Investigating Equally
Likely Outcomes
Objective To provide experiences with equal-chance events.
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Common
Core State
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Ongoing Learning & Practice
Key Concepts and Skills
Writing the Numbers 3 and 4
• Represent numbers using tally marks. Math Masters, p. 304
Children practice writing the numbers
3 and 4.
[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]
Home Link 1 8
Math Masters, p. 10
Children practice and maintain skills
through Home Link activities.
• Make predictions about the outcomes of
dice rolls. [Data and Chance Goal 3]
Key Activities
Children 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.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
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.
ENRICHMENT
Playing Rock, Paper, Scissors
Math 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.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 3. [Number and Numeration Goal 6]
Materials
Math Journal 1, p. 3
per partnership: die, craft sticks (optional) slate
Advance Preparation
For 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
Lesson 1 8
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Getting Started
Mental Math and Reflexes
Call 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)
Interactive whiteboard-ready
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PROBLEM
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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.
Adjusting
the Activity
ELL
Have children bundle craft sticks by 5s for
each ////\ tally count.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
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.
Journal page 3
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]
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Ask partnerships questions about their results, such as the
following:
●
●
Student Page
Date
LESSON
How many times did you roll 1? 2? 3? 4? 5? 6?
Dice-Roll and Tally
18
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?
Roll a die. Use tally marks to record the results
on this chart. Answers vary.
Tallies
Total
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
Math Journal 1, p. 3
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INDEPENDENT
ACTIVITY
(Math Masters, p. 304)
NOTE Remember to reserve time every day
Use Math Masters, page 304 to provide more practice writing the
numbers 3 and 4.
Home Link 1 8
to complete the number-line and attendance
routines.
INDEPENDENT
ACTIVITY
(Math Masters, p. 10)
Home Link Master
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.
Name
HOME LINK
Date
18
Numbers Are Everywhere
Family
Note
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.
Cut examples of numbers from scrap papers you find
at 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!
Invite children to continue bringing in examples of various
numbers and their uses throughout the school year.
Math Masters, p. 10
Lesson 18
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3 Differentiation Options
NOTE For each partnership, cut five 3" by 5"
index cards in half. Draw tally marks for the
numbers 1–10 on the cards.
PARTNER
ACTIVITY
READINESS
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.
PARTNER
ACTIVITY
ENRICHMENT
NOTE Make enough copies of Math Masters,
page 352, so that each child will have one
half-sheet. Cut the copies in half.
Playing Rock, Paper, Scissors
5–15 Min
(Math Masters, p. 352)
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:
Game Master
Name
rock
paper
scissors
Date
1 2
4 3
Rock, Paper, Scissors
Tallies
Tied Game
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.
Name
Date
Rock, Paper, Scissors
1 2
4 3
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.
Tallies
Tied Game
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.
Math Masters, p. 352
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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.
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.
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.
Lesson 18
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