www.everydaymathonline.com

294 Unit 4 Multiplication and Division

Advance PreparationYou may wish to gather carpet squares or blotters to reduce noise and bounce for the coin toss.

Teacher’s Reference Manual, Grades 1–3 pp. 116, 117, 120, 121

Key Concepts and Skills• Record the results of a coin-toss

experiment.  

[Data and Chance Goal 1]

• Analyze results of a coin-toss experiment

and draw conclusions about equally

likely results. 

[Data and Chance Goal 2]

• Use the terms equally likely and fair to

summarize the results of a coin-toss

experiment. 

[Data and Chance Goal 3]

• Predict the outcome of a coin-toss

experiment and test the prediction

using coins. 

[Data and Chance Goal 4]

Key ActivitiesChildren perform a coin-toss experiment

to confirm that some outcomes are

equally likely.

Ongoing Assessment: Recognizing Student Achievement Use journal page 98. [Data and Chance Goal 1]

Key Vocabularyheads � tails � fair � equally likely

MaterialsMath Journal 1, p. 98

Home Link 4�9

Class Data Pad (optional) � per partnership:

10 coins, carpet squares or blotters

(optional) � calculator � half-sheet of paper

Practicing Measuring Line SegmentsMath Journal 1, p. 99

ruler

Children measure the line segments to

the nearest 1

_ 2 inch,

1

_ 4 inch, and

1

_ 8 inch.

Math Boxes 4�10Math Journal 1, p. 100

Children practice and maintain skills

through Math Box problems.

Home Link 4�10Math Masters, p. 113

Children practice and maintain skills

through Home Link activities.

ENRICHMENTMaking Predictions about Rolling DiceMath Masters, p. 114

per partnership: 1 six-sided die

Children roll a die to explore equally likely

outcomes.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 132

Children add the term fair to their Math

Word Banks.

EXTRA PRACTICE

Drawing a Scaled Bar GraphMath Journal 1, p. 98

Math Masters, p. 118A

Children represent their coin-toss data on a

scaled bar graph.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

A Coin-Toss ExperimentObjective To guide children as they develop intuition

about equally likely events.a

��������

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

294_EMCS_T_TLG1_G3_U04_L10_576809.indd 294294_EMCS_T_TLG1_G3_U04_L10_576809.indd 294 2/11/11 1:59 PM2/11/11 1:59 PM

Lesson 4�10 295

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

Ask children whether they have seen a coin toss used to decide the order of play for games. Remind them that a coin has two different sides—heads and tails. Have a volunteer demonstrate how to toss a coin to decide the order of play.

1. A player or official tosses a coin into the air.

2. Another player calls out either heads or tails while the coin is in the air.

3. If the player correctly calls the side that is faceup after the toss, then that player, or that player’s team, wins the toss. If the player calls incorrectly, then the other player or team wins the toss.

4. The player or team that wins the toss chooses the order of play; for example, to play first or second, to serve or receive.

Use the following questions to prepare children for the coin-toss experiment.

● What are all of the possible outcomes of tossing a coin? It will land either heads up or tails up.

● How likely is a coin to land heads up? To land tails up? Most children will say that heads and tails are equally likely or that each of these outcomes has the same chance. One objective of this lesson is to collect coin-tossing results that should convince children that heads and tails are equally likely outcomes.

Getting Started

Home Link 4�9 Follow-Up Review answers and strategies. Point out that for many of the comparisons, it is not necessary to use the map scale to get a measurement. For example, in Problem 1 the scale is 1 inch = 300 miles. So, 1,000 miles is a little more than 3 inches. On the map, the distance from New York to Los Angeles is much more than 3 inches. Also, the distance from New York to Los Angeles is greater than the distance from Chicago to Dallas.

Mental Math and ReflexesPose multiplication facts. Suggestions:

2 × 2 4 2 × 3 6 2 × 4 8 2 × 5 10

4 × 3 12 4 × 4 16 4 × 5 20 4 × 6 24

6 × 6 36 6 × 7 42 6 × 8 48 6 × 9 54

Math MessageMaria and Joe toss a coin to decide who goes first when they play a game. Is this a fair way to decide? Explain why or why not on a half-sheet of paper.

295-299_EMCS_T_TLG1_G3_U04_L10_576809.indd 295295-299_EMCS_T_TLG1_G3_U04_L10_576809.indd 295 2/11/11 2:04 PM2/11/11 2:04 PM

296 Unit 4 Multiplication and Division

Work with a partner. You need 10 coins.

1. You will each toss all 10 coins 5 times.

For each toss you make,

record the number of HEADS

and the number of TAILS in the table.

2. Use the information in both your partner’s and your tables to fill in the blanks below.

My total: HEADS TAILS

My partner’s total: HEADS TAILS

Our partnership total: HEADS TAILS

3. Record the number of HEADS and the number of TAILS for the whole class.

Number of HEADS: Number of TAILS:

4. Suppose a jar contains 1,000 pennies. The jar is turned over. The pennies are

dumped onto a table and spread out. Write your best guess for the number of

HEADS and TAILS.

