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Lesson 5�12 379

Advance PreparationMake copies of Math Masters, pages 159 and 160 and position them next to the Sunrise-Sunset wall chart

and the class Sunrise and Sunset Record.

Teacher’s Reference Manual, Grades 1–3 pp. 121–124

Key Concepts and Skills• Find the maximum, minimum, and

range using data from the Sunrise and

Sunset Record.  

[Data and Chance Goal 2]

• Draw conclusions from a line graph.  

[Data and Chance Goal 2]

• Draw line segments on a line graph.  

[Geometry Goal 1]

Key ActivitiesChildren make a line graph of the Length-of-

Day data they have collected so far. Adding

to the graph will be part of the yearlong

weekly sunrise-sunset routine.

Key Vocabularyline graph

MaterialsMath Journal 1, pp. 27 and 125

Home Link 5�11

Math Masters, pp. 159 and 160

transparency of Math Masters, p. 159 � 

Place-Value Book � straightedge � slate

Playing Beat the Calculator (Multiplication)Math Journal 1, p. 156

Student Reference Book, p. 279

calculator

Children practice multiplication facts.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip 

Math Masters, p. 398

[Operations and Computation Goal 3]

Math Boxes 5�12Math Journal 1, p. 126

Children practice and maintain skills

through Math Box problems.

Home Link 5�12Math Masters, p. 161

Children practice and maintain skills

through Home Link activities.

ENRICHMENT

World Population GrowthMath Masters, p. 162

Student Reference Book, p. 234

Children calculate changes in world

population as they read and interpret data

from a chart and line graph.

EXTRA PRACTICE

Heights of 8-Year-Old ChildrenStudent Reference Book, pp. 79–81 and 235

half-sheet of paper

Children find landmarks for a set of data.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Sunrise-SunsetLine Graphs

Objectives To guide children as they analyze data from the

sunrise-sunset routine; and to demonstrate how to make and

read a line graph.

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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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380 Unit 5 Place Value in Whole Numbers and Decimals

Sunrise and Sunset RecordLESSON

1�13

Date Time

Date Time of Sunrise Time of Sunset Length of Day

hr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr minhr min

Math Journal 1, p. 27

Student Page

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Children share strategies for finding the difference between the lengths of the longest and shortest days.

� Making a Line Graph WHOLE-CLASS ACTIVITY

of the Lengths of Days(Math Journal 1, pp. 27 and 125;

Math Masters, pp. 159 and 160)

In today’s lesson, the data from the Sunrise and Sunset Record is going to be transferred to a Length-of-Day line graph.

Draw an enlarged date box on the board. (Model it after the ones on the bottom of the Length-of-Day graph.) Using a transparency of Math Masters, page 159, show children how to copy the dates from journal page 27 to the date boxes below the grid on journal page 125. Explain that the slash separates the month and the day.

Explain the scale on the vertical (upright) axis. The labelsrepresent the lengths of days in hours and minutes. The heavy horizontal rules indicate whole hours. To support English Language learners, label the graph with the terms vertical axis and horizontal axis.

PROBLEMBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMEMMBLBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBLBBLBLLLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROOROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEELELELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOBBBLBLBLBBLBLBBROROOROROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGLLLLLLLLLLLLLVVINVINVINVINVINNNVINVINVINVINVINVINVINGGGGGGGGGGOLOOOOOLOOLOLOO VINVINVLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOLOLOLOLOLOLOLOOOLVVVVVVLLLLLLLLLLVVVVVVVVVOSSOOSOSOSOSOSOSOSOSOSOOOOOOSOSOSOSOSOSOSOSOSOSOSOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLLVVVVVVVVVLLLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING

ELL

Getting Started

Math Message Look at your Sunrise and Sunset Record on journal page 27. Which day was the longest day so far? Which was the shortest? How much longer was the longest day than the shortest day? Write the answers on your slate.

Home Link 5�11 Follow-Up Partners or small groups take turns reading the number sentences in Problems 1–8 aloud to the class.

Mental Math and Reflexes Dictate decimals while children display them with their Place-Value Books. In decimal numbers greater than 1, the decimal point is read as “and.”

Suggestions:

fifty-three hundredths 0.53 two and thirty-five hundredths 2.35

four-hundredths 0.04 twenty and seven-hundredths 20.07

one and four-tenths 1.4 forty and nine-tenths 40.9

For each number, ask questions such as the following:

• Which digit is in the tenths place?

