Carmen Manoil(100334505, Section 1A), Oct 2/2007

PROBABILITY KIT /

Description - The “Probability Kit” is a comprehensive kit that includes:

a deck of cards

didactic coins

color and number spinners

transparent spinners

few polyhedral dice (with 4,8,10,12,20 faces)

six sided cube dice

activity cards

teacher’s notes

Purpose

The media is full of predictors and students should understand how these numbers are determined and how to interpret them

Probability concepts are pretty abstract and the manipulative included in this kit help students visualize these abstract concept

Probability experiments are an important step in beginning to understand probability concepts and predictions

The latest research have showed that hands-on activities are very important for learning process

The manilupatives are suitable for cooperative learning, individual learning, as well as whole class instruction. + They are FUN!!!

In grades 7-8 all students should:

perform simple probability experiments involving two independent events

design studies, collect and record data

select, create, and use appropriate graphical representations of data (histograms, stem-and-leaf plots, box plots, and scatterplots)

find, use, and interpret measures of center and spread, including mean, median, mode;

distinguish between the experimental probability and the theoretical probability of a specific outcome etc.

Many other mathematical concepts such as factor, multiple, prime number, composite number, divisors, etc. can be incorporated in probability questions and activities.

The kit contains:

1. A deck of cards /
Examples of activities:
P(4)=? – probability to get a 4 (after removing all the face cards and considering ace=1).
P( heart )=?
P(any heart and any 4)=?
Students can be asked to calculate the theoretical probabilities of different events, and then to calculate the experimental probability by drawing cards without looking, recording the outcomes, and analyzing their results
2. Didactical coins (quarters, dims, nickels, pennies) /
Examples of questions and activities:
Consider flipping a coin.
How many possible outcomes are there?
Without flipping the coin, P(H)=?, P(T)=?. What kind of probability is this, theoretical or experimental?
Use a quarter. Flip the coin 20 times and record all the outcomes in a frequency table. Find out P(H). What kind of probability is this? Why?
3. Number Dice /
Examples of questions and activities:
Introducing tree diagrams (draw a tree diagram that illustrates all the possible/favorable outcomes)-for 2 dice
P (two even numbers)=?
P (an odd, and an even number)=?
P (a prime number, a composite number)=?
P (6, a factor of 4)=?
4. Color spinners /
Examples of questions and activities:
Using 2 color spinners
How many possible outcomes are there?
Draw a tree diagram.
Decide on a way to represent your data, spin both spinners 20 times, and record your results using tally charts.
5. Number spinners /
Examples of questions and activities using a color spinner and a number spinner:
Draw the tree diagram for the possible outcomes.
P ( a multiple of 2, and blue )=?
P (a prime number, and not get yellow)=?
6. Transparent spinners /
A set consisting of 5 spinners, each with a transparent base and a metal arrow.
The transparent base of the spinner allows the teacher to use them on the overhead projector.
Students can place the spinners over colorful drawn circular, spinners bases found on textbooks, and worksheet to complete probability experiments.
They can be customized to fit any situation.
7. Polyhedral Dice (with 4,8,10,12,20, faces) /
Examples of questions and activities:
P (a prime number)=?
P (3, 5 or 7)=?
P (a factor of 4)=?
Activities for the die with 3 numbers on a face:
P (the sum of the numbers is a multiple of 2)=?
P (a number greater than 3 is on the side)=?
P (the sum of the numbers on the side is a factor of 24)=?
8. Probability Activity Cards /
The probability activity cards have two sides. The “activity side” of the card asks the student to conduct an experiment and suggest ways of recording data.
The “problem side” of the card poses questions concerning the mathematics of an experiment.
Students are expected to use their knowledge of mathematics and probability to formulate the answers to the questions

Virtual Probability Kit:

Activity 1 – “Target Mean”

Activity 2 - “Roll And Roll”

see handouts bellow

Carmen Manoil, Oct 2/2007

Target Mean (or Median)

Ideal for consolidation after teaching measures of central tendency (mean, median)

Number of players: 2 or more

The goal of the game is to make 4 numbers (or 5, 6 if enough time is available and the students’ competence allows) that, when averaged, equal or are close to a target mean.

Rules:

  1. The students have to decide on a target number between 11 and 66, for example 35.
  2. Each player gets 2 dice and the table from “handout 1”.
  3. Each time they role the dice, the players will get 2 numbers. One of the two numbers will be the tens’ digit, and the other number will be the ones’ digit. The players can decide which number will be the tens’ digit, and which one will be the ones’ digit. For example, if a player gets a 4 and 5, the player can choose 45 or 54.
  1. Each player records his numbers in the table from “handout 1”.
  1. Players take turn rolling the two dice and deciding on the result number (45 or 54).
  2. After four turns, each of the players has to calculate the mean of the four numbers, and to round it to the closest integer. The player whose mean is closest to the target number wins one round - 1 point.
  3. The Ss can play 3 rounds and the player who reaches 3 points first is the winner.

For example if Stefan and Dave play together:

Roll1:

-Let’s say Stefan got a 4 and a 2, and he decided to form the number 24 (not 42, although he could).

-Let’s say Dave got a 3 and a 6, and he decided to form the number 36 (not 63)

-Let’s say that for the second, third, and forth rolls they got:

Round 1: Stefan

Tens / Units / The Mean
First number / 2 4 / 34,5
Rounded to the closest integer is 35.
Second number / 1 6
Third number / 6 2
Forth number / 3 6

Round 1: Dave

Tens / Units / The Mean
First number / 3 6 / 34
Second number / 3 5
Third number / 4 1
Forth number / 2 4

So Stefan won round 1.

Observations:

  1. Instead of using dice, 2 spinners (number spinners) can be used.
  2. If the teacher wants to make the game more complicated, or if he/she wants to use the game to reinforce the concept of “median”, students can be asked to calculate the median of the 4 numbers.

Handout 1

Player:______

Round 1:

Tens / Units / The Mean
First number
Second number
Third number
Forth number

Round 2:

Tens / Units / The Mean
First number
Second number
Third number
Forth number

Round 3:

Tens / Units / The Mean
First number
Second number
Third number
Forth number

Carmen Manoil, Oct 2/2007

Roll and Roll

Work in groups.

Consider the four sided die and the six sided cub die.

One die will have sides labelled 123, 124, 134, 234, and one will have sides with the numbers 1, 2, 3, 4, 5, 6.

  1. How many outcomes are there? ______
  2. What is the probability of getting 3 and 134?______
  3. P (5, 234) = ______
  4. P (2, 123) =______
  5. P (an even number, 234) = ______
  6. Roll both dice 24 times and record your findings as tally charts, in the table given bellow.
  7. Use your data to calculate the experimental probability of each outcome.
  8. Compare the theoretical probability of each outcome from steps 2,3, and 4 with the experimental probability calculated at step 7. What do you notice? Why is that?

Group: ______

123 / 124 / 234 / 134
1
2
3
4
5
6

1