Box Cars and One-Eyed Jacks MATH GAMES THAT BUILD THE BRAIN "MATTER" Jane Felling John Felling [email protected] [email protected] phone 1-866-342-3386 / 1-780-440-6284 fax 1-780-440-1619 boxcarsandoneeyedjacks.com BoxCarsEduc BoxcarsEducation Teaching Tips from Box Cars And One-Eyed Jacks Box Cars And One-Eyed Jacks Inc. Organizing Your Cards & Card Management Use three large buckets (1 gallon or 4 liter each}. Gather a lot of decks of cards. Approximately 1 deck per student but 1 deck per 3 students is a good start (purchase, donated, brought from home}. The joke "not playing with a full deck" applies here. We don't play with full decks as it's not important to the math of the games. Full decks are not necessary when organizing the cards, and not worrying about full decks speeds getting cards out and putting them away (as seen below) at the beginning and end of classes. In the first bucket, put your low cards. For example, John likes to put his 1's, 2's, 3's, 4's and 5's. The cards match the fingers on the hand, keeps sums to 10, products to 25, denominators to 1/5s. On the other hand, Jane likes to have 1's through 6's as this allows matching the cards to a typical 6-sided die. This also allows sums to 12, products to 36 and fraction denominators to 1/6s. The key here is that as teacher, decide what cards go into your buckets based on your classroom routines. In the second bucket, put the rest of your single-digit cards. John - 6's, 7's, 8's, 9's, and 0's (Kings for 0 if using a regular deck). Jane - 7's, 8's, 9's, and 0's (Kings for 0 if using a regular deck). The cards in this bucket along with cards in the first bucket allow for Place Value (0-9 digits), sums to 18, products to 81 and fraction denominators to 1/9s. In the last bucket, put everything else- 10's 11's 12s (Jacks for 11, Queens for 12 if using regular decks) and any wild cards or jokers . GETTING CARDS OUT Once a teacher has identified a game and shown how to play,the students are told to get a "small" or "big" handful of cards from either a specific bucket or buckets SHUFFLING AND DEALING Cards are "mushed up" and quickly separated into as many groups as players (typically 2 for 2 players, 3 for 3 players). The player Mushing the cards is the last to pick a pile (piles do not have to be exactly equal. If "winning" is important, the winner is whoever has the most cards in their "point pile" at the end}. CLEANING UP Players quickly place the cards into 3 piles. First pile has 1s 2s 3s 4s and 5s. Second pile has 6s 7s 8s 9s and 0s. Last pile has 10s 11s 12s Wild Cards,Jokers,etc. The piles are then placed into their corresponding bucket Organizing Your Dominoes & Dominoes Management A typical class will need a minimum of one set of dominoes for every two students (about 12 sets). If feasible , 1 set per student is even better. First and Foremost Use Dominoes of Different COLORS! This makes it easier to determine each student's or group's set while playing and when putting dominoes away. If you already have sets of the same color, get an adult (parent?) volunteer with 6 colors of permanent spray paint. The adult volunteer takes one set, lays them face-down on newspaper (outside or other well-ventilated area) and sprays the back of the set all one color (for example "green"). The volunteer then takes the other sets and repeats the same process but with a different color for each set until the first 6 sets are done. The volunteer continues to do sets of 6 in this way until the entire collection of dominoes has been done. Keep the dominoes in their sets inside easily opened and closed see-through containers such as Mesh Bags, Traveling Soap containers, heavy duty sandwich sized freezer bags etc. 2 For each week that the students are using the Dominoes, have the students make sure they have a complete set by using their set to fill in the Dominoes Outcomes Chart (page 78 in Domino Games - Connecting The Dots, page 77 in Domino Games - Linking The Learning). When students are done using the dominoes for the class, have them make stacks of 4 dominoes (a complete set of 28 double-6 dominoes will have 7 stacks). If they have a complete set, they put the dominoes into the container and then