Unit 3: Understanding Measurement, Length, and Time

All the resources on this page come from the GADOE Framework 2nd Grade Unit 3 Overview. Reviewing this information before or during planning can help ensure your instruction is aligned with the standards and is at the depth expected.

Unit 3 Overview

In this unit students will:

• Know the following customary units for measuring length: inch, foot, yard

• Recognize the need for standard units of measure

• Use rulers and other measurement tools with the understanding that linear measure involves an iteration of units.

• Recognize that the smaller the unit is, the more iterations needed to cover a given length.

• Know the following metric units for measuring length: centimeter and meter

• Compare the relationship of one unit of measurement to another, within the same system

• Check by measuring to determine if estimates are accurate for length

• Determine the appropriate tool for measuring length: inch ruler and yardstick, centimeter ruler, and meter stick

• Tell time to the nearest five minutes (This should be part of your daily routine for the remainder of the year through Math Maintenance. For more information see the Grade Level Overview.)

• Understand the relationship of hours and days • Understand the importance and usefulness of reasonable estimations

• Connect the whole-number units on rulers, yardsticks, meter sticks and measuring tapes to number lines showing whole-number units starting at 0

• Use these measuring tools to model different representations for whole-number sums and differences less than or equal to 100 using the numbers 0 to 100.

• Be able to represent the length of several objects by making a line plot

Second graders are transitioning from measuring lengths with informal units to measuring with these standard units: inches, feet, centimeters, and meters. The measure of length is a count of how many units are needed to match the length of the object or distance being measured. Students have to understand what a length unit is and how it is used to find a measurement. They need many experiences measuring lengths with appropriate tools so they can become very familiar with the standard units and estimate lengths. Use language that reflects the approximate nature of measurement, such as the length of the room is about 26 feet.

Chapter 8 in Teaching Student Centered Mathematics K-3 by John A. Van de Walle focuses on measurement. Revisiting/Reading this chapter provides information about measurement and how young children learn measurement skills.

Have students measure the same length with different-sized units then discuss what they noticed. Ask questions to guide the discussion so students will see the relationship between the size of the units and measurement, i.e. the measurement made with the smaller unit is more than the measurement made with the larger unit and vice versa.

Insist that students always estimate lengths before the measure. Estimation helps them focus on the attribute to be measured, the length units, and the process. After they find measurements, have students discuss the estimates, their procedures for finding the measurements and the differences between their estimates and the measurements.

NUMBER TALKS

Between 5 and 15 minutes each day should be dedicated to “Number Talks” in order to build students’ mental math capabilities and reasoning skills. Sherry Parrish’s book Number Talks provides examples of K-5 number talks. The following video clip from Math Solutions is an excellent example of a number talk in action. https://www.teachingchannel.org/video/numbertalk-math-lesson-2nd-grade

During the Number Talk, the teacher is not the definitive authority. The teacher is the facilitator and is listening for and building on the students’ natural mathematical thinking. The teacher writes a problem horizontally on the board in whole group or a small setting. The students mentally solve the problem and share with the whole group how they derived the answer. They must justify and defend their reasoning. The teacher simply records the students’ thinking and poses extended questions to draw out deeper understanding for all.

The effectiveness of Numbers Talks depends on the routines and environment that is established by the teacher. Students must be given time to think quietly without pressure from their peers. To develop this, the teacher should establish a signal, other than a raised hand, of some sort to identify that one has a strategy to share. One way to do this is to place a finger on their chest indicating that they have one strategy to share. If they have two strategies to share, they place out two fingers on their chest and so on.

Number Talk problem possible student responses:

Number talks often have a focus strategy such as “making tens” or “compensation.” Providing students with a string of related problems, allows students to apply a strategy from a previous problem to subsequent problems. Some units lend themselves well to certain Number Talk topics. For example, the place value unit may coordinate well with the Number Talk strategy of “making ten.” For additional information on Number Talks, see the Grade Level Overview.

STANDARDS FOR MATHEMATICAL PRACTICE

This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.

1. Make sense of problems and persevere in solving them. Students will determine what unit is best for measuring an item and follow through to find the exact measurement.

2. Reason abstractly and quantitatively. Students will make correlations between comparing an item with two forms of measurements.

3. Construct viable arguments and critique the reasoning of others. Students will compare and contrast measurements of each other’s objects. Students will share estimates and discuss whether or not the estimates are reasonable based on their knowledge of measurement.

4. Model with mathematics. Students will construct and use a ruler to measure different objects.

5. Use appropriate tools strategically. Students will estimate measurements and decide the appropriate unit for getting the exact measurement.

6. Attend to precision. Students understand that a ruler is a representation of units (not simply counting marks) and focus on the spaces between the marks for measurement.

