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176 Unit 3 Linear Measures and Area

Advance PreparationCut the rulers from the bottom of the transparency of Math Masters, page 65. You may wish to precut the rulers

on Math Masters, page 413 for children who have difficulty cutting accurately.

Teacher’s Reference Manual, Grades 1–3 pp. 157, 165–167

Key Concepts and Skills• Name the marks on a ruler that divide

inches into halves, fourths, and eighths.  

[Number and Numeration Goal 2]

• Use a ruler to find equivalent halves, fourths,

and eighths. [Number and Numeration Goal 5]

• Select measuring tools and appropriate

units for particular measuring tasks.

Measure to the nearest inch, 1

_ 2 inch,

1

_ 4 inch,

centimeter, 1

_ 2 centimeter, and millimeter. 

[Measurement and Reference Frames Goal 1]

Key ActivitiesChildren select measuring tools and choose

appropriate units of length. They measure line

segments to the nearest inch, 1

_ 2 inch,

1

_ 4 inch,

centimeter, 1

_ 2 centimeter, and millimeter.

Ongoing Assessment: Informing Instruction See page 179.

Ongoing Assessment: Recognizing Student Achievement Use journal page 58. [Measurement and Reference Frames Goal 1]

Key Vocabularyinch (in.) � line segment � centimeter (cm) �

millimeter (mm)

MaterialsMath Journal 1, p. 58

Student Reference Book, pp. 137 –139, 143,

and 144

Home Link 3 �1

Math Masters, p. 413

transparency of Math Masters, p. 65 �

scissors � red crayon (optional)

Playing Subtraction Top-ItStudent Reference Book, pp. 310

and 311

per group: 4 each of number cards

0–10 and 1 each of number cards

11–20 (from the Everything Math

Deck, if available)

Children develop automaticity with

basic subtraction facts.

Math Boxes 3�2Math Journal 1, p. 59

Children practice and maintain skills

through Math Box problems.

Home Link 3�2Math Masters, p. 66

Children practice and maintain skills

through Home Link activities.

READINESS

Making a Number Linesheet of paper

Children create number lines and label with

whole numbers and fractions.

ENRICHMENTBeginning with a Nonzero Mark on a RulerMath Journal 1, p. 58

Math Masters, p. 413 (Ruler E)

Children measure line segments from a

nonzero mark on a ruler.

ELL SUPPORTBuilding a Math Word Bank Differentiation Handbook, p. 133

Children add the terms inch, centimeter, and

millimeter to their Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Measuring with a RulerObjective To guide children as they measure line segments

to the nearest inch, 1

_ 2 inch,

1

_ 4 inch, centimeter,

1

_ 2 centimeter,

and millimeter.

t

�������

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Name Date Time

Rulers

10

23

45

67

8Inches (in.)

Ruler A

10

23

45

67

8Inches (in.)

Ruler B

12

10

23

45

67

8Inches (in.)

Ruler C

2412

3414

Centim

eters (cm)

Ruler D

130

12

34

56

78

911

1012

1416

1517

1819

20

65

78

910

1112

13Inches (in.)

Ruler E

Math Masters, p. 413

Teaching Aid Master

Lesson 3�2 177

16

29

24

30

40

30

119

60

59

Getting Started

Mental Math and ReflexesWrite the following multiple-addend problems on the board. Encourage children to look for combinations that make the addition easier.

7 + 3 + 6 = 15 + 9 + 5 + 1 = 25 + 19 + 75 =

12 + 8 + 9 = 11 + 4 + 9 + 16 = 16 + 19 + 24 + 1 =

15 + 5 + 4 = 21 + 3 + 0 + 6 = 16 + 18 + 24 + 1 =

Math Message Suppose you and your classmates are going to have a watermelon seed-spitting contest. How would you measure the distance the seeds travel? How would you pick the winner? Discuss with a partner.

