Singer, M. Investigations in Number, Data, and Space:

Between Never and Always. Dale Seymour, 1998.

Proposed Time Frame:

Between

Never and

Always

Probability

Unit Goals:

•

Understand what probability means

•

Estimate using probability

•

Using probability to decide if a game is

fair

Materials:

◊

Paper and pencil

◊

Deck of playing cards (each card

represents the numeral equal to it’s

face value, ex; 2 is the numeral 2)

◊

Ace represents 1, Jacks represent 0,

remove Queens and Kings from the

deck.

Procedure:

◊

Shuffle the deck and deal each

player eight cards.

◊

Each player selects six cards to cre-

ate a three-digit addition problem

that will come closest to 1000.

◊

Take the sum of the addition prob-

lem and subtract it from 1000. This

is your score.

◊

Play ten rounds and whoever has the

least points, wins!

Investigations in

Schools

Web Resources

You will find web resources at:

http://www.everett.k12.wa.us/math

www.illuminations.nctm.org

Probability Games

http://www.bbc.co.uk/education/mathsfile/

shockwave/games/fish.html

http://www.rainforestmaths.com/

Glossary

Probability

— How likely it is that

something is going to happen.

Likely —

A very good chance that

something may occur.

Unlikely —

Nearly no chance that

something may occur.

On-Line Glossary

http://www.amathsdictionaryforkids.com/

Close to 1000

2

0

4

7

6

8

1

5

7

2

8

1

5

+

4

9 9 9

Cards Dealt:

3-digit addition

problem

---

Tips for Helping at Home

∗

Help students see a connection between sports

statistics and probability

∗

When playing games at home, have your child

tell you about the probability of winning.

∗

Emphasize that probability is not the same as

being certain.

Listed below are questions to help teachers dur-

ing observations and assessments.

Getting Started

* What is it that you don’t understand? (Have

your child be specific.)

∗

What do you need to find out?

∗

What do you need to know?

∗

What terms do you understand or not under-

stand?

While Working

∗

How can you organize the information?

∗

Do you see any patterns or relationships that will

help solve this?

∗

What would happen if…?

Reflecting about the Solution

∗

How do you know your answer is reasonable?

∗

Has the question been answered?

∗

Can you explain it another way?

At Home:

1 An activity your child will be doing at

home is tossing a bottle cap many

times to see how likely it is to land

with the top up. You can help your

child keep track of the results of this

experiment and try to draw some

conclusions from it.

2 We will be talking about games of

skill and games of chance, and how

to judge the “fairness” of a game.

Listen to your child’s explanation of

what makes a game fair.

3 In another activity at the end of the

unit, your child will experiment with

pulling family members’ names out of

a hat as a fair way of deciding hwo

does a household chore. Although

students only pretend to allocate

chores this way, you might actually

try it out for a while. If you do, be

sure to keep track of the results and

discuss with your child whether or not

it seems fair.

At School:

1

Attend Open House, Back to School

Night, and after school events.

2 Join the parent-teacher organization

Singer, M. Investigations in Number, Data, and

Space: Between Never and Always. Dale

Seymour, 1998.

Mathematics in

Investigations

Investigation 1:

∗

Associate verbal descriptions with numerical

descriptions of probability

∗

See that repeating a probability experiment

several times yields a variety of results

∗

Using probability to predict how often an

event may occur in a given number of trials

∗

Estimate probabilities from results of ac-

tual trials

∗

Predict and analyze features of distribu-

tions

∗

Learning to add probabilities of simple

events

Investigation 2:

∗

Interpret fairness of a game as equal prob-

ability of winning

∗

Developing systematic ways to generate a

list that includes all the ways an event can

occur

∗

Apply knowledge of probability to design a

fair game, and analyze the fairness of

games

∗

Distinguish between games of chance and

games of skill

∗

Understand variability in the results of fair

games.