investigating equally likely outcomes - everyday math · objective to provide experiences with...

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Lesson 1�8 47

Advance PreparationFor the optional Readiness activity in Part 3, you will need to make tally cards using 3" by 5" index cards.

For the optional Enrichment activity, make copies of Math Masters, page 352. See Part 3 for details.

Teacher’s Reference Manual, Grades 1–3 p. 11

Key Concepts and Skills• Represent numbers using tally marks.

[Number and Numeration Goal 6]

• Create a tally chart to organize data.

[Data and Chance Goal 1]

• Answer questions and make predictions

based on data organized in a tally chart.

[Data and Chance Goal 2]

• Make predictions about the outcomes of

dice rolls. [Data and Chance Goal 3]

Key ActivitiesChildren roll a die and record the results with

tally marks. Then they speculate whether

one number is more likely to be rolled than

another. Children answer questions about

the data.

Ongoing Assessment: Recognizing Student Achievement Use journal page 3. [Number and Numeration Goal 6]

MaterialsMath Journal 1, p. 3

per partnership: die, craft sticks (optional) �

slate

Writing the Numbers 3 and 4Math Masters, p. 304

Children practice writing the numbers

3 and 4.

Home Link 1�8Math Masters, p. 10

Children practice and maintain skills

through Home Link activities.

READINESS

Matching Numbers and Tallies per partnership: number cards 1–10

(from the Everything Math Deck, if available),

tally cards

To provide experience with tallying, children

match numerals and tally marks.

ENRICHMENTPlaying Rock, Paper, ScissorsMath Masters, p. 352

Children play Rock, Paper, Scissors and

record the results with tally marks. They

speculate whether one gesture is more likely

to win than another.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Investigating Equally Likely Outcomes

Objective To provide experiences with equal-chance events.

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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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48 Unit 1 Establishing Routines

////\ // /// ////\ /// ////\ ////\ /// ////\ /

Ongoing Assessment: Recognizing Student Achievement

Use journal page 3 to assess children’s ability to make tally marks. Children are

making adequate progress if they show each set of 5 as ////\. [Number and Numeration Goal 6]

Journal page 3 �

Getting Started

Mental Math and ReflexesCall out single-digit numbers. Children write tallies for the numbers on their slates. After displaying their answers, children count the tally marks in unison, always beginning with 5 if the number is 5 or more.

If children are ready, try tally counts for numbers from 10 through 15.

NOTE Some children may benefit from doing

the Readiness activity before you begin Part 1

of the lesson. See the Readiness activity in

Part 3 for details.

1 Teaching the Lesson

� Dice-Roll and Tally PARTNER ACTIVITY

(Math Journal 1, p. 3)

Ask children which number they think will come up most often when they roll a die. Tell them that they will roll a die to find out. Explain that they will record the rolls using tallies.

Divide the class into partnerships and review the partnership principles: Guide, Check, Praise.

On the board, make a tally chart for the numbers 1 through 6. (See margin.) Then describe the activity:

Directions

1. Partners take turns rolling a die.

2. Both children make tally marks next to the appropriate die in the chart in their journals.

3. After 2 minutes, ask children to pause. Invite them to predict which number or numbers will come up most often. Record children’s predictions, but do not take sides.

4. Children continue to roll a die and record the results for 3 more minutes.

5. After 3 minutes, have children record the total number of times each number was rolled.

NOTE Theoretically, each number has the same chance of being rolled.

However, in practice, it is unlikely that all numbers will come up the same number

of times. This is a sophisticated idea that will be discussed in later grades. At

this time, children should simply observe that the results were not the same for

all partnerships.

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Interactive whiteboard-ready

ePresentations are available at

www.everydaymathonline.com to

help you teach the lesson.

Adjusting the Activity

Have children bundle craft sticks by 5s for

each ////\ tally count.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

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Your child will bring home assignments called “Home Links.” The assignments will not take

much time to complete, but most of them involve interaction with an adult or an older child.

There are good reasons for including Home Links in the first-grade program:

� The assignments encourage children to take initiative and responsibility. As you

respond with encouragement and assistance, you help your child build independence

and self-confidence.

� Home Links reinforce newly learned skills and concepts. They provide thinking and

practice time at each child’s own pace.

� These assignments relate the mathematics your child is learning to the real world,

which is very important in the Everyday Mathematics program.

� Home Links will give you a better idea of what mathematics your child is learning.

Listen and respond to your child’s comments about mathematics. Point out ways in

which you use numbers (time, TV channels, page numbers, telephone numbers, bus routes,

shopping lists, and so on). Everyday Mathematics supports the belief that children who have

someone do math with them, learn math. Fun counting and thinking games that you and

your child play together are very helpful for such learning.

For this first Home Link, your child might look for a newspaper ad for grocery items,

a calendar page, or a picture of a clock. The purpose of this activity is to expand your child’s

awareness of numbers in the world.