Number of HEADS: Number of TAILS: 500 500Sample answers:

Toss Record

Toss HEADS TAILS(10 coins)

1

2

3

4

5

Total

Coin-Toss ExperimentLESSON

4� 10

Date Time

�

Math Journal 1, p. 98

Student Page● Is tossing a coin a fair way to determine the order of play?

Possible responses: “The person who calls heads or tails does it when the coin is in the air, so he or she can’t know how it will land. It is fair.” “The coin lands heads up as often as it lands tails up. So, the one who calls it will be right about half the time. That’s fair.” “I’ve seen them toss like this to start football games. They wouldn’t do it this way if it were not fair to both sides.”

NOTE Fair means that each player has an equal chance of winning. Sometimes

children misinterpret fair to mean that one player has a better chance of winning.

� Conducting and Analyzing PARTNER ACTIVITY

a Coin-Toss Experiment(Math Journal 1, p. 98)

Tell children that they are going to conduct a coin-toss experiment to determine whether heads and tails are equally likely.

Partners share 10 coins. They take turns tossing all 10 coins 5 times. For each turn, they shake 10 coins and drop them about one foot above a surface. (A carpet sample or blotter is an ideal surface for this activity.) Children count the number of coins landing heads up and the number landing tails up. They each record the results of their own coin tosses in the table at the top of journal page 98.

Children calculate the total number landing heads up from all five tosses and the total number landing tails up. Ask them to check their calculations by adding the two totals: (total heads up) + (total tails up) should equal 50. Finally, partnerships combine totals for heads and tails. The combined number should equal 100.

Ongoing Assessment: Journal Page 98 �Problem 1Recognizing Student Achievement

Use journal page 98 Problem 1 to assess children’s progress toward collecting

and organizing data. Children are making adequate progress if they are able to

complete the Toss Record chart. Some children may be able to draw conclusions

from their own and their partner’s tables.

[Data and Chance Goal 1]

PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEEMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBLBLBLBLBLLLLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB ELEELEEMMMMMMMMMMOOOOOOOOOOBBBLBBLBLBBLBBBLROOOORORORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNNVINVINNVINVINVINVINV GGGGGGGGGGGGOLOOOLOOOOLOLOO VVINVINLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVIVINV NGGGGGGGGGOOOLOLOLOLOLOLLOLO VVVVLLLLLLLLLLVVVVVVVVVOSOSOSOOSOSOSOSOSOSOOSOSOSOOOSOSOOOSOOSOSOSOSOSOSOOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLLVVVVVVVVVLLLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING

EM3cuG3TLG1_295-299_U04L10.indd 296EM3cuG3TLG1_295-299_U04L10.indd 296 12/20/10 5:56 PM12/20/10 5:56 PM

Use your ruler to measure each line segment.

Measure to the nearest inch.

1.

about inches

2.

about inches

3.

about inches

Measure to the nearest inch.

4.

about inches

5.

about inches

Measure to the nearest �18

� inch.

6.

about inches

14

4

12

Date Time

Measuring Line SegmentsLESSON

4� 10

2�12

�

5�12

�

3�14

�

4�34

�

5�18

�

Try This

Math Journal 1, p. 99

Student Page

Lesson 4�10 297

Heads38475662444650544841

Total: 486

Tails62534438565450465259

Total: 514

Each partnership calls out the numbers of heads and tails for their 100 tosses, and you record the results on the board or Class Data Pad. You and the children use calculators to find the total number of heads and the total number of tails for the entire class. Children record the class totals in Problem 3 on the journal page.

Sample class data

The class totals should show nearly equal numbers of heads and tails, confirming children’s intuition that these results are equally likely. Help them summarize the results. Use language such as, “We got nearly equal numbers of heads and tails,” “Heads and tails are equally likely,” and “You get heads on 1 out of 2 tosses if you toss a lot.”

2 Ongoing Learning & Practice

� Practicing Measuring INDEPENDENTACTIVITY

Line Segments(Math Journal 1, p. 99)

Children measure the line segments on journal page 99. This page reviews content covered in Lesson 3-3.

EM3cuG3TLG1_295-299_U04L10.indd 297EM3cuG3TLG1_295-299_U04L10.indd 297 12/20/10 5:56 PM12/20/10 5:56 PM

298 Unit 4 Multiplication and Division

py

gg

p

Name Date Time

Family Note text

Please return this Home Link to school tomorrow.

FamilyNote

A Fair Game?HOME LINK

4�10

The class is exploring probability. Play Rock, Paper, Scissors with your child. After 20 rounds,have your child decide whether the game is fair and tell you why or why not. (A game is fair if all players have an equal chance of winning or losing.)

Please return this Home Link to school tomorrow.

Play the game Rock, Paper, Scissors with someone at home. Play at

least 20 times. Keep a tally of wins and losses.

Rock, Paper, Scissors

Materials � players’ hands

Players 2

Object of the Game To choose a hand

position that beats your partner’s choice.