Home Link 3�1 Follow-UpChildren show and discuss their lists and pictures of items with measurements. Remind children to continue to look at home for pictures that show measurements.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Have children describe what they would do to measure the distances in a seed-spitting contest. Which measuring tool would they use to find the distances? Which unit of length would they choose? Probably inch or centimeter; someone might suggest fractions of an inch or millimeters. What other units of length do children know? Foot, yard, mile, meter, kilometer, and so on Why are larger units not as appropriate for measuring the distances in the contest? With larger units, it is harder to get precise measurements of shorter distances.

� Reading a Ruler and WHOLE-CLASS ACTIVITY

Measuring to the Nearest Inch, 1 _ 2 Inch, and 1 _ 4 Inch(Math Journal 1, p. 58; Math Masters, pp. 65 and 413; Student Reference

Book, pp. 143 and 144)

If children are fairly skilled at measuring with a ruler, you may want to omit parts of the following activity.

Have children carefully cut out Rulers A, B, C, D, and E from Math Masters, page 413. Set aside Ruler D until later in the lesson. Ruler E is used in the optional Part 3 Enrichment activity. Point out that Rulers A, B, and C are divided into inches. The inch, abbreviated in., is a standard unit of length in the U.S. customary system. Review reading an inch ruler with the class.

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178 Unit 3 Linear Measures and Area

Name Date Time

Measure the line segments with the rulers.

1. Use Ruler A to measure to the nearest inch (in.).

2. Use Ruler B to measure to the nearest �12� inch (in.).

3. Use Ruler C to measure to the nearest �14� inch (in.).

1 2 3 4 5 6

Inches (in.) Ruler C

02412

14

34

10 2 3 4 5 6

Inches (in.) Ruler B

12

10 2 3 4 5 6

Inches (in.) Ruler A

LESSON

3�2 Measuring Line Segments

3 in.5 in.4 in.

4�12� in.

2 in.3�

12� in.

1�14� in.

3�12� in.

4�34� in.

Math Masters, p. 65

Teaching Master

Adjusting the Activity

Measuring Line SegmentsLESSON

3 � 2

Date Time

Ru

ler A

about in.

about in.

about in.

4 5 3

Ru

ler D

about cm

about cm

about cm

9 13 8

Ru

ler B

about in.

about in.

about in.

2 4� 12 �

Ru

ler D

about cm

about cm

about cm

9 11

Ru

ler C

about in.

about in.

about in.

Ru

ler D

aboutm

m

about m

m

about m

m

11987 34

1.

Use R

uler A to measure to the nearest inch (in.).

Use R

uler D to m

easure to the nearest centimeter (cm

).

2.

Use R

uler B to measure to the nearest � 12 �inch (in.).

Use R

uler D to m

easure to the nearest � 12 �centimeter (cm

).

3.

Use R

uler C to m

easure to the nearest� 14 �inch (in.).

Use R

uler D to m

easure to the nearest millim

eter (mm

).

5� 12 �

3� 12 �

3� 12 �

1� 14 �

4� 34 �

�

Try This

Math Journal 1, p. 58

Student Page

NOTE The measures of the line segments

on journal page 58 are not exactly whole

inches, 1

_ 2 inches,

1

_ 4 inches, whole centimeters,

or 1

_ 2 centimeters. The focus of this lesson is

to measure to the nearest or closest inch,

1

_ 2 inch,

1

_ 4 inch, centimeter,

1

_ 2 centimeter,

and millimeter.

Look at Ruler A. Each inch is divided into 2 equal parts by a mark that is halfway between the inch marks. These 1 _ 2 -inch marks help when measuring to the nearest inch. Guide children to think of 1 _ 2 inch as one out of two equal parts of the inch. Using the transparency of Ruler A, have a volunteer measure a line segment to the nearest inch on the transparency of Math Masters, page 65. These line segments are the same length as those on journal page 58. Point out that the ruler and line segments on the screen are larger than real life. Ask children how the inches on the screen are different from the inches on their rulers. Tell them that the screen inch is at a different scale than a real inch and that they will explore more about scale at a later time.

Review the following ideas:

� Line up one edge of the line segment with the 0-mark on the ruler.

