VIEWS: 51 PAGES: 11 POSTED ON: 11/13/2011
Histograms Topic: Histograms Focus: Connections – Students will make connections to previous information on data displays that they have acquired. Students will compare bar graphs and histograms since many misconceptions of histograms stem from a lack of understanding in the distinction between the two data displays. Students will then compare histograms with stem and leaf plots to analyze which would be more helpful and/or efficient in different situations and compare the two representations of the same data. Sources: http://www.learnnc.org/lessons/DebbieNewton5232002546 https://ims.ode.state.oh.us/ODE/IMS/Lessons/Content/CMA_LP_S05_BA_L06_I 01_01.doc Objectives: Level One: Students will be able to create and analyze a histogram to interpret information. Level Two: Students will be able to explain the difference between a bar graph and a histogram. Level Three: Students will be able to explain the connection between a histogram and a stem and leaf plot. Materials: Transparencies, Over Head Projector Histogram/Barrel Graphic organizer Pencils Motivation: (1-3 minutes) Students will enter the class and complete the Do Now written on the board. Students will copy down their homework and the objectives of today’s class. Do Now: Think about what activities you do when you get home from school. What are your favorite TV shows? How many hours a week do you spend watching TV? Put a tally on the overhead projector in the box over the barrel that you belong in. W hen you are finished, immediately get together with your rows and discuss the answers to the homework and compare with the answers displayed on the overhead. Be sure to help each other out! A picture of what will be on the board is attached, Attachment A, will be displayed on the overhead projector. A student will then be selected at random to read the class goal for the day, which will also be written on the board before class: “What is a histogram?” Procedure: 1. Address any individual questions with the homework. 2. Group work and class discussion (5-10 minutes) Students will be given a picture of a Histogram (Attachment B). Students will get into groups with their rows (3 across) and will discuss the histogram. Each group will come up with some properties of a histogram based on the picture of the histogram. 3. Students will discuss as a class a few properties of a histogram. 4. The definition of a histogram will be presented: - Histograms are a graph that uses bars to display the frequency of data within equal intervals. Think of histograms as “sorting bins”. There is one variable and the data is sorted by this variable by placing the data into “bins”. The pieces of data in each bin are counted. 5. Guided Discussion (30 minutes) Using the same histogram, students will view attachment B on the overhead and answer the questions that follow. - How many kids spend 20 minutes or less per week doing chores? - How many kids spend more than 80 minutes per week doing chores? - What is the most common amount of time spent doing chores? - What is the least common amount of time spent doing chores? - How is a bar graph different from a histogram? o Histograms are often confused with bar graphs Histograms: The height of the rectangle drawn on top of each bin is proportional to the number of pieces in that bin. Histograms show one set of data and are designed to show trends. Bar graphs Have several measurements of different items that allow comparison. Bar graphs display numerical information with labels for each bar and a scale to show amount for each bar. 6. The students will then refer back to the data from the Do Now. Students will total the tallies and transfer the tallies and totals from the barrels onto a frequency table. - What numbers go on the x-axis - What information goes on the y-axis - Where do the barrels fit on the histogram? - How can we construct a histogram of the number of hours a week our class watches TV? 7. The class will work together to construct the histogram onto Attachment D, through guided discussion, based on the data of the Do Now. 8. Discussion (20 minutes) Students will work in groups of 6 (two rows of 3 will work together) on Attachment C. Each student will hand in their own work. In the event the group does not have time to finish, students will complete the assignment for homework. Closure: Using a piece of notebook paper, students will list at least two interesting facts that they learned today and something that is still unclear to them. Students will hand this in at the end of the period. Assessment: Students’ participation in the guided discussion will give an idea of how well the students are at drawing conclusions and how well they comprehend the data