Understanding Centimeters and Meters Unit of Study 9: Length in Metric Measure Global Concept Guide: 1 of 3

Content Development A common misconception students have when measuring is that they overgeneralize the numbers on the ruler. In the example below the child might say that they crayon is 11cm long. Lining up unit cubes next to the crayon will reinforce the idea that the ruler is a representation of the units to be counted. “Measurement reasoning involves unit-length iteration, that is, determining the number of fixed unit lengths that fit end-to-end along the object, with no gaps or overlaps.” (Battista, 2007 p. 894) When measuring with a ruler of this type or a “broken ruler,” children must recognize the fact that the length of an object is the number of units from one end of the object to the other. Throughout this GCG, students will iterate units to measure the lengths of objects. “Iterating a unit repeatedly along the length of an object. Children with little understanding of this concept often leave gaps between subsequent units or even overlap the units” (Bamberger, Oberdorf, Shultz-Ferrell, 2010) Learn Zillion video ~ Quick code 3646 –Measure in Centimeter and Meter- length Units Quick code 3648-Choose the Appropriate Measurement Tool Quick code 3649- Solve measurement problems using a broken ruler

Day 1 Essential Question: How do you use unit cubes to measure the lengths of objects? The focus of day 1 is have students build a concrete understanding of a centimeter by using centimeter cubes to measure the length of objects.

Day 1 continued The unit cube, which is approximately one centimeter, is used for a non-standard unit of measure to develop concrete understanding of the the centimeter. Sample engage: Have students measure the length of a common object such as a pencil using only 1 unit cube. Elicit discussion about: Have students share their results. Discuss why the results were different. (The expectation is that students will get a different result because of inaccurate measurements and an inefficient tool). What made measuring with one unit cube difficult? How do you know your answer is accurate? What would you do to check your measurement? What could we do to make it easier (or more efficient) to measure? Discuss the efficiency of this measuring tool and how it can be improved. We want to lead the students to realize that one unit cube can be used to measure, but there are more efficient strategies. It would be more efficient if they had more unit cubes to work with. Efficiency would be further improved if the unit cubes had been connected (leading them to want a ruler). Students can continue to measure various objects around the classroom and record the units used on the Measurement record chart-

Day 1 continued Lesson 9.1 is referenced in the GCG as a possible lesson to do on Day 1. If you use the Measurement Record Chart and have students measure various objects around the classroom, you do NOT need to complete Lesson 9.1 as it covers the same concept. As evidence of learning, students can complete one of the possible daily journal questions. By the end of Day 1, students will be able to use unit cubes to measure the length of various objects.

Day 2 Essential Question: How do you use a centimeter ruler to measure lengths? The focus of day 2 is for students to connect the unit cubes to a more efficient way of measuring (centimeter ruler) to measure the lengths of objects. Have students measure another common object (glue stick, eraser, etc.) with their unit cubes. Facilitate discussion about a more efficient tool to measure with. Students should make the connection from using the inch ruler with color tiles to using the centimeter ruler with unit cubes. Students should line up their unit cubes on the centimeter side of the ruler to discover the unit of centimeter. Students should be encouraged to use a centimeter ruler to measure objects around the classroom and record their results in centimeters on the Centimeter record chart listed in the lesson ideas. Students need to practice measuring items on paper as well but it is essential to expose them to real life measuring opportunities first. Elements of Lesson 9.3 can be used once students have had hands on experience measuring with a centimeter ruler. By the end of Day 2, students will be able to precisely measure a variety of objects using a centimeter ruler. As students line up the unit cubes that will see that 12 cubes is the same as 12 cm.

Day 3 Essential Question: How is measuring in meters different from measuring in centimeters? The focus of Day 3 is to build students understanding of measuring in meters and how it relates to centimeters. Possible Engage:

Day 3 continued Possible lesson idea for Day 3: Use masking tape to mark a few different distances on the floor (make sure some of the distances are a meter or larger). Have students use centimeter rulers to measure the length of the tape. Discuss with students if there might be a more efficient tool to measure the tape with. Students may select a meter sick to measure with. Have them measure the same piece of tape again using a meter stick. Facilitate a discussion about how the meter stick was a more efficient tool to use to measure the longer pieces of tape with. Create stations around the classroom that include objects similar to the ones found in Go Math Lesson 9.5. Have students record the length of the object in both centimeters and meters. Have them discuss which unit was more efficient to use when measuring. By the end of Day 3, students will understand that meters are more efficient for measuring longer objects.

Day 4 Essential Question: How do you know if you should measure in centimeters or meters? The focus of day 4 is for students to better understand which is the more appropriate tool (centimeter ruler or meter stick) to use when measuring the length of an object. Students need to be provided with several opportunities to determine what the appropriate tool would be. For example: Would it make more sense to use centimeters or meters to measure the length of a textbook? Students should select centimeter because it is going to give a more accurate measurement and 1 meter is larger than the length of the textbook. Students could be given specific objects to measure in the classroom and it would be their job to determine the appropriate unit of measurement to measure the object. They should justify their reasoning. The Appropriate measurement- task could be used to help students select the appropriate tool for measurement situations. Note: you may need to change the listed objects to fit your classroom By the end of Day 4, students will be able to precisely measure objects in both centimeters and meters and select the appropriate unit based on the object being measured.

Enrich/Reteach/Intervention Tier 2 Lesson 9.1 TE p.433B Tier 2 Lesson 9.3 TE p.441B Reteach p.R90 Animated Math Model: Measure with Centimeter Models Animated Math Model: Centimeters Animated Math Model: Centimeters and Meters Enrich: Enrich p.E90 Enrich activity TE p.449B Provide each student with a piece of centimeter grid paper. Have students place a point in the center of the paper and label it as Point A. Give students various directions such as: Move 3 spaces to the left and 2 spots down. Label the new point as Point B. Measure the distance from Point A to Point B. Continue from Point B and have students move 6 spaces of the right and 4 spaces up. Label as Point C. Measure the distance from Point B to Point C.