Big Idea: Attributes, units, and measurement sense

Expectations:

• E2.2 use metric prefixes to describe the relative size of different metric units, and choose appropriate units and tools to measure length, mass, and capacity

• E2.3 solve problems involving elapsed time by applying the relationships between different units of time

teacher background

E2.2:

• The metric system parallels the base ten number system. One system can reinforce and help with visualizing the other system.

• The same set of metric prefixes is used for all attributes (except time) and describes the relationship between the units. For any given unit, the next largest unit is 10 times its size, and the next smallest unit is one-tenth its size.

• Conversions within the metric system rely on understanding the relative size of the metric units and the multiplicative relationships in the place-value system.

E2.3:

• Elapsed time describes how much time has passed between two times or dates. Clocks and calendars are used to measure and/or calculate elapsed time.

• Addition, subtraction, and different counting strategies can be used to calculate the difference between two dates or times. Open number lines (time lines) can be used to track the multiple steps and different units used to determine elapsed time.

• Elapsed time problems often involve moving between different units of time. This requires an understanding of the relationships between units of time (years, months, weeks, days, hours, minutes, seconds), including an understanding of a.m. and p.m. as conventions to convert the 24-hour clock into a 12-hour clock.

Describe the following scenario to the class:

“A timeline is an effective organizer for recording important events and innovations. Over the next several days you will be creating your own personal timeline, detailing the first decade of your life. Your timeline will include significant personal events, world events, and important innovations. In order to complete this timeline, you will be required to gather information from home as well as from secondary resources, such as informational texts or the Internet. Your timeline will be shared with your classmates and used to investigate interesting facts from the first decade of your life.”

Note: When discussing elapsed time on the sample timelines, direct conversation to the appropriateness of the unit used to describe the duration, frequency, and time between events. Select a variety of events or innovations in order to ensure that various units are used to describe elapsed time. Model the language of approximation when describing elapsed time.

STAGE ONE: CREATING A PERSONAL TIMELINE

Before beginning this task, give students time to reflect and connect by brainstorming what they know about timelines. Working with the students as a group, review sample timelines to examine and note organizational structures and features. Discuss the supplies that are available (for example, Bristol board, chart paper, or butcher paper; markers; glue / iPad apps: Pages, Explain Everything, Keynote). Have the students do research on resources (informational texts or the Internet). Provide direction on the number of events and innovations that should be included per year on each timeline. Encourage students to strive for a balance between personal events, world events, and important innovations.

To facilitate comparison through shared discussion, you may decide to select specific events that must be represented on all timelines. Examples of questions related to personal events might include:

• “When did you learn to talk?”

• “When did you learn to walk?”

• “When did you start school?”

• “When did you get your first tooth?”

Note: When discussing key events on a sample timeline, it is best to focus on elapsed time, given the time and duration of specific events. In discussions and shared investigations, elapsed time can be expressed in intervals of five minutes or in hours, days, weeks, months, or years. A key feature of each timeline will be notations indicating the amount of elapsed time within and between events. Specify a reasonable number of notations per time line. It is important for students to recognize that certain notations indicating elapsed time will require a greater degree of precision than others.

As students work on their personal timelines, circulate and conduct individual conferences. During this phase, you will be able to assess students’ understanding of elapsed time by discussing their notations of the duration of specific events, milestones, or innovations. Focus on whether students have selected an appropriate unit of measurement, and also on their recognition of the degree of precision required. Students can then share their completed time lines in a Gallery Walk (where students display their work for others to view) or in Sharing Circles (where students share their work in small or large group settings).

Note: Using the language of approximation, relate events that occur naturally throughout the school day to various units of time. Experiences that allow students to estimate, measure, and record time intervals to the nearest minute will provide foundational knowledge for this learning task. Everyday references and experiences will help students to develop benchmarks for time, thus providing an anchor for reasonable estimation.

STAGE 2: ESTIMATING TOOTH BRUSHING TIME

Say to the students:

“You have been sharing personal events, world events, and important innovations, using your personal timeline of the first decade of your life. Every day, we spend considerable time completing daily routines. Toothbrushing is one of those routines. In the next part of the timeline activity you will be adding time anchors related to toothbrushing. You will be working with a partner to consider these questions:

• Approximately how much time might a person spend brushing his or her teeth in one year?

• Approximately how much time might that person spend brushing his or her teeth in one
  decade?

• Approximately how much time could that person spend brushing his or her teeth in half
  a century?”

“Let’s begin by estimating, to the nearest minute, how long it takes to brush your teeth:

• Approximately how much time do you think it takes you to brush your teeth?

• How many times per day do you brush your teeth?

• Approximately how much time do you think you spend on toothbrushing each day?”

