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Length Measurement
Students develop the fundamental skills of measuring length by exploring metric and customary measurement. They also develop an understanding of number lines and line plots.
Math
Unit 3
2nd Grade
Unit Summary
In Unit 3, 2nd grade students build on their understanding of length and measurement by learning about standard units of length measurement and tools used to measure the length of objects. In first grade, students measured indirectly and by iterating length units like paperclips and linking cubes. In this unit, students are introduced to standard metric and customary units including centimeters, meters, inches, and feet. Students use rulers to measure the length of objects on paper and in real life. They then connect this idea of measurement to the number line, exploring similarities and differences between rulers and number lines. Students represent whole numbers as lengths on a number line and use a number line to represent sums and differences within 100. With their growing understanding of measurement and number lines, students then display measurement data on line plots and answer questions about these line plots.
In Topic A, students are introduced to the standard unit of centimeters and use centimeter cubes to measure the length of objects. They then make their own centimeter ruler to help them understand this new measuring tool. Some important concepts around measuring with a ruler include:
- “length-unit iteration. E.g., not leaving space between successive length-units;
- accumulation of distance. Understanding that the counting “eight” when placing the last length-unit means the space covered by 8 length-units, rather then just the eighth length-unit.
- alignment of zero-point. Correct alignment of the zero-point on a ruler as the beginning of the total length, including the case in which the 0 of the ruler is not at the edge of the physical ruler;
- meaning of numerals on the ruler. The numerals indicate the number of length units so far;
- connecting measurement with physical units and with a ruler. Measuring by laying physical units end-to-end or iterating a physical unit and measuring with a ruler both focus on finding the total number of unit lengths” (Progressions, p. 96).
With this understanding of centimeters, students start to estimate length in centimeters and learn about another unit, meters. Students learn about different tools such as meter sticks and tape measures and learn to select appropriate tools to measure based on the object they are measuring. Students also use their knowledge of measurement to solve story problems involving metric length within 100, encountering two-step story problems for the first time.
After being introduced to metric units in Topic A, students encounter inches and feet as another unit of length measurement in Topic B. Students measure the lengths of objects to the nearest inch and draw lines of specified length. They use inch rulers and yardsticks as measuring tools to measure and estimate lengths in inches and in feet. Students also come to understand that when measuring an object with two different units of measure, the measurement value is relative to the size of the unit. For example, if a student were to measure a pencil in centimeters and then in inches, they would reason that the higher valued measurement is centimeters since a centimeter is smaller than an inch and it therefore takes more of them to measure the length of the same object. Similarly, to measure the length of the same pencil, they would need fewer inches than centimeters. In this topic, students also apply their problem solving skills to one-step and two-step story problems involving customary measurement.
In Topic C, the focus shifts to number lines. Now that students understand the distance between tick marks on a ruler represents a standard unit of measure, they can connect this idea to a number line, which is more abstract. Through this topic students represent lengths from zero on a number line and identify missing tick marks on a number line when counting by 1s, 5s, or 10s. Students will also estimate the value of a point on an open number line.
In Topic D, students put their knowledge of measurement and number lines together to generate measurement data and create line plots. Students measure the length of real-world objects and create line plots to show those lengths. They then answer questions based on the generated line plot.
The work of this unit connects to work students will do in Units 4 and 5 where they will use number lines to understand magnitude, proximity, and order of numbers as well as use them as a tool to represent addition and subtraction. In future grades students will continue to develop their understanding of measurement and number lines in various ways, including measuring more attributes such as area, volume, mass, etc. as well as understanding a fraction as a number on the number line 3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. or a rational number (such as -4) as a number on the number line 6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. , the foundation of which can be seen in this unit.
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Assessment
The following assessments accompany Unit 3.
Mid-Unit
Have students complete the Mid-Unit Assessment after Lesson 10.
Post-Unit
Use the resources below to assess student understanding of the unit content and action plan for future units.
Unit Prep
Intellectual Prep
Intellectual Prep for All Units
- Read and annotate "Unit Summary" and "Essential Understandings" portion of the unit plan.
- Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind.
- Take the Post-Unit Assessment.
Unit-Specific Intellectual Prep
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Read pp. 86-99 on Geometric Measurement in the Progressions.
Essential Understandings
- Standardized objects can be used to measure other objects by lining up the standardized unit from end to end with no gaps or overlaps, or with a standardized measuring tool (centimeter rulers and meter sticks) that include markings of equal length.
- When measuring, the longer the unit used to measure, the fewer units it takes to span the length of the object, and the shorter the unit used to measure, the more units it takes to span the same length.
- Rulers and number lines have similar features that include equally-spaced intervals and increasing count values from the starting point of zero to the end. Number lines can be used to represent values and as a model to add or subtract.
- Measurement data can be collected and represented in a line plot that can be used to visualize trends and answer questions. The numerical axis of a line plot is a segment of a number line.
Materials
- Centimeter cubes (20 per student or student pair if students are working in pairs)
- Paper clips (20 per student or student pair if students are working in pairs) — These should measure about 3 cm
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Shoe Print PDF cut out (1 for teacher only) — Print and cut out more than one shoe print if wanted
- Optional: Masking tape (1 roll for teacher only)
- Cardstock (1 strip per student) — Cut into 2 inch wide strips for rulers
- Ruler (1 per student and 1 for teacher) — Ensure the ruler has centimeters
- Centimeter Measuring Tape (1 per group)
- Meter stick (1 per group)
- Animal Prints Measuring Document (1 per student)
- Optional: Alternate Measurement Document (1 per student) — See Set Up for L5 AT2
- Number Line 0– 100 (1 per student) — These should be inserted into sheet protectors to be reused
- Sheet protectors (1 per student)
- Dry erase marker (1 per student)
- Optional: Objects of various length (8-10 items per group) — See Set Up for L5 AT2
Vocabulary and Models
Unit Vocabulary
centimeter
estimate
foot/feet
inch/inches
line plot
meter
number line
To see all the vocabulary for Unit 3, view our 2nd Grade Vocabulary Glossary.
Models
| Model | Example |
| number line | |
| line plot | |
| tape diagram | Example: Armando buys 16 peppers for a barbecue. 7 of the peppers are red and the rest of the peppers are orange. How many orange peppers did Armando buy? |
Unit Practice
Lesson Map
Topic A: Metric Measurement
Topic B: Customary Measurement
Topic C: Foundations of Number Lines
Topic D: Line Plots and Data
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
Measurement and Data
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2.MD.A.1 — Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
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2.MD.A.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.
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2.MD.A.3 — Estimate lengths using units of inches, feet, centimeters, and meters.
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2.MD.A.4 — Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
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2.MD.B.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.
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2.MD.B.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-number sums and differences within 100 on a number line diagram.
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2.MD.D.9 — Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
Foundational Standards
Measurement and Data
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1.MD.A.1
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1.MD.A.2
Operations and Algebraic Thinking
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1.OA.A.1
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1.OA.B.4
Future Standards
Measurement and Data
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3.MD.A.2
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3.MD.C.5
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3.MD.C.6
Number and Operations—Fractions
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3.NF.A.2
Operations and Algebraic Thinking
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3.OA.D.8
Standards for Mathematical Practice
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CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
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CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
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CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
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CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
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CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
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CCSS.MATH.PRACTICE.MP6 — Attend to precision.
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CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
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CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
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