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 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