LESSON 8.2 Hands On • Make and Use a Ruler · 1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length

LESSON AT A GLANCE

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547A Chapter 8

Hands On • Make and Use a Ruler

LESSON 8.2

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your OwnLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 537J.

FOCUS COHERENCE RIGOR

Learning ObjectiveMake an inch ruler and use it to measure the lengths of objects.

Language ObjectiveChild pairs rephrase what they learned about why using a ruler is similar to using a row of color tiles to measure length.

MaterialsMathBoard, color tiles, color pencils or crayons, paper strips (8 inches)

F C R Focus:Common Core State Standards2.MD.A.1 Measure the length of an object by selecting and using appro-priate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

F C R Coherence:Standards Across the GradesBefore1.MD.A.2 1.MD.A.1

Grade 22.MD.A.1

After3.MD.A.2

Why Teach This?Children may wonder why they are making a ruler when they could use one of the rulers in the classroom.

•By building a ruler, children deepen the connection between the measurement unit (inch tiles) they have been using and the spaces between the marks on the ruler. It builds concrete understanding of the abstract tool.

•As children use alternating colors to shade each inch, it helps them visualize the length of an inch.

•Children should be aware that when they are measuring an object in inches, they are using a unit of measure. A unit is something that does not change as it is used over and over. Explain the importance of writing the unit when expressing length. Merely writing a number, such as 5, has no meaning as a length if a unit label is not shown.

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Multimedia and Technology

ENGAGE1Daily Routines

Common CoreDaily Routines

Common Core

Why is using a ruler similar to using a row

of color tiles to measure length?

Lesson 8.2 547B

Literature ConnectionFrom the Grab-and-Go™ Differentiated Centers Kit

Children read about a walk in the woods and measuring the lengths of various things.

Nature Walk

Fluency BuilderPlace ValueName the place value of the digit 1 in each number.

1. 318 tens 7. 691 ones

2. 129 hundreds 8. 139 hundreds

3. 612 tens 9. 15 tens

4. 851 ones 10. 190 hundreds

5. 214 tens 11. 731 ones

6. 301 ones 12. 184 hundreds

with the Interactive Student Edition

Essential QuestionWhy is using a ruler similar to using a row of color tiles to measure length?

Making ConnectionsAsk children what they know about measuring in inches.

Why is it helpful to know the length of an object? Acceptreasonableanswers. Have you ever used a ruler before? Tell the class about your experience. Acceptreasonableanswers.

Learning ActivityWhat is the problem the children are trying to solve? Connect the story to the problem. Ask the following questions.

• Use your fingers to show about how long one inch is. Checkstudentwork.

• How is using tiles to find the length of an object helpful? How are they unhelpful? Sampleanswers:youcancountthemasyouplacethem;theyarenotnumberedanditisdifficulttoplacethemexactlysidetoside.

Literacy and MathematicsView the lesson opener with the children. Then, choose one or more of the following activities:

• Have children write a story about finding the lengths of several objects in their desk. At the end of class, have them use the rulers they made to measure the objects.

• Have children investigate the history of inch rulers in the library or online and share their findings with the class.

Problem of the Day 8.2Word of the Day inch

Choose three objects in the classroom. Measure their lengths in inches, using color tiles.

Encourage children to explain how they used the tiles to measure and to share their measurements.

Vocabulary• Interactive Student Edition• Multimedia Glossary e

Common Core Fluency Standard 2.OA.B.2

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EXPLORE2

Name

Make and Use a Ruler

Use a paper strip. Mark the sides of a color tile. Mark 6 tiles. Color each part.

Each part is about 1 inch —— long.

Line up the left edge of the bracelet with the first mark. Count the inches.

The bracelet is about 5 — inches long.

Measure the length with your ruler. Count the inches.

1.

about 4 — inches

2.

about 3 — inches

Lesson 8.2Reteach

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8-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

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about inches2about inches4

about inches5

about inch1

about inches4

Name

Writing and Reasoning If all of the tools were placed in a row, what would the total length be? Explain.

Measure the ToolsMeasure all of Carpenter Dan’s tools with your ruler. Below each tool, write its length. Circle the tools that are shorter than 5 inches.

Lesson 8.2Enrich

16 inches; 1 added the lengths of the tools.

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8-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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Listen and DrawListen and DrawHands

On

MATHEMATICAL PRACTICES 6MathTalk

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Chapter 8 fi ve hundred forty-seven 547

Make and Use a RulerEssential Question Why is using a ruler similar to using a row of color tiles to measure length?

4 inches

2 inches

3 inches

Use color tiles. Make the given length. Trace along the edge to show the length.

HOME CONNECTION • Your child used color tiles as 1-inch models to show different lengths. This activity helps to make inch units a more familiar concept.

