Using Ratios to Taste the Rainbow Lesson Plan Cube Fellow: Amber DeMore

Teacher Mentor: Kelly Griggs

Goal: At the end of the activity, the students will know that the actual ratio of colored skittles is not what the Mars company claims. They will also be able to calculate different ratios and percentages associated with the number of colored skittles given to their group. Grade and Course: Math 7th grade KY Standards: MA-7-NPO-S-RP1 Students will compute percentages and use percentages in proportional reasoning. MA-7-NPO-S-RP2 Students will determine and solve proportions in real-world and mathematical situations. MA-7-NPO-S-RP3 Students will develop proportional reasoning and apply to real-world and mathematical problems (e.g., rates, scaling, similarity). MA-07-1.4.1 Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, sales tax, discounts, rate). MA-7-NPO-U-4 Students will understand that proportional reasoning is a tool for modeling and solving problems encountered in everyday situations. MA-7-DAP-S-CD1 Students will make predictions, draw conclusions and verify results from statistical data and probability experiments. Objectives: Resources/materials needed: 15 bags of 25 skittles (1 for each pair), worksheets, smartboard/whiteboard Description of Plan: First have the students do the following bell ringer: Write out a step by step method for changing the fraction 1/8 to a percent. Write it so that a fourth grader could repeat your steps and get the same answer. Then go over the two different methods for finding a percent using student participation. Second, hand out the worksheet to each pair of students. For my students, I made sure to stress that we would stop doing the activity if anyone was off task or playing with the Skittles in an inappropriate manner. Next, hand out the Skittles, stressing to the students not to open the bags until you say to. Then have them read aloud number one (choose a volunteer). Have them estimate what the ratios would be for number two (you may have to lead them through this). Then tell them to count up the colored Skittles and record their answers in number 3. Then have them bag up the Skittles again, and collect them.

Tell them they will be able to eat the skittles at the end of class, provided they are behaved. Have them do 4-6 on their own. Then choose a group’s numbers to use, and go over how it is supposed to be done. Have them read the different answers for number 6 critiquing how simple the process is. Then have them complete number 7. Discuss number 8 as a class. There should be some interesting answers. Have them complete the rest of the worksheet. Choose another group’s data to use. Go through 9-13 with this data set. Make the students answer the questions, and tell how they arrived at this answer. Then go through and write on the board the individual group’s questions. Have the class answer the questions. Go through as many questions as you can with the time you have. Then, if your students were behaved, pass the Skittles out again, being careful to give each group the bag they originally had. Turn on your smart board and have the class play a ratio game: http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/g ame.shtml Lesson Source: An adaptation from Rossman and Chance (2000), Workshop Statistics: Discovery with Data, 2nd Edition. gk12.uark.edu/lessons/skittle%20math.doc

Instructional Mode: Worksheets, Smartboard/Web, Whiteboard Date Given:

Nov.19th

Estimated Time: 1.5 hours

Date Submitted to Algebra3: Nov.26th

Form 8-18-07

Skittles Activity Names of group members: Group Number on your Skittles bag: 1. The Skittles company claim that there are the same amount of each color in each bag of Skittles. I have divided a large bag of Skittles into several smaller bags for you. Make sure not to eat the Skittles before finishing the activity. You will be given permission to do so if the class as a whole has behaved, and after the activity is completely finished. 2. First, estimate the following proportions/ratios: a. Red Skittles to Total Skittles: b. Green Skittles to Total Skittles: c. Yellow Skittles to Total Skittles: d. Purple Skittles to Total Skittles: e. Orange Skittles to Total Skittles: 3. Count the number of Skittles in your bag, and how many of each color are in your bag. Record the numbers here: Total number of Skittles: Number of Orange Skittles: Number of Yellow Skittles: Number of Green Skittles: Number of Purple Skittles: Number of Red Skittles:

4. What is the ratio of orange Skittles to total number of Skittles?

5. Figure out the proportion of orange Skittles out of 100. Number of orange Skittles Total Number of Skittles

= _______ = ______

100

6. What steps did you go through to get the number of orange Skittles out of 100?

There may be a different way to figure out the number of orange Skittles out of 100. Write the example here: 7. Repeat steps 2 and 3 with all of the Skittles. What proportions do you get? Record your answers in this chart: Color of Skittles

Number of Skittles

Fraction (Ratio)

Reduced Fraction (Ratio)

Percent

Red Green Yellow Purple Orange 8. Is the proportion you just calculated the same as what you predicted? Why do you think this is?

