Measuring in Meters

Expectations:

E2.2 explain the relationship between centimetres and metres as units of length, and use benchmarks for these units to estimate lengths

E2.3 measure and draw lengths in centimetres and metres, using a measuring tool, and recognize the impact of starting at points other than zero

Measurement Principles

• Sometimes you measure directly, sometimes you use indirect means.

• Familiarity with certain measurements referents help you estimate.

• In order to measure, a series of uniform units must be used or a single unit must be used repeatedly.

• The unit chosen for a measurement affects the numerical value of the measurement; a bigger unit results in a smaller number of units. This is why a measurement without a unit is meaningless.

materials Math Language/Vocabulary

• Metre Sticks

• Rulers

• Tape measures (every student needs to bring one in)

• Masking tape

• Sticky notes

Source: Barrett, J., Cullen, C., Behnke, D., & Klanderman, D. (2017) A Pleasure to Measure” Tasks for teaching measurement in the elementary grades.Lesson:Third Time’s the Charm! Pg. 97-100

Ask students to find the distance across a large room (consider social distancing) by counting the number of steps needed to walk across the room and have them record the distance. Counting steps while walking from one side of a room to the other is a way of measuring if it involves counting regular steps as units of distance (or length). Have them discuss their results with a classmate. Is one student wrong and the other right if their results differ? Note that students may not notice the effect of the varying lengths of their strides.

Next, ask students to walk across the same room again and record the number of steps again. Challenge students to compare their second measurement of this distance with their first measurement. Ask them to write both of their measurements on a sticky note and circle the better measurement. How should they decide which measurement is better? Encourage students to solve this dilemma by checking the distance one more time. This third measurement should sway them toward their first and second measure. The third measure is a charm!

Ask students to post their findings on the front wall and discuss the entire collection of measures (Distance Learners can use Padlet). What is the most common number of steps taken? It is OK if students struggle with this question before the data are organized. Posing the question before they have organized the data helps them realize the value of doing so.

Source: Barrett, J., Cullen, C., Behnke, D., & Klanderman, D. (2017) A Pleasure to Measure” Tasks for teaching measurement in the elementary grades.Lesson:Third Time’s the Charm! Pg. 97-100

Now ask students to help arrange the data from this set of measures in order along an empty number line on the front board. Look for groups of data that cluster together along the number line. Can you find at least one such cluster of numbers? Which number is located at the center of that cluster? Are there extremely small measures or large measures posted along the number line? Mathematicians call the numbers that are isolated from the clusters at the middle outliers. These numbers may be ignored if we are interested in finding the best number to report the measurement of the distance across the room. Some numbers would not fit for this measurement. Encourage students to think of some numbers that would not have made sense. Perhaps they will say ½, 1, or 3 steps would be too few steps to get across the room. Similarly, they may suggest that 1 000 steps is not a realistic measurement.

It is important to discuss the reason that students’ measurements were not all the same. What do students say about this? Explain that variation is a way to describe different results. Students may mention that they do not have the same foot size or shoe size, or that they take different strides. Maybe some took regular strides and others took longer strides (super steps!).

If a new student enrolled in the class tomorrow and measured the same distance in steps, how many steps would we expect him or her to take? Do students expect the measurement to be close to the centre of a cluster?

• Measure using measuring tapes the length and width of the room together starting at 10 cm on the measuring tape. They will watch as the teacher demonstrates how to measure. How the teacher calculated/ calibrated the measure as they didn’t start from zero. They compare these measures with their step measurements. Discuss accuracy. Discuss measuring not from zero and how to calibrate the measure.

Independent Task / Assessment Opportunities:

Students are measuring now using a measuring tape the length width of a large room/hallway. You may want to go to the gym.

Student Self Assessment: https://docs.google.com/document/d/17GcyC2TSmljE5_VX4m9xEnHvFDt_kN_KcujFnpypZR4/edit?usp=sharing

Teacher Rubric: https://docs.google.com/document/d/1C28aCyHpZFAwz6C7AGxu_hAvPTSUKbHtNvH3R-d9yDM/edit?usp=sharing

To further investigate measuring not from zero refer to this grade three lesson: https://docs.google.com/document/d/1E73TGB81TQ0WhZVe7GaTIQa9B9NoveX7ZWmxH4nDYVA/edit