HANDS ONLesson 8.2

Measurement and Data—2.MD.A.1

MATHEMATICAL PRACTICESMP5, MP6

Describe how you knew how many color tiles to use for each length.

Check children’s work.

Math Talk: Possible answer: I used the same number of tiles as the number of inches because 1 color tile is about 1 inch long.

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547 Chapter 8

Enrich 8.2Reteach 8.2

LESSON 8.2

Listen and Draw Materials color tilesDistribute color tiles to children.

Make a row of color tiles to show a length of 4 inches. Then trace along the edge of the row of tiles to show the length.

• How many color tiles do you need to show a length of 4 inches? Explain. Possible answer: Each tile is about 1 inch long, so I need 4 tiles.

If they have trouble keeping the tiles from moving, suggest that they work with a partner. One child can hold the tiles while the other child traces along the edge.• How do you know that you showed a

length of 2 inches in the middle section? Possible answer: I used two tiles. Each tile is about 1 inch long, so I know the mark is about 2 inches long.

• Why do you have to make sure that there are no gaps between the tiles you use to show a length? Possible answer: If there are gaps, the length will not be correct.

MathTalk MP6Attendtoprecision.

Use Math Talk to focus on children’s understanding of using tiles to show lengths.

ELL Strategy: Scaffold Language

Draw 3 pencils on the board.• Have children use their rulers to measure

the lengths.• Ask: How did you measure the pencils? • Encourage children to use this sentence

frame: First I _________. Then I___________. So, I know that the pencil is __________ inches long.

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. 1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

HandsOn

This lesson continues the process of conceptually bridging the measurement principles presented in grade 1. Additionally, children take what they have learned in the previous lesson and use that understanding to construct their own inch ruler— essentially transitioning from a concrete representation in Lesson 8.1 to a less concrete more abstract representation of linear measurement. At the conclusion of this lesson, children will have a stronger conceptual understanding of linear measurement and a deeper connection between the measurement process and the underlying principles for measurement.

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MeetingIndividualNeeds

DifferentiatedInstruction

Model and DrawModel and Draw

Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowMATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

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Use a color tile to make a ruler on a paper strip.Color 6 parts that are each about 1 inch long.

1.

about 4 — inches

2.

about 3 — inches

3.

about 5 — inches

How to use your ruler:Line up the left edge of an object with the first mark.



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Quick Check

If

Rt I 1

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Then

EXPLAIN3

COMMON ERRORS COMMON ERRORS Advanced LearnersAdvanced Learners

Lesson 8.2 548

a child misses the checked exercises

Differentiate Instruction with • Reteach8.2

• PersonalMathtrainer2.MD.1

• RtITier1Activity(online)

Model and DrawMATHEMATICAL PRACTICES

MP5Useappropriatetoolsstrategically.Distribute 8-inch paper strips and color tiles. Explain that the ruler they will make is a tool that can be used to measure lengths. Work through the model. Have children make alternating-color marks on their paper strips, marking on the sides of the tile. Have children save their rulers.• What happens if you line up the edge of an

object with the end of the ruler instead of the first mark?Themeasurementisnotcorrect.

Share and Show MATHBOARDMATHBOARD

Connect Exercises 1–3 to the learning model.• In Exercises 1–3, which object is longest?

thechainWhich is shortest? thestringExplain. Possibleanswer:Ilookatthelengthsininchesoratthepicturesoftheobjects.

Use the Checked Exercises for Quick Check.Children should use their MathBoard to show their answers to these exercises.

Error Childrenaligntheleftedgeofobjectswiththeedgeoftherulerinsteadoftheleftedgeofthefirstinch.

Example

SpringboardtoLearning Havechildrendrawaverticalarrowontheirrulerpointingtotheleftedgeofthefirstinchsectiontohelpthemrememberwheretostartmeasuring.

Visual / KinestheticIndividual / Partners

Materials paper rulers made in class using color tiles, small classroom objects

•Ask each child to measure the same classroom object with his or her paper ruler.

•Ask partners to compare their measurements. Ask: Are the measurements the same or different? Have children discuss possible reasons why they could be different.

•Ask children to estimate and then measure the length of another object in the classroom. Have partners compare their estimates and share their measurements.


DifferentiatedInstruction

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Chapter 8 • Lesson 2 fi ve hundred forty-nine 549


4.

about 3 — inches

5.

about 4 — inches

6.

about 6 — inches

7.

about 5 — inches

8.

about 2 — inches

On Your OwnOn Your Own


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About 1 inch long

About 3 inches long

About 5 inches long

4 ELABORATE

549 Chapter 8

On Your OwnIf a child answers the checked exercises correctly, assign Exercises 4–8.

DEEPER

MP3 Construct viable arguments and critique the reasoning of others. Continue to deepen children’s understanding of an inch by asking them to draw pictures of other classroom objects that are about 1 inch long, about 3 inches long, and about 5 inches long.

