Walk or Ride Student Handout
Walk or Ride?
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Students use unit fraction or decimal addition, multiplication, or number line placement to explore the question “is it faster to walk or ride public transit?” for trips on a local transit route. This lesson can be modified to any neighborhood with public transit, and has suggestions for adaptations for grades 3, 4, or 5. See Trolley Trips for a 5th grade version of this lesson that focuses only on decimals.
- One per group: Map of a local train, bus, or trolley route that is to scale and has all streets visible for as much of the route as possible. Busses or trolleys which can stop on almost every block may work better for this activity.
- Projectable version of the same map.
- List of some popular parks, stores, restaurants, and other locations along the route with their cross streets.
- Projectable schedule for the train/bus/trolley route.
- Use Google Maps or a Google search to find out how many blocks there are per mile in the neighborhood surrounding your school, on average. Round or estimate this number to adjust the difficulty level of the exploration. In Philadelphia (Center City) there are 12-15 on average, in New York 10 blocks/mile, and in Chicago 8 blocks/mile. If you work with 12 blocks/mile, students will have opportunities to reduce fractions. If you round to 10 blocks per mile, you can switch to simple decimals by working with tenths for this part of the project. Choosing 13 blocks/mile and then converting to an unusual decimal can give students the chance to add and multiply more complex decimals.)
Invite students to share their experiences and knowledge about trains, busses, or trolleys. Elicit ideas from them by asking:
- Which train, bus, or trolley lines have you taken?
- How do you decide if you’re going to take the train/bus/trolley or walk?
- If students don’t bring it up, consider time (faster travel time, more waiting time), distance (if it’s “too far to walk”), and cost (free weekday passes for school, paying for passes on weekends).
- Discuss which decisions are easier to make (cost, because it’s either a flat fee or free) and harder (distance and time, because they vary).
After students share, project the neighborhood map and highlight the train/trolley/bus line you will discuss. Ask students to describe some locations that they might like to visit that are along the line and label 10 to 12 destinations on the map. Start with students’ knowledge of the neighborhood and add destinations from your own list if necessary. If students are unsure of exact cross streets, have a student to look them up or use approximations.
Decide as a class on a sample trip. Choose destinations that are 15 or 20 blocks apart to model fractions or decimals greater than 1. Choose destinations that are only 4 to 8 blocks apart to model fractions or decimals that are less than one.
Ask students to brainstorm about what additional information they might need to choose whether to walk or ride. For example, they might need to know the distance between the points in blocks or miles, how long it takes to walk a block or a mile, and how long it takes to ride a block or a mile. They might suggest using a train schedule, walking a block to test it, etc.
Guide students in setting up reasonable estimates to answer these questions. The numbers you choose here, how you present them, and whether you use fractions or decimals will impact the difficulty of the task. For each question, first elicit ideas from the class to get a sense of their conceptions of distance and time, and then either move toward consensus or give students the amounts that you have prepared.
- Tell students how many blocks there are in a mile, using the estimate you found in preparation for this activity.
- Ask: How long is one block, in miles? (Draw a number line from 0 to 1 miles and subdivide it into the number of blocks from the first question. Demonstrate that if there are b blocks in a mile, each block is 1/b. If applicable, convert your rate to a decimal.)
- Practice finding the distance in miles if you went 1 block, 2 blocks, 3 blocks, 10 blocks, and 20 blocks and add those distances to the number line as fractions and/or decimals.
- To support students in working with the number line as a model, you may want to ask questions like the following (here 10 blocks/mile is used as an example):
- What would it mean if you went more than ten blocks? What would it mean if you traveled fewer than ten blocks? What are some different ways that we can represent those numbers?
- For grades 4 and 5: Is there a more efficient way to determine the total distance traveled than repeatedly adding 0.1 or 1/10 for each block? (Guide students to think about multiplication.)
- How could you calculate the total distance walked if you went 58 blocks? What would that look like as a fraction? As a decimal?
- How could you calculate the total distance if you went x blocks?
- Ask: How long does it take to walk a mile? (Typical times are 15-20 minutes. You may wish to choose a time that is a multiple of the number of blocks from the earlier question to get a simple rate, or a time that is unusual like 17 minutes/mile to get an interesting decimal answer.)
