It’s a Stats World After

All

   

Activity 1

 MTH 2060 Math for the Elementary School Teacher II Activity #1 Activity: It’s a Stats World After All Sources: http://illuminations.nctm.org/LessonDetail.aspx?id=L856       (adapted) http://montemath.com/alg1unit7boxwhiskerplotpractice041411.pdf

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0CEoQFjAG&url=http%3A%2F%2Fteacher.edmonds.wednet.edu%2Fmths%2Fdjohnston%2Fdocuments%2Fbox__whisker__summary_stats_ws.pdf&ei=jSk0T9zAIcHu0gG_qMDZAg&usg=AFQjCNFxrag2eaWIFi2LmCkPLB7IFEPbeQ http://www.mathworksheets4kids.com/statistics/median-quartiles-medium.pdf http://fcit.usf.edu/math/resource/bibs/data.htm

Goals:

1. The students will learn to create box-and-whisker plots. 2. The students will use graphs to interpret data. 3. The student will understand how statistics applies to real world careers.

Objectives:

1. Given the voki about remodeling a Disney World attraction, the students will engage in an experiment and record their data.

2. Given the list of class data, the student will construct a box and whisker plot, including all five elements.

3. Given two box-and-whisker plots, the students will compare the data and draw at least 3 correct inferences.

Age Level: 6th grade Evaluation: This activity is appropriate for sixth grade students because it aligns with the NYS Common Core Math Standards for statistics and probability. In order to complete this activity, the students should have prior knowledge on determining the mean, median, quartiles, range, and interquartile range. This activity is developmentally appropriate for sixth graders because it motivates the student with a real-world situation. It may even motivate the students to pursue a career in mathematics or engineering. The students could develop an interest in developing rides or attractions for amusement parks. The hands-on nature of this activity will also encourage active participation by all of the students. New York State Standards

NYS Standard 3: Students will understand the concepts of and become proficient with the skills of mathematics; communicate and reason mathematically; become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations, algebra, geometry, measurement, statistics, and probability Common Core: Statistics & Probability 6.SP Summarize and Describe Distributions 6.SP.4. Display numerical data in plots on a number line, including dot plots,

histograms, and box plots. 6.SP.5. Summarize numerical data sets in relation to their context, such as by:

c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Vocabulary Words for Activity: Mean: the average of a set of numbers Median: the middle number in an order list of numbers Quartile: values that divide a set of data into 4 equal parts Range: the difference between the highest and lowest values Box-and-whisker plot: shows the distribution of a set of data along a number line, dividing the data into four parts using the median and quartiles. Materials Required:

Computer with smart board Voki used to describe the students’ task 6" × 6" squares of heavy duty aluminum foil (four squares per student) Four plastic containers, approximately 8" wide, 8" long, and 4" deep Hundreds of 4-gram Baby Bears™ plastic teddy bears (about 50 per student) Water to fill each container Math Journal Paper and pencils

Object of the Activity: The purpose of this activity is for students to gain practice creating and interpreting box and whisker plots and see how math is relevant to the real world and interesting career paths. Process: Prior to the lesson, you will need to:

Fill each plastic container about halfway with water. The water needs to be deep enough so that the aluminum foil boats made by students will eventually sink when filled with bears. The plastic containers must be at least 8" wide, 8" long, and 4" deep, although larger containers work better.

Arrange the lakes throughout the room so that students have ample space to work. It is best to place only one lake on a table.

Next to each lake, place about 100 bears. (Note that other objects can be used if plastic bears are not available. Unifix cubes or any small plastic items that are uniform in weight and size will work, but the approximate weight of each item should be 3-5 grams.)

Introduce the activity with a voki explaining the task for the students to complete. The voki will represent a Walt Disney World Imagineer who creates the attractions for Disney parks. He will explain that are remodeling one of the most famous attractions; “Small World,” to make it more updated and efficient more modern and efficient. However, the imagineers are having trouble deciding on the design of a boat that the guests go in for the ride. They want to choose the design that will hold the most guests, while ensuring their safety. The Imagineer will explain that he needs the help of the students in order to come up with the best design!

The teacher will explain to the students that they will use the foil to create a "boat" by folding it in any manner they choose. Warn them not to rip, tear, or make a hole in the foil. If they do, their boat will sink. Tell them that after constructing their boat, it will be floated in water and filled with bears (to represent guests). Their goal is to keep the bears afloat (dry); they do not want the boat to sink. Tell them that they will test their boat by placing it in the water and loading it with bears until it sinks. Divide the class into five groups so that they are split evenly among the water tables. One at a time, students should place their boats in the water table and carefully load the boat with bears. The students' goal is to get as many bears as possible into their boats. They will quickly learn to balance the load and place the bears carefully.

