 Author:
 DAWNE COKER
 Subject:
 Mathematics
 Material Type:
 Activity/Lab, Lesson, Lesson Plan
 Level:
 Lower Primary
 Tags:
 License:
 Creative Commons Attribution
 Language:
 English
 Media Formats:
 Downloadable docs
Education Standards
T4T We're Both Right!
Overview
This resource is from Tools4NCTeachers.
In this lesson, partners use both centimeters and inches to measure objects to develop their understanding of the relationship between the length of a unit and the resulting measurement. With teacher guidance, they will solidify their understanding that the objects themselves do not change when measured using different units. Students should have had multiple experiences measuring using standard units before attempting this lesson.
Here is a sample of this resource. Click the attachment to download the entire fullyformatted lesson and support materials.
We’re Both Right!
Finding Patterns Using Multiple Units of Measurement
In this lesson, partners use both centimeters and inches to measure objects to develop their understanding of the relationship between the length of a unit and the resulting measurement. With teacher guidance, they will solidify their understanding that the objects themselves do not change when measured using different units. Students should have had multiple experiences measuring using standard units before attempting this lesson. 
NC Mathematics Standard(s):
Measurement and Data
NC.2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
Additional/Supporting Standards:
NC.2.MD.1 Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, metersticks, and measuring tapes.
Standards for Mathematical Practice:
3. Construct viable arguments and critique the reasoning of others.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
Student Outcomes:
 I can use a ruler to measure to the nearest centimeter and/or inch.
 I can describe how the size of the unit I use is related to the number I get when I measure.
Math Language:
What words or phrases do I expect students to talk about during this lesson?
unit, measure, more, less, inch, centimeter, accurate, size, length
Materials:
 Rulers with centimeters on one side and inches on the other
Advance Preparation:
 Gather enough rulers for each child to be using them simultaneously
 Prepare sentence frames
Launch:
 Systems of Measurement (8 minutes)
Adapt the following scenario to your classroom, but be sure to measure the object(s) beforehand.
Mr. Wells wants to move his desk out of the room and trade it for a smaller one, but he was worried the desk was too wide to fit through the (32 inch) doorway. Javy measured the desk as (about 28) and while Maya measured the desk as (about 72) Bryan surprised everyone when he said that they were both right. What was Bryan thinking? Today we are going to do some measuring of our own so that we can answer questions like this one whether we are making measurements in or out of school.
Look at your rulers. What do you notice? (There are lines., Some of the lines are numbered., The two different sides have spaces that are different lengths., etc.) What do you wonder? (Why are the spaces on each side different?, Why are some of the lines numbered, but others are not?, What do cm. and in. or other labels mean?)
(The next two paragraphs will not be necessary if students already know about systems of measurement.)
Did you know that people in different parts of the world use different systems of measurement? In the United States, we often measure objects using inches, feet, yards, and miles and we call these types of measurement “customary measurement.” In most of the rest of the world, people use a system of measurement called the “metric system” which uses units such as centimeters, meters, and kilometers.
Most of the rulers we use have centimeters on one side and inches on the other. Look at the rulers you and your partner have. Find the side that has centimeters, labeled “cm”. The partner with the shortest hair will be using this side to measure the objects you select. Now find the inches side labeled, “in”. The partner with the longest hair will be using the inches side to measure today.
In second grade we measure to the nearest complete unit, so briefly model how to estimate which whole number of units an object is closest to.
Briefly introduce and make available (post, preprint, etc.) these or similar sentence frames to structure students’ conversations within their partnerships. The teacher can draw students’ attention to and model these frames as necessary during the Explore and Discuss sections of the lesson.
Sentence Frames:
Identify or State
When I measured (the object) it was about (____) long.
My measurement was (________) more than my partner’s measurement.
My measurement was (________) less than my partner’s measurement.
Describe or Explain
My measurement was more because my unit was (_______).
My measurement was less because my unit was (_______).
When we measured we had different totals because (_______).
I (agree or disagree) with my partner’s measurement because (______).
Explore:
 Measuring Around the Room (1520 minutes)
Allow ample time for students to measure many objects. Designate a few standard objects for all students to measure such as a specific text book, the seat of a chair, etc. These standard objects will be a way for you to quickly check to be sure that their measurements are reasonable. Otherwise, they should measure as many objects as possible because the more examples they have, the more likely they are to recognize and describe the relationships between the different units of measure. Prompt students to use the sentence frames during their partner conversations, but do not take over the conversation.
As students work, observe:
 The act of measuring. Are they being precise to the nearest whole unit?
 Their collaboration. Are they paying attention to and considering the measurements their partner is making?
 Their conversations. Are they using the vocabulary (unit, measure, etc.) and syntax (My measurement was ____., Our measurements were different because _____., etc.) that demonstrate an understanding of what they are doing?