9. If you had three bags of Skittles, exactly like the one you just had, how many green skittles would there be? What would be the unreduced fraction/ratio? The reduced fraction/ratio?

10. What is the ratio of the total skittles in one bag to the number of red skittles?

11. How many purple Skittles would there be in 20 bags? How many total skittles would there be in 20 bags?

12. What percentage of Skittles are red and green?

13. What percentage of Skittles are not yellow?

14. Please make a bar chart of your data: 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Green Orange Purple

Red

Yellow

15. Write two questions that you would like the class to answer. The questions should be like numbers 9-13. Make the questions reasonable so they can be answered by your classmates. Question 1:

Question 2:

19.9 My 27.2 My 10.3 My

5.1 My 2.6 My

4.9 My

1.8 My 0.8 My

1.3 My 0.38 My

0 My

Locker Problem Activity

A Thousand Lockers Imagine you are at a college that still has student lockers. There are 1000 lockers, all shut and unlocked, and 1000 students. Here's the problem: 1. Suppose the first student goes along the row and opens every locker.

2. The second student then goes along and shuts every other locker beginning with number 2.

3. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.)

4.

The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the thousand students have followed the pattern with the thousand lockers. At the end, which lockers will be open and which will be closed? Why?

Looking for Patterns: a. Which lockers will only be touch once? b. Which lockers will only be touch twice? c. Is there any locker that will be touch three times? If so, which ones? d. Which locker has been touch more? Locker 36 or locker 48? e. After the 36th student opens/closes lockers, which lockers are open? Which are closed? f. After the 100th student opens/closes lockers, which lockers are open? Which are closed?

Estimating Deer (Marshmallow) Population Lesson Plan Cube Fellow: Eric Clark

Teacher Mentor: Sandra Fugett

Goal: Use proportions to determine the deer population in a given area. Grade and Course: 9th grade Algebra I KY Standards: MA-HS-NPO-U-5, MA-HS-NPO-S-RP1 Objectives: The students will be able to apply ratios and proportions to real life problems. They should be able to collect data, make observations and use the data to solve problems. Resources/materials needed: White and colored marshmallows, small paper bags, Styrofoam cups, paper plates, worksheet. Description of Plan: Students will be in groups of three. They will use white and colored marshmallows to simulate the process of capturerecapture to estimate deer population. Lesson Source: Algebra I by Holt, Rinehart, and Winston Instructional Mode: Group work Date Given: 12/10/07

Estimated Time: 1-2 days

Date Submitted to Algebra3: 12/10/07

Form 8-18-07

Estimating Deer (Marshmallow) Population Name: ________________

Imagine that you are an employee of the Kentucky Fish and Wildlife Service. Hunting season is coming up and you have been asked to estimate the deer population in the state. Trying to count them by catching them all would take too long, so you decide to use the capture-recapture method. This is a method that uses proportions to estimate the population of animals. In this activity we will simulate this by using marshmallows.

Tools: Each group will need: ̶ 1 paper sack – the “forest” ̶ A supply of white marshmallows – the “deer” ̶ A supply of colored marshmallows – the “tagged deer” ̶ 1 styrofoam cup – the “trap” ̶ 1 paper plate

Procedure: 1. Collect the Data a. Capture i. Each group will receive a bag with white marshmallow inside. ii. With the cup, “trap” several white marshmallows and place them on the paper plate. iii. Count the number of white marshmallows you trapped and write that number down. ______________. DO NOT put these back in the bag (in fact, you can eat them!) iv. Replace the number of white marshmallows you caught with colored marshmallows. These represent the “tagged” deer. v. Put these colored marshmallows in the bag and mix thoroughly.

b. Recapture i. Use the cup again to trap some marshmallows. ii. Count the TOTAL number of marshmallows you caught and record it the table below. iii. Count the number of COLORED marshmallows in this sample and record it in the table below. iv. Return ALL of these marshmallows to the bag and mix. v. Repeat this process until you fill out the entire table.

Sample

1 2 3 4 5 6 7 8 9 10 AVERAGE

Total number of Number of Marshmallows in colored Marshmallows in sample sample

2. Analyze the Data a. To find the AVERAGE number of marshmallows in each sample, add up the number of marshmallows in each sample and then divide by 10. Do the same to find the average number of colored marshmallows in each sample. b. Using these averages, we can write a RATIO of colored marshmallows in the sample to the total number of marshmallows in the sample. How should this ratio compare to the ratio of colored marshmallows to the total number of marshmallows in the bag? ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ c. Set up a proportion to estimate the number of marshmallows in the bag.