put the container away. If a set is missing a domino, it is important that the teacher knows so it can either be found or, if all else fails, the container for the set is marked as "incomplete" until a replacement can be found. Younger students may find it easier to put them into stacks of 2 (14 stacks for a complete set). Organizing Your Dice & Dice Management Keep dice that are the same together in one container (for example 0-9 dice in one containe r, + and - dice in another container, 1-12 dice Iin a third container, etc.). See-through re-sealable Tupperware containers or heavy duty mid-sized freezer bags work well. One student per group or game gets the dice for the game and returns the dice at the end of the game. Have the students roll the dice into their hands! Roll their dice into the "Hockey Net", "Soccer Goal", "Dug out" etc. In other words the dice rolled by one hand and are blocked from going too far by the other hand. Another effective example is to have the students roll the dice with both hands, "trap" the dice in both hands and then "hide" the dice as they fall the 2 cms from their hands onto the playing surface. The roll is "revealed" when they remove their hands from over the dice. For noisy dice -roll on somethi ng " soft" Fun Foam, Felt liners or pads, table setting mats etc all work well. In a pinch, have the students roll on 5-10 sheets of paper stacked on top of each other. The stacked paper muffles a lot of the sound. Organizing & Managing Your Dice Trays (36 dice in a tray) When taking the dice out of the tray. Remove the tray from the bag, turn the tray upside-down (black on top) and take the black tray off of the clear lid (the dice remain in the lid). The dice are now easily "poured out" of the lid onto the playing surface. Play on the floor when possible. The dice don't "fall off' the floor and most students enjoy the experience of playing on the floor as it gives them room to "spread out". Have the students roll the dice into their hands! Roll their dice into the "Hockey Net", "Soccer Goal", "Dug Out" etc. In other words the dice rolled by one hand and are blocked from going too far by the other hand. Another effective example is to have the students roll the dice with both hands, "trap" the dice in both hands and then "hide" the dice as they fall the 2 cms from their hands onto the playing surface . The roll is "revealed" when they remove their hands from over the dice. For noisy dice - roll on something "soft". Fun Foam, Felt liners or pads, table setting mats etc all work well. In a pinch, have the students roll on 5-10 sheets of paper stacked on top of each other. The stacked paper muffles a lot of the sound. When putting the dice back into the trays at the end of a class have the students start with the lid, using one hand to "separate" one half of the lid from the other. The students take all of ONE COLOR of the dice and pour them into ONE HALF of the lid. They spread the dice into the half, "patting down" the dice so the dice are flat and in place. Then all of the dice of the OTHER COLOR are poured into the other half of the lid. Again, the students "pat down" the dice so the dice are flat and in place. The black tray is then fitted on to the top of the dice in the lid. The tray is now complete and can be slipped back into the ziplock bag. Use rubber bands to separate parts of the tray. This is useful when using the trays for place value and you want to limit size to less than 100,000 or you want to have a "decimal place". 3 By: 4 Table of Contents GAME NUMBER GAME NAME CONCEPTS COVERED 5 Math Glossary WORD MEANING OR EXAMPLE 6 Game Number: Title: Players: Skills: Equipment: How to Play: Goal: 7 Adding and Subtracting Strategies With Cards and Dice 1. Adding with Cards • • • • • Counting on >Addend / bracelets on the left Fun Foam Mats Making tens / missing part +9 visual / -9 extension with manipulatives 2. Subtracting with Cards • Concrete • Counting back • Missing part / fact families 3. Adding with Dice • Squeezing out the greatest addend "birthday" • Belly button dice / double regular • Identify > • Identify>and name number • Identify>and count on from>to get the sum 4. Doubles • Master the doubles • Nicknames, knocking the doubles out • Doubles +1, +2, -1, -2 8 DOUBLES + PATTERNS DOUBLE DOUBLE + 1 even NICKNAME odd 1+1=2 1+2= 3 Goal Post 2+2= 4 2+3= 5 Rabbit, Kangaroo, Caribou 3+3= 6 3+4= 7 Dental 4+4= 8 4+5= 9 Spider, Octopus 5 + 5 = 10 5 + 6 = 11 Ten Tickly Fingers 6 + 6 = 12 6 + 7 = 13 "Box Cars", Egg Carton, Farmers 7 + 7 = 14 7 + 8 = 15 Valentine's Day 8 + 8 = 16 8 + 9 = 17 Driver Double 9 + 9 = 18 9 +10 = 19 Adult Double • Learn doubles - cards 1-6 or 1-9, regular dice, 10 sided 0-9 dice • +1 Trick counting on • Doubles + 1 Then transfer to symbolic work PATTERNS FOR DICE PLAY 1 2 3 +4 10 2 4 6 +8 20 6 7 8 +9 30 SIMPLE SIXES SUCCESSFUL SEVENS EASY EIGHTS NIFTY NINES TERRIFIC TENS ENORMOUS ELEVENS TREMENDOUS TWELVES 9 10 0 0 1 2 3 2 1 1 two one 4 5 2 3 three 6 7 3 4 four 8 9 4 5 five 10 6 six 11 5 12 7 seven 8 7 14 eight 13 6 Box Cars & One-Eyed Jacks inc. NUMBER LINE WORK 15 9 nine 16 8 17 10 ten 18 9 11 eleven 19 20 10 12 twelve PRIMARY SUPER MUSH LEVEL: K–2 SKILLS: fact fluency, addition facts to 12, number patterns PLAYERS: 2 (cooperative team) EQUIPMENT: GOAL: 1 tray, recording sheet to fill up the tray with 36 dice matching the selected fact family GETTING STARTED: The teacher selects a fact family for teams to work on: Simple Sixes Successful Sevens Easy Eights Nifty Nines Terrific Tens Enormous Elevens Tremendous Twelves All dice are removed from the tray and “super mushed” – i.e. scrambled all together and rolled for about 20 – 30 seconds. The teacher calls stop and the dice are then set for the activity. Together both players now hunt for combinations of dice that match the set fact family and place them into the tray. EXAMPLE: Round of Easy Eights: 11 PRIMARY SUPER MUSH MATH JOURNAL WORK AND EXTENSIONS: 1. Students can be very creative problem solvers as they fill up their tray and have fewer choices and/or spaces left to use. As spaces fill up they may “share” open spaces as follows: Easy Eights Players put a 3 in here, and make 4 1 3 4+1+3 in a corner. Players can share the 4 from the 4+2+1+1 sentence, and the 1 from the 3+4+1 sentence, using them to make a new one. 12 PRIMARY SUPER MUSH _________________ _________________ 13 HORSE RACE - PRIMARY ADDITION LEVEL: K-2 SKILLS: adding to 12, commutative property of addition, fact families PLAYERS: 2 (1 vs 1) EQUIPMENT: GOAL: tray of dice (each player needs 18 of their own color), gameboard to have the greatest number of dice on your side of the “racetrack” at the end of the game GETTING STARTED: Each player takes 18 dice of one color and picks a side of the dice tray to be their “racetrack”. Each player picks up a pair of dice, rolls, and calculates their sum. The player with the greatest sum puts their dice into their side of the racetrack. Both players verbalize their sums. EXAMPLE: + + = 8 PLAYER ONE MATH TALK + + = 6 PLAYER TWO Player One says “8 is a greater sum than 6” The player with the greatest sum places their dice in their side of the racetrack. The player with the least sum tosses their dice into the lid. Players each pick up another pair of dice, roll and compare their next sums. In the event of a EQUAL SUM – both players put their two dice into their side of the racetrack. TIE or Play continues until both players’ 18 dice have been rolled out. The player with the greatest number of dice on their side of the racetrack wins. Level 1 : Addition to 12 - Players roll two dice and add them Player One Player Two Level 2 : Addition to 18 - Players roll three dice and add them. Level 3: Multiplication to 36 - Players roll two dice and multiply them Level 4: Multiplication to 72 - Players roll three dice, choose two to add together, then multiply the sum by the third. Add dice to the track along a curving path to simulate the race! 14 HORSE RACE STRATEDICE PLAYER ONE PLAYER TWO ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ ____ + ____ = ___ 15 WARP 18 LEVEL: K-3 SKILLS : adding to 18 with three addends , fact families , associative property of addition, working with patterns PLAYERS: 2 (1 vs EQUIPMENT: 1) tray of dice (each player needs 18 of their own color), gameboard GOAL: to have the most dice in the "racetrack" at the end of the game GETTING STARTED : MATH TALK