As students work, record:
 student thinking as you listen to and interact with students. These moments will help to guide your discussion; however, you may interrupt the class a few times to share ideas that come up during the discussion. What words and phrases are students using? How are their discussions showing what they understand and unveiling misconceptions?
 questions that students wonder and/or answer during their exploration. What do their questions reveal about their thinking and about the concepts of measurement and units? How did they answer their own questions?
 comments that you overhear that relate to the big idea of measuring using multiple units.
 student strategies that will encourage others to share and will lead to clear understanding and efficient processing for the class.
 a progression in which you want students to share their thinking and/or examples. What order will create the most discussion and lead students to a clearer understanding? Which student examples serve as clear examples of patterns of thinking for many students?
Discuss:
3. Who is Right and Why? (25 minutes)
Begin by sharing questions and thoughts you recorded during the explore section including what students noticed and wondered. It is best, when possible, to have students share their own examples or to mention them and then have students explain what they were thinking or what they found out. However, you may decide to share on behalf of students in some cases.
Share example measurements and have students determine which measurement is “right” and justify their argument. Allow students to rehearse and revise their points in partners or small groups before sharing with the class. Encourage students to use the question stems when explaining their thinking and agreeing or disagreeing with each other. Take advantage of disagreements and have students demonstrate and explain proper use of their rulers and how they are attending to precision.
Encourage students to look for and describe patterns. For instance, “When the units are bigger, the numbers are smaller.” or “It takes more little units to measure something.”
Refer back to the problem from the launch. Have students discuss and defend their responses in partnerships or small groups. After a discussion of their reasoning, ask students to explain how each unit is related to their final measurement and use this discussion to wrap up before assigning the formal assessment.
Possible points to address and questions to ask:
 Who agrees/disagrees with (the student)? Why? Or Who was right? Why?
 Are you noticing any patterns? How would you describe the pattern you have found? Did the Evidence and Examples recording sheet help you to recognize or describe any of these patterns?
 How was the unit you used related to the measurement you made? How does this explain the difference in measurements?
 What challenges did you deal with during this lesson?
 What connections did you make to other experiences?
 What would you and your partner do differently if we repeated this activity tomorrow?
Evaluation of Student Understanding
Informal Evaluation:
Recorded observations and notes from the exploration and discussion phases of the lesson
“Evidence and Examples” forms collected from students
Formal Evaluation/Exit Ticket:
Either:
Draw and label a diagram that can be used to explain how the size of the unit used is related to the measurement. Include a brief caption to explain the diagram. or
Sketch a comic strip using stick figures and simple shapes to show how the size of the unit used is related to the measurement. Use speech bubbles for your characters to explain your thinking.
Meeting the Needs of the Range of Learners
Intervention:
Engage students in a similar experience by iterating multiple objects such as inch tiles, Unifix cubes, or paperclips. Have students work through the same thinking of comparing their results after measuring the same object using different units. Centimeters and inches are relatively abstract concepts. We can root their reasoning in their world when students think and speak about the difference between the number of cubes and paperclips it takes to measure a book, shoe, etc. This simple change avoids mistakes with using and reading rulers as well as confusion with labels. The same questions, activity sheet, and sentence frames can be used.
This activity can be substituted for the original exploration at any point or can be an additional opportunity for small groups or individuals who are not yet able to demonstrate their understanding during the discussion and/or assessment after having used the rulers in the explore section of the lesson.
Extension:
If students quickly realize and articulate that the smaller unit results in a higher number when measuring an object, have them measure a few more objects to test their theory before moving on. Now have these students generalize the pattern they have recognized. What are other instances to which this pattern applies? What possible problems could be caused when people use different units and are not clear about which units they have used? Why is it important that we label our units when we communicate measurements to others? This extension is meant to take their thinking farther and deeper but should not add extra work.
Possible Misconceptions/Suggestions:
Possible Misconceptions  Suggestions 
Students consistently measure inaccurately.  Observe the child measuring carefully and instruct them on how to begin measuring at zero mark and to accurately read the marks on the ruler to determine the length of the object. 
In this exploration and discussion, students realize that more than one measurement can accurately describe an object, but there is a chance that they overgeneralize and believe that any measurement a student shares is accurate.  This, like many overgeneralizations, is best counteracted with nonexamples. Have the student test their conjecture, but be sure to include inaccurate measurements that might sound reasonable. 
Students may begin to think that inches are in some way better than centimeters or vice versa.  Ask students to explain their thinking and then clarify that different units are more accurate in different situations. Centimeters are more precise when estimating to the nearest whole because they are smaller units. Inches are likely to be more precise when measuring objects that were created using the customary system. 
Special Notes:
 At this age, students can be inflexible with their understanding of what a number represents. This is an opportunity to expand their understanding of numbers as being able to represent widely different values as in the weight of 7 mice and 7 elephants. Be prepared for students to need time when explaining why an object was both ___ inches and ____ centimeters.
 There is no reason for 2^{nd} grade students to know a specific ratio between metric and customary units.
Evidence and Examples
Object Measured  My Partner’s Measurement  My Measurement  What we notice and wonder about these measurements. 



