� Caution children that sometimes the 0-mark is the edge of the ruler, and sometimes the 0-mark is away from the edge.

� Note that Rulers A, B, and C have an arrow at the 0-mark to help children line up one edge of the line segment.

� Remind children to use such phrases as about inches and between and inches to indicate that measurements are not exact.

Have children color the 0-mark with a red crayon to highlight it.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Children measure the first line segment in Problem 1 on journal page 58 to the nearest inch. When most children have finished, have them share their measurements. When they agree that the measurement is about 3 inches, have children continue measuring the other line segments in Problem 1. Circulate and assist as needed.

Look at Ruler B. Ask children to identify the 1 _ 2 -inch marks and to write the fraction 1 _ 2 below each of those marks. The first one is done for them.

● What is the distance from the 0-inch mark to the 1 _ 2 -inch mark? 1 _ 2 inch

● What is the distance from that 1 _ 2 -inch mark to the 1-inch mark? 1 _ 2 inch

Point out that each 1 _ 2 -inch distance on Ruler B is divided into two equal parts.

● How many equal parts does each inch have on the ruler? 4 equal parts Think of 1 _ 4 as one out of four equal parts of the inch.

Tell children that the 1 _ 4 -inch marks help when measuring to the nearest 1 _ 2 inch.

ELL

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Lesson 3�2 179

NOTE These ruler activities can be

summarized by reading Student Reference

Book, pages 143 and 144 with the class.

The second example on page 144 can be

used to clarify the skills needed to use

Ruler C correctly.

Links to the FutureProblem 3 on Math Journal 1, page 58 provides

an opportunity for children to begin working

with 1

_ 4 inches and millimeters when measuring.

Children use rulers marked with 1

_ 8 inches to

measure to the nearest 1

_ 4 inch. They use rulers

marked with millimeters to measure to the

nearest millimeter. Measuring to the nearest

1

_ 4 inch is a Grade 4 Goal. Measuring to the

nearest millimeter is a Grade 5 Goal.

Measurement

Find the length of the pencil to the nearest quarter-inch.

The quarter-inch marks between 3 and 4 arewritten below the ruler. The tip of the pencil isclosest to 33–

4.

The pencil is 3�34� inches long, to the nearest quarter-inch.

There are times when you do not need an exactmeasurement. Measuring to “the nearest �

12� inch”

or “the nearest �14� inch” may be good enough.

What is the length of the eraser?

Always line up the end of the object with the 0-mark of the ruler.

If the 0-mark is at the end of a ruler, the number 0 may not be printed on that ruler.

There are 2 small spaces between the 2-inch mark and the end of theeraser. Each small space is 1–

16 inch long.

So the eraser is 2 2��16 inches long. Because 2��16 � �

18�, the

length can be written as 2 2��16 in., or 2 �

18� in.

Student Reference Book, p. 144

Student Page

Adjusting the Activity

Children should measure the first line segment in Problem 2 to the nearest 1 _ 2 inch while a volunteer demonstrates how to make the measurement on the overhead with the transparency of Ruler B. When everyone agrees that the measurement is about 4 1 _ 2 inches, children should measure the other line segments.

Ongoing Assessment: Informing Instruction

Watch for children who have difficulty understanding that a measurement to the

nearest 1

_ 2 inch can be at a whole-inch mark. Discuss the possibility that when

measuring to the nearest 1

_ 2 inch, some lines may be a whole number of inches.

Look at Ruler C. Ask children to identify the 1 _ 4 -inch marks and to read the fractions 1 _ 4 , 2 _ 4 or 1 _ 2 , 3 _ 4 , and 1 (or 4 _ 4 ) below those marks between the 0-inch and 1-inch marks. Count the labeled marks in an inch space in unison.

● What is the distance between each of the labeled marks from the 0-inch mark to the 1-inch mark? 1 _ 4 inch

Point out that each 1 _ 4 -inch distance is divided into two equal parts. Those marks help when measuring to the nearest 1 _ 4 inch.