ESTIMATED NUMBER: ________________________ d. Now count the total number of marshmallows in the bag. TOTAL NUMBER: __________________ e. How close was your estimate?

Using Proportions to Estimate Lesson Plan Cube Fellow: Stuart Traxel

Teacher Mentor: Tara Barnett

Goal: Show how proportions can be useful for prediction th

Grade and Course: 9 grade Pre-Algebra KY Standards: MA-HS-1.4.1 Objectives: The student will be able to: 1) Given a ratio, calculate corresponding proportions 2) Begin to understand the error involved when using proportions to estimate 3) Calculate and understand the importance of unit rates

Resources/materials needed: The attached worksheet is needed along with the following, which are classified by each station: 1. Remote Controlled Car, tape, timer 2. Timer 3. Hershey Kisses, timer 4. Pennies, jar/cup, timer

Description of Plan:

Hand out the worksheet in Appendix A. If you have three or four teachers/aids in the class, you can split the class into four groups and have them rotate by groups. If you only have one or two teachers/aids in the class, it is probably better to ask for volunteers for each station. The rest of this description will be based upon the fact that you only have one/two teachers/aids and have asked for volunteers. First, ask for a volunteer to time the remote controlled (RC) car. Mark off 10 feet and 15 feet before class. Have a teacher/aid drive the RC car for 10 feet and time it. Make the students use a proportion to calculate how long they think it will take for the RC car to go 15 feet. After that, time and drive the RC car for 15 feet. Ask the students how close they think their estimate was and what might have caused the error. The students can calculate all unit rates at the end of class or for homework. Have a student volunteer to do jumping jacks for 20 seconds. Record how many jumping jacks the student performed and have the students use a proportion to calculate how many jumping jacks they think the student will complete in 30 seconds. Time the student to see how many jumping jacks the student completes in 30 seconds. Ask the students to compare their estimate and the measured number. Have a student volunteer to see how many Hershey Kisses he/she can eat in 20 seconds. Have the students use a proportion to calculate how many Hershey Kisses they think the student will eat in 45 seconds. Experiment to see how many the student can eat in 45 seconds. Again, compare these previous two values. Have a student volunteer to see how many pennies they can put in a cup one at a time for 30 seconds. Record this number and make the students calculate how many pennies they think

the volunteering student can put in for 50 seconds. Ask the students to compare these two values.

Lesson Source: Yours truly Instructional Mode: Experiments Date Given: 03-20-2008

Estimated Time: 1 class period (45 minutes) 3

Date Submitted to Algebra : 03-22-2008

Appendix A: Name: ____________________________________

Using Proportions to Estimate

While at a station answer the questions below that label. You can work problems to the right of the tables.

1. Remote Controlled Car Time a How long does it take for

Unit

the car to travel 10 feet?

b

Use the ratio from the problem above to calculate how long you think it will take for the car to travel 15 feet?

c

How long did it actually take for the car to travel 15 feet?

d

What is the unit rate using the ratio in part a? (Hint: How far does the car travel in 1 second?)

2. Jumping Jacks Jumping Jacks

a

How many jumping jacks can you do in 20 seconds?

b

Use the ratio from the problem above to calculate how many jumping jacks you think you can do in 30 seconds?

c

How many jumping jacks can you actually do in 30 seconds?

d

What is the unit rate using the ratio in part a? (Hint: How long does it take for 1 jumping jack?)

Unit

3. Hershey’s Kisses

a

How many Hershey's Kisses can you eat in 20 seconds?

b

Use the ratio from the problem above to calculate how many you think you can eat in 45 seconds?

c

How many can you actually eat in 45 seconds?

d

What is the unit rate using the ratio in part a? (Hint: How long does it take to eat one Hershey kiss?)

Hershey Kisses

Unit

pennies

Unit

4. Pennies

a

How many pennies can you put in a bowl (ONE AT A TIME) in 30 seconds?

b

Use the ratio from the problem above to calculate how many you think you can put in the bowl in 50 seconds?

c

How many pennies can you actually put in a bowl (ONE AT A TIME) in 50

seconds?

d

What is the unit rate using the ratio in part a? (Hint: How many pennies can you put in per second?)

