
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
 Given sets of data in realworld contexts, students will use technology (either graphing calculators or Geogebra, depending on teacher choice) to create graphic displays of the data.
 Students will use their graphs to justify their interpretations of the data in context.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should have working knowledge of measures of central tendency (i.e., mean and median), measures of variability (i.e., range, IQR, variance, absolute deviation and mean absolute deviation, and standard deviation), outliers, box plots, dot plots, and histograms.

Guiding Questions: What are the guiding questions for this lesson?
Which hotel is the better choice for your family to attend based on the ratings each received?

Teaching Phase: How will the teacher present the concept or skill to students?
Activate Prior Knowledge: To open the lesson, the teacher will give students the opportunity to "show what they know" about: measures of central tendency, measures of variability, outliers, box plots, dot plots, and histograms.
The teacher will use the webbased program "Poll Everywhere" so that students may respond in real time to questions/prompts either by using their cell phones or computers. Student responses are displayed on the SmartBoard and provide material for discussion.
The following questions can be used to determine what background knowledge the students have:
 What is the significance of the median? It is the middle number in a given data set.
 When is the mean a good measure of center to use? When the distribution is relatively symmetric.
 What effect does an outlier have on measures of center and measures of variability? An outlier can skew the mean and make the range larger. The median and the IQR are resistant to the effects of outliers.
 What information can be seen in a dot plot that is not represented in a box plot? Each individual piece of data is represented in a dot plot but not in a box plot.
 What is the purpose of a histogram? To place data in categories for comparative purposes, to make it easier to understand and to identify trends.
If this technology is unavailable, the "ThinkPairShare" method can be used to assess prior knowledge. The teacher posts the topics listed above on the board and gives students time to think individually and to write what they know. After 5 minutes, students pair with a partner to discuss their answers and then finally they share with the whole group ideas that they have generated. If there are any gaps in the knowledge, the teacher can address them before proceeding with the lesson.
Next, the teacher will present a PowerPoint that demonstrates comparing data for two restaurants, based on customer ratings. The restaurant ratings will have the similar means, necessitating the use of other measures for comparison. The PowerPoint will show box plots, created in Geogebra (or using the graphing calculator if preferable) that show variability in the data. The teacher can toggle back and forth between slide 7 and 8 to discuss interpretations of measures of center and variablity. The teacher will demonstrate choosing one restaurant and justifying the choice using information from the graphs. For example, the restaurant with the lower mean but higher median and smaller IQR might be viewed as the better choice. The teacher will allow for question and answers during the lesson presentation.
There should be student commentary during the lesson presentation. For example, a student might notice that the lower mean is the result of an outlier in the data. The teacher should encourage student dialogue throughout the lesson directing students back to the context of the data when necessary.
Throughout the lesson encourage students to investigate and interpret center, variation, distribution, and outliers. Students should consider any factors that might affect these values. For example, students should question the reliabilty of the data. For example, could the sample be biased? How reliable is a voluntary response sample? Could the source of the data impact the quality?
Note: When creating box plots in GeoGebra or when using other technology, sometimes an "x" or asterisk appears at the upper or lower extreme of the box plot. This is an indication that the value is an outlier.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will be arranged in groups of three. There will be roles that students will decide on: recorder, timekeeper/facilitator, and tech expert. Students will be given data (student averages) for 3 Algebra classes. They will complete worksheets that ask a series of questions about the three classes. They will also generate box plots for each Algebra class using technology. Students will cite evidence from the data to answer the question, "Which class is performing at the highest level?"
Prior to this activity, the teacher may want to discuss/review a modified boxplot (i.e., a modified boxplot is a boxplot that is utilizes symbols (e.g., an asterisk) to identify outliers. The horizontal line extends only as far as the minimum data value that is not an outlier and/or the maximum data value that is not an outlier.)

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Home learning will serve as the independent practice. The students will be given data on two hotels, use technology to create a box plot for each hotel. Based on the graphs, which hotel would you recommend for a family going on vacation? Explain your response using evidence from the graphs.
Students will be given numeric data: Each hotel will have a number of 5 star ratings, 4 star ratings, 3 star ratings and so on.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Closure will take place the following class session. Students will be asked to group themselves according to their answers to the home learning assignment (which hotel they recommended). Students will be given time to discuss their conclusions and to have a representative explain their choice to the whole group. After both groups have presented their ideas, students will be given the opportunity to "switch sides" if they wish.

Summative Assessment
Students will demonstrate their understanding by completing (individually) a home learning assignment. This assignment will be graded using the included rubric.
The home learning assignment will be:
Given data on two hotels, use technology to create a box plot for each hotel. Based on the graphs, which hotel would you recommend for a family going on vacation? Explain your response using evidence from the graphs.
Students will be given numeric data: Each hotel will have a number of 5 star ratings, 4 star ratings, 3 star ratings and so on.
Students may be asked to respond to the following questions.
During this presentation, the teacher should address any concepts that do not arise organically in the dialogue.
 How can data be used to draw conclusions?
 How can box plots be used to display and compare sets of data?
 How can you use statistical values gathered from data to support or refute claims?

Formative Assessment
Formative Assessment: Throughout the lesson, the teacher will monitor students' work and ask probing questions to ensure that students are working toward a reasonable solution. Even when student work is mathematically sound, the teacher should ask for justification.

Feedback to Students
Students will receive feedback throughout all phases of the lesson. Students will receive verbal feedback during the lesson opening and while they are working collaboratively in groups. Students will receive written feedback on their individual assignments (home learning).