Introduce the associative property of addition, which states:"the sum stays the same when the grouping of addends is changed" (6 + 4) + 2 - 10 + 2 = 12 6 + (4 + 2) - 6 + 6 = 12 Each player takes 18 dice of one color and picks a side of the dice tray to be their "racetrack". Each player picks up three dice, rolls, and calculates their sum. The player with the greatest sum puts their dice into their side of the racetrack , and the player with the least sum tosses their dice into the lid. Both players verbalize their sums and the winner verbalizes : MATH TALK "15 is a greater sum than 12." More importantly, we have students move their dice and set them how their brain put it together . Players each pick up three more dice, roll and compare their next sums. In the event of a TIE or EQUAL SUM both players put their three dice into their side of the tray . Play continues until both players' 18 dice have been rolled out. The player with the most dice on their side of the "racetrack" wins . 16 17 What's Under My Thumb? Copyright Box Cars and One-Eyed Jacks 2013 Level: Grades K-3 Concepts: Missing Addend, Subtraction, Counting On or Back Players: 1 vs 1 Equipment: Stratedice Tray, One Game board, pencil Goal: To figure out the number under the other player's finger. Setting Up: Each player has their own color dice. Player One turns their back to Player Two and secretly rolls two of Player Two's dice (rolled 5 and 1, covered the 1 with a finger), adds the two dice together to get the sum of 6. Player One then turns back around so Player Two can see the 5 and the other covered die (1). Player One then says "Six is my sum! What's under my thumb?" Player Two figures out that 1 added to 5 equals 6 and says "ONE". Player Two records the 5 on the line for one addend, records the 1 in the box for the missing addend and records the sum (6) into the sum location. Since player Two was correct, Player Two places both dice into their side of the Black Tray. Players continue to alternate turns secretly rolling two of the other player's dice, adding them and saying the rhyme. If players say the correct missing addend, they get to put their dice into the Black Tray. If they are incorrect, they place their dice into the clear lid. The player with the most dice in the Black Tray at the end of 9 rounds wins the game. Example: Player One rolled 1 and 5 and covered the 1 and said "Six is my sum! What's under my thumb?" Player Two filled in the 5 + 1 = 6 on the paper and said "ONE". Since Player Two was correct, they placed their dice into the Black Tray. (incorrect answers go in lid) Player One Player Two ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = ____ + ____ = Total Dice in Black Tray = ____ + ____ = Total Dice in Black Tray = 18 19 PRIMARY RACE WITH RULES DIFFERENCE OF 1 ODD SUM PLAYER TWO PLAYER ONE EVEN SUM Each player takes 18 dice of own color. Players will be cycling through the following: EVEN SUM, DIFFERENCE OF 1, ODD SUM Each player rolls 2 dice each turn, first looks for EVEN SUM. If EVEN, they can place into their side. Next roll they need a DIFFERENCE OF 1 answer and so on. First player to fill in entire side is the winner. 20 KNOCK YOURSELF OUT LEVEL: 2–6 SKILLS: adding, subtracting, probability, problem solving, multiplication, division for variation, creating outcomes charts, analyzing outcomes PLAYERS: 2 (1 vs 1) or 4 (2 vs 2) EQUIPMENT: GOAL: tray of dice (each player needs 6 dice of their own color plus 2 of their opponent’s color, and one half of the tray for their gameboard) to be the first player to remove all six of their dice from their side of the tray. GETTING STARTED: Players set up the gameboard as follows: PLAYER ONE PLAYER TWO The dice in the tray are arranged in a numeric sequence 1 – 6 and remain in that order for the entire game. Once the tray is set up, play can begin. Players alternate turns and play as follows: The two extra dice are rolled on each player’s turn. The dice may be either added for a sum OR subtracted for a difference. The answer must be a number from one to six. A player can choose which operation to perform and remove only one die per turn. The removed die must not be changed, i.e. if the die removed is the (three), it