7. Look for and make use of structure. Students will use skip counting by 5’s to help tell time.

8. Look for and express regularity in repeated reasoning. Students will continue to use a number line and skip counting to help with telling time to the nearest 5 or 10 minutes and for finding the hour.

STANDARDS FOR MATHEMATICAL CONTENT

Measure and estimate lengths in standard units.
MGSE2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

MGSE2.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. Understand the relative size of units in different systems of measurement. For example, an inch is longer than a centimeter. (Students are not expected to convert between systems of measurement.)

MGSE2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

MGSE2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard-length unit.

Relate addition and subtraction to length.
MGSE2.MD.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.

MGSE2.MD.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.

Work with time and money.
MGSE2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Represent and Interpret Data.
MGSE2.MD.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.

MGSE2.MD.10 Draw a picture graph and a bar graph (with single- unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems

BIG IDEAS

By the conclusion of this unit, students should be able to demonstrate the following:

• Standard units for measuring length (inch, foot, yard, centimeter, and meter).

• Measuring items with two different units makes it possible to determine the relationship of the two different units.

• Estimated lengths should be reasonably close to the actual measurement.

• Appropriate tools should be used to measure length.

• Tell time to nearest 5 minutes and using a.m. and p.m. using both analog and digital clocks.

• Create, read, and interpret a line plot graph.

• Use a number line to help solve problems using addition and subtraction.

• Use addition and subtraction within 100 to solve word problems about length.

• Represent lengths on a number line.

• Understand measurement is used to quantify a consistent duration and/or distance.

• The length of objects can be measured using customary units (inch, foot, and yard).

• The length of objects can be measured using Metric units (centimeter, meter).

• An inch or centimeter would be an appropriate unit to measure small items such as the length of a pencil or crayon.

• A yard or meter would be an appropriate unit to use when measuring the length of a large item, such as the length of the classroom or hallway.

• A ruler, yardstick, and a meter stick are special types of number lines (they show fractions, too). • A ruler, yardstick, and a meter stick are tools used for linear measurement.

• Line plots are useful tools for collecting data because they show the number of things along a numeric scale.

• A number line has evenly spaced points corresponding to numbers.

ESSENTIAL QUESTIONS

• How can we decide on appropriate units of measurement (i.e. inch, foot, yard, centimeter, meter, seconds, minutes, hours, days)?

• Why is it important for us to know how to measure different objects using different tools of measurement?

• How can we tell if an estimate is reasonable?

• How does using a different unit change our measurement?

• Why do we need to be able to estimate a measurement or value?

• Why is it important for us to know how to measure different units of measurement?

• How does a line plot help me share my data?

• How can using a number line help us when we are solving math problems?

• Why is it important to be able to organize and graph data?

CONCEPTS/SKILLS TO MAINTAIN

Fluency: Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Fluent problem solving does not necessarily mean solving problems within a certain time limit, though there are reasonable limits on how long computation should take. Fluency is based on a deep understanding of quantity and number.

Deep Understanding: Teachers teach more than simply “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives. Therefore, students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of foundational mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.

Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency and automaticity. Fluency implies a much richer kind of mathematical knowledge and experience.

Number Sense: Students consider the context of a problem, look at the numbers in a problem, and make a decision about which strategy would be most efficient in each particular problem. Number sense is not a deep understanding of a single strategy, but rather the ability to think flexibly between varieties of strategies in context.

Fluent students:

• Flexibly use a combination of deep understanding, number sense, and memorization.

• Are fluent in the necessary baseline functions in mathematics so that they are able to spend their thinking and processing time unpacking problems and making meaning from them.

• Are able to articulate their reasoning.

• Find solutions through a number of different paths.

For more about fluency, see: http://www.youcubed.org/wp-content/uploads/2015/03/FluencyWithoutFear-2015.pdf and https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/nctm-timedtests.pdf

Skills from 1st Grade:
It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

• Developing understanding of linear measurement and measuring lengths as iterating length units; and

• Reasoning about attributes of, and composing and decomposing geometric shapes.

Second Grade Year Long Concepts:
Organizing and graphing data as stated in MD.10 should be incorporated in activities throughout the year. Students should be able to draw a picture graph and a bar graph to represent a data set with up to four categories as well as solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Specifically, it is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

• Telling time to the nearest hours and half-hours

• Measurement – estimating, comparing, and ordering

• Basic geometric figures and spatial relationships

STRATEGIES FOR TEACHING AND LEARNING
(Information adapted from North Carolina DPI Instructional Support Tools)

Measure and estimate lengths in standard units.
MGSE2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

MGSE2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

MGSE2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Instructional Strategies
It is important to note that in the Georgia Standards of Excellence, nonstandard measurement is explored after students have explored standard measurement. See below, from the work of Doug Clements:

Another important issue concerns the use of standard or nonstandard units of length. Many curricula or other instructional guides advise a sequence of instruction in which students compare lengths, measure with nonstandard units (e.g., paper clips), incorporate the use of manipulative standard units (e.g., inch cubes), and measure with a ruler. This approach is probably intended to help students see the need for standardization. However, the use of a variety of different length units, before students understand the concepts, procedures, and usefulness of measurement, may actually deter students’ development. Instead, students might learn to measure correctly with standard units, and even learn to use rulers, before they can successfully use nonstandard units and understand relationships between different units of measurement.