Directions

1. Each player hides one hand behind his or her back and puts it in the

rock, paper, or scissors position.

2. One player counts, “One, two, three.”

3. On “three,” both players show their hand positions.

4. Players choose the winner according to these rules.

If both players show the same position, no one wins.

1. Is this a fair game? (Fair means each player has the same chance

of winning.)

2. On the back of this paper, explain why or why not.

yes

rock paper scissors

Rock dents scissors. Scissors cut paper.

Paper wins. Scissors wins.Rock wins.

FamilyNote

Paper covers rock.

Math Masters, p. 113

Home Link Master

Math BoxesLESSON

4� 10

Date Time

5. Write the number that has

5 hundreds

7 thousands

8 ones

4 tens

2 ten-thousands

Read it to a partner.

3. What is the perimeter of the

rectangle?

The perimeter is .(unit)

68 in.

2. Is a 6-sided die more likely to land

on an odd number or on an even

number? Explain.

either.

equal chance of landing on

3 odd numbers. There is an

6-sided die has 3 even and

Sample answer: Neither. A

4. Complete the Fact Triangle. Write

the fact family.

� �

� �

� �

� � 4624

6424

2446

2464

6. Use �, �, or �.

5,001 1,005

55,001 51,005

55,001 55,100

505,105 505,105�

�

�

�

1. 18 marbles are shared equally.

Each child gets 5 marbles.

How many children are sharing?

Use counters to solve.

(unit)

How many marbles are left over?

(unit)

3 marbles

3 children

73

150 151 55

18 19 13 20

12 in.

22 in.

•

4 6

24

�,�

27,548

Math Journal 1, p. 100

Student Page

� Math Boxes 4�10 INDEPENDENTACTIVITY

(Math Journal 1, p. 100)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-8. The skills in Problems 5 and 6 preview Unit 5 content.

� Home Link 4�10 INDEPENDENTACTIVITY

(Math Masters, p. 113)

Home Connection Children play the game Rock, Paper, Scissors with someone at home. They tally wins and losses and tell whether they think the game is fair.

Remind children that fair means that all players have an equal chance of winning.

EM3cuG3TLG1_295-299_U04L10.indd 298EM3cuG3TLG1_295-299_U04L10.indd 298 12/20/10 7:47 AM12/20/10 7:47 AM

Lesson 4�10 299

Name Date Time

LESSON

4 10 Making Predictions about Rolling Dice

Think about how you would know that a die is fair.

1. Make predictions. If you roll the die 30 times,

which number will come up the most?

How many times might you roll a 5?Explain how you made your predictions.

2. Roll a die 30 times. Use tally marks to record your results in the table below.

one might come up 5 times in 30 rolls.Since there are 6 numbers on the die, each

I might roll it 5 times.Answers vary.

3. Compare your results with your predictions.

4. Do you think your die is fair?

Explain.

an equal chance of being rolled.Sample answer: Yes, each number has

Answers vary.

Number Times Rolled

1

2

3

4

5

6

Answers vary.

Sample answers:

Math Masters, p. 114

Teaching Master

Name Date Time

Graphing a Data SetLESSON

4�10

Number of Heads for Each Toss

Nu

mb

er

of

He

ad

s

0

2

4

6

8

10

Toss Number

1 2 3 4 5

Title:

Make a bar graph for your set of data. Sample answer:

EM3cuG3MM_U04_085-118.indd 118A 1/25/11 12:44 PM

Math Masters, p. 118A

Teaching Master

3 Differentiation Options

ENRICHMENT PARTNER ACTIVITY

� Making Predictions 5–15 Min

about Rolling Dice(Math Masters, p. 114)

To apply children’s knowledge of equally likely results, have them explore the outcomes of rolling a die. Begin by discussing what it means to say that a die is fair. The die is equally likely to land on any side for each roll. Have children complete Math Masters, page 114. When they have finished the page, discuss their predictions and their results.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 132)

To provide language support for probability, have children use the Word Bank template found on Differentiation Handbook, page 132. Ask children to write fair, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.

EXTRA PRACTICE PARTNER ACTIVITY

� Drawing a Scaled Bar Graph 5–15 Min

(Math Journal 1, p. 98; Math Masters, p. 118A)

To provide experience with creating graphs, have children use Math Masters, page 118A to draw scaled bar graphs representing their coin-toss data. They may select either the heads data or the tails data from the Toss Record on journal page 98. Remind children to label the vertical axis with intervals of 2.

295-299_EMCS_T_TLG1_G3_U04_L10_576809.indd 299295-299_EMCS_T_TLG1_G3_U04_L10_576809.indd 299 1/26/11 1:25 PM1/26/11 1:25 PM

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

Name Date Time

118A

Graphing a Data SetLESSON

4�10

Title:

Make a bar graph for your set of data.

EM3cuG3MM_U04_085-118.indd 118AEM3cuG3MM_U04_085-118.indd 118A 1/25/11 12:44 PM1/25/11 12:44 PM