Children can check the lengths of their drawings by measuring them with their rulers.


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Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

MathMath Problem Solving • ApplicationsProblem Solving • Applications

MATHEMATICAL PRACTICES COMMUNICATE • PERSEVERE • CONSTRUCT ARGUMENTS

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about — inches

9. SMARTER Work with a classmate. Use both of your rulers to measure the length of a bulletin board or a window. What is the length?

TAKE HOME ACTIVITY • Choose one object in this lesson. Have your child find objects that are longer, about the same length, and shorter.

10. MATHEMATICAL

PRACTICE 6 Explain Describe what you did in Exercise 9. How did you measure a length that is longer than your rulers?

11. SMARTER Measure the length of the yarn with your ruler. Does the sentence describe the yarn. Choose Yes or No.

The yarn is 2 inches long. Yes No

The yarn is 3 inches long. Yes No

The yarn is less than 3 inches. Yes No

The yarn is longer than 2 inches. Yes No

Answers may vary. Check for understanding of continuing to count

spaces/inches as their rulers are moved from section to section of

the length that they are measuring.



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EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

MATHEMATICAL PRACTICES

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

Lesson 8.2 550

Essential QuestionReflect Using the Language Objective Have child pairs rephrase what they learned to answer the Essential Question.Why is using a ruler similar to using a row of color tiles to measure length? Possible answer: I can find the number of inches being measured with the inch sections on a ruler or with the row of color tiles.

Math Journal Math

Would you rather use color tiles or your ruler to measure the length of an object? Explain your choice.

SMARTER

Exercise 9 requires children to find a way to measure an object that is longer than the length of one ruler. Make sure children do not overlap their rulers. Have them hold the rulers so that the inch marks are along the top edge as they use them.

ActivitiesSuper Subs

Children complete orange Activity Card 17 by comparing the lengths of everyday

objects using paper clips.

LiteratureNature Walk

Children read about a walk in the woods and measuring the lengths of various things.

MP6 Attend to precision. Exercise 10 requires students to explain the method they used in Exercise 9. Ask questions to assist students in verbalizing the work they did.

SMARTER

Children will need to use an inch ruler to measure the length of the piece of yarn. They should remember to align one end of the yarn with the 0 on the ruler and then read the mark on the ruler closest to the other end of the yarn. Children who select incorrect answers likely did not correctly align the ruler.

Math on the Spot Video TutorUse this video to help children model and solve this type of Think Smarter problem.


Meeting Individual Needs

Problem Solving • ThinkingProblem Solving • Applications

Problem SolvingProblem Solving

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Practice and Homework

COMMON CORE STANDARD—2.MD.A.1 Measure and estimate lengths in standard units.

Lesson 8.2

Chapter 8 fi ve hundred fi fty-one 551

Make and Use a Ruler


1.

about 5 — inches

3.

about 4 — inches

2.

about 2 — inches

4. Use your ruler. Measure the width of this page in inches.

about 8 _ inches

5. Math Would you rather use color tiles or your ruler to measure the length of an object? Explain your choice.



Practice and HomeworkUse the Practice and Homework pages to provide children with more practice of the concepts and skills presented in this lesson. Children master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine children’s understanding of content for this lesson. Encourage children to use their Math Journals to record their answers.

551 Chapter 8

COMMON CORECOMMCOMMCOMMON CON CON COREOREOR

PROFESSIONALDEVELOPMENT Math Talk in Action

Ben is learning about rulers. In this discussion, his teacher talks to him about what rulers are used for and where he may have seen them before.

Teacher: Look at the ruler you made. How can you describe it?

Ben: It has straight edges and marks showing inches.

Teacher: What can you use a ruler for?

Ben: I can use a ruler to measure the length of an object or draw a picture of an object that has a certain length.

Teacher: What else have you seen or used that is like the ruler you made?

Ben: a yardstick, an inch ruler, a measuring tape

Teacher: Suppose I have a piece of string and measure it with my pencil. Will we know the length of the string in inches?

Ben: No, because we do not know how long the pencil is in inches.

Teacher: Right! Your ruler has inches marked on it, so you could use it to find the length of the string in inches.

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Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Spiral Review (2.OA.C.4, 2.NBT.B.7, 2.MD.C.7, 2.MD.C.8)

2. What time is shown on this clock?

3 _ : 45 _

3. What is the total value of these coins?

60 _ cents

4. The first group collected 238 cans. The second group collected 345 cans. How many cans did the two groups collect?

5. There are 2 children in each row. How many children are in 5 rows?

10 _ children

1. Use your ruler. What is the length of this ribbon?

about 4 _ inches

Lesson Check (2.MD.A.1)

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Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage children in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

Lesson 8.2 552

Documents

LESSON 8.2 Hands On • Make and Use a Ruler · 1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length