must remain a three, and it must be placed back into the third position if required during the course of the game. 21 KNOCK YOURSELF OUT If a player is unable to either add or subtract to equal any of the numbers left on their side of the tray, the player receives a STRIKE and they must CHOOSE and REPLACE any die that has been earlier removed. If there are no dice to replace, the player simply misses that turn. ROLL WARNING: Double 6’s, double 5’s and double 4’s are automatic strikes. The player will either miss a turn or put a die back if these rolls occur. EXAMPLE: Player One only Roll 1: 6 & 2 6 – 2, removes 4 5 4 3 1 2 Roll 2: 3 & 2 3 + 2, removes 5 Roll 3: 2 & 1 2 + 1, removes 3 Roll 4: 6 & 5 6 – 5, removes 1 Roll 5: 6 & 1 6 – 5 = 1, which is already out 6 + 1 = 7, which is not an option Player must now put a die back. Player chooses 1 Players continue to alternate turns rolling, analyzing, adding and subtracting combinations until one player has successfully removed all six of their dice at once. 22 SLAM DUNK DIFFERENCES MY ROLLS MY ROLLS STEP 1 STEP 1 STEP 2 STEP 2 MY ROLLS MY ROLLS STEP 1 STEP 1 STEP 2 STEP 2 23 SLAM DUNK WITH REGROUPING MY ROLLS MY ROLLS MY ROLLS MY ROLLS 24 10 UP . LEVEL: SKILLS PLAYERS: EQUIPMENT: GETTING STARTED: Grade 1- 2 Adding to 10 Solitaire or cooperative pairs 2 0-5 dice, 1 gameboard Each player has a gameboard. The goal is to fill in a column (10 up) in as few rolls as possible. The player rolls the dice and adds the two numbers to find a sum. It is recorded in a space above the answer. The player continues to roll and record answers until one column is filled in. Players may add the numbers to find a sum and subtract the numbers to find a difference. Both answers may be recorded ie. Roll 6 and 2 and record 6 + 2 = 8 and 6 -2 = 4. Have players compare the shapes of their graphs when the game has been played using addition only, compared to addition and subtraction. VARIATION: 0 1 2 3 4 5 6 7 8 9 10 25 26 2 1 3 three 4 four Roll 2 dice and add. Record math sentence above answer. First to "Reach the Top" wins. two one 5 five 6 six 8 eight 9 nine 10 ten 6+2=8 6-2 =4 6÷2=3 6 x 2 = 12 Record all 4. K's use 1-12 die or spotted 12 sided die. Can use multi-operations: e.g. roll 6 and 2 7 seven Box Cars & One-Eyed Jacks inc. Reach For The Top 11 eleven 12 twelve 0 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Box Cars & One-Eyed Jacks inc. 0 - 20 Graph© ADDITION TIC TAC TOE 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18 Adapted From Dice Works page 44. Use cards 0 (K) through 9. Mix the cards up. Players take turns flipping over two cards at a time. One card is located at the top, the other is located at the left side. Players trace their fingers from the two numbers to the sum (answer) on the board. For example 3 and 7 are flipped over. 3 is placed on the top and 7 is placed on the left. The player runs their left finger along the "7" row and runs their right finger down the "3" column" until they meet at the "10". They place a chip at that location. The player then switches the cards and places the 7 at the top and the 3 on the left side. The player runs their left finger along the "3" row and runs their right finger down the "7" column until they meet at "10". They place a chip at that location. Most turns will have players place two chips. Players continue to alternate turns until one player places a chip that completes 3-in-a-row, 4in-a-row or 5-in-row Tic Tac Toe. When this happens, the player removes the chips for that Tic Tac Toe and places them into their "point pile". Tic Tac Toes usually occur two at a time. Stealing points - If a player has a turn where an answer already has a chip on it, the player.removes that chip, places it into their point pile and then places a new chip on the answer. For example, if a player flipped a 3 and 7 and the 10 answer already has a chip on it. 28 Multiplication Board 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 3 4 5 6 7 8 9 10 11 12 2 2 4 6 8 10 12 14 16 18 20 22 24 3 3 6 9 12 15 18 21 24 27 30 33 36 4 4 8 12 16 20 24 28 32 36 40 44 48 5 5 10 15 20 25 30 35 40 45 50 55 60 6 6 12 18 24 30 36 42 48 54 60 66 72 7 7 14 21 28 35 42 49 56 63 70 77 84 8 