Please return this Home Link to school tomorrow.

Family Note

Name Date

Numbers Are Everywhere

Cut examples of numbers from scrap papers you findat home.Glue some examples on the back of this page.Bring examples that will not fit on this page to school.Do not bring anything valuable!

HOME LINK

1�8

Math Masters, p. 10

Home Link Master

Lesson 1�8 49

Dice-Roll and TallyLESSON

1�8

Date

Roll a die. Use tally marks to record the results on this chart.

Tallies Total

�Answers vary.

EM3MJ1_G1_U01_001-006.indd 3 12/28/10 10:48 AM

Math Journal 1, p. 3

Student Page

NOTE Remember to reserve time every day

to complete the number-line and attendance

routines.

Ask partnerships questions about their results, such as the following:

● How many times did you roll 1? 2? 3? 4? 5? 6?

● How could you figure out how many times your partnership rolled the die altogether? Sample answer: Count the tally marks in all of the rows by 5s.

● Which did you roll more times, 5 or 6 (or any combination of two numbers)? How many more times?

● Which did you roll fewer times, 2 or 3 (or any combination of two numbers)? How many fewer times?

End the activity with a cumulative tally of the results for all partnerships. You can expect the numbers to come up about the same number of times, even though some partnerships may have had one number come up much more often than the others. Discuss the results.

2 Ongoing Learning & Practice

� Writing the Numbers 3 and 4 INDEPENDENTACTIVITY

(Math Masters, p. 304)

Use Math Masters, page 304 to provide more practice writing the numbers 3 and 4.

� Home Link 1�8 INDEPENDENTACTIVITY


Home Connection Have children write their names and today’s date at the top of the page.

Discuss the purpose of Home Links and what children should do with them. For example:

● Always put your name on your Home Link.

● Be sure to take it home.

● Discuss and complete the assignment with someone at home—a parent, a guardian, a caregiver, or an older brother or sister.

● Bring the completed Home Link back to school the next school day. (Some assignments may take longer to complete. If that is the case, the Family Note in the Home Link will indicate that.)

For Home Link 1-8, children collect examples of numbers and bring them to school. They look for more examples during the next few days.

Invite children to continue bringing in examples of various numbers and their uses throughout the school year.


50 Unit 1 Establishing Routines

Name Date

Tallies

Tied Game

Tallies

Tied Game

Rock, Paper, Scissors 132

4

Name Date

Rock, Paper, Scissors 132

4

Math Masters, p. 352

Game Master

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Matching Numbers and Tallies 5–15 Min

To provide experience with tallying, have children work together to match number cards with corresponding tally cards. Spread the number cards and tally cards for 1–10 faceup on the table. Mix them up. Ask partners to work together to match the number cards to the corresponding tally cards. Have partners double-check their work.

ENRICHMENT PARTNER ACTIVITY

� Playing Rock, Paper, Scissors 5–15 Min


To further explore tallying as a data-collection strategy, have children use tallies to record the results of a Rock, Paper, Scissors game. Some children may be familiar with this well-known game. It is known by many other names and is played all over the world. The game is for two players.

Three objects—a rock, a piece of paper, and scissors—are represented by the following hand gestures:

rock paper scissors

Players make one of the three hand gestures behind their backs. One player counts to 3, and then both players quickly show their hands. The following rules determine the winner of the round:

� Scissors and paper: Scissors wins because scissors can cut paper.

� Paper and rock: Paper wins because paper can be wrapped around a rock.

� Rock and scissors: Rock wins because it can blunt the scissors (make them less sharp).

� If both players choose the same gesture, it is a tie.

Players play 20 rounds. After each round, they make a tally mark in the chart on their half-sheet of paper to indicate either the winning gesture or that the round ended in a tie.

NOTE For each partnership, cut five 3" by 5"

index cards in half. Draw tally marks for the

numbers 1–10 on the cards.

NOTE Make enough copies of Math Masters,

page 352, so that each child will have one

half-sheet. Cut the copies in half.


Lesson 1�8 51

Encourage children to speculate about whether one gesture will win more often than the others, but do not take sides. You may wish to discuss the chance of winning a game compared to the chance of tying. Children can use tally marks to record the results and discover that winning happens about twice as often as tying.

Planning Ahead

Starting in Lesson 1-10, children will use full decks of number cards. If you are using the cards from the back of the children’s journals, you will need to prepare decks of cards from Activity Sheet 2. As before, the number cards must be cut apart and marked with the same distinctive marks, letters, shapes, or colors as the first set.

When combined with the cards from Activity Sheet 1, which you may have distributed in Lesson 1-6, each deck of number cards will consist of 22 cards, 0–22.

NOTE Some children may think that certain

gestures are more likely to win than others.

Point out that if that were true, then players

would choose that gesture every time and

games would always end in a tie.


investigating equally likely outcomes - everyday math · objective to provide experiences with...

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