Isn’t Math Yummy??!! Often I am asked: “What am I ever going to use this for?” Today you will see many different applications of math through one of your favorite things: junk food! Basically we are going to explore and experiment with every type of math that can be done using a bag of skittles! Don’t worry; you will get to eat them eventually…but not yet! You have your work cut out for you and you will work up an appetite! You will be doing some basic math that is a review of 7th grade (and the 8th grade curriculum that you are skipping) and you will be seeing a preview of what is to come this year in Algebra 1. Many of the topics today will just be introduced. The “why” and “how” part will come later as we build up our algebra skills! At the end, you will be writing an essay describing all the math you found in these activities! Let’s get started! Supplies Needed: Bag of Skittles, ruler, cup, calipers, paper plate Part 1: Basic Math Review 1. Before opening your bag, predict how many total Skittles will be in your bag (don’t feel the bag!) Which color do you think will occur most often? Why? 9. Fill out the following chart based on the skittles in your bag. 10. Assume your teacher has a large bag that contains 630 skittles. Use your data above to predict how many of each color will be in your teacher's bag. Show all work below. (Try using proportions.) c) Do you think that every skittle is exactly the same size and shape? Explain why or why not. d) Attempt to find two skittles that appear to be different sizes, one that appears normal and one abnormal. Use a pair of Vernier calipers to measure the dimensions of the two skittles. Find the percent change in the dimensions of the two. 15 . Do all the candy bags contain the same number of candies and colors? How can you explain this? 16. Pull out the following combination of colors and put them in a cup. 5 Red, 7 Yellow, 5 Orange, 2 Green, 1 Purple. Conduct a Probability experiment. Shake the cup hard in between each pull. Reach in and grab a color without looking and record the color that is pulled out. After 10 pulls, calculate the experimental and theoretical probability of each color in the next chart. Compare them and decide if you are lucky or unlucky and why. Color Tally Experimental Probability Theoretical Probability Lucky or Unlucky? Red Yellow Orange Green Purple Part 2: Graphs – Do this at home by yourself for homework. You know a LOT about graphs. Your task is to make THREE graphs using any of the data that you have collected so far in part 1. The challenge for you is to make three very different graphs that show three different kinds of data. You are to draw a CONCLUSION from each graph. Use a separate piece of graph paper to make these graphs and then answer the questions below about each graph. Make sure each graph is PERFECT with all its parts! Graph #1 Types of Graph Why did you choose that type of graph? What data question does your graph answer? What conclusions can be drawn from your graph? Graph #2 Graph #2 Part 3: Skittle Pie? 1. Draw a straight line in the middle of a blank piece of paper. Then line up somewhere between 5 and 10 (your choice) Skittles on the line and mark off the beginning and end of the line of Skittles. This will establish the diameter of your circle using one Skittle as our fundamental unit of length. 2. Using your compass and ruler construct the perpendicular bisector of the diameter to find the center for the circle. Draw the circle using your compass. 3. Line up Skittles on the circle until the circumference is filled in. If necessary, split a Skittle in half to complete the circumference. 4. Record the number of Skittles required to complete the circumference. 5. Divide your circumference by your diameter and describe the significance of and accuracy of your result. Part 4: What, more graphs? Linear Growth Experiment 1. Make a FIVE color Skittle pattern using at least THREE different colors of Skittles. Write down your pattern here. 2. Continue your pattern of Skittles for five more iterations (repeats). 3. Pick your favorite color in your pattern: 4. After each iteration, record how many Skittles of your favorite color that there are total so far. Use the table at the right. 5. Make a graph from the data you have collected. Put the iteration number on the x-axis. 6. Explain the shape of your graph. What connection does the shape have with the data collection experiment with Skittles? Exponential Growth Experiment 1. Fill a cup about 2/3 full of Skittles. 2. Pour out your candy onto the plate and count all of them. Record this as Trial 0 in the table. 3. Put all the candy back into the cup. Pour out the candy onto the plate again, but this time only count the ones that are face up--that is, have the "S" showing. Record this in your table. 4. Put only the candies that were face up back into the cup. Remove all of the candy that was face down. 5. Repeat steps 3 and 4 until you have no candy left. 6. On a coordinate plane, plot your data as coordinate points. Trial Number should be on the x-axis. 7. Explain the shape of your graph. What connection does the shape have with the data collection experiment with Skittles? 8. If time, ask me how to enter your data into your calculator. Part 5: Problem Solving: (do on your own for homework) The Problem: (Skittles and bags not actually needed!) There are 5 paper bags. There are 100 Skittles total in all the bags. The first and second have 52 Skittles. The second and third have 43 Skittles. The third and fourth have 34 Skittles. The fourth and fifth have 30 Skittles. How many Skittles are in each bag? Strategy: Work: Solution: Part 6: Reflection and Essay Besides reviewing math skills, what have you learned from this experiment with Skittles. Give at least FIVE DEEP THOUGHTS! Use more space if needed or type.