Manipulative: DICE (Jonathan Ball)
Dice are small throwable objects with multiple resting positions, used for generating random numbers.
Dice have been used since before recorded history, and it is uncertain where they originated. The oldest known dice were excavated as part of a 5000-year-old backgammon set at the Burnt City, an archeological site in south-eastern Iran.
Source: Wikipedia
Sides / Shape / Notes4 / tetrahedron / / Each face has three numbers: they are arranged such that the upright number (which counts) is the same on all three visible faces. Alternatively, all of the sides have the same number in the lowest edge and no number on the top. This die does not roll well and thus it is usually thrown into the air instead.
6 / cube / / A common die. The sum of the numbers on opposite faces is seven.
8 / octahedron / / Each face is triangular and looks like two square pyramids attached base-to-base. Usually, the sum of the opposite faces is 9.
10 / pentagonal trapezohedron / / Each face is a kite. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet. The ten faces usually bear numbers from zero to nine, rather than one to ten (zero being read as "ten" in many applications). Often all odd numbered faces converge at one sharp corner, and the even ones at the other. The sum of the numbers on opposite faces is usually 9 (numbered 0–9) or 11 (number 1–10).
12 / dodecahedron / / Each face is a regular pentagon. The sum of the numbers on opposite faces is usually 13.
20 / icosahedron / / Faces are equilateral triangles. Icosahedrons have already been made in Roman/ Ptolemaic times, but it is not known if they were used as gaming dice. Modern dice with 20 sides are sometimes numbered 0–9 twice as an alternative to 10-sided dice. The sum of the numbers on opposite faces is 21 if numbered 1–20.
Source: Wikipedia
Dice as a Thinking Tool
Dice are inexpensive and simple ways to generate impartial random numbers, an impossible task for the human mind. Dice can be used in a variety of ways in the classroom in many subjects. Dice can: indicate a required number of sets of a specific exercise in gym; be used to move playing pieces along in a student-developed board game; be used to generate flash-card numbers for math practice; be used to play Yahtzee (a classic probability and multiplication game).
Lesson Title: SKUNK/Grade: 6/Source: Illuminations
Learning Goal: To pose and solve simple probability problems,and solve them by conducting probability experiments.
1)Minds On
- Write the following questions on the board:
- It might rain today. Should I wear rain boots?
- The Leafs might make playoffs next year. Should I reserve post-season tickets?
- I might find a quarter in the vending machine. Should I check?
- Discuss responses and the concepts of choice, chance, and probability.
- Discuss Learning Goals (I can play strategically in a game of chance, I can recognize whether an action has a high or low degree of risk in a game of chance)
2)Hands On (courtesy of Illuminationsilluminations.nctm.org/)
A helpful youtube video: youtube.com/watch?v=jfHCIZ8fN7I
To start the game each player makes a score sheet like this: S | K | U | N | K
Each letter of SKUNK represents a different round of the game; play begins with the "S" column and continue through the "K" column. The object of SKUNK is to accumulate the greatest possible point total over five rounds. The rules for play are the same for each of the five rounds.
- At the beginning of each round, every player stands. Player 1 rolls a pair of dice.
Player 1 gets the total of the dice and records it in his or her column, unless a "one" comes up.
- If a "1" comes up, play is over for that round and all player's points in that column are wiped out.
- If "double ones" come up, all points accumulated in prior columns are wiped out as well.
- If a "1" doesn't occur, the player may choose either to try for more points on the next roll (by continuing to stand) or to stop and keep what he or she has accumulated (by sitting down).
Note:If a "one" or "double ones" occur on the very first roll of a round, then that round is over and each player must take the consequences.
Playing SKUNK with the Whole Class
The best way to teach SKUNK to the class is to play a practice game.
Draw a SKUNK score sheet on the chalkboard or overhead transparency on which to record dice throws. Have all students make their own score sheets on their own scrap paper. Have all students stand up next to their chairs. Either you or a student rolls the dice. Suppose a "four" and a "six come up, total 10. Record the outcome of the roll in the "S" column on the chalkboard:
On the first roll, all the players get a total of the dice or a zero if any "ones" come up. Kerry and Lisa are standing up, so they also write "10" in their score sheets.
After each roll, players may choose either to remain standing or to sit down. Those who are standing get the results of the next dice roll; those who sit down keep the score they have accumulated for that round regardless of future dice rolls. Once someone sits down, that person may not stand up again until the beginning of the next round.
3)Consolidation
Post the top 5 scores on the wall. Have these students share their strategies and answer questions.
Have groups play another round with these new strategies in mind.
Choose 2 new high scorers and connect these scores to learning goals.
Assessment: Have groups prepare a point-form poster titled “A Beginner’s Guide to SKUNK: How to Beat the Odds and Win!”
J. Ball