Building a Train Track

[Mathematics, Grade 5, Construction Learning]

Type and Purpose of Learning

While being mock engineers and construction workers, students had the opportunity to feel what it was like to organize, create, and solve problems in the real world. Through construction learning, students thought and designed, pre-planned and experimented with objects and materials, using logic and spatial reasoning to build a train track. In doing so, the math concepts of linear measurement, money matters, connection to time and distance, volume, and even adding with decimals became more meaningful and realistic to the students.

Learning Story (overview)

As a culminating measurement activity, our grade five students designed and constructed a railway track using straws, centimetre cubes, glue and tape.

To add interest to this activity, each group was told it had a budget of $100 – they could purchase straws for $0.10 per centimetre, and centimetre cubes for $0.50 each. Additional charges included $0.20 per bend in the track and an extra $1.25 for any construction of a bridge. Once completed, the students were required to build and figure out the volume of a train engine using centimetre cubes. Next, they figured out how long it would take the train to travel once around their track keeping in mind it moved one-second every 3cm on a straight section, and one-second every 2cm on a curve.

Said one grade five student upon completion of the activity, “This activity was so much fun because you got to be a like a real architect and build your own train track!” Little did I know at the time, this played-based learning task would be one of the most enjoyable math activities of the year.

It all began as a culminating measurement activity which took my students from architects to construction workers within a matter of a few periods. From the get-go, they were enthusiastic as I explained the task of designing and constructing a railway track using straws, centimetre cubes, glue and tape. They became even more engaged when I gave them a budget. Eyes lit up, inquiring glances were shared and a murmur of excitement spread throughout the classroom.

During the planning process, student inquiry and engagement remained high. Groups worked collaboratively to create the direction, size and background of their railway track designs, while keeping in mind the construction costs of their blueprint. Since we are an inclusive learning community, a safe and accepting environment was already established so everyone felt comfortable openly sharing an idea or opinion, knowing all input was appreciated by other group members.

The building of the railway track was the most exciting part. One student put it succinctly, “It was a fun way to end our measurement unit because it helped us be responsible with money so when we’re older, we’ll know how to budget.” Another student commented, “It was a good activity in budgeting with $100. It kept us focused on how many straws we actually needed and we didn’t waste any materials.” We did have a few challenges such as sustaining the height of the bridge and keeping the straws on the bulletin board with glue. However, being an inclusive learning community, we focused on staying positive and not giving up until we found a solution. In the end, some students decided to use tape instead of glue to ensure the strength of their bridge and to secure the track to the bulletin board; however, the results were not as aesthetically pleasing.

Once they completed their railway track, the students were asked to build and then figure out the volume of a train engine using centimetre cubes as well as the time it would take this engine to travel once around their track. One student pointed out, “I liked building a train engine and figuring out its volume, then calculating the time it would take to go around the track. This really got us thinking about what we learned in our math unit.”

Reinforcing math concepts through play-based learning proved truly effective and engaging. In the end, everyone requested that other unit activities be summarized in a similar hands-on, creative way.

Lesson Focus

Students will use the problem solving process to design and construct a train track.

Assessment/Reflections for future lessons:

While observing the students engaged in the activity, I looked to observe the following:

1. Do students communicate using mathematical terminology such as linear measurements, centimetres (cm), mass (kilograms (kg), tonnes (t)), volume (cm3), money (dollars ($) and cents (¢)), and time, minutes (m) and seconds (s)?
2. Are the students able to compare kg to t?
3. How well are the students measuring and calculating the total cost of the train track?
4. In what ways do the students show a connection between time and distance?

Overall, this activity truly summed up the main concepts of this unit – linear measurement, time, money, volume and mass. The students were very excited at the prospect of completing a construction learning activity and worked collaboratively to complete all sections within the given timeframe. In fact, one student was shocked to learn that this was a math activity rather than one of our daily fun energizers.

During the process, we stumbled over a few challenges such as the popsicle sticks not sticking to the Bristol board, and the bridges continually falling over. In the end, students chose tape instead of glue to adhere the train track and bridges to the Bristol board; however, the results were not as aesthetically pleasing. Possibly in the future, Popsicle sticks or Lego may replace the straws to further strengthen the railway track. With accommodations and differentiated teaching, most students were able to complete the purchasing of materials as well as the distance and time questions. For those who struggled with these concepts, further lessons were required.

Curriculum Expectations:

• Estimate, measure, and record perimeter, area, temperature change, and elapsed time, using a variety of strategies;
• Select and justify the most appropriate standard unit (i.e. millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance, and to measure the perimeter of various polygons;
• Determine, through investigation using a variety of tools (e.g. concrete materials, dynamic geometry software, grid paper) and strategies (e.g. building arrays), the relationships between the length and width of a rectangle and its area and perimeter and generalize to develop the formulas [i.e. Area = length x width; Perimeter = (2 x length) + (2 x width)];
• Solve problems involving the multiplication and division of multi-digit whole numbers and involving the addition and subtraction of decimal numbers to hundredths, using a variety of strategies;
• Read and write money amounts to $1,000 (e.g. $455.35 is 455 dollars and 35 cents or four hundred fifty-five dollars and thirty-five cents).