Each student should record the number of bears that their boat was able to hold. The capacity of the boat is the number of bears in the boat just before the boat sinks. For example, if the 28th bear placed in a boat caused it to sink, then the capacity of that boat was 27. Record the capacity of each student’s boat. Sort the capacities and place them in a table. It is not unusual to have capacities that range from lows of 9 or 10 to highs greater than 60. The following is a typical sample for a group of 13 students:

Student Ada Ben Cal Dee Eve Fae Gia Hal Isa Jen Kay Lue Mai

Capacity 10 15 18 20 20 30 34 36 38 40 44 58 61

From the data collected, work with the class to identify the five-point summary, which includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. For the set of data shown above:

Minimum: 10 First Quartile: 19 Median: 34 Third Quartile: 42 Maximum: 61

The teacher will then introduce a song for remembering how to create a box and whisker plot. The teacher will display the lyrics on the smart board and sing the song to the tune of “It’s a Small World After All.” After singing the song once, the teacher will have the students join in and give them their own copies of the lyrics. Construct a large box-and-whisker plot of the data set on your whiteboard. The teacher will discuss the 5-point summary and the different values that the students got. The teacher will ask the students with low, middle, and high capacities to explain the design of their boats. From this, the class will be able to make inferences about the design that would hold the most bears. Teacher talk: Which types of boats seem to hold the most bears? Why do certain structures hold more bears without sinking? What would make this task easier? What is the mean of the data? What is the mode of the data? Why would it be important for an attractions designer to conduct this experiement? Application: This activity will help the students learn to organize their data so they can interpret it appropriately. This will be important as the students move on to more upper level mathematics. This activity will also help the students see how math is relevant to different career opportunities. Modifications: Visual Learners: will benefit from creating a table box and whisker plots to organize the data Auditory Learners: will benefit from the teacher giving directions orally and asking questions while monitoring the students’ work Tactile Learners: will benefit from being able to make their own boats and figuring out how many bears they can fit into it ELL Students: will be given support from the teacher or a partner in completing their math journal. They can also draw a picture for their math journal. Early master students: can be given two squares of aluminum foil to make a boat and complete another trial to compare their findings Hearing Impaired Students: Will be seated up close to the board

Behavior Issues: These students will have a contract with rewards for appropriate behavior Literature Connection:  Looking  for  Cinderella  Handprint  Staff   In her U.S. debut, Dutch illustrator Dematons tickles her readers' imaginations by plunking a modern girl into a fairy tale world. Hilda looks out of her bedroom window to see signs of life at the deserted old windmill outside of town. When she goes there to investigate, she steps into a world where she is repeatedly mistaken for Cinderella. Characters from various stories mingle: the seven dwarfs help reroof the gingerbread house of the witch in Hansel and Gretel, for example. Finally Hilda finds the real Cinderella, hands her the glass slipper she has been mistakenly given, and Cinderella's coach takes her home. In some ways, the juxtaposition of modern/old, real/make-believe just doesn't seem to be mined thoroughly enough. Yet Dematon's ingenuous, old-new illustration style hits the mark, and her premise could easily spark some flights of fancy in would-be Cinderellas. *This book discusses the relationship between shoe size and height which we will compare to the design if the boat and the amount of weight it can hold during our activity* Worksheets: Practice: Box and Whisker Plots Practice Worksheet 11-10 Quartiles Worksheet Math Journal Math Journal Entry: The students will write back to the imagineer about how the boats for the “Small World” attraction should be designed. The student should discuss how they designed their own boat and any changes they would make. The student should also back up their reasoning with data. Technology:

BAMZOOK: Mean, Median, Mode and Range http://www.bbc.co.uk/schools/ks2bitesize/maths/data/mode_median_mean_range/play.shtml This interactive video reviews the concepts of mean, median, mode and range and challenges students to use them to play games. This website also has further reading if a child is struggling or needs review, as well as a quiz to test students’ knowledge. Voki.com Used to create a talking character (in this case a Disney Imagineer) to introduce the problem and hand.

Name:  ________________________________      

Math Journal  Directions:  It’s  time  to  write  back  to  our  Imagineer  friend!  Discuss  the  type  of  boat  you  designed  and  what  changes  you  would  make  to  improve  on  your  design.  Also,  include  what  you  think  is  the  best  design  and  why.  (Make  sure  to  use  the  data  in  your  reasoning  )        _________________________________________________________________________________________________

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It’s time to draw a box and whisker plot Gather up your data, look at what you’ve got Now order your list You’re getting the gist It’s a mathematical world It’s a stats world after all It’s a stats world after all It’s a stats world after all It’s a mathematical world Now find the median and draw a dot Find the first and third quartiles make a plot Draw a rectangle around You’ll be safe and sound It’s a stats world after all It’s a stats world after all It’s a stats world after all It’s a stats world after all It’s a mathematical world Find the lowest and the highest values, draw two dots Now we’ll connect the rectangle with these two spots Simply draw a line Yes, you’re going to be fine It’s a stats world after all