Lesson 16

The purpose of this Math Talk is to elicit strategies and understandings students have for determining distances on a ruler. These understandings help students develop fluency and will be helpful later in the Algebra lesson when students will need to be able to use distances like these to collect data.

Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

• “Who can restate \(\underline{\hspace{.5in}}\)’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to \(\underline{\hspace{.5in}}\)’s strategy?”
• “Do you agree or disagree? Why?”

The goal of this activity is for students to practice comparing two data sets that are both represented with a box plot. Students will use two box plots to interpret the data sets and, as they answer the questions, they will have to compare the data sets. This will prepare students for a later lesson because they will interpret their own data sets after they have collected the data and created representations of them.

Remind students to answer the questions based on the information they can gather from the box plots. For example, students should not calculate the mean when asked about measures of center, because these representations do not show individual data points.

Discuss how students used the graph to help analyze the data. Here are sample questions to promote class discussion:

• “What does it mean for data sets to overlap?” (It means that numbers from one data set fall between numbers from the other data set.)
• “What are ways to determine and compare variability?” (You can calculate the range, interquartile range, or standard deviation. To answer question 2, you have to compare the two measures of variability and see which one is higher.)
• “Are there other data displays that you think would have made analyzing this data easier?” (Yes, if we used a dot plot, we would know more about variability, because we could calculate the standard deviation, too.)

The goal of this activity is for students to combine the skills they have learned throughout the unit. Students create graphical representations of data, calculate important measures, and compare two data sets. This will prepare students for the accompanying Algebra lesson when they will use a data set to create a graphical representation and interpret the data by answering questions.