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Ever wonder about the differences in heights between boys and girls in grade 8? In this lesson, students will use data they collect and analyze with multiple box plots and 5-number summaries to make inferences about how height and gender may or may not be related.
Learning Objectives: What should students know and be able to do as a result of this lesson?
Interpret the 5-number summary of a given box plot
Explain/compare the differences in measures of center and spread for two or more box plots
Infer/predict/explain how additional data values would change the measures of center (median) and spread (IQR)
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should have an understanding of box plots and be able to successfully interpret the data display (analysis of 5-number summary and spread) with appropriate vocabulary.
Guiding Questions: What are the guiding questions for this lesson?
How does gender play a role in the height of students in Algebra I?
How does statistics help us analyze our data?
Teaching Phase: How will the teacher present the concept or skill to students?
This lesson goes through four phases:
1. Warm-up/bellringer with a whole group discussion afterwards. (see Formative Assessment)
2. Guided comparative box plot analysis. Given the data set and 5-number summary, students will construct box plots and answer guided/probing questions. (see Guided Practice)
3. Independent Practice: Collecting the class data set, students will construct three box plots for the class and then write comparative statements. They will then answer questions (see analysis questions attachment), evaluating what affect adding or eliminating data values would have on the display. (see Independent Practice)
4. Homework: Students will write to direct a friend to buy a new car at a particular dealership based on data displays for car prices for three dealerships. (See Summative Assessment)
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Guided Practice data is attached as a file for student use and includes an answer key for the teacher. Teachers should use the downloaded file of student heights to create box plots. These heights are given in a spreadsheet with the whole class data in column A as well as girl and boy data in columns B and C. Teachers can make copies of the data or project it for the class.
Students will construct a number line on a blank sheet of paper (landscape).
Students will then draw a box plot above the number line to represent the given 5-number summary for all the students in Algebra I.
Students will then draw a second box plot below the number line representing the data given for the girls in Algebra I.
Students will then draw a third box plot below the number line representing the data given for the boys in Algebra I.
In their notebooks, students will answer questions comparing the 5-number summary and the spread for the three data sets.
Guided Practice questions from Tall Lesson Analysis Questions attachment:
Which data set has a greater range? What does this tell us?
What are the medians for the data sets? What does the median tell us about the measure of center?
In examining the quartiles, how is the data spread for each of the data sets? Are there any outliers or clusters?
Which data set represents a taller group of students? Justify your answer using the 5-number summary.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
In pairs or small groups, students will measure and record the heights in centimeters for the students in their current class (It is suggested that this is completed on a previous day to save time and have data projected).
Using this information, they will then analyze the data and construct three box plots (boys, girls and combined) and record their findings on chart paper.
They will then write three statements about the data displays. The statements must refer to information about the 5-number summary.
Other questions from Tall Lesson Analysis Questions for Independent Practice:
A new student enters the class and is 175 cm tall. Where would this data fall on the box plot for the whole class? Which measures of analysis would this affect?
Assume this new student is a boy. How would this affect the box plots and their comparisons between the boys and the girls?
A female student who is the tallest in the class transfers to another school. Explain how this would affect the 5-number summary, specifically the measure of center and the spread of the data.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students will post their data displays around the classroom and complete a gallery walk, taking notes to compare their data sets and conclusion statements to those of their peers. Use the opportunity of peer review as an assessment of the independent practice and individual students' work. Notes can be discussed as time permits.
For homework, students will apply their understanding and mastery of comparative data in answering questions on a problem of buying a new car (which entails comparing 3 box plots). Both the handout and the answer key are attached.
A warm-up/bellringer (.ggb file) is attached to initiate this lesson. This is a Geogebra file; teachers will need to have downloaded the free Geogebra software. Questions from Tall Lesson Analysis Questions attachment to be used for warmup:
What does the 5-number summary tell us about this data set? The minimum? Quartile 1? Median? Quartile 3? Maximum?
How is the data spread? Are there any outliers? Is there any clustering of data in any of the quartiles?
The teacher can monitor the room, reading individual responses and asking probing questions to students, prior to sharing as a class to complete the formative assessment. The teacher should review any missing pieces as needed.
Feedback to Students
Students will be given feedback during the warm-up and during guided practice as the teacher goes over answers.
Students will get feedback from peers on the gallery walk from Independent practice.
Students will receive written feedback after the homework assessment is complete.
Accommodations & Recommendations
Accommodations for this lesson include having the students use GeoGebra to generate their box plots and analytical data. This technological tool will eliminate some of the work and allow them to focus more on the visual analysis.
The teacher could also have the students work with smaller data sets (less than 10 values).
This lesson could be extended to grocery shopping. Students will be asked to analyze box plots which display the price spread for three grocery products of their choosing. They will then answer guiding questions to decide where is the best place to shop and defend with statistical reasoning.
Suggested Technology: Document Camera, Computer for Presenter, Computers for Students, Internet Connection, Interactive Whiteboard, Basic Calculators, LCD Projector, Overhead Projector, GeoGebra Free Software, Scientific Calculator
Special Materials Needed:
tape measures, notebooks, chart paper, markers
Model with Mathematics
Look for and make use of structure
Source and Access Information
Name of Author/Source: Stephanie Martin
District/Organization of Contributor(s): Miami-Dade