Introduction: (MINDS ON)

The students have just been hired by an engineering company to design and construct a new railway track and bridge using straws, centimetre cubes, glue, tape and a piece of Bristol board.

Materials:

• straight and bendable straws
• scissors
• Bristol board
• pencils and markers
• glue stick or white glue
• tape
• calculator
• centimetre cubes

Teacher-Directed Lesson

By reviewing the anchor charts created for each of the learning goals listed above, students will be better prepared to begin this activity. If any students need further assistance, teachers can provide individual or small group lessons while the rest of the class begins the design of their railway track.

Student Tasks (WORKING ON IT)

The class will be split into groups of three to four students and asked to complete the following tasks:

1. Design and construct a railway track with at least one bridge using straws, centimetre cubes, glue, tape and a piece of Bristol board. Straws may be cut. To add interest to the activity, each group will be given $100 from which they are to purchase straws for $0.10 per centimetre, and centimetre cubes for $0.50 each. Additional charges will later be added at $0.20 per bend in the track and an extra $1.25 for any construction of a bridge.
2. Introduce a chart on which students will keep a tally of the track’s length in centimetres (cm), the cost of the track in dollars ($), any extra charges accumulated, and the total cost of the railway. See blank chart provided.
3. Students will then build and calculate the volume of a train engine using centimetre cubes. At this point, the teacher may want to relate this activity to a real life situation such as imagining that each boxcar holds 60,000 kilograms (kg) of cargo, how many boxcars would you need to carry 240 t of cargo?
4. Using their model train engine, students are asked to figure out how long it will take for the train to travel once around their track, keeping in mind that it moves three cm every second on a straight section of the track, and two centimetres (cm) on a curve every second.

Other Applications (Extensions)

As an extension to this activity, students may create then answer an altered or new question related to their model railway. This may include an alteration of distance and time, cost per centimetre of straw, or even a passenger car picking up a certain weight of travellers every time the train travels around the track. Students may even choose to add a question about capacity such as how many millilitres of water could be sold to 60 passengers, assuming each water bottle contains 500 ml? What would this amount be in litres (L)? Students may also vary the model idea, for example changing it to a re-creation of a rollercoaster ride at Canada’s Wonderland, a race car track or even an ancient Roman aqueduct.

Share and Connect

Students benefit from sharing their work with others in the classroom. In doing so, the measurement concepts of time and distance, volume, mass as well as making change are further reinforced. Students are more likely to put forth a better effort to complete their task when they know their work will be shared.

Accommodations/Modifications

Meeting the learning needs of all students is vital in an effective lesson. By providing a visual and concrete example of a straw’s measurement and cost, teachers are able to guide students with their computations. For example, one straw equals 20 centimetres in length. At $0.10 per centimetres, each straw costs $2.00. Since there is an additional cost of $0.20 per bendable straw, these straws would therefore cost $2.20. Furthermore, teachers can display a sample chart of straw lengths and corresponding costs to assist students in organizing their observations. To help students understand the connection between distance and time, teachers can show students a three cm length of straw and explain that the train takes one second to travel this distance. Similarly, a two centimetre curved section of the track will take one second.

Differentiation

Through a differentiated approach, teachers can enable the various learning styles of students within the classroom. In doing so, students of varying abilities have the opportunity to process and construct meaning of new information using their own unique way of learning. This activity covers a variety of Gardner’s multiple intelligences such as logical-mathematical, interpersonal, bodily-kinesthetic and visual-spatial. Problem-solving through a collaborative approach is also evident as students discuss their design, the cost of materials to build it and the construction of the straight sides versus the curves in the track. Even the more challenging questions relating to time and distance can be completed within a team.

Impact Quotes (Impact Analysis)

“I thought it was fun because you got to be like a real architect and build your own train track.”

“It was a fun way to end our measurement unit because it helped us be responsible with money so when we’re older we’ll know how to budget.”

“It was a good challenge in budgeting with $100. It kept us focused on how many straws we actually needed and we didn’t waste any materials.”

“I also liked building a train engine and figuring out its volume and how much time it would take to go around the track once. This really got us thinking about what we learned in our unit.”

“I want to do more of these activities in the future because they are creative and lots of fun!” “The most challenging part of this activity was building the bridge. We had trouble keeping it up with the materials we had. After a while, our group problem solved and used tape instead of glue to keep the bridge up.”

“By setting our goals, we were able to finish our train track successfully.”

Research Quotes

Play-based learning is closely connected to brain-based learning. The brain naturally learns through emotional connections exhibited during creative, enjoyable activities which “develop the pathways in the brain that affect future health, learning and behaviour; and even the shape of the brain” (ETFO, 2011, from My Playbook, www.ultimateblockparty.ca).

Establishing a Safe Place to Learn

During the lesson I was mindful of maintaining a safe and accepting environment. This was accomplished by following our classroom norms. Within heterogeneous groupings of four to five students, everyone had the opportunity to share their ideas openly and feel comfortable knowing their opinions were validated and appreciated by others.

Resources

Building a Train Track Unit Problem