Foundations for Functions. Correlation: Cookie Cost Vs. Cookie Quality

Transcription

1 Activity: TEKS: Overview: Materials: Grouping: Time: Correlation: Cookie Cost Vs. Cookie Quality (A.) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (D) collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. In this activity, students will taste and rate store-bought cookies, collect and organize the data in tables, create scatterplots of the data, and analyze the scatterplot. They will then calculate the correlation to determine whether there is a relationship between the price and the quality of the cookies investigated. 8 to different brands of chocolate chip cookies; teacher will need to divide these into enough similarly sized samples for each student to taste Bags or containers labeled with capital letters to hold the cookie samples Paper plates (or paper towels) and cups, for each student Cookie Data Sheet - one per student Group Data Tables (one table per sample) - one set per group Class Data Tables (8 tables on large poster paper) Two-Column Tables Graphing calculators Handout, poster, or transparency stating the price and weight for each labeled cookie sample Notebook paper for T tables Graph paper for scatterplots Teacher assigned groups of to students class periods; 50 to 55 minutes per period Lesson: Procedures. Preparation for Activity Before Class: Assign students to groups with to students per group. Assign each group a number. Notes Teacher assigned groups that provide a balanced level of ability from group to group tends to work best. Correlation: Cookie Cost Vs. Cookie Quality Page

2 Procedures. Prepare samples for testing: Obtain the packages of cookies to be tested. Place similarly sized samples of each brand of cookie in a bag or container and randomly assign each brand a capital letter label, beginning with A. Use a large container for each brand and pass the container from group to group after each sampling or use small containers one for each group for each brand.. There will be scatterplot for each attribute investigated. Each scatterplot will have data point for each sample investigated, A-H. The teacher needs to determine the procedures for tasting the samples. A suggested procedure for collecting, recording and sharing data and for determining the price per weight for each sample (price per ounce, price per gram, price per cookie, price per pound ) is provided in the following procedures.. Day : Ask students, Is there a relationship between the price of a cookie and its quality? and How could such a relationship be investigated? ( minutes) Notes The data recording sheets provided allow for 8 cookie samples labeled A-H. There should be enough samples for each participant to have at least one; some participants may want to taste additional samples, so have extras available. The Cookie Data Sheet allows students to rate attributes of the cookies: taste, texture, appearance and overall. Make copies of handouts and transparencies provided, or create your own if the attributes to be investigated and the number of samples differ from the ones provided. Allow groups minutes to discuss the question. Then have or groups present their responses. 5. Explain to the class that today they will be collecting data ranking the quality of several different brands of chocolate chip cookies by tasting and rating various attributes for each cookie sample. Tomorrow they will use the data to make scatterplots and to analyze the results in order to answer the question: Is there a relationship/correlation between cookie price and cookie quality? ( minute) Correlation: Cookie Cost Vs. Cookie Quality Page

3 Procedures 6. Distribute materials: cookie samples, cups of water, paper plates, Cookie Data Sheetone per student, and Group Data Tables-one set per group. ( minutes) 7. After tasting each cookie sample, have each student rate the attributes (Taste, Texture, Appearance, and Overall) of each cookie on a scale from (poor) to 5 (excellent) and then record the ratings on the Cookie Data Sheet. Each group should taste the samples in a different order; i.e., group # should begin with sample A, group # with sample B, and so on (to avoid any order effect). (0 minutes) 8. Each group should record its individual student data ratings of each attribute for each sample on the Group Data Tables. Then each group should calculate the average ratings for each attribute for each sample A-H. (0 minutes) 9. Have each group post its average rating for each attribute of each sample on the appropriate Class Data Table. (5 minutes) 0. Assign each group a specific sample s Class Data Table (i.e., group #-sample A, group #-sample B and so on). Each group then calculates and posts the class average ratings for each attribute for their assigned sample. (8 minutes) Notes If any students do not wish to participate in the tasting, include them as helpers in distributing the samples and refilling water cups as needed. It is very important that students do not mix up the samples! Emphasize to the students the importance of individually scoring without discussing their thoughts with their neighbors, tasting quietly, and taking this seriously so as not to skew the data. The teacher may need to review the procedure for finding the mean or how it may be calculated using graphing calculators. Students will use this data to make tables of ordered pair to create scatterplots. Assign anyone who did not participate in the taste-testing to a group or make a group with those students. According to the number of samples and the number of groups, some groups may be assigned the same sample.. Homework: Post or distribute the price and weight information for each sample. Have students calculate the price of each cookie sample in cents per ounce (to the nearest tenth of a cent). Correlation: Cookie Cost Vs. Cookie Quality Page

4 Procedures. Day : Have students begin class by comparing their homework calculations with other students in their group. Then have each group post the price and cents per ounce for the sample assigned the previous day. (5 minutes). On notebook paper have each student create four two-column tables of ordered pairs, one for each attribute. The Two- Column Tables hand-out can be used as a model for this. Notes Ask students to discuss with their group members what are independent and dependent variables in each table. For each ordered pair in the two-column table x = the price per ounce and y = the mean rating (class average rating) for the specified attribute for each cookie. (5 minutes). Have each student create a scatterplot for each attribute using the ordered pairs from the tables. (0 minutes) The teacher may need to discuss scale as well as discrete and continuous graphs. 5. Have students discuss with group members any trends or patterns they observe. (5 minutes) 6. Facilitate the whole class discussion calling on various groups to report their findings. Discuss the following questions as a class: a) What would a scatterplot of the data look like if two things were linearly related (i.e. one has an effect on the other)? (Points should form a pattern that looks somewhat linear.) What would it look like if the two things were not related? (The points would be randomly spaced over the graph and/or not appear linear.) Be sure to let each group/student have a chance to participate in the discussion. Listen carefully to the responses the students give, and give specific guidance to the discussion to ensure that students are getting the concepts they need. This is an opportunity to see if students truly understand scatterplots and correlation. b) The measure of the strength and direction of the relationship is described by the term correlation. Correlation: Cookie Cost Vs. Cookie Quality Page

