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Lesson Plan S.ID.l: Dot Plots, Histograms, and Box Plots S.ID.l: Dot Plots, Histograms, and Box Plots Summarize, represent, and interpret data on a single count or measurement variable 1. Represent data with plots on the real number line (dot plots, histograms, and box plots). Overview of Lesson - activate prior knowledge - present vocabulary and/or big ideas associated with the lesson - connect assessment practices with curriculum - model an assessment problem and solution strategy - facilitate guided practice of student activity - facilitate a summary and share out of student work Optional: Provide additional problem sets Optional HW - Write the math assignment. univariate A set of data involving one variable. multiivariate A set of data involving more than one variable. A dot plot consists of data points plotted on a simple scale. Dot plots are used for continuous, quantitative, univariate data. Data points may be labelled if there are few of them. The horizontal axis is a number line that displays the data in equal intervals. The frequency of each bar is shown by the number of dots on the vertical axis. Example: This dot plot shows how many hours students excercise each week. Fifteen students were asked how many hours they exercise in one week. A histogram is a frequency distribution for continuous, quantitative, univariate data. The horizontal axis is a number line that displays the data in equal intervals. The frequency of each bar is shown on the vertical axis. Example: This histogram shows the number of students in Simpson’s class that are in each interval. The students were asked how many hours they spent playing video games in one week. Lesson Plan A box plot, also known as a box and whiskers chart, is a visual display of a set of data showing the five number summary: minimum, first quartile, median, third quartile, and maximum. A box plot shows the range of scores within each quarter of the data. It is useful for examining the variation in a set of data and comparing the variation of more than one set of data. Example: Annual food expenditures per household in the U.S. in 2005 median $5630 minimum $3101 $3000 3rd quartile $6431 1st quartile $4827 $5000 $7000 maximum $10520 $9000 $11000 REGENTS PROBLEMS 1. Robin collected data on the number of hours she watched television on Sunday through Thursday nights for a period of 3 weeks. The data are shown in the table below. Using an appropriate scale on the number line below, construct a box plot for the 15 values. Lesson Plan S.ID.l: Dot Plots, Histograms, and Box Plots Answer Section 1. ANS: Strategy: Follow these step-by-step procedures for creating a box and whiskers plot. STEP 1. Organize the data set in ascending order, as follows. Be sure to include all the data.: 1, 1.5, 1.5, 2, 2, 2.5, 2.5, 3, 3, 3, 3.5, 4, 4, 4.5, 5 STEP 2. Plot a scale on the number line. In this case, the scale is 0 to five in equal .5 units. intervals of STEP 3. Plot the minimum and maximum values: minimum = 1 and maximum = 2. STEP 4. Identify the median. In this problem, there are fifteen numbers and the median is the middle number, which is 3. There are seven numbers to the left of 3 and seven numbers to the right of 3. STEP 5. Plot and label the median = 3 (also known as Q2 or the second quartile). STEP 6. Identify Q1, which is the median of the bottom half of the organized data set. The bottom half of the data includes all numbers below the median, which in this problem, includes the following numbers 1, 1.5, 1.5, 2, 2, 2.5, 2.5 The middle number in an organized list of seven numbers is the fourth number, which in this case is a 2. STEP 7. Plot and label Q1 = 2. STEP 8. Identify Q3, which is the median of the top half of the organized data set. The top half of the data includes all numbers above the median, which in this problem, includes the following numbers 3, 3, 3.5, 4, 4, 4.5, 5 Again, the middle number in an organized list of seven numbers is the fourth number, which in this case is a 4. STEP 9. Plot and label Q3 = 4. STEP 10. Finish the box plot by drawing boxes between the plotted points for Q1, Q2, and Q3. PTS: 2 REF: 061432a1 NAT: S.ID.1 TOP: Box Plots Lesson Plan START PART 1. PART 2. PART 3. PART 4. PART 5. PART 6. Standard “Writing the Math” Assignment Write your name, date, topic of lesson, and class on your paper. Copy the problem from the lesson and underline/highlight key words. State your understanding of what the problem is asking. Answer the problem. Explanation of strategy. Create a new problem that addresses the same mathematical understandings. State the answer to your new problem. Clearly label each of the six parts. Grading Rubric Each homework writing assignment is graded using a four-point rubric, as follows: Part 1. Statement of the problem. 1 point is awarded for correctly restating the 2 original problem. Part 2. Statement of what the problem is really asking. 1 point is awarded for correctly identifying 2 what the problem is asking you to find or do. Part 3. Solution to the problem. Part 4. Written analysis of the mathematics and solution strategy involved in the problem. Part 5. An alternative version of the problem. Part 6. Solution to the alternative version of the problem. 1 point is awarded for a correct solution to 2 the problem. Up to 1 point is awarded for an explanation of the mathematics and solution strategy involved in the problem. Up to 1 point is awarded for creating a new problem that involves similar mathematics and a similar solution strategy. 1 point is awarded for correctly solving the 2 new problem that you have created. This assignment/activity is designed to incorporate elements of Polya’s four step universal algorithm for problem solving with the idea that writing is thinking. Rationale for Assignment Each New York Regents Algebra I (Common Core) examination contains 13 open response problems. An analysis of the first three Algebra I examinations revealed that approximately 51% (20 out of 39) of these open response problems instructed students to: 1) describe; 2) state; 2) explain; 3) justify or otherwise write about their answers. It is theorized that students can benefit from explicit instruction and writing routines that are applicable to solving these problems. Lesson Plan EXEMPLAR OF A WRITING THE MATH ASSIGNMENT Student’s Name Topic: Date: Class: Part 1. The Problem TOP Electronics is a small business with five employees. The mean (average) weekly salary for the five employees is $360. If the weekly salaries of four of the employees are $340, $340, $345, and $425, what is the salary of the fifth employee? Part 2. What is the problem asking? Find the salary of the fifth employee. Part 3. Answer The salary of the fifth employee is $350 per week. Part 4. Explanation of Strategy The arithmetic mean or average can be represented algebraically as: X x1 x2 ... xn n I put information from the problem into the formula. The problem says there are 5 employees, so n 5 . The problem also gives the mean (average) salary and the salaries of 4 of the employees. These numbers can be substituted into the formula as follows: 340 340 345 425 x5 5 1800 340 340 345 425 x5 360 1800 1450 x5 1800 1450 x5 350 x5 340 340 345 425 350 1800 360 Check: 360 5 5 Part 5. A New Problem Joseph took five math exams this grading period and his average score on all of the exams is 88. He remembers that he received test scores of 78, 87, 94, and 96 on four of the examinations, but he has lost one examination and cannot remember what he scored on it. What was Joseph’s score on the missing exam? Part 6. Answer to New Problem Joseph received a score of 85 on the missing examination. EVALUATION Name and Proper Heading Part 1. Problem copied correctly? Part 2. Understand the problem? Part 3. Correct and complete answer? 1/2 Point 1/2 Point 1/2 Point Part 4. Explanation of strategy. Part 5. New problem. Part 6. Solution to new problem. TOTAL 1 Point 1 Point 1/2 Point 4 Points