8 16 24 32 40 48 56 64 72 80 88 96 9 9 18 27 36 45 54 63 72 81 90 99 108 10 10 20 30 40 50 60 70 80 90 100 110 120 11 11 22 33 44 55 66 77 88 99 110 121 132 12 12 24 36 48 60 72 84 96 108 120 132 144 Box Cars & One-Eyed Jacks inc Multiplication Tic Tac Toe Player one rolls 2 x 0-9 or 2 x 1-12 dice and finds the product (eg 4x6=24; 6x4=24) Cover spaces with bingo chips (one space only would be covered if doubles are rolled) Player Two takes their turn. Players continue to alternate turns Build Tic Tac Toe, three or more in a row horizontally, vertically or diagonally One point per chip and remove from board so spaces are open again Roll your partner's space and capture for 2 points per chip Play for a set period of time 29 30 Nine Plus LEVEL: Grade 2 and up SKILLS: Addition facts, adding with 9 PLAYERS: 2 EQUIPMENT: 1 deck of cards Ace – 9 (Ace = 1) GETTING STARTED: Each player plays on their own gameboard. Each player draws a card and puts it onto the square space on their gameboard. Players add the number on the card to the 9 on the board. Players should notice that the number in the ones place of their answer is one less than the number they drew (3 + 9 = 12, 2 is one less than 3). Players can write their equations down, or say them out loud. They can also say or write down what they notice about the number they drew and the ones digit of their answer. For example, a player who draws 4 would say or write: “4 + 9 = 13” and “3 is one less than 4.” Play through a certain number of cards, or for a period of time. VARIATION: You can also use the rules to Addition Snap. Use one gameboard and pile of cards for both players. 31 To Sum It Up LEVEL: Grade 3 and up SKILLS: Adding 3 digit numbers PLAYERS: 2 or more EQUIPMENT: 1 deck of cards Ace – 10 (Ace = 1, 10 = zero), paper and pencil GETTING STARTED: Each player draws a 3 by 3 grid as a gameboard and the cards are shuffled. Then a card is drawn and placed face up. All players write the number on the card into a space on their gameboard. Eight more cards are drawn and players fill in the rest of their gameboards. Once all nine spaces are full, players add the three numbers they've made together. The player with the greatest sum scores a point. Play to 10 points. EXAMPLE: VARIATION: The nine cards drawn, in order, are 5, 7, 4, 6, 5, 10, Ace, 3 and 9. Three players build their gameboards as follows. Player Three wins with a sum of 2,326. Player One Player Two 7 3 4 7 5 0 Player Three 7 3 5 6 5 0 6 5 1 6 4 0 + 5 =1, 9 9 1 4 9 9 5 1 7 5 + 3 =1, 7 5 0 =2, 3 2 6 + For less experienced students, you can draw six cards and make two three-digit numbers, or draw only four cards and make two two-digit numbers. 32 What's the Difference? LEVEL: Grade 2 - 5 SKILLS: Subtraction of three-digit numbers PLAYERS: 2 or more EQUIPMENT: 1 deck of cards Ace – 10 (Ace = 1 and 10 = zero), 1 gameboard for each player. GETTING STARTED: Each player draws a 3 by 2 grid as a gameboard and the cards are shuffled. Then a card is drawn and placed face up. All players write the number on the card into a space on their gameboard. Five more cards are drawn and players fill in the rest of their gameboards. Once all six spaces are full, players subtract the bottom number they made from the top number. The player with the smallest difference scores a point. If the bottom number is larger than the top, they “strike out” and can't score for the round. Play to ten points. The six cards drawn, in order, are 6, Ace, 7, 4, 10 and 8. Three players build their gameboards like below. Player One strikes out, while Player Three wins with a difference of 141. EXAMPLE: Player One 6 4 0 – VARIATION: 8 7 – 4 8 Player Three 7 8 1 4 0 – 6 = 1 9 1 Strikeout! = 1 4 1 For less experienced players, draw only four cards and build two two-digit numbers. Source: All Hands on Deck for Families copyright Box Cars and One Eyed Jacks Inc. www.boxcarsandoneeyedjacks.com 1 Player Two 6 7 1 0 33 36 SLAM DUNK PLAYER ONE PLAYER TWO Each player takes 18 dice of own color. Each player rolls 2 dice, multiplies. Player with greatest product places them into their side of the tray, least product places in lid. Player with the most dice in their side of the tray at the end of the