ground absorbed during the day from radiating back up into space. If the temperature is low enough on these clear nights and there’s no wind, frost may form.”

Music Selection

B.J. Thomas - Raindrops Keep Falling on My Head

Advance Preparation

Prepare one of the following

1. A pre-recorded weather forecast from the local weather station,

2. A weather forecast with a percent chance of rain on it from the local newspaper or Internet, or

3. A transparency of the forecast map provided on the next page. Note the map foreshadows weather symbols and information to be discussed in latter modules. Modify the percent chance of rain in the journal / bell work question to match the forecast you select.

Divide the class up into groups.

Prepare the precipitation containers.

Review the concept of probabilities.

Teaching Suggestions

Step 1 – Journal / Bell Work

What does it mean when the meteorologist says there is a 30% (note – substitute in the percentage chance of precipitation to match your advance preparation forecasts) chance of precipitation? This question is the same question that ended the previous learning module. It is used to reinforce the probability nature of precipitation forecasts and tie the two learning modules together.

Field and discuss responses from the students or have students record their answers in their journal to the journal / bell work question.

Answer to bell work question: the probability of precipitation is defined as the likelihood of occurrence (expressed as a percent) of a measurable amount of liquid precipitation (or the water equivalent of frozen precipitation) during a specified time period at any given point in the forecast area.

A simple view would be - If we provide a meteorologist with historical rainfall data and ask the meteorologist to tell us the probability of having rainfall on a given day, she/he would go through complex computations. A simple way

Forecast Map

[pic]

Precipitation Forecast for the Central U.S. is a 30% chance of precipitation.

What does it mean when the meteorologist says there is a 30% percentage chance of precipitation?

to compute a percent chance of rain is to compute the ratio of the number of rainy days on a given day to the total number of years of the historical data. For example, if over the last 100 years in College Station, Texas it rained 48 days on October 26; the computed chance of rain is 48%.

Step 2 – Review / Introduce Probabilities - Optional

This review is provided to the students as part of the Probable Cause Experiment.

Calculating probabilities and percents

Student review - a percent or probability is the number of times an event occurs relative to the total number of events. Probabilities need to sum to 1 in decimal form or 100% in percent form. For example, if 6 times out of 20 draws you obtained a rain strip, the probability of rain would be [pic] in decimal form and [pic] in percent form.

Step 3 - Probable Cause Experiment

Student directed lab experience which introduces / reinforces the concept of probabilities in the context of rainfall forecasts.

[pic] Probable Cause Experiment [pic]

Objective

The objective of this lab is to understand probabilities associated with rainfall forecasts. You will recognize that a forecasted chance of rain does not mean it will always rain. The unit reviews the concepts of probabilities using both percentages and decimals.

Materials

Each group needs a container with an unknown number of rain / clear weather strips.

Procedures

1. Without looking inside the container, reach into the container and draw one strip out of the container.

2. Record if the strip was a rain or clear day on the Data Chart by checking the correct column.

3. Place the strip back in the container.

4. Shake the container to redistribute the strips in the container.

5. Repeat steps 1-5, 20 times.

6. Add up the checks in each column and place in the total row to indicate the total number of rainy and clear days.

7. Answer the questions using the data in the Data Chart.

1. Record Data on the Data Chart – use the steps from the above procedures to create your data. Each draw from the container represents one day that had the precipitation forecast associated with your container.

Forecast Number on Container ____________

Answers will depend on the draws.

|Data Collection Table |

|Draw # |Rain |Clear |

|1 | | |

|2 | | |

|3 | | |

|4 | | |

|5 | | |

|6 | | |

|7 | | |

|8 | | |

|9 | | |

|10 | | |

|11 | | |

|12 | | |

|13 | | |

|14 | | |

|15 | | |

|16 | | |

|17 | | |

|18 | | |

|19 | | |

|20 | | |

|Total Rain Days | |xxxx |

|Total Clear Days |xxxx | |

2. Graph Your Data - Complete the following bar graph using the data from your data chart. Plot the total number of days with rain and days that were clear.

|Number of Rain and Clear Days |

|T |20 | | | |

|O | | | | |

|T | | | | |

|A | | | | |

|L | | | | |

| | | | | |

|N | | | | |

|U | | | | |

|M | | | | |

|B | | | | |

|E | | | | |

|R | | | | |

| | | | | |

|O | | | | |

|F | | | | |

| | | | | |

|D | | | | |

|A | | | | |

|Y | | | | |

|S | | | | |

| |19 | | | |

| |18 | | | |

| |17 | | | |

| |16 | | | |

| |15 | | | |

| |14 | | | |

| |13 | | | |

| |12 | | | |

| |11 | | | |

| |10 | | | |

| |9 | | | |

| |8 | | | |

| |7 | | | |

| |6 | | | |

| |5 | | | |

| |4 | | | |

| |3 | | | |

| |2 | | | |

| |1 | | | |

| | |Rain | |Clear |

Calculating probabilities and percents

Student review - a percent or probability is the number of times an event occurs relative to the total number of events. Probabilities need to sum to 1 in decimal form or 100% in percent form. For example, if 6 times out of 20 draws you obtained a rain strip, the probability of rain would be [pic] in decimal form and [pic] in percent form. For the following questions, record your answers in both decimal and percent form using your data from the Data Chart.

