# Measurement

Students develop the foundational skills of measuring length by exploring metric measurement and develop the understanding of number lines and measurement data with line plots.

Math

Unit 3

## Unit Summary

In Unit 3, 2nd grade students build on their understanding of length and measurement by learning about standard units of measurement and tools used to measure objects. In first grade, students measured indirectly and by iterating length units. In this unit, students are introduced to the metric units centimeters and meters. Students use rulers to measure 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 they use a number line to represent sums and differences within 100. Given 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 centimeters by using a one's base ten block which measures 1 centimeter. They use centimeter cubes to iterate a centimeter unit, building on their Grade 1 work and extending this to make their own centimeter ruler (2.MD.A.1). As they explore measuring with standard measuring tools they come to understand that when measuring they start at zero and measure an object to its endpoint on a ruler. They also come to understand that the distance between each tick mark on a ruler represents a standard unit, so in the case of a centimeter ruler, the distance between each tick mark represents a centimeter.

As students develop their measuring skills they use benchmarks to estimate and check their measurements with centimeter rulers (2.MD.A.3). They further expand their measurement knowledge by learning about different tools such as meter sticks and tape measures to measure different objects and learn to select appropriate tool to measure based on the object they are measuring. As their work in Topic A continues, students learn how to measure and compare objects of different sizes and express the difference in terms of standard unit of measure (2.MD.A.4). Instead of simply recognizing an object as longer or shorter, students represent the difference in terms of centimeters or meters. Students also use their knowledge of measurement to solve word problems involving length within 100 (2.MD.B.5).

In Topic B, the focus shifts to their understanding of number lines. Now that students understand the distance between tick marks on a ruler represents a standard unit of measure, they can equate that to the more abstract version on a number line. Through this topic students represent lengths from zero on a number line and based on intervals are able to identify missing tick marks on a number line when counting by 1s, 5s, or 10s (2.MD.B.6). Students are also able to use given tick marks to estimate whole numbers on a number line. The work of this topic builds on their skills of counting within 1,000 (2.NBT.A.2).

In Topic C, students put their knowledge of measurement and number lines together to generate measurement data and create line plots. Students measure real world objects and create line plots to show the measurements of objects to the nearest whole unit (2.MD.D.9). Using a horizontal scale students mark x’s to represent each object that measures that same length and 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 continue to use number lines to place and order numbers as well as use them as a tool to represent addition and subtraction. In Unit 6 students will build on their measurement skills as they apply them to customary units. They will further build their understanding of measurement and the understanding that the length of the unit affects the measurement of an object in situations where you are measuring an object using two different standard units of measure (2.MD.A.2).

In future grades students will continue to iterate on their understandings of measurement and number lines as they expand to looking at non-whole units of measure and expand their number lines to negative numbers, the core foundations of which can be seen in the learnings in this unit.

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## Assessment

The following assessments accompany Unit 3.

### Mid-Unit

Have students complete the Mid-Unit Assessment.

### Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Mid-Unit Assessments and Answer Keys to help assess progress with unit content and inform your planning.

## 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

• Read pp. 86-991 on Geometric Measurement in the Progressions.

• Read the following table that includes models used in this unit.

 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?

### 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 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.
• When measuring two different objects, students can compare the relative sizes by expressing the difference in length using a standard unit of measure.
• 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 locate 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.
•

### Vocabulary

benchmark number

centimeter

line plot

measurement data

meter

number line

To see all the vocabulary for Unit 3, view our 2nd Grade Vocabulary Glossary.

### 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
• 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

## Unit Practice

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

## Lesson Map

Topic A: Metric Measurement

Topic B: Foundations of Number Lines

Topic C: Line Plots and Data

## Common Core Standards

Key

Major Cluster

Supporting Cluster

### Core Standards

#### Measurement and Data

• 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.
• 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.
• 2.MD.A.3 — Estimate lengths using units of inches, feet, centimeters, and meters.
• 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.
• 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.
• 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.
• 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.

• 1.MD.A.1
• 1.MD.A.2

• 1.OA.A.1

• 3.MD.A.2
• 3.MD.C.5
• 3.MD.C.6

• 3.NF.A.2

• 3.OA.D.8

### Standards for Mathematical Practice

• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

• CCSS.MATH.PRACTICE.MP6 — Attend to precision.

• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Unit 2

Unit 4

Place Value with Numbers to 1,000 & Money

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