- Ask: How long does it take to walk a block? (The answer to this is the time to walk a mile divided by the number of blocks in a mile, though rates are usually a 6th grade skill. You may wish to just give students a value like 2 minutes per block, or let them brainstorm ways to figure it out. For example, if there are 10 blocks in a mile and it takes 20 minutes to walk, you can divide both numbers by 10 to get 2 minutes for 1 block. You can also draw a double number line, lining up 0 minutes with 0 blocks, and the number of minutes with 1 mile. Then, subdivide the number of minutes the same number of times that the mile has been subdivided into blocks.)
- Have students work independently or in small groups to figure out the number of blocks, number of miles, and walking time (in minutes) for the class trip using strategies of their choice. Students may draw number lines, add, or multiply. Encourage students to use multiple strategies, and then have them share the strategies that they used.
Repeat the process for transit information by eliciting student knowledge, providing carefully-chosen rates, and supporting students in making calculations.
- Project the transit schedule and have students share what they know about it or what they notice. Observe that most transit schedules provide arrival times at a few major stops, but do not provide information for each block along the way.
- Ask: How could you use the schedule to figure out the amount of time it would take to ride one block? (Let students brainstorm ideas. Guide students as necessary into finding two stops that are near your class trip, finding how long it takes to travel from one to the other, counting the blocks between them, and then dividing the time by the number of blocks.)
- Note that the time between blocks is often different for different parts of the route. For an additional challenge, you may wish to calculate different rates for different areas and have students figure out how to add them together appropriately.
- Have students use their own strategies to calculate the time it takes to ride one block. Students may use number lines, subtraction and division, or other strategies. Have students share their strategies with the class.
- Ask: If you arrive at the stop just as a bus, trolley, or train is leaving, how long might you have to wait for the next one to come? (Support students in recognizing that they need to look at the time between when one vehicle and the next arrive at the same stop. Use number lines or subtraction to find the elapsed time.)
Have students use their own strategies of number lines, addition, or multiplication to find the riding time. Then, add the maximum waiting time to the riding time for the final column.
Have students create their own trips. Encourage students to try short, medium, and long trips, and also to make a guess about a trip that would take about the same amount of time to walk and to wait for and then ride public transit.
For each trip, have them record the following information in the table on the handout: Number of Blocks, Number of Miles, Walking Time, Riding Time, Max. Waiting + Riding Time.
Have a few groups share their trips and the strategies they used to calculate the miles and time.
Lead a discussion of how students used various strategies to reach the same goal, and how they used mathematics to make real-world decisions about transportation:
- What strategies did you use to calculate the miles, walking time, and riding time?
- Using one example that students shared, write a general rule for when it is faster to walk, when it is faster to wait and ride, and when it both options are about equal. (For example, if you want to take the 64 bus and leave at around 3pm, it is faster to walk if you are going less than 18 blocks, but faster to wait for the bus and ride if you are going more than 18 blocks.)
- Do you think that your rule would be the same for other transit routes? Why or why not? (Students should recognize that some transit routes have more stops, more people getting on and off, more traffic, etc. while others have less. It may be interesting to look at another transit route for comparison.)
To build on students interests and skills developed in this lesson, try some of the following activities:
- Using the same transit schedule, notice if there are parts of the route where you travel faster or slower. For example, the 34 trolley takes 9 minutes to travel the 12 blocks between 61st and 49th streets at a rate of 0.75 minutes per block, but it takes only 11 minutes to travel the 27 blocks from 40th and 13th at a rate of 0.41 minutes per block. Give students compound problems where they must combine two travel times for two different parts of the city. For example, find locations on the map that would require them to travel 9 blocks at 0.75 minutes per block and then 30 more blocks at 0.41 minutes per block. Have students show how they used a combination of adding and multiplication to find the total time.
- Have students calculate the total traveling time and rate for visiting friends and family in other cities. For example, calculate the time it takes to walk to the bus stop, wait an average wait-time for the bus, arrive at the MegaBus station, take the MegaBus to NYC, and then take the subway to visit someone. Have students calculate the number of minutes required to travel each mile for each leg of the journey, then compare them. Notice that those with the least minutes per mile are the fastest. Discuss that typically we think about traveling in terms of speed, or distance per unit time, such as miles per hour. Calculate the speed for each leg of the trip and notice that those with the most miles per hour are fastest.
- Take a neighborhood walk with a camera. Create a map mural with pictures of favorite destinations and the times it takes to travel to them by public transit or on foot as a public display to help others make good decisions about walking or riding.
- Follow up this lesson with other CBMP lessons about public transportation.
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