game wins. 34 SLAM DUNK PLAYER ONE PLAYER TWO ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ ____ x ____ = ___ 35 72 SLAM DUNK - MULTIPLICATION LEVEL: 3–6 SKILLS: multiplication, products to 72, 144, associative property of multiplication, factors PLAYERS: 2 (1 vs 1) or 4 (2 vs 2) EQUIPMENT: GOAL: tray of dice (each player needs 18 of their own color) to have the most dice in the “racetrack” at the end of the game GETTING STARTED: Introduce the associative property of multiplication which states: MATH TALK “The product stays the same when the grouping of factors is changed” i.e. (6 x 4) x 2 = 24 x 2 = 48 6 x (4 x 2) = 6x8 = 48 Students will explore this concept as they play out this variation of 72 Slam Dunk. Each player takes 18 dice of one color and picks a side of the tray to be their “racetrack”. Each player picks up three of their dice, rolls and calculates their product. The player with the greatest product puts their dice into their side of the racetrack, and the player with the least product tosses their dice into the lid. Both players verbalize their products and how they grouped their dice for multiplying. EXAMPLE: Player One Player One says “4 x 3 = 12 x 6 = 72” Player Two Player Two says “6 x 5 = 30 x 2 = 60” MATH TALK Player One says “72 is a greater product than 60”. 36 MULTIPLICATION SCRAMBLE From "Dice Works" page 69. Roll two special 1-12 dice at a time. Multiply the factors, place the math sentence on the appropriate space on your side. If the space is already filled, then no space is filled in for that turn. First player to fill in their side is the winner. 0 - 9 0 - 9 10 - 19 10 - 19 20 - 29 20 - 29 30 - 39 30 - 39 40 - 49 40 - 49 50 - 59 50 - 59 60 - 69 60 - 69 70 - 79 70 - 79 80 - 89 80 - 89 90 - 99 90 - 99 100 - 109 100 - 109 110 - 119 110 - 119 120 - 129 120 - 129 130 - 139 130 - 139 140 - 149 140 - 149 THE BIG ROUND UP From "Dice Works" page 72. Roll two special 1-12 dice at a time. Multiply the factors and round the product to the nearest 10's place. Circle the answer on your row. If the space is already filled, then no answer is circled for that turn. First player to fill in their side is the winner. 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 37 Place Value Teaching Tips Games support the instruction of place value concepts with baseten manipulatives. Always sit players side by side so they are reading numbers properly; use tens bracelets, thousands bracelets, playing mats / fun foam for building place values. For cards, sort out all tens, Jacks, Queens and Kings and use cards from 0-9 only. Place Value dice come in a variety of values which you can use to build differentiation and a variety of concepts into your instruction. Use number lines: 0 - 9, 0-100, or tape ten together for a 0-1000 line. Use chunking place value strategies with regular dice or in 3in-a-cube dice. Foam mats/ Dry Erase Boards 38 Betweeners Primary Roll Least Between Greatest 1 2 3 4 5 6 7 8 9 10 1. Three players, each need the same type of dice. 2. Each player rolls their dice. 3. Players arrange the three numbers: Least, Between, Greatest. 4. Between WINS the round and scores one point 5. Record the rolls. 6. In the event of a tie, no points are awarded. 39 Who's In The Middle? LEVEL: Grade 1 – 3 SKILLS: Place value to 100, betweeness PLAYERS: 2 EQUIPMENT: 1 deck of cards Ace – 9 (Ace = 1), paper and pencil, 1 – 100 chart GETTING STARTED: Each player draws four cards and makes two twodigit numbers with them. After players have made their numbers, two more cards are turned over to make a new two-digit number. The first card turned over takes the tens place and the second takes the ones place. Player score a point if the new number falls between the two numbers they have made. They may need to use a 1 – 100 chart to determine if they score a point. Making a large spread between their two numbers will help a player score more often. Players continue drawing four new cards, making two new numbers each and drawing new two-digit numbers for comparison. The first player to reach twenty points is the winner. VARIATION: For K – 1 students, play with a deck of cards from Ace – 10 and turn only one card over at a time. EXAMPLE: 6 3 4 3 5 2