• What is the value of the digit x?

• How many hundredths are there?

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Adjusting the Activity

Links to the Future

Lesson 5�12 381

LESSON

5�12

Name Date Time

Length-of-Day Line Graph

16 hr 0 min

30 min

15 hr 0 min

30 min

14 hr 0 min

30 min

13 hr 0 min

30 min

12 hr 0 min

30 min

11 hr 0 min

30 min

10 hr 0 min

30 min

9 hr 0 min

30 min

8 hr 0 min

Date

Math Masters, p. 159

Teaching Master

NOTE Math Masters, page 159 is similar to

journal page 125.

LESSON

5�12

Name Date Time

Length-of-Day Line Graph continued

16 hr 0 min

30 min

15 hr 0 min

30 min

14 hr 0 min

30 min

13 hr 0 min

30 min

12 hr 0 min

30 min

11 hr 0 min

30 min

10 hr 0 min

30 min

9 hr 0 min

30 min

8 hr 0 min

Date

Math Masters, p. 160

Teaching Master

Write the word whole on the board and explain its meaning. Whole

hours means entire or complete hours. This will prevent children from hearing

and thinking the word hole.

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

Each interval between consecutive whole hours is divided into six equal parts, each part representing 10 minutes. The halfway point between consecutive whole hours is labeled 30 min.

Show the class how to graph the length of day above the first date. Children make a dot in the appropriate place on the vertical rule above the first date box. This dot will most likely fall between twoconsecutive 10-minute marks. Children continue to graph the lengths of days from journal page 27 onto the grid on journal page 125. Use the overhead to demonstrate correct graphing technique.

The activities in this lesson are an early exposure to creating and using line

graphs. Creating and using line graphs is a Grade 4 Goal.

After everyone has graphed all the data, ask children to use their straightedges to connect consecutive dots. The graph created is a line graph. The line graph is a representation of the data that the children are collecting. Children can look for patterns in the data table and in the data on the line graph.

Spend a few minutes sharing observations about the graph. For example:

● Find the highest point on the graph. Which date corresponds to this point? Is that the longest day so far? The longest day of the year, the summer solstice, is around June 21.

● Find the lowest point on the graph. Which date corresponds to this point? Is that the shortest day so far? The shortest day of the year, the winter solstice, is around December 21.

● What does it mean when the lines connecting the points go down? The days are getting shorter. What does it mean when the lines go up? The days are getting longer.

● Is there a turning point at which the lines change direction (either up or down)? At each solstice

ELL

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382 Unit 5 Place Value in Whole Numbers and Decimals

5. Write the number that has

4 in the tenths place

0 in the hundredths place

6 in the ones place

9 in the thousandths place

6 . 4 0 9

3. Which is more?

1.36 or 1.6 1.6

0.4 or 0.372 0.4

0.69 or 0.6 0.69

0.7 or 0.09 0.7

Date Time

2. What is the

maximum

number of

points?

25

What is

the mode? 25 points

4. One side of this square is

4 cm long.

4 cm

Perimeter = 16 cm

6. This polygon has 12 sides.

Name the shape. dodecagon

1. Color 0.08 of the grid.

33 34

36

79 8186

150 151

35 102 103

Math BoxesLESSON

5 �12

A B C D E05

1015202530

Num

ber o

f Poi

nts

Players

Point Totals

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Math Journal 1, p. 126

Student Page

Name Date Time

HOME LINK

5�12

Make a ballpark estimate. Subtract and show your work. Check to see if

your answer makes sense.

1. Use the counting-up method.

754

-299

2. Use the trade-first method.

754

-299

Multiplication. Write facts that you know.

3. × 2 facts 4. × 3 facts 5. × 4 facts

Answers vary.

455

4 × 2 = 8

455

Sample answer: 450

Sample answer: 450

Subtraction & Multiplication Practice

Unit

Ask your child to explain the counting-up and trade-first subtraction methods.

Please return this Home Link to school tomorrow.

Family Note

60 61 63

(Ballpark estimate)

(Ballpark estimate)

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Math Masters, p. 161

Home Link Master

Tell children that from now on, whenever they record the sunrise-sunset data for a certain day, they will also plot the length of that day on their line graphs.

NOTE By the time children finish Math Journal 1, the Sunrise and Sunset

Record, page 27, and the Length-of-Day line graph, page 125, will most likely be

complete. In Math Journal 2, children will find a new Sunrise and Sunset Record

on page 279, and a new Length-of-Day line graph on pages 280 and 281.

