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## The Clucking Chicken

Food Court
3-5
1

Students choose meals from a menu and then construct a box plot. They use the plot to identify the mean, mode, median and range of the data set.

Teacher Note: In this lesson, students will learn a different way to graph data, the box plot. This graph displays clearly the endpoints and range of quantitative data, and the median. Its construction begins with ordering the data.

Call the class together and assign them to pairs. Distribute file cards, calculators, and one copy of The Clucking Chicken Activity Sheet to each pair.

Tell them to choose a lunch for the two of them from the menu, based upon their personal preferences. If necessary or appropriate, students can use a calculator to find the cost of the two lunches.

When they have computed the price, ask them to write it on an index card. When they have done so, call on a volunteer to write the prices on the board as one student from each group calls them out. Have the students use their calculators to find the mean cost of the two lunches and write the amount on the board, labeled "Mean."

Ask the students from the pairs to come to the front of the room and order themselves according to the number on their file card. (If more than one student has the same number, they should stand side by side.)

Give the student with the smallest number (for example, \$4.75) a card on which you have written "Minimum." Now give the student with the highest total a card on which you have written "Maximum." Ask the students to find the range of the data. (To find the range, subtract the minimum from the maximum.) Record the range on the board. Next, have the students determine if any amount occurs more times than all others. Identify that value as the mode, and record it on the board under the mean.

Next, to find the median, ask the students at the two ends of the line to say "1" at the same time, then the students next to then to say "2." Continue counting off in this fashion until the middle of the line is reached. If there is an odd number of students, this will be one student; if there is an even number, it will be two students. If there is one student, the number he or she holds is the median. If there are two students, the arithmetic average of their numbers is the median.

Write the median on the board under the mean and mode, and label it. Provide the student(s) who represent the median with a card on which you have written "median." Inform the students that the halfway mark is called the 50th percentile.

Now have the students on either side of the median find the median of just their side. Provide a card that says "75th percentile" to the center student on the higher end and a card that says "25th percentile" to the center student on the lower end.

Give the student with the smallest amount a piece of yarn and give the other end of it to the student at the 25th percentile. Similarly, give the student with the largest amount a second piece of yarn and give the other end of it to the student at the 25th percentile.

Present the student in the 75th percentile with one end of a long piece of yarn to hold in his or her right hand. Holding the yarn, walk to the student who holds the 25th percentile card and place yarn in that student's right hand. Walk in front of that student and place the yarn in his or her left hand as well. Then, carrying the yarn, walk back to the student holding the 75th percentile card and put the other end of the yarn in his or her left hand to complete the loop. Now have those students hold out their arms, so that a yarn "box" is formed. Explain that they have made a human box plot.

Call on a volunteer to draw the figure on the board.

Finally, collect the yarn and the cards and ask all the students to take their seats and copy the plot, labeling and naming the high and low scores and the median. Now give the rest of the class a chance to construct a human box plot.

Call students' attention to the mean, median, and mode, and tell them that these are called averages, or measures of center. (The mode, which cannot be determined from a box plot, is the data point that occurs most often. The mean is the arithmetic average. The median is the halfway point in the ordered data, one half the observations are above it and one half are below it.)

Ask the students what they notice about the three numbers and which one they think best describes the "average" cost of two meals. [The averages are probably not the same. The median is the best average in this case.] Finally, ask the students to write the measures of central tendency under their copy of the box plot so they can have a record for their files.

To conclude the lesson, go to the Box Plotter Tool.

Students can choose from given sets of data to create box and whisker plots, or they can enter their own data.

Assessment Options

1. At this stage of the unit, students should be able to:
• construct and read a box plot
• identify the mean, median, mode and range in a set of data
2. As you use the key questions, the students might raise other questions. These will enrich the discussion and help both you and your students focus on their current level of understanding.
3. After the lesson, you may wish to add more comments to the Class Notes. Revisited later in the year, this information may suggest ways to apply these learnings in other subjects.
4. Put the students into pairs and ask each pair to plan a party for eight people. If they wish to order something that is not on the menu, they may wish to use the prices from a different menu or estimate the prices for the items.

When they are ready, ask them to write the price of the party on the board. Then have the pairs construct a box plot from the data, and to find the mean, median, and mode of the price of the party. When all have had time to complete the task, identify one pair and call on a volunteer from that pair to describe the menu and to exhibit their box plot. Repeat with each pair.

Extension

Move on to the last lesson, The Pizza Palace

Questions for Students

1. What graph did we make today?

[The box plot.]

2. What price for two meals was most common in our class? What name is given to this measure of central tendency?

[Answers will depend upon the student choices; The mode.]

3. What was the least expensive total in the class? The most expensive? How did we show these values on the box plot? What was the difference between these numbers? What do we call that difference?

[Answers will depend upon the student data; The difference is called the range.]

4. What were the mean and median of the data set? What does each term mean? How did we find the mean? The median?

[Answers will depend upon the student data; Mean is the average of the data set; Median is the middle number; To find the mean, take the sum of all of the data and divide by the number of data values; To find the median, order the data from least to greatest and find the middle number.]

5. How many students in the class had totals higher than the total at the 75th percentile? How many students had totals less than the total at the 25th percentile?

[Answers will depend upon the student data.]

6. Suppose the median is like a half dollar. What amount is the 25th percentile like? What does 25th percentile mean? How about the 75th percentile? How were these points shown on the plot?

[25 cents or a quarter; 25 per cent of the class is accounted for when we get to this piece of data; They form the ends of the box.]

Teacher Reflection

• Which students easily found the range and mode? The median? The mean?
• Which students could compare the measures of central tendency with understanding?
• Were there students not yet able to draw a box plot? What did they have trouble with? What were they able to do without prompting?
• How can I extend this instructional experience?
• What will I do differently the next time I teach this lesson?

3-5
In this lesson, students conduct a survey and create bar graphs from the data they have collected.

### The Pizza Palace

3-5
Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data.

### The Pizza Palace

3-5
Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data.

### Learning Objectives

Students will:

• Compute prices from a menu
• Construct and read box plots.
• Identify the mean, median, mode, and range of a set of data

### NCTM Standards and Expectations

• Collect data using observations, surveys, and experiments.
• Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
• Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed.
• Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.