5 Procedures Do any of your scatterplots appear to have some correlation? What kind of correlation? (Answers will depend on the data collected.) Notes c) Think about the slope of a line. What kind of slope does a line have that goes up from left to right? (positive) What kind of correlation would a scatterplot have, then, if the data trends sloped upward left to right? (Y increases an average amount for each increase of x.) d) What can you conclude from this correlation in the context here? In other words, interpret what this means for this data. (One possible interpretation is the higher the cost of the cookie the better the quality.) e) What would a negative correlation look like? (a linear relationship with a negative slope) What would it mean in this situation? (The cheaper the cookies the higher the quality ratings). f) What would a scatterplot look like if there was no correlation between the data collected? (The data would not appear to have a pattern.) What would it mean in this situation? (That the quality of the cookie does not depend on the cost.) (5 minutes) 7. Chose attribute for the whole class or assign different groups different attributes. Do not assign the Overall rating. Save it for the homework. Allowing the students to write their first paragraph in class and discuss it with their group. This will help students build confidence and allow another opportunity to Correlation: Cookie Cost Vs. Cookie Quality Page 5

6 Procedures Using the assigned scatterplot have each student write a paragraph describing in detail the correlation or lack of correlation for a given attribute and interpret the correlation (what does it mean) in the context of the situation being analyzed. (5 minutes) Notes assess student understanding. Have students share their analysis with the members of their group and then with the entire class. (0 minutes) 8. HOMEWORK/PROJECT: Have students write a paragraph describing in detail the correlation or lack of correlation for each of the remaining attributes (or for the Overall Rating) and interpret the correlation ( what does it mean) in the context of the situation being analyzed. Scatter plots and paragraphs can be turned in for a grade. Homework: See procedures and 8 Assessment: Extensions: On-going assessment is necessary so that the teacher can determine the depth of student understanding. The questions outlined above will generate open discussion of the key concepts; the teacher should pay close attention to the responses and guide the discussion carefully. The writing assignment helps students to communicate their understanding, and allows the teacher to assess the depth of understanding. After the investigation is complete discuss the way the data was organized and collected. Ask students if they would have organized the investigation differently. Some things to consider include: () Population: What other cookies could be tested? Would you test hard cookies, soft cookies, or both? Would you want to include cookie dough? What about deli-baked cookies? () Sample and sample size: How many different products (brands, varieties) could be tested? How could you choose the brands to use for your sample? () Details: Should appearance be part of the overall test for quality? How many times should testers be allowed to taste? Is the tastetesting for comparison to another brand or to some idea or Correlation: Cookie Cost Vs. Cookie Quality Page 6

7 standard of what makes a good cookie? What does make a high-quality cookie? () Measurement: How should the cookies be ranked? What other attributes could be considered? (5) What other ratios could be used to compare cost: Price per ounce? Price per gram? Price per cookie? Price per pound? Have students create their own investigation. Criteria could include: Item being investigated List of types or brands of item to be tested Identify cost comparison to be used Calculate price per unit for each type or brand List attributes to be considered List the rating scale Make a prediction of the outcome Resources: This activity was adapted from an activity found on-line from Tom Moore, Dartmouth University. Modifications: This activity could be modified to use other products such as chips, cheese, fruit, computers, etc. It could also be adapted to compare stocks, interest rates of lending institutions, score differences in professional sports, etc. Correlation: Cookie Cost Vs. Cookie Quality Page 7

8 Cookie Data Sheet Ratings: Using a scale from to 5, rate each cookie on each of the categories listed below: = poor, = fair, = good, = very good, 5 = excellent. Cookie Taste Texture Appearance Overall A B C D E F G H Correlation: Cookie Cost Vs. Cookie Quality Page 8

9 Group Data Tables: Group # Sample A: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample B: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample C: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample D: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample E: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample F: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample G: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Sample H: Student Taste Texture Appearance Overall Group Average Ratings: Taste: Texture: Appearance: Overall: Correlation: Cookie Cost Vs. Cookie Quality Page 9

10 Class Data Table Sample A: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page 0

11 Class Data Table Sample B: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page

12 Class Data Table Sample C: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page

13 Class Data Table Sample D: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page

14 Class Data Table Sample E: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page

15 Class Data Table Sample F: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page 5

16 Class Data Table Sample G: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page 6

17 Class Data Table Sample H: Group Taste Texture Appearance Overall Class Average Ratings: Taste: Texture: Appearance: Overall: Cents per ounce: Correlation: Cookie Cost Vs. Cookie Quality Page 7

18 Two-Column Tables Sample A Sample B Sample C Sample D Sample E Sample F Sample G Sample H TASTE X = cents per oz. Y = rating Sample A Sample B Sample C Sample D Sample E Sample F Sample G Sample H Texture X = cents per oz. Y = rating Sample A Sample B Sample C Sample D Sample E Sample F Sample G Sample H Appearance X = cents per oz. Y = rating Sample A Sample B Sample C Sample D Sample E Sample F Sample G Sample H Overall X = cents per oz. Y = rating Correlation: Cookie Cost Vs. Cookie Quality Page 8