Can You Measure This?

Introduction:

• Have students sit together in an area where they can clearly see a ruler/metre stick and a large object such as a book.
  • Ask students: If I wanted to measure this object, how would I do it?
  • Allow students to take turns providing or demonstrating their ideas.
  • As students explain or demonstrate, highlight the key points to remember about measuring objects with a ruler (i.e., always start at 0 cm, stop where the object ends, round to the nearest whole number, line the object up parallel to the ruler, etc.)
• Ask students:
  • What would happen if I didn’t line my object up at 0 cm? How would I measure it? What is different and what stays the same? What size is it now?
  • Students may have difficulty recognizing that the object has not changed size. Some may jump to the conclusion the new measurement is wherever the object ends on the ruler without realizing it no longer starts at 0 cm. Encourage students to understand the object is the same size. If necessary, ask students:
    • Has anything about the object changed? If the object itself has not changed, then is it still the same size no matter where we measure it on the ruler?
    • If students require further support, select a straight object that can be used as a means of measurement to provide proof. First, measure the object starting at zero and record that measurement. Next, start at a number that is not zero, such as three, and measure from that position. Record the measurement and indicate that the lengths are the same.
  • Finally, ask students:
    • What can I do to get the correct measurement if the object does not start at 0 cm on the ruler?
    • Students may simply state to move the object.
      • While this is a good strategy, objects printed on paper cannot be moved. Encourage students to think of strategies besides moving the object.
    • Listen for strategies such as counting on, friendly numbers, renumbering, or subtraction. Make sure to explain and highlight these strategies.
  • Advise students they will be doing an activity where they measure objects, but the object will not be lined up at 0 cm on the ruler.

Part 1: Can You Measure This Slides

• Have students sit back at their desks and project Appendix A. Ensure each student has an unobstructed view of the slides.
• On each slide, there is a measurement problem that the students must answer. Remind students that all the objects are being measured in centimetres.
• Ideally, students will use mental math strategies to answer each challenge.
  • Ask students to answer each problem using strategies such as counting on or subtraction.
  • Prompt student thinking by asking questions, such as:
    • Is it easier to count on or subtract? Does this change as the object gets larger?
    • What are different strategies we could use to make subtraction more friendly?
    • If the object being measured starts at 0 cm, what would its size be?
  • When each student has an answer, ask them to write it down on their paper or whiteboard and place it face down until the rest of the class is finished.
    • Ensure the whiteboard or paper is only being used to write their answer. Students must use mental math strategies to answer the challenge.
    • Students may also forget or omit the unit of measurement being used. Encourage students to avoid having “naked numbers” by adding centimetres (cm) after their numerical answer.
  • When all students are finished, invite students to reveal their answer. Ask student volunteers to explain how they got their answers by showing the class on the projector. As a class, students can work through each answer to find the correct one.
    • Encourage students to explain the strategy they used for all answers, whether they are right or wrong.
  • As the slideshow progresses, the measurement challenges increase in complexity.

Part 2: Partner Challenge

• Have students work with a partner to challenge each other to measure objects of choice.
• Advise students that their only rule is that the object cannot line up at zero and students should not move their object back to 0 cm.
• Have Partner 1 choose an object and set it beside their ruler or metre stick while Partner 2 closes their eyes.
  • Allow for 30 seconds to set up the measurement.
• When everything is set up, the partner can open their eyes to solve the problem.
• When both partners think they have the correct measurement, they can “lock in” their answers by writing it down on GOOS paper on their desk. Make sure students have their paper positioned so the answer is not visible.
• Have partners switch with another group. Partners will now work together to determine the other group’s measurement. Once they believe to know the answer, they will flip the paper to see if it matches the original group’s answer.
  • If the answer is right, have groups return to their original spots and reverse roles.
  • If the answer is not right, have both teams come together to find the right answer, then return to their spots and reverse rolls.
    • Look for collaboration between partners and groups, as well as the use of measurement and spatial language to explain their reasoning.
  • Repeat this process until both partners have had at least two turns at choosing and measuring an object.