Children should continue to enter data on these pages. The classroom copies

of Math Masters, pages 159 and 160 positioned next to the Sunrise-Sunset chart,

will serve as the yearlong record of the children’s data. Each week, as children

record the data in their journals, one child should record the data on the class-

room copies of the journal pages.

2 Ongoing Learning & Practice

� Playing Beat the Calculator SMALL-GROUP ACTIVITY

(Student Reference Book, p. 279; Math Journal 1, p. 156)

Children develop automaticity with multiplication facts by playing Beat the Calculator. Have children add a check mark on the Fact Power Table (journal page 156) for each fact that they solve correctly when playing the role of the Brain. For Fact Power Table directions, see Lesson 4-5. For game directions, see page 279 in the Student Reference Book.

Ongoing Assessment: Exit Slip�Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 398) to assess children’s progress toward

demonstrating automaticity with multiplication facts through 10 × 10. Children

record the facts from the Fact Power Table for which they earned at least one

check mark. Children are making adequate progress if they record at least 15

facts from the unshaded portion of the record sheet. Some children may record

more than 15 facts.

[Operations and Computation Goal 3]

� Math Boxes 5�12 INDEPENDENTACTIVITY

(Math Journal 1, p. 126)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-10. The skill in Problem 6 previews Unit 6 content.

Writing/Reasoning Have children write an answer to the following: For Problem 3, explain how you know which number in each pair is more. Sample answer: I wrote the

pairs of numbers one under the other. Then I compared each digit starting with the ones. If they were the same, I compared the tenths. If they were the same, I compared the hundredths. If the digits weren’t the same, the larger digit was in the larger number.

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LESSON

5�12

Name Date Time

World Population Growth

Use the data about world population on Student Reference Book, page

234 to help you answer the questions below.

1. About how many people were added to

the world population between 1500 and 1804?

How many years is that?

2. About how many people were added to

the world population between 1804 and 1960?

How many years is that?

3. About how many people were added to

the world population between 1960 and 1999?

How many years is that?

4. Compare your answers for Questions 1, 2, and 3. What do you

notice about population growth?

Sample answer: Population is increasing more rapidly in recent years.

5. Look at the World Population Graph. What does the line graph

illustrate, or show, about world population?

Sample answer: The population has grownmuch larger and faster in the last 500 yearsthan in the previous 1,500 years.

6. Use the World Population Table to predict when the world population will

reach 8,000,000,000. Explain. Use the back of this page, if needed.

Sample answer: About 24 years. 1 billion more people were added from 1987 to 1999;that’s 12 years. In 24 years, 2 billion wouldbe added.

39 years

3,000,000,000

156 years

2,000,000,000

304 years

500,000,000

Math Masters, p. 162

Teaching Master

Lesson 5�12 383

World Population GrowthThere are more than 6 billion people in the world today.The table and graph below show how the world’s populationhas grown.

By the year 2050, the world will have about 10 billion people.

Data Bank

World Population

World Population TableDate Population Date Population

1000 B.C. 50,000,000 1927 2,000,000,000A.D. 1 300,000,000 1960 3,000,000,0001250 400,000,000 1974 4,000,000,0001500 500,000,000 1987 5,000,000,0001804 1,000,000,000 1999 6,000,000,000

Source: United Nations Population Division

Student Reference Book, p. 234

Student Page

� Home Link 5�12 INDEPENDENTACTIVITY

(Math Masters, p. 161)

Home Connection Children practice multidigit subtraction using two different strategies. They write multiplication facts they know.

3 Differentiation Options

ENRICHMENT INDEPENDENTACTIVITY

� World Population Growth 5–15 Min

(Math Masters, p. 162; Student Reference Book,

p. 234)

To further explore interpreting data on a line graph, have children answer questions on Math Masters, page 162 using data from the World Population Table and the graph on Student Reference Book, page 234.

EXTRA PRACTICE PARTNER ACTIVITY

� Heights of 8-Year-Old Children 15–30 Min

(Student Reference Book, pp. 79–81 and 235)

To provide additional practice in finding data landmarks, have children determine the maximum 148 cm, minimum 107 cm, range 41 cm, mode 126 cm, and median 126 cm

for the Heights of Third Graders data set on page 235 in the Student Reference Book. Children record their answers on a half-sheet of paper. They may refer to pages 79–81 in their Student Reference Books as needed.

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