Global Concept Guides: Understanding Centimeters and Meters, Estimating Metric Length, Compare Metric Length
Prior Learning: MACC.1.MD.1, MACC.1.MD.2
Progressions Document Link
Sample Show What You Know Task:Use the Go Math Ch. 9Show What You KnowTE p. 430 or the Diagnostic Interview Task TE p. 430
Common Core State Standards for Mathematical Content :
Measure and estimate lengths in standard units.
MACC.2.MD.1.1-Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
MAC.2.MD.1.2-Measure the length of as object twice, using the length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
MACC.2.MD.1.3-Estiamte lengths using units of inches, feet, centimeters, and meters.
MACC.2.MD.1.4-Measure to determine how much longer one object is than another, expressing the length differences in terms of a standard length unit.
Relate addition and subtraction to length.
MACC.2.MD.2.5-Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g. by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
MACC.2.MD.2.6-Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,…, and represent whole-numbers sums and differences within 100 on a number line diagram. / Comments:
Notes on Assessment:
Unit 10 Assessment – Go Math Ch. 9
See common performance task link below.
Unpacking the Standards for this Unit:
Students will build upon their knowledge of customary units of measurement from Ch. 8. Students will apply their knowledge of customary units of measurement to measure lengths using metric units of measurement like centimeters and meters. Students will have to measure objects using two units of different lengths such as centimeters and meters. This is a difficult concept for young children and will require numerous experiences for students to predict, measure, and discuss outcomes. As students estimate, the student has to consider the size of the metric unit. Estimation creates a problem to be solved rather than a task to be completed.
Common Performance Task for this Unit:
Shoes: In this performance task students will measure the length of shoes and determine the difference in lengths. Students will also use a number line to determine the different lengths of shoes. Students will be expected to explain their thinking with written responses.
Click here for the performance task and rubric.
Future learning:
Students need to be comfortable with metric units of measure so that in third grade they will be able to measure accurately to the nearest centimeter and meter. They will use their knowledge of metric units when they are measuring lengths to determine perimeter and area.
2nd / Global Concept 1 of 3 for this Unit of Study: Understanding Centimeters and Meters
This GCG is focused on building students concrete understanding of a centimeter and a meter. Students develop an understanding of what these units of measurement are and they measure using these customary units of measurement. / Projected Time Allotment:
4 Days
Sample Essential Questions:
Day 1: How do you use a centimeter model to measure the lengths of objects?
Day 2: How do you use a centimeter ruler to measure lengths?
Day 3: How is measuring in meters different from measuring in centimeters?
Day 4: How do you know if you should measure in centimeters or meters?
Related Unit 10 Assessment: Go Math Ch. 9: #1, 2, 3, 9, 10, 12, 18, 19
Instructional Resources
Manipulatives:
- Centimeter cubes to measure the length of objects and build a concrete understanding of a centimeter
- Centimeter ruler to measure the length of objects
- Meter stick to measure the length of objects
- Go Math Lesson 9.1-Essentials:Reteach Tier 1 TE p. 433B, Listen and Draw TE p. 433 (use the guiding questions in the margin of the TE),Model and Draw TE p. 434 (use guiding questions in TE margin), Problem Solving TE p. 436
- Go Math Lesson 9.3-Essentials:Reteach Tier 1 TE p. 441B, Model and Draw TE p.442 (use guiding questions in TE margin), Problem Solving TE p. 444
- Go Math Lesson 9.5-Essentials:Reteach Tier 1 TE p. 449B,Engage TE p. 449, Listen and Draw TE p. 449 (use guiding questions in TE margin), Problem Solving TE p. 452
- Measurement record chart-Students can record their measurements (using centimeter cubes) of objects around the classroom.
- Centimeter record chart-Students can record their measurements (using a centimeter ruler) of objects around the classroom.
- Appropriate measurement-Givestudents specific objects to measure and they would determine if they should use cm or m.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Is it more efficient to measure using 1 unit cube or several unit cubes? Explain your thinking.
- How could you measure the length of the teacher’s desk using only a centimeter ruler?
- Can you use the meter stick to measure the width of your math book? Explain your thinking.
- Is there ever a time where you would measure the length of an object using both centimeters and meters? If so give an example.
Students are better able to…
- Select the most appropriate unit of measurement to measure lengths of objects in the classroom. (SMP 5)
- Understand the relationship between centimeters and meters. (100cm is the same as 1m) (SMP 7)
- Are providing the students opportunities to measure objects hands-on. (SMP 5)
- Provide concrete opportunities for students to discover the relationship between centimeters and meters by having the students use centimeter cubes to explore the relationship. (SMP 7)
2nd / Global Concept 2 of 3 for this Unit of Study: Estimating Metric Length
This GCG is focused on students building understanding for estimating lengths in centimeters and meters. By building this understanding students will be more proficient at gaging the accuracy of their measurements. / Projected Time Allotment:
3 Days
Sample Essential Questions:
Day 1: How do you use known lengths to estimate unknown lengths?