Repeat the procedure for measuring the line segments in Try This Problem 3 to the nearest 1 _

4 inch.

Have children name the marks that divide the 1

_ 4 -inch spaces in half on

ruler C. 1

_ 8 inch Ask how many equal parts these marks divide each inch into.

8 equal parts Explain that each of the marks between consecutive whole inches

names 1

_ 8 of an inch. Ask children to name the marks that have more than one

name. 2

_ 8 and

1

_ 4 ;

4

_ 8 ,

2

_ 4 , and

1

_ 2 ;

6

_ 8 and

3

_ 4 To support English language learners, write

these fractions, using numbers and words, on the board. Guide children to think

of 1

_ 8 as one out of eight equal parts of the inch.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Ongoing Assessment:Recognizing Student Achievement

Journal Page 58 �Problem 1

Use journal page 58, Problem 1 to assess children’s progress with measuring

line segments to the nearest 1

_ 2 inch. Children are making adequate progress if

they are able to measure the line segments to the nearest inch in Problem 1.

Some children may be able to measure to the nearest 1

_ 2 in.,

1

_ 4 in.,

1

_ 2 cm, and mm

to complete Problems 2 and 3 successfully.

[Measurement and Reference Frames Goal 1]

ELL

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180 Unit 3 Linear Measures and Area

Measuring Length in Centimeters and MillimetersLength is the measure of a distance between two points. Length is usually measured witha ruler. The edges of your Pattern-BlockTemplate are rulers. Tape measures, yardsticks, and metersticks are rulers that are used for measuring longer distances.

Rulers are often marked with inches on one edge and centimeters on the other edge. The side showing centimeters is called the centimeter scale. The side showing inches is called the inch scale.

Each centimeter is divided into 10 equal parts called millimeters. A millimeter is �

110� or

0.1 of a centimeter. The word centimeter is abbreviated cm. The word millimeter is abbreviated mm.

Measurement

In January 2003, Chinesescientists found the body ofa four-winged dinosaur thatwas about 75 centimeterslong from head to tail.

The centimeter marks arenumbered 0, 1, 2, and so on.

Millimeter marksare not numbered.

Student Page

Student Reference Book, p. 137

If the 0-mark is at the end of a ruler, then the number“0” may not be printed on the ruler. When this happens,line up the end of the object with the end of the ruler.

How many millimeters long is the arrow?The 0-mark is at the end of the ruler. Line up the end of the object with the end of the ruler.

There are 40 millimeters from the end of the ruler to the 4 cm mark. The arrow tip is another 5 millimeters past the 4 cm mark.

So the arrow is 45 millimeters long.

We write this as 45 mm.

How long is the key?Always line up one end of the object with the 0-mark on the ruler.

The other end of the key is at the 3-centimeter mark.

The key is 3 centimeters long.

We write this as 3 cm.

Measurement

Student Page

Student Reference Book, p. 138

� Measuring to the Nearest WHOLE-CLASS ACTIVITY

Centimeter, 1 _ 2 Centimeter, and Millimeter(Math Journal 1, p. 58; Math Masters, p.413; Student Reference Book,

pp. 137–139)

Ruler D is marked in centimeters and millimeters. Remind children that centimeters, abbreviated cm, and millimeters, mm, are standard units of length in the metric system. The ruler also has marks to show half the distance between consecutive whole centimeters. These marks help when measuring to the nearest whole centimeter. Briefly discuss pages 137–139 in the Student Reference Book to review measuring with these units.

Children use Ruler D to measure the nine line segments on journal page 58 to the nearest centimeter, 1 _ 2 centimeter, and millimeter.

2 Ongoing Learning & Practice

� Playing Subtraction Top-It PARTNER ACTIVITY

(Student Reference Book, pp. 310 and 311)

Children play Subtraction Top-It to maintain and/or develop automaticity with basic subtraction facts. Review the rules for Subtraction Top-It on pages 310 and 311 in the Student Reference Book.

