The purpose of this activity is for students to use what they know about fractions on a number line to make sense of a map of a race course. As they make sense of the map, they also are encouraged to consider the decisions the race planners may have made as they designed the course. In the Activity Synthesis, students discuss the decisions they made during the activity and those they think the race designers may have made. This reasoning will help them make their own decisions in the next activity.

• Invite 2 or 3 students to share where they placed the music station and why.
• If no students place the music station at a fractional length or describe where they placed their station, using a fraction, consider labeling a music station at mile on the map and asking students to identify its distance from the starting line.
• “You had to make a decision about where to put the music station. What other decisions do you think the race planners made? How do you think they made their decisions?” (They had to decide where to put the water stations and how many. I think they thought people might get thirsty while they ran. I think they had to think about safety because they have so many water stations and a first-aid station.)
• Consider asking:
  • “What might happen if stations were placed too close together?” (There might be long lines if there are a lot of people. It might be hard to find the stations. People might get thirsty at different spots, so the water stations need to be spread out.)
  • “Do you think the planners were thinking more about safety or about having fun when they planned these stations? Why?” (I think they were worried about safety because I see a lot of water stations and a first-aid station, but not many fun things. They could add some fun stations near the finish line.)

The purpose of this activity is for students to use what they know about fractions to design their own fun run. Planning the fun run has some constraints that require students to make decisions about which stations to include in their run. When students model a situation, using a number line, and think about the real-world implications of their model, they model with mathematics (MP4). These constraints also force students to use what they know about fractions on the number line to locate and label the location of their stations. It may be helpful to review the stations with all students to elicit student experiences with each station type.

As students place their stations on their course maps, they may use a variety of strategies to partition the course. Some students may use visual inspection to estimate their partitions, while others may use the tools available (for example, the string or flexible rulers) to create more precise partitions. Monitor for the different ways students reason about and explain how they partition. Also, although most students likely will express the locations of their stations from the start of the number line, without using mixed numbers (for example, mile rather than 1 miles), some students may begin to use mixed numbers to describe locations. Students will learn more about mixed numbers in grade 4.

This activity can also be extended to invite students to think about other aspects of their fun run theme, including researching charities that align with causes that are important to themselves, their families, or their greater community. This also might provide opportunities for students to add and subtract within 1,000, and multiply and divide within 100, as they consider other factors when designing their run, including setting a fundraising goal, establishing ticket prices, and thinking about which stations might attract more people.

• Invite previously selected students to display their map for all to see.
• “What questions do you have for ____ about the decisions they made for their race?”