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I have been using dice to generate random digits for activities in my 7-12 classrooms for several years. I attended a workshop at the November 2000 regional NCTM conference in Omaha, NE, put on by Box Cars & One Eyed Jacks. From there the ideas for elementary activities began to grow. I purchased a few of their materials for ideas and made modifications that would fit my own situation. After experiencing some frustration with the lack of consistent basic number fact knowledge in the upper elementary grades, I purposely designed some simple activities in the forms of games that gave students opportunity and motivation to practice their number facts and cultivate number sense at the same time. Dice and card games are tremendously adaptable—I have used them from grades 3 through 10.
Going Up, Coming Down—Multiplication, addition & subtraction
Guess My Product—Multiplication and maximum/minimum concepts (plan only, not yet tested, easily adapted to other operations)
War—multiplication (easily adapted to other operations)
Salute—integer multiplication (easily adapted to other operations)
Needed Materials: Two decahedron (10-sided) dice for every 4 students, a piece of paper and writing utensil for each team (2 students). You can use 6-sided dice, but it limits the number facts practiced. Another idea is to use blank 6-sided dice and put the numbers on them you want to use. You can also cut up address labels, write on them, and put them over the faces of regular dice. Another method is to use a random number generator on a calculator, but I prefer that the students have the tactile experience of rolling the dice. Mouse pads or drawer liner make good rolling surfaces and cut down the noise levels. It is possible to buy foam dice, but I’ve never seen the decahedron dice in foam. Please email me if you find a source.
Directions:
1. Two students make a team; two teams play the game. The “going up” team will start at 0 and add to reach a target number. (In the fourth grade we used 100). The “coming down” team will start at the target number and subtract to reach 0. Teams should switch roles between games.
2. One partner rolls the dice. The other partner must independently multiply the faces. Together the partners determine the sum (or difference) of the product with their running score. All calculations are done mentally with verbal explanations of how the students know their answers are right. The number sentences are recorded on the team paper, but the paper is not used for calculation.
3. The opposing team is responsible for catching any mistakes. If a team misses the multiplication fact or adds/subtracts incorrectly and the other team catches them, the playing team loses that opportunity to “go up” or “come down”.
4. Play ends when either team goes beyond their goal, however, both teams must have rolled the same number of times. (If the team that went first goes beyond their goal first, the other team gets one more roll.)
5. The winning team is the one that is the closest to their target, above or below.
The mathematical goals are to practice multiplication facts, to practice mental addition/subtraction and justification of answers, and to think about the magnitude of numbers and their relationship to the team target. These are a part of developing good number sense. Class discussion can also introduce the element of probability.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
This activity followed the No Need to Borrow lesson. Because of the time between sessions (we met only once each week), it was difficult to establish continuity. The students were beginning to work on multiplication facts during regular math class, so I designed this activity to practice both. It was a rather bold objective since mental subtraction/addition was not yet automatic for them and multiplication facts were new. However, the game did work—it just progressed at a much slower pace and with more errors than I expected. Some students were easily frustrated when they or their partner made a mistake that prevented them from being able to progress toward their goal (leading to a teachable moment on good sportsmanship).
_4_ Was the purpose of the activity clear to me?
_3_ Was the purpose of the activity clear to my students?
_3_ Did the activity support a range of learning styles?
_3_ Were the students engaged during this activity?
_13_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
…telling them at the beginning we were going to play a game that I really liked. I asked them to be thinking about what we were doing because at the end of our time together I would ask them why they thought I liked the game.
The part of the lesson that was student-centered was…
…the actual play of the game. Students are practicing mental arithmetic with verbal justification. Their peer opponents must listen in order to assess their accuracy.
Needed Materials: A pair of dice, a piece of paper, and writing utensil for every 2 students. (Can be played as a whole class activity.) Vary the kind of dice used depending on the skill level of the students. (I would use 10-sided dice with fourth graders.)
Directions:
1. Students play in pairs. One person rolls the dice while the other person records guesses. The players switch roles after each round.
2. One player rolls so that the other player cannot see the result and then finds the product of the two faces.
3. The other player begins guessing the product. The player who rolled the dice simply responds “higher” or “lower”. The player guessing should record each guess and indicate whether the product is higher or lower. Once the correct number is guessed, the guesser must also determine what numbers were rolled. (E.g., if the product is 12, the guesser must also determine is the faces were 2 and 6 or 3 and 4.
4. Play ends after a certain number of rounds or an allotted amount of time. (I would probably have 4th graders play a total of 6 rounds, 3 guessing rounds per player.)
5. Have each player count his total number of guesses. The winner is the player with the fewest guesses.
The mathematical goals are to practice multiplication, think about possible factors for the multiple discovered, and strategize which guesses are the most helpful. After the game has been played several times, class discussion can develop the concept of probability.
The class period planned for trying this game was usurped by another school activity, so it has not yet been tested with students. Please feel free to tell me how it worked in your classroom by contacting me at rokershner@alumni.okbu.edu
Needed Materials: A deck of cards for each two students. A local casino might provide used playing cards to schools at no cost.