� Math Boxes 3�2 INDEPENDENTACTIVITY

(Math Journal 1, p. 59)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 3-4. The skill in Problem 6 previews Unit 4 content.

� Home Link 3�2 INDEPENDENTACTIVITY

(Math Masters, p. 66)

Home Connection Children take body measurements of someone at home. Remind them to continue to collect and bring in pictures and lists of items that show measurements.

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5.

Maximum number of books read:

4 books

3. Write <, >, or =.

69 < 96

101 < 110

2‰ = 5Í

1,000 > 999

Date Time

2. Measure to the nearest }14

} inch.

about 2 1

_ 4

in.

Draw a line segment 1 1 __

2 inches

long.

4. Pamela had $38. She spent money

on shoes. She has $15 left.

Number model: $38 − ? = $15

Answer: $ 23

1. Count by 6s.

57 , 63 , 69 , 75 ,

81 , 87 , 93 , 99 ,

105, 111, 117, 123,

129, 135, 141, 147

Math BoxesLESSON

3 �2

143–144

254 25513

77–79 73

Start EndChange

$38 −? $15

0 1 2 3 4

XXX

XXX

XXXXX

XXXXX

X

X

Numberof

Children

Books Read

Book Club Totals 6. Courtney has 8 pennies. She shares

them equally with Nicholas. How

many pennies do they each get? Fill

in the circle for the best answer.

A. 16 pennies

B. 8 pennies

C. 4 pennies

D. 2 pennies

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Math Journal 1, p. 59

Student Page

Name Date Time

Body MeasuresHOME LINK

3�2

Help your child measure an adult at home. Use a tape measure if you have one, or use a piece of string. Mark lengths on the string with a pen, and then measure the string with a ruler.

Please return this Home Link to school tomorrow.

FamilyNote

Measure an adult at home to the nearest �12� inch. Fill in the information below:

Name of adult: Around neck: about inches

Height: about inches Around wrist: about inches

Length of shoe: about inches Distance from waist to floor:

about inches

Forearm: about

inches

Hand span: about

inches

Arm span: about

inches

arm spanhand spanforearm

Reminder: Find more pictures that show measurements. Bring them toschool if possible (ask an adult first) or write descriptions of them.

UnitPractice

Write these problems on the back of this page.Fill in a unit box. Write number modelsfor your ballpark estimates. Show your work.

1. 83 � 25 � 2. � 35 � 47 3. 58 � 89 �

80 � 25 � 55 35 � 50 � 85 60 � 90 � 1501478258

Math Masters, p. 66

Home Link Master

Lesson 3�2 181

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Making a Number Line 5–15 Min

To explore modeling fractions as equal parts on a number line, have children fold a strip of paper in half vertically and label the fractional parts. Along the folded edge, they make a tick mark, for 0 and 2 near the edges of the paper and a tick mark for 1 in the middle. (Children may fold the paper the opposite way to find the middle, if they wish.) Then children fold the number line and label tick marks to indicate the halfway points between 0 and 1 and between 1 and 2. Some children may be able to create markings for fourths and eighths. Children may use their number lines for reference as they identify fractional increments on a ruler.

0112

1 21 2

ENRICHMENT SMALL-GROUP ACTIVITY

� Beginning with a Nonzero 5–15 Min

Mark on a Ruler(Math Journal 1, p. 58; Math Masters, p. 413)

To apply children’s understanding of measuring, have them remeasure the line segments on journal page 58 with Ruler E (from Math Masters, p. 413), beginning with the 5-inch mark instead of the 0-inch mark. Discuss ways of measuring with such a ruler. Their measurements should match those recorded earlier. Some children may suggest counting unit segments. Others may suggest lining up the 5-inch mark with the left endpoint of a line segment, recording the number for the mark nearest the right endpoint, and subtracting 5 from that number.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 133)

To provide language support for units of measure, have children use the Math Word Bank template found on Differentiation Handbook, page 133. Ask children to write the terms inch, centimeter, and millimeter; draw pictures representing the terms; and write other related words that describe them. See the Differentiation Handbook for more information.

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