This Math Talk focuses on finding distances on a ruler. It encourages students to think about the difference between two numbers and to rely on what they know about fractions to mentally solve problems. The strategies elicited here will be helpful later in the Algebra 1 lesson when students use distances like these to collect data.

To find distances on a ruler, students need to look for and make use of structure (MP7).

The goal of this discussion is to review students’ strategies for finding the distance between two points on a ruler.

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 ’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 ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to earlier problems do you see?”

The goal of this activity is for students to practice comparing two data sets that are both represented with a box plot. Students reason abstractly and quantitatively (MP2) when they use two box plots to interpret and compare the data sets. This prepares students for a later lesson because they will interpret their own data sets after they have collected the data and created representations of them.

The purpose of this activity is to 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 find and compare variability?” (We can calculate the range, interquartile range, or standard deviation. To answer the question about which cohort has more variability, we 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 1 lesson when they will use a data set to create a graphical representation and interpret the data by answering questions.

Monitor for students who create each type of data display:

• Box plot
• Dot plot
• Histogram

The goal of this discussion is to compare the same data represented in different data displays. 

Display 2–3 displays from previously selected students for all to see. If time allows, invite students to briefly describe their display and why they chose the data display they used. Use Compare and Connect to help students compare, contrast, and connect the different displays. Here are some questions for discussion:

• “What do the displays have in common? How are they different?”
• “Are there any benefits or drawbacks to one representation compared to another?”
• “How do the mean, median, IQR, and standard deviation show up in each method?”