Directions:
1. Decide upon values for the face cards. These can vary depending on your goals. (In the fourth grade we used Jack=11, Queen=12, King=0, and Ace=1 and left the Jokers out.)
2. Students play in pairs. Begin by shuffling the deck and dealing all cards out to the two players. This game is played quite similarly to traditional “war”.
3. The players each turn a card over at the same time. The first person to correctly state the product they see wins the two cards. (I required the students to say the number sentence, e.g. “9 times 2 is 18” instead of just “18”.)
4. If there is a tie in naming the product, “war” begins. Each player places 2 cards face down, then they simultaneously turn 1 card face up. This continues until one of the players is quicker in giving the number sentence and product. The winner gets to keep all the cards that were placed on the table.
5. Play ends when either player has all the cards or after an allotted time. The winner is the player with the most cards.
The mathematical goals are to practice multiplication facts and to introduce/reinforce the commutative property of multiplication. When students play facing each other, they will instinctively read the cards they see from left to right—so each round will state the number fact both ways.
This game is highly adaptable. It can be used with its traditional rules at the K-1 level to reinforce magnitude of numbers. Use it in grades 1-3 to reinforce addition facts. It can be used in grades 6-8 to practice integer operations by making red negative and black positive.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
This activity came as a strategy to make internalizing the multiplication facts a game that could be practiced at home with siblings or parents. Repetition is NOT the only way to learn facts, but it is one way. This game combined well with the Show Me 48 activity used at another time. I let the students pick their own partners, and by coincidence (?) they paired themselves with students of about equal ability.
As I walked around the room during game play, I helped some students think of ways to remember or reason out facts by demonstrating reasoning based on number sense—jumping up or back from known (benchmark) facts. For a special needs student I used rhythmic skip counting to foster success. I discovered that one student was trying to use a multiplication table (taped on a nearby desk), but that he didn’t know how to make the table work for him. I gave him a mini-lesson in reading the table, let him use it a few rounds, then came back and covered it up (his partner thought that was much fairer, and I agreed).
This is not a quiet game! We talked about using “inside” voices, but a group of inside voices still makes a dull roar! Teachers who use active student-centered lessons must learn to deal with a classroom noisier than it is when they are the only ones talking. It is sometimes one of the most difficult transitions for a teacher accustomed to being “in control”. In building settings where noise travels (like ours), care must be taken that learning in other classrooms is not interrupted—but that must not prevent teachers from using activities that involve active student participation.
_4_ Was the purpose of the activity clear to me?
_4_ Was the purpose of the activity clear to my students?
_2_ Did the activity support a range of learning styles?
_4_ Were the students engaged during this activity?
_14_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
I told them at the beginning that knowing their multiplication facts would make lots of math easier down the road and that we were going to play a game to help them practice. We talked about the importance of practice when you want to improve a skill, whether it’s dribbling a basketball, playing the piano, or riding a dirt bike. I told them I would be there to help if needed while they played and to listen to their progress. I stressed how easy it would be to play this game anywhere with siblings or parents.
The part of the lesson that was student-centered was…
…the actual play of the game. Students helped each other with forgotten facts, sometimes with amazing animation!
Needed Materials: A deck of cards for the entire class. (You may want to break your class into groups if the class is large.)
Directions:
1. Decide upon values for the face cards. These can vary depending on your goals. (In the seventh & ninth grades we used Jack=11, Queen=12, King=0, and Ace=1 and left the Jokers out. In the ninth grade, black suits were positive numbers and red suits were negative numbers.)
2. Begin by shuffling the deck and placing it, face down, in a pile at the front of the room. Two students go to the front of the room; each draws a card without looking at it.
3. The players face the class and each “salutes” the class by bringing the card to his forehead. The class then tells the two players only the product of the two cards.
4. The players turn and face each other simultaneously with the cards still held to their foreheads. The winner is the student that can correctly identify the card he is holding.
5. The winner stays at the front of the room and another student comes forward to challenge. Play continues until the deck is used or for an allotted period of time.
The mathematical goals are to practice basic multiplication facts and to think about the relationship between multiplication and division. The game is very adaptable to addition and subtraction.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
My seventh through ninth graders love this activity! I have introduced it at the different levels depending on student needs. At first the game is very challenging and results in lots of jumping up and down as they try to figure out the answer. I “caught” a group of kids playing it before school one morning when they discovered I had left a deck of cards out on the supply table.
_4_ Was the purpose of the activity clear to me?
_4_ Was the purpose of the activity clear to my students?
_3_ Did the activity support a range of learning styles?
_4_ Were the students engaged during this activity?
_15_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
…telling them at the beginning that knowing their integer multiplication facts would make solving equations more efficient as well as help with lots of other math. This game would be a fun way to practice. I told them I would be listening to their play in order to assess their progress.
The part of the lesson that was student-centered was…
…the actual play of the game. The only teacher activity was introducing the game. I was free to listen and assess both the individuals playing and the group participation.