Additional questions: 1. What might have made your answer in part (b) different from your answer in part (c) for: a. The Remote Controlled Car:

b. Doing Jumping Jacks:

c. Eating Hershey’s Kisses:

d. Picking Up Pennies:

Puerto Rico – In the Eye of the Storm Background Information Hurricanes (and their cousins Typhoons and Tropical Cyclones) form in the tropics, over the ocean, and in particular where sea surface temperature is greater than 80°F. This warm water provides the energy that drives the storm. When a hurricane moves over colder water or over land the energy supply is cut off and the storm will weaken quickly. Hurricanes are essentially just areas of low air pressure with a closed air circulation and sustained wind speeds in excess of 74 miles per hour. In the northern hemisphere that air circulates in a counter-clockwise direction. The opposite is true in the southern hemisphere. This difference is due to the Coriolis Force. Tropical Storms are similar but their wind speeds are slower – between 35 and 74 miles per hour. The greatest wind speeds in a hurricane occur near the center. At the center there is often an “eye” and here there is almost no wind. The eye of a hurricane is typically between 20 and 40 miles across. Outside the eye is the zone of hurricane force winds (winds faster than 74 mph). This zone may be more than 100 miles across. Beyond that is the zone of tropical storm force winds (winds between 35 and 74 mph), which may also extend more than 100 miles. The largest Atlantic hurricane, in terms of width, was 2010’s Hurricane Igor which had tropical storm force winds extend almost 350 miles from either side of the eye.

Exercise Imagine you live on the Caribbean island of Puerto Rico and you have a home in the capital city San Juan (See Figure 1). Every year between the months of May and December there is a chance that the island will be hit (~8%) or ‘brushed’ (~30%) by a hurricane.

Figure 1: A map of Puerto Rico, and its capital San Juan (red star)

One significant hit was Hurricane Hugo on September 18th 1989. Hugo brought 125 mile per hour winds and passed just northeast of San Juan. In nearby Culebra there was extensive damage. Hurricane force winds extended 45 miles out from the center of the storm, and tropical storm force winds extended 150 miles from the center. (http://www.stormpulse.com/hurri cane-hugo-1989)

For this exercise we will imagine that a hurricane with the following dimensions will pass along the north coast of Puerto Rico. 1) Center of the storm will pass 20 miles north of the north coast of Puerto Rico 2) Hurricane force winds extend 25 miles from the center of the storm 3) Tropical storm force winds extend 50 miles from the center of the storm Notice how the island of Puerto Rico is almost a rectangle. The island is approximately 35 miles wide (north to south) and 100 miles long (east to west). Here we will assume it is a perfect rectangle with those dimensions, and that San Juan is right on the north coast exactly halfway between the eastern- and westernmost ends of the island. It might help to draw the island and the hurricane on graph paper. 1) When the hurricane is directly north of San Juan what length of coast will be experiencing hurricane force winds? 2) When the hurricane is directly north of San Juan what length of coast will be experiencing tropical storm force or greater winds? 3) When the hurricane is directly north of San Juan what length of coast will be experiencing tropical storm force winds but not hurricane force? 4) If the storm is moving from east to west at 10 miles per hour, for how long (in hours) will San Juan experience tropical storm force winds? 5) If the storm is moving from east to west at 10 miles per hour, for how long (in hours) will San Juan experience hurricane force winds?

Name _____________________ Date_____________________ MATH 193 Road Trip Project This summer, your family has decided to take a road trip. You will start in Albuquerque and travel to five other U.S. cities before returning to Albuquerque. It is your job to decide what cities to visit and calculate how far you will travel.

Step 1: Plan your trip. You may only visit cities that are included on the given map. Choose which 5 cities you will be visiting during your summer vacation. Specify both the city and the state. Starting City

Albuquerque, New Mexico

City #1 City #2 City #3 City #4 City #5 Ending City

Albuquerque, New Mexico

Step 2: Using a ruler, draw a straight line connecting each city you will be visiting. (Draw a straight line from Albuquerque to City #1. Then, draw a straight line from City #1 to City #2, etc.) Step 3: Using the ruler, measure the length of the line connecting each city in your trip. ROUND EACH DISTANCE TO THE NEAREST QUARTER INCH. Fill out the following table: Starting City

Ending City

Distance on Map (in Inches)

Albuquerque, NM

Albuquerque, NM

Step 4: Use the scale on the map to write a ratio of distance on map to distance in real life. Your ratio should be written as a fraction. Be sure to include units.

http://mathequalslove.blogspot.com/2012/07/pre-algebra-road-trip-project.html

Name _____________________ Date_____________________ Step 5: Calculate the distance of each leg of your trip using the ratio you just found. Set up a proportion and cross multiply to find the distance in real life between each of the cities. ROUND TO THE NEAREST MILE. List 2 Cities and Distance in Inches

Proportion

Show Work

Distance in Miles

Step 6: Find the total distance traveled during your road trip.

http://mathequalslove.blogspot.com/2012/07/pre-algebra-road-trip-project.html