Students will be able to:
- Represent data appropriately using frequency tables, histograms, and box plots.
- Draw conclusions from the data displayed.
- Analyze data provided in various plot forms and draw conclusions from the data displayed
- Identify similarities and differences in shape, center and spread of various data sets across and within specific representations.
Math Content Standards
- S.ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S.ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, Standard deviation) for two or more data sets.
Math Practice Standards
- MP.1 Make sense of problems and persevere in solving them.
- MP.4 Model with mathematics.
- MP.5 Use appropriate tools strategically.
- Two of the main indicators the United Nations use to measure the degree to which people in countries around the world have adequate food are:
- The prevalence (in %) of children <5 who are underweight
- The percent of adults with body mass index (BMI) <18.5
- Explain that we will spend the next few lessons examining these indicators. Today we will begin with the first one: the prevalence of children<5 who are underweight. Project the map of the prevalence (in %) of children <5 who are underweight according to regions and countries in the world.
- Tell students that the next two lessons focus on our own estimations on how many children in the world are underweight, then we will go deeper into the United Nation’s data.
- Have students visit one of the following sites:
- Ask students to use the most recent date data for countries (between 2000-2010) and consider how they might use some of this data to estimate the number of underweight children in the entire world. Inform them that according to the UN population division the total number of children under 5 in the world is about 642 million (for example, add percentages of China, India and USA + other large countries) Approximately 20% of the children under the age of 5 live in India. India’s population is over 1.2 billion.
- Create a number line on the board that includes the range 1-150 million. Share with students that the number of children under 5 who are underweight is between 1-150 million. Within that range, ask students to estimate the actual number of children under 5 who are underweight in the world (based on their preliminary review of the data). Ask students to round their estimation to the closest million.
- Give each student a 4x6 post it and ask each student to record his/her estimation on the post it and place it on the appropriate place on the number line. Have students hold the post it vertically (so that the sticky portion is on the left side rather than the top; it is oriented as portrait rather than landscape format.). Show a sample and have them write their number as large as possible with a dark marker, using the full height of the post it so it is easy to read. (e.g., 5, 12, 30, 34, 40, 40, 52, 55, 55, 60, 75, 75, 75, 80, 80, 80, 80, 85, 85, 95, 100, 100, 125, 125, 130, 130, 150, 150, 150, 150 on number line)
- Once students are back in their seats, distribute Handout #1 in which students are asked to calculate the five number summary and create a box plot of their class data.
a) Arrange the class data from lowest to highest (left to right) as in the table below. An example for a class of 30 is below.
Example of data on number line
b) Find the five number summary for the class data:
Minimum (lowest estimation):
Maximum (highest estimation)
[Answers: Minimum: 5; First Quartile: 55; Median: 80; Third Quartile: 125; Maximum: 150]
c) Draw a box plot that represent this data above the number line [if needed, give students a refresher handout on how to draw a box plot]
d) Find the mean and range of this data set.
[Answers: Mean: 83.43; Range: 145]
e) Is the median higher or lower than the mean? What does it mean if the median is higher or lower than the mean?
Small Group Work
- Divide students into small groups (2-3)
- Announce that students in another class were asked the same question. We do not have the raw data of the frequency table that represents their data, but we do have the box plot.
- Tell students that their task will be to derive all the information they can from the box plot of the other (mystery) class.
- Distribute Handout #2 (which includes the box plot of the mystery class data)
- On a projector post the questions from Handout #2 one by one. After each question have students discuss them in their small group and share 2-3 solutions from different groups. Encourage the rest of the students to challenge and counter their answers each presentation. Be sure to ask different groups for full representation.
Handout #2 Mystery Class Box Plot
- Looking at the mystery class’ box plot, can you determine how many students are in that class?
- In this box plot, the median does not seem to be in the middle of the box. How can that be? What does it tell you about the distribution of the estimates?
- What percent of the students from the mystery class thought the number of children <5 in the world who are hungry is between 70 and 80 million?
- What percent of the students in that class thought the number of underweight children is lower than 125 million?
- What does this box plot tell you about the spread of estimated numbers in the mystery class? How does it compare to the spread of estimated numbers in our class?
- Can you create a histogram that will match this box plot? Is there only one possible histogram?
Differentiation and Supports
Struggling: Provide students with a written step-by-step instruction on how to construct a box plot
Struggling: Provide students with a written step-by-step instruction on how to calculate the five number summary.
Advanced: In addition to answering question f in handout #2 (Can you create a histogram that will match this box plot? Is there only one possible histogram?) Have student(s) prove their answer.
- Support students when using websites, providing guidance about how to navigate the sites.
Handouts 1 & 2 will provide assessment data on student learning.