Grade 5: "Hiking the Bruce Trail 2"

(Adapted from: Guide to Effective Instruction in Mathemathics, Grade 4-6: Measurement)
This activity is an extension from the previous lesson “Hiking the Bruce Trail Part 1”

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Content

Big Idea: Measurement relationships

Expectations:

E2.2 solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units

Learning Goals

We want students to...

solve problems requiring conversion from metres to centimetres and from kilometres to metres.
determine the relationships among units and measurable attributes, including the area of a rectangle and the volume of a rectangular prism.
estimate and determine elapsed time, with and without using a timeline, given the durations of events expressed in minutes, hours, days, weeks, months, or years.
estimate, measure, and record perimeter, area, temperature change, and elapsed time, using a variety of strategies.

Build relationships with peers and communicate effective to collaborate and solve challenging problems

Success Criteria

I can choose appropriate standard units while problem solving
I can convert metres to centimetres and kilometres to metres
I can estimate and measure elapsed time
I can create a broken line graph and use the data to make conclusions
I can use my ideas and the ideas of others to help solve challenging problems
I can ask questions if I want to know more or need help

Materials

Smartboard to project math problem / Screen share on Zoom
sheets of chart paper (2 per group of students)
sheets of grid paper (3 per group of students)
markers (1 set per group of students)
rulers (1 per group of students)

Vocabulary

Conversion
Data
Distance
elapsed time
Rate
units of distance (kilometre, metre) • time intervals (minute, hour)

Pedagogy

Minds On

Another hiker travels the 9 km trail at the rate of 2.4 km/h. This hiker leaves at 9:00 a.m. and stops at all the same locations to take photographs. Determine the time at which each photograph will be taken. Ask:

“What impact will this different rate of travel have on the time at which each photograph will be taken?”

Action!

Note: In the previous lesson, students developed and shared efficient strategies to identify and apply the relationship between time and distance. Problem 2 will allow students to work from what they already know to be true, rethink the problem within a new context, and search for related information that may be helpful.

Have students work in triads to determine the time each photograph was taken. While they are engaged in this task, circulate and encourage them to reflect on strategies shared in stage one of the task. Ask:

“Which strategies do you think will be most useful in approaching this new challenge? Explain your thinking.”

At key points in the process of solving the problem, there may be a need for shared discussion or guided math instruction. Questions and prompts that encourage student reflection have been embedded in each stage of this learning task. Draw students’ attention to different visual formats that could be used to represent and solve the problem. Sharing opportunities that demonstrate and model a wide range of efficiency in strategy use allow students to focus on the process. Students benefit from comparing approaches. Such comparisons help them to self- assess and to set goals as they continue to work on the problem. Provide opportunities for students to ask questions of one another, share ideas, and justify their reasoning.

Consolidation Of Learning

SHARING IDEAS: There are many formats for communicating observations on the comparison of the two sets of data. You may wish to:

have a class discussion;
have each triad share graphs and observations;
have students reflect individually in a math journal.

Once triads have determined the time at which the second hiker took each photograph, reconvene the class and have students communicate their findings. During sharing, record (or have a student record), on a second class T-chart, calculations related to this problem.

After students have completed this stage of the task, ask them to summarize the information on the same graph used in Problem 1 (that is, two broken-line graphs will be drawn on the same grid or set of axes, with time on the horizontal axis). Before they plot the new values, have students anticipate how this data set will compare with the representation of values from Problem 1. The graphs will be straight lines, since the distance/time rates are constant (3 km/h and 2.4 km/h). However, the steepness (or slope) of the graph lines will differ: the faster the rate, the steeper will be the graph line. Ask:

“How do you think the graphed data for the second hiker will compare with the plotted values for the first hiker?”

Completed graphs provide a rich opportunity for comparing two related sets of data. Ask:

“What can be determined by comparing the two related sets of data?”

Differentiated Support

This measurement task provides many opportunities for differentiated instruction; it requires students to make choices and it promotes cooperative learning.
As students progress through this task, you have the opportunity to circulate and assess student needs, provide feedback, and scaffold instruction.
The task allows for multiple entry points. You have the opportunity to control the number of variables students are using, and can thus make the calculations more manageable.
For example, you might decide to provide the rate of travel for the first problem, enabling students to focus solely on the relationship between time and distance.
Some students may require help to organize their data and calculations. Differentiate instruction for these students by assisting them in the creation of a table or graphic organizer.

Independent Task / Assessment Opportunities

Ongoing assessment opportunities are embedded throughout this learning activity. Suggested prompts and questions have been provided in the Getting Started and Working on It sections. Focus your observations in order to assess how well students:

express their understanding of measurement relationships (time, distance, rate);
work flexibly with conversions (kilometres to metres);
select and compare units of measure and justify their reasoning;
draw upon their understanding of quantity and fractional relationships with respect to time;
apply reasoning and logical thinking;
communicate and justify their solutions.

Assessment Checklist

SEL Self-Assessments (English) and Teacher Rubric

Extension Opportunities

Staggered Starting Times. Create a scenario in which the hikers’ starting times are staggered and students are challenged to predict outcomes. For example, if one hiker leaves the trail- head at 9:00 a.m., travelling at a rate of 2.4 km/h, and another hiker leaves the trailhead at 9:30 a.m., travelling at a rate of 3 km/h: Will the hikers meet on the trail? Who will be the first to take photograph number 4? Who will be first to complete the hike?

Graphical Stories. Provide small groups of students with a variety of line graphs (like the one shown on the right) representing distance and time. Ask the groups to select a particular graph and create a related math story.

Hiking Story. Ask students to create a story involving distance travelled over time. For example, the following story could match the graph shown below: “I started at 8 a.m. I walked at a rate of 4 km/h for 15 minutes. I stopped for 10 minutes to talk to a friend. We walked together for 5 minutes, covering a distance of 400 m. We stopped for a break. Then I walked home at a rate of 5 km/h. The whole trip took 60 minutes.” Notice that a steeper slope indicates a faster rate. Advise students that they may choose to write math stories with realistic contexts related to their own experiences or they may create and use imaginative, fictional scenarios.

Technology

Pages

Students could use the Pages app to document their findings and create a line graph.

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