The purpose of this Warm-up is to elicit the different things students notice when they make sense of maps. This will be helpful when students interpret increasingly complex maps over the course of the lesson activities. While students may notice and wonder many things about the map, students’ use of the key to interpret the symbols and the connections students may make to fractions on the number line are the important discussion points.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
What do you notice? What do you wonder?
Student Response
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Advancing Student Thinking
Activity Synthesis
“How did you use the key to make sense of the map?” (I think it’s a trail because there’s a symbol for the start and finish. I think it’s for a race because it looks like it’s in a city and the key shows water stations.)
“How is the map the same as the number line? How is it different?” (Both have the same symbols and some of the same numbers. It looks like the water stations are halfway between each number on both. The number line is straight, but the map shows curves and bends. The number line shows fractions, like .)
“This is the map of a 3-mile race. What do you know about running in a race? Have you ever run in a really long race?”
Activity 1
Standards Alignment
Building On
3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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.
Launch
Groups of 2
Display the image from the student book.
“What do you notice? What do you wonder?” (It’s another map. The course is a straight line. It looks like a number line. There are marks every mile. Is this a map of a race, too?)
“This is a map for a 3-mile fun run. A fun run is a friendly race that people join for fun rather than for trying to win a prize. Fun runs can be used to raise money for causes that are important to a community. Some fun runs involve wearing funny costumes or include special obstacles.”
Activity
5–7 minutes: partner work time
Monitor for the different ways students:
Use what they know about the number line to locate and describe stations on the map.
Wonder or speculate as to why the stations were included in the race or how they are spaced.
Describe the locations of the stations using fractional lengths.
Consider asking:
“How did you locate the __ station?”
“How did you decide where to put the music station?”
What do you notice? What do you wonder?
How far is each water station from the starting line?
Water Station 1: __________
Water Station 2: __________
Water Station 3: __________
What do you notice?
How far is the first-aid station from the starting line?
How far is the bathroom from the starting line?
The planners want to add a music station to the race to help energize the runners. Show on the map where you would put it. Explain to your partner where your station is on the map and why you put it there.
Student Response
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Advancing Student Thinking
Activity Synthesis
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.)
Activity 2
Standards Alignment
Building On
Addressing
3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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.
Launch
Groups of 2 or 4
Give each group access to string, rulers, and colored pencils or markers.
Activity
Read the Task Statement with students.
“Take a minute to read through the different station options that you can use on your course. You can use the same station more than once.”
1–2 minutes: group work time
As needed, review each station with students, or invite students to share their experiences.
Give each group one of the three map options.
“Look at your course map, and read the information about your city. Talk with your group about what stations might be the most important.”
1–2 minute: group discussion
As needed, invite students to share their initial responses.
“Now work with your group to plan your race. Use the number line to plan your stations if it is helpful.”
14 minutes: group work time
Monitor for a variety of students who:
Clearly label and describe the locations of their stations, using their understanding of fractions.
Place stations at different fractional lengths (for example, groups who use -mile intervals,-mile intervals, or combinations of fractional lengths).
Make clear choices, based on the information they are given (for example, they decide to include more water stations because they know it will be hot).
Consider asking:
“How would you describe how far this station is from the starting line, using what you know about fractions?”
“How did you decide which stations to include?”
“How did you decide where to put each station?”
“What tools could you use to partition your course precisely?”
“Why is the Baltimore course longer than 3 miles? What could you do with the extra length?
Activity Synthesis
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?”
Lesson Synthesis
“Today you used what you know about fractions to plan a 3-mile fun run.”
“How did you decide to use the information that you were given to plan your race?” (We had to think about what would make a fun race, but also what we learned about the city that might be important to make sure the race was safe. The map wasn’t in a straight line, so we had to figure out how we could locate and label the stations on the map. We used estimation and what we know about fractions to plan our stations and describe where they were on the map.)
“How did you use what you knew about fractions to plan or describe your race?” (We partitioned a number line to plan our race there first, before we put it on the map. We thought about using halves and fourths. We labeled our map with fractions to help show how far the stations were from the starting line.)
Consider having students respond to the previous question as a journal prompt.
Standards Alignment
Building On
3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