displayed on a histogram. The closure activity will help to assess how well the students understood the material. Based on the depth of detail used in their response, their understanding and clarity of histograms can be evaluated. The group work will assess the class’ abilities to work represent data correctly in a histogram and draw conclusions from the display. Homework: Since the group work is very detailed and will most likely take them much more than 20 minutes, students will finish the group work for homework. Each student will hand in their homework and it will be graded on an individual basis. Each student will be graded on their accuracy, detailed responses to questions, and neatness. Textbook Spiral Review pg 324 #19-30 This will not be collected. Answers will be on a transparency in the beginning of class tomorrow and students will ask questions on individual problems. This is assigned at the request of the teacher since this is a routine for the students. It does not cover the material we are teaching and she normally does not take much time to review this homework. Reflections/ Self Evaluations: What Barrel do you belong in? <1 hour 6-10 hours 1-5 hours 11-15 hours 16+ hours 1. How many kids spend 20 minutes or less per week doing chores? 2. How many kids spend more than 80 minutes per week doing chores? 3. What is the most common amount of time spent doing chores? 4. What is the least common amount of time spent doing chores? 5. How is a bar graph different from a histogram? Histograms Jumping Into Histograms Name_______________________________ Date__________________________ Work in groups to complete the activity. Each person will hand in their own work. Each person will be graded on their accuracy, detailed responses to questions, and neatness. Ms. Varacallo had her students measure how high each student could jump. The students were then instructed to graph their data as a class. Use the information in the table below to create a histogram, stem and leaf plot, and box and whisker plot. Be sure to label the x-axis, y-axis and title. Use both the histogram, stem and leaf, and box and whisker plot to answer the questions below. Name Jump Name Jump Name Jump Height (cm) Height (cm) Height(cm) Frank 5 Mack 29 Brianne 27 Christian 11 Vicente 50 Ms. Schenker 13 Nicole 75 Anish 37 Ayesha 51 Carlos 55 Michael 14 Avik 54 Sana 25 Lauren 62 Kathleen 62 Kaitlyn 27 Amy 73 Kunal 56 Ms. Varacallo 6 John 10 Aakash 12 Kevin Jackson 62 Karen 44 Logan 79 Jennifer 52 Paul 14 Sabrina 29 Kevin Joyce 36 Ryan 65 Sarah 32 Lily 15 Veronica 15 Tiffany 20 Hope 53 Allison 60 Emily 27 Kevin Lim 44 Mr. Canik 47 Mr. McGurney 70 Po 13 Will 33 Ms. Perhacs 19 Alex 47 Andy 66 Corey 49 Name: Date: Histogram <<Title>> <<Y Axis>> <<X Axis>> Stem and leaf plot 1. What are the mean, median, mode, and range of this data? (You can use a calculator to calculate the mean) 2. How many people jumped a height of 30 centimeters or less? ____________________ 3. How many people jumped a height of 61 centimeters or more? ___________________ 4. What is the most common height jumped in centimeters? _______________________ (using histogram) 5. What is the least common height jumped in centimeters? ________________________ (using histogram) 6. Turn the stem and leaf plot on its side so that the “stem” is on the bottom and the “leaves” are vertical. Compare the shape of the stem and leaf plot and the histogram. What do you notice about their appearances? Explain how a stem and leaf plot and a histogram are related. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Name:______________________________________________ Date:_______________ Histogram Lesson Directions: Use the notes discussed in class to define the term below. Histogram: Directions: Use the lines below to list some properties of the histogram discussed in group work. Properties __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Directions: Identify the differences between a bar graph and histograms. Histogram Bar graph Answer Key: Attachment B 1. 10 2. 15 3. 41-60 minutes 4. 0-20 minutes 5. Answers will very, however a main difference is that bar graphs are categorical while histograms display the frequency within an interval. A discussion should include ideas related to the physical appearances of both graphs. Answer Key Jumping into Histograms Stem Leaves 0 56 1 0123344559 2 0577799 3 2367 4 44779 5 0123456 6 022256 7 0359 1. mean: 1745 45 38.8 median: 37 mode(s): 27, 62 range: 79 – 5 = 74 2. 19 students 3. 9 students 4. 11-20 centimeters 5. 0- 10 centimeters 6. A stem-and-leaf plot does resemble a histogram turned sideways. The stem values could represent the intervals of a histogram, and the leaf values could represent the frequency for each interval.