# Determining Length

Alignments to Content Standards: 2.MD.A.1 2.MD.A.3 2.MD.A.4

#### Materials

• ruler, meter sticks, yard sticks, measuring tape

• paper

• crayons

#### Actions

Part 1

1. Explain that students will be working in pairs to determine the length of each partner’s foot. Ask what tools would be appropriate for determining length.  Chart student thinking about appropriate tools, and today’s goal of  using standard measurement tools such as rulers, yard sticks, meter sticks, or measuring tape.

2. Ask student pairs to consider the unit(s) that would give the most precise measure of the length of a student’s foot.  If students struggle with this idea, the teacher might model using his/her foot as an example considering yards, meters, feet, inches and centimeters.

3. Ask student pairs to identify the unit they will work with and predict the length of each partner’s foot and record their estimations.  Estimates should be recorded in units.

Part 2

1. Have one student from each pair stand on a blank sheet of paper and have his/her partner make a mark at the student’s heel and another at the toe.

2. Then, together, have the pair measure the distance between the two marks to determine the length of the first student’s foot and record the length.  Students may have to find the closest unit.

3. Have students then find the difference between the estimation and actual length.

4. Repeat with the second student, using a different color to make the marks.  The second student should stand at the same endpoint as the first student so that students can visually compare the two representations and compare the number of the distance in units in part three.

Part 3

1. Working in pairs, have students compare the distances between the lengths of each student’s foot.

#### Class Discussion

Engaging in a class discussion will support students in thinking about the mathematical ideas embedded within the task.

• What tool did you use and why?

• How was that tool helpful?

• If you were going to measure _____ (a desk, a whiteboard, an eraser), would you use the same tool? Why?

• How long was your foot? What was your estimate? What was the difference?

• What unit did you use to measure? How did you decide to use ______? Why is the unit important?

• How long was your partner’s foot? What was his/her estimate? What was the difference?

• What was the difference between the length of your foot and the length of your partner’s foot? How did you find the difference?

• What did you notice about finding the difference? Is there more than one way to find the difference? (This might be an opportunity to discuss finding the difference by measuring how much longer one length is than the other or by using an operation such as addition to add up from the smallest length to the larger length or by subtracting the smaller length from the larger length.)

## IM Commentary

This task was designed to support students to estimate, measure, and compare lengths using standard units. To be successful with this task, students must have experience measuring lengths and be familiar with the units. Within the task students have the opportunity to measure and compare lengths of their own foot and that of a partner. As students work on the task, teachers should circulate and address misconceptions that may arise including the need to understand the idea of starting at the zero part of their tool and how to identify the zero on different tools. Teachers can support student attention to precision, MP6, as they engage in the task. The task gives students an opportunity to engage in MP5, use appropriate tools strategically, as students need to consider which tools would be appropriate for measuring length as well as which tool and unit would lend itself to a more precise measurement. For example, measuring a student’s foot using inches or centimeters would likely be more precise than rounding to the nearest foot or yard. A consideration when using this task is whether or not to choose a measurement system to focus on, standard or metric. Focusing on each system separately may be less confusing for students. The class discussion component of the task is a critical piece, providing teacher and students with opportunities to probe and extend their thinking about measurement, units, tools, as well as different strategies for finding the difference.

## Solution

Some of the key points that should be covered in the follow up discussion:

• Using appropriate tools strategically. A variety of tools can be used to measure and some will lead to more precise measures than others.
• Attending to the unit is important when describing length. For example, 2 means something different than 2 inches, 2 feet, or 2 yards.
• Multiple operations and strategies can be used to find the difference between estimated length and actual length.
• Addition or subtraction can be used to find the difference in length.
• Differences in length can be found through direct comparison, laying two objects sided by side and measuring the difference.
• Attending to precision and using comparative language when discussion length, "My foot is 3 centimeters shorter than Peyton's."