3. What is the probability of drawing a rain day? (Show your work)

Decimal form

Hint: [pic]

Percent form _________%

Hint: decimal form x 100 or move the decimal place two spaces to the right

4. What is the probability of drawing a clear day? (Use above hints)

Decimal form _____________

Percent form ___________%

5. Check your work, do rainy days plus clear days add up to 100%?

Total % rain _____________

Total % clear + _____________

Total % _____________

If the total is not 100%, you need to check your work on questions 3 and 4.

Conclusions

6. Given your data and calculated probabilities what percent chance of rain do you think your container represents? (Circle your answer)

20% 40% 80%

7. If a container represented a 0% chance of rain, how many rain days would you have drawn out of your 20 draws?

8. If a container represented a 100% chance of rain, how many rainy strips would you have drawn out of your 20 draws?

Reporting to the Class

Your group will report to class the following information.

9. Ask your teacher to give you the following information for your container. What is the correct percent chance of rain represented by your container?

10. What was your guess, question 5, as to the percent chance of rain represented by your container?

11. How many days did it rain out of the 20 days? (see question 3).

______ days rain out of 20 days

12. What is the percent chance of rain given your draws? (question 3)

Step 4 - Whole Class Discussion

At this point it is suggested the whole class discusses one or all three of the following questions.

1. Why do you think it is possible for a particular forecast that the number of rain days differed between the groups? Keep in mind the containers for a particular forecast had the same information in them for each group.

Answer: the calculated probabilities are based on 20 draws and not a very large number of draws. Also, the draws are random. The teacher could lead the students to this answer by exploring the relationship between the number of draws and probability starting with assuming only one draw. Will the calculated probability be the same as the container? Assume any probability of rain, for a single draw the calculated probability will be either 100% chance of rain or 0% chance of rain depending on the single draw. Then asking the students what will happen as the number of draws increase.

2. Return to the journal / bell work question “What does it mean when the meteorologist says there is an x% chance of rain?” The discussion should tie the first module with this module.

Answer – the probability of precipitation is defined as the likelihood of occurrence (expressed as a percent) of a measurable amount of liquid precipitation (or the water equivalent of frozen precipitation) during a specified time period at any given point in the forecast area.

Step 5 Assessment / Homework

[pic]

Assessment Options

1. Probable Cause Lab

2. Homework Options

3. Journal reflection: List of events or experiences when weather has affected/impacted you.

4. Journal reflection: What information did you learn today?

[pic]

Homework Options

1. Continue Weather Journal

2. Enrichment Options

3. Make a list of other events, besides the weather, that may have uncertain outcomes that impact your life.

[pic]

Enrichment Options

Probabilities and Draws

1. Assume you have a container that represents a 10% chance of rain. How many rain weather strips would you expect to pull out of the container in 10 draws ___________?

1 rain strip

2. Assume you have a container that represents a 50% chance of rain. How many rain weather strips would you expect to pull out of the container in 10 draws ___________?

5 rain strips

3. Assume you have a container that represents an 90% chance of rain. How many rain weather strips would you expect to pull out of the container in 10 draws ___________?

9 rain strips

Probabilities – Other Areas

Ask students to explain how probabilities are used in other areas; examples include sports, lottery, cards, games, and science.

Probabilities – Other Forecasts

Suppose that you were going to be the teacher for the next class period and you were going to put 30 strips into each container. How many strips representing rain and clear days would you put into each container to represent these percentages?

30% chance of rain

Number of clear strips ___21________

Number of rain strips ____9________

60% chance of rain

Number of clear strips ______12_____

Number of rain strips ______18_____

70% chance of rain

Number of clear strips _______9_____

Number of rain strips ______21_____

[pic]

Struggling Learners

Students should be divided into groups such that the struggling learners are paired with peer tutors.

Container Labels

| |

|Forecast 1 |

|[pic] [pic] |

| |

|Forecast 2 |

|[pic] [pic] |

| |

|Forecast 3 |

|[pic] [pic] |

Weather Strips

Forecast 1 Forecast 2 Forecast 3

|1 |2 |3 |

|Rain [pic] |Rain [pic] |Rain [pic] |

|1 |2 |3 |

|Rain [pic] |Rain [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Rain [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Rain [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Clear [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Clear [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Clear [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Clear [pic] |Rain [pic] |

|1 |2 |3 |

|Clear [pic] |Clear [pic] |Clear [pic] |

|1 |2 |3 |

|Clear [pic] |Clear [pic] |Clear [pic] |

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Teacher Edition 1 day

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