Day 2: How do you estimate the lengths of objects in meters?
Day 3: How do you know if you should estimate length using centimeters or meters?
Related Unit 10 Assessment: Go Math Ch. 9: #4, 7, 8, 13, 17
Instructional Resources
Manipulatives:
- Centimeter cubes to check their estimated measurements in centimeters.
- Centimeter ruler to check the estimated measurements they make.
- Meter stick to check the estimated measurements they make.
- Ten rods are approximately 10cm long and can be used as a “known” length to estimate the length of unknown objects.
- Go Math Lesson 9.2-Essentials: Reteach Tier 1 TE p. 437B, Listen and Draw TE p. 437 (use the guiding questions in the margin) Model and Draw TE p. 438 (use the guiding questions in the margin), Problem Solving TE p. 440
- Go Math Lesson 9.6-Essentials: Reteach Tier 1 TE p. 453B, Listen and Draw TE p. 453 (use the guiding questions in the margin) Model and Draw TE p. 454 (Refrain from using the student page and focus on the T.E. guiding questions), Problem Solving TE p. 456
- Estimate length in centimeters chart-This chart can be used to help students gain proficiency when estimating lengths in centimeters.
- Estimate length in meters chart-This chart can be used to help students gain proficiency when estimating lengths in meters.
- Estimate using centimeters and meters-Students will have to estimate measurements in centimeters and meters by looking at a picture and not having direct access to the object.
- Learn to estimate-Could be used as a remediation page for students to go over estimating using centimeters and meters.
- Let me Refer You To-Lesson from “Voyages” that helps students use referents to make better estimates.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Sammy said that 100 meters is the same as 1 centimeter. She estimated the length of her math book to be 12 meters long. Do you agree or disagree with Sammy’s estimate. Please justify your reasoning.
- Vrunda and Krupa are arguing over the best way to estimate the height of their younger sister, who is in kindergarten. Vrunda thinks they should use centimeters and Krupa thinks they should use meters. Who do you think is correct and why?
- Sharon wants to measure her pencil using a meter stick. Do you think that Sharon has selected a good unit of measurement? Explain why you agree or disagree with her.
Students are better able to…
- Estimate the length of objects because they have begun to develop an understanding of the structure of centimeters and meters. (SMP 7)
- Decide what the appropriate unit of measurement to use when estimating based on the relationship of the size of the unit to the length being measured. (SMP 5)
- Provide students a number of opportunities to estimate measurements and then confirm their accuracy. (SMP 7)
- Provide opportunities for students to explore the relationship between the size of the unit and the size of the object being measured. (SMP 5)
2nd / Global Concept 3 of 3 for this Unit of Study: Compare Metric Length
This GCG is focused on students comparing the lengths of measurements using a variety of strategies like drawing a quick picture and number lines. / Projected Time Allotment:
4 Days
Sample Essential Questions:
Day 1: How can drawing a quick picture help when solving problems about length?
Day 2: How can using a numberline help when solving problems about length?
Day 3: How do you find the difference between the lengths of two objects?
Day 4: How can using estimation ensure that your measurements are accurate?
Related Unit 10 Assessment: Go Math Ch. 9: #5, 6, 11, 14, 15, 16
Instructional Resources
Manipulatives:
- Centimeter ruler to create a referent or to measure 2 or more lengths to compare the lengths
- Meter stick to create a referent or to measure 2 or more lengths to compare the lengths
- Go Math Lesson 9.4-Essentials:Access Prior Knowledge TE p. 445, Try Another Problem TE p. 446 (use the guiding questions in the margin), Share and Show TE p. 447
- Go Math Lesson 9.7-Essentials:Access Prior Knowledge TE p. 457, Listen and Draw TE p. 457 (use the guiding questions in the margin),Model and Draw TE p. 458 (use the guiding questions in the margin), Problem Solving TE p. 460
- Problem Solving Metric-Word problems to draw a quick picture to solve problems about metric length
- Estimate Measure-Word problems to estimate answers to help students check reasonableness of their answers
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1 , 3)
- When in real life would you need to compare the lengths of objects?
- Cynthia estimated that her pencil was 10 meters long. When she measured it she thought her estimate made sense and that her answer was reasonable. Do you agree with Cynthia’s estimate and answer?
- What strategy makes the most sense to use when comparing lengths and why? (example student responses-quick picture, number line, number sentence, placing the objects next to each other)
Students are better able to…
- Use correct vocabulary when comparing lengths and estimating to check for the reasonableness of their answers. (SMP 6)
- Use a variety of tools like cm rulers, meter sticks, number lines, and quick pictures to solve math word problems. (SMP 5)
- Are using precise language like centimeters, meters, estimate, greater than, less than, and equal to. (SMP 6)
- Have tools like cm rulers and meter sticks readily available for students to use and we have modeled how to use number lines and quick pictures.