The class can decide on a specific tooth brushing time per session and a frequency of toothbrushing sessions per day that all students will use while working on this task. This specific length of time and frequency could be based on the toothbrushing video or on the two-minute recommended guidelines. Now is an ideal time to clarify students’ understanding of the task. Ask them:

• “What is this problem asking you to determine?”

• “What strategies could you use to begin solving this problem?”

• “What materials and tools could you use to solve this problem?”

• “How might you organize your thinking effectively so that you can share your solution with
  your classmates?”

NOTE: It might be useful to create an anchor chart with your students to display the relationships between minutes and hours, hours and days, days and weeks, weeks and years, years and decades, and decades and centuries.

Working in pairs, students record their thinking on chart paper. As they investigate the relationships between years and decades, and between decades and centuries, they will be engaging in computations with increasingly large values. Calculators will allow them to focus on mathematical reasoning and communication during this task. The task will culminate in a whole-group sharing session, after which students will indicate on their personal timelines time anchors drawn from the calculations.

As the students work on this task, observe how effectively they use the relationships between minutes and hours, hours and days, days and weeks, weeks and years, years and decades, and decades and centuries.

Rich assessment data can be gathered while you observe the degree to which students work flexibly with units of time. The solution to the problem could be presented in minutes, but a student who works flexibly will be able to recognize and use larger units of time

Skilfully led discussions provide opportunities for students to ask questions of one another, to share ideas, and to justify their reasoning. As students reflect and connect through shared discussion, they deepen their understanding of attributes, units, measurement sense, and measurement relationships. Draw students’ attention to the different formats used to create their personal timelines. Discuss the toothbrushing problem, focusing on the process. In sharing sessions, such as a Gallery Walk or Sharing Circles, students can compare approaches, self-assess, and set goals as they continue to work on the problem. Draw a horizontal bar on the board, placing a 0 at the start of the bar and a 10 at its end. Explain to students that this bar represents their first decade. Ask them to consider what portion of this decade was spent on toothbrushing and whether it is possible to represent this portion visually on the bar by shading the portion of the bar that represents the total tooth brushing time. Students should realize that it would be difficult to do this, because toothbrushing is a very short activity. Ask them to brainstorm daily activities that take longer than toothbrushing – for example, sleeping, walking, or talking. Ask them to estimate the portion of the decade spent on each of these activities by indicating the portion of the decade bar that might be shaded. For example, if someone sleeps an average of 8 hours per night, then one-third of the decade bar will be shaded.

• This learning activity provides excellent opportunities for differentiated instruction; it requires students to make choices and offers multiple entry points. The open-ended nature of the Fermi question allows students to use varying levels of sophistication to interpret information and select units.

• Ongoing assessment will allow you to provide feedback and to scaffold instruction. For example, you might simplify the time line task by having students use more approximate, larger units of time to calculate elapsed time.

• Some students may require individual assistance to organize their information. Anchor charts, particularly those created by the class, as well as sample timelines, will be critical reference tools for some students.

Ongoing assessment opportunities are embedded throughout this activity as suggested prompts and questions. Some additional assessment questions are:

• “How did you decide what degree of precision was required when calculating elapsed time?” • “How did you use benchmarks to estimate time?”

• “How did you use relationships between units to solve problems?”

Grade 4 Assessment Checklist (From: Guide to Effective Instruction in Mathematics, Measurement Grade 4-6)

SEL Self-Assessments (English) and Teacher Rubric

Wasting Water. According to Environment Canada, the average Canadian uses 335 L of water per day. Daily water use in Canada is higher per person than in most other countries. Conservationists are urging Canadians to protect our freshwater supplies and not waste them. Every time someone leaves the tap running while brushing his or her teeth, 10 L to 20 L of water are wasted. Challenge students to determine the answer to the following Fermi question: If you were to leave your tap running every time you brushed your teeth, how much water would you use in one year, one decade, and one century?

Happiness Scale. A second possible extension involves the measurement of happiness in relation to events on the timelines. As students reflect on significant events, some events may evoke a stronger emotional response than others. Ask students to assign happiness values to a selection of events, using a scale of 0–10. The results may then be represented by a broken-line graph, where the horizontal axis is the timeline and the vertical axis is the happiness scale.

Accounting For Our Time. Have each student create a personal timeline to track, record, and account for a 24-hour period of his or her life. The data will be used to determine elapsed time and to analyse how time is being spent. Students will represent elapsed time using a variety of units, which can then be converted to fractions. For example, “I sleep for about 8 hours each day; therefore, I spend approximately one-third of my day sleeping.”

Exploring Additional Questions: How much time might a person spend sleeping in one year? In one decade? In a lifetime?