Note that this trajectory of learning about measurement is one of the few areas in which Van de Walle and the Georgia Standards of Excellence do not align.

From the K-5 Measurement Progressions:

Second graders begin to use tools to measure with these standard units: inches, feet, centimeters, and meters. The measure of length is a count of how many units are needed to match the length of the object or distance being measured. Students have to understand what a length unit is and how it is used to find a measurement. They need many experiences measuring lengths with appropriate tools so they can become very familiar with the standard units and estimate lengths. Use language that reflects the approximate nature of measurement, such as the length of the room is about 26 feet.

In order for students to have a better understanding of the relationships between units, they need to use measuring devices in class. The number of units needs to relate to the size of the unit. They need to discover that there are 12 inches in 1 foot and 3 feet in 1 yard. Allow students to use rulers and yardsticks to discover these relationships among these units of measurements. Using 12-inch rulers and yardstick, students can see that three of the 12-inch rulers, which is the same as 3 feet since each ruler is 1 foot in length, are equivalent to one yardstick.

Have students record the relationships in a two-column table or t-charts. A similar strategy can be used with rulers marked with centimeters and a meter stick to discover the relationships between centimeters and meters. Present word problems as a source of students’ understanding of the relationships units of measurement. Have students measure the same length with different-sized units then discuss what they noticed. Ask questions to guide the discussion so students will see the relationship between the size of the units and measurement, i.e. the measurement made with the smaller unit is more than the measurement made with the larger unit and vice versa.

Insist that students always estimate lengths before they measure. Estimation helps them focus on the attribute to be measured, the length units, and the process. After they find measurements, have students discuss the estimates, their procedures for finding the measurements and the differences between their estimates and the measurements.

Instructional Strategies
Connect the whole-number units on rulers, yardsticks, meter sticks and measuring tapes to number lines showing whole-number units starting at 0. Use these measuring tools to model different representations for whole-number sums and differences less than or equal to 100 using the numbers 0 to 100.

Use the meter stick to view units of ten (10 cm) and hundred (100 cm), and to skip count by 5s and 10s.

Provide one- and two-step word problems that include different lengths measured with the same unit (inches, feet, centimeters, and meters). Students add and subtract within 100 to solve problems for these situations: adding to, taking from, putting together, taking apart, and comparing, and with unknowns in all positions. Students use drawings and write equations with a symbol for the unknown to solve the problems.

Have students represent their addition and subtraction within 100 on a number line. They can use notebook or grid paper to make their own number lines. First, they mark and label a line on paper with whole-number units that are equally spaced and relevant to the addition or subtraction problem. Then they show the addition or subtraction using curved lines segments above the number line and between the numbers marked on the number line. For 49 + 5, they start at 49 on the line and draw a curve to 50, then continue drawing curves to 54. Drawing the curves or making the ―hops‖ between the numbers will help students focus on a space as the length of a unit and the sum or difference as a length.

Work with time and money.
MGSE2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Instructional Strategies
Second graders expand their work with telling time from analog and digital clocks to the nearest hour or half-hour in Grade 1 to telling time to the nearest five minutes using a.m. and p.m.

As students continue to practice telling time (orally and in writing) using both analog and digital clocks they should also be encouraged to use the terms a.m. and p.m. Teachers should help students make the connection between skip counting by 5s (MGSE2.NBT.2) and telling time on an analog clock.

MGSE2.MD.10 Draw a picture graph and a bar graph (with single- unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Instructional Strategies

Standard MGSE2.MD.9 calls for students to represent the length of several objects by making a line plot. Students should round their lengths to the nearest whole unit.

Example: Measure objects in your desk to the nearest inch, display data collected on a line plot. How many objects measured 2 inches? 3 inches? Which length had the most number of objects? How do you know?

SELECTED TERMS AND SYMBOLS

The following terms and symbols are not an inclusive list and should not be taught in isolation. Instructors should pay particular attention to them and how their students are able to explain and apply them (i.e. students should not be told to memorize these terms).

Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

For specific definitions, please reference the Georgia Standards of Excellence Glossary. • analog clock • centimeter • digital clock • estimate • foot • hour • inch • line plot • measuring tape • meter • meter stick • minute • number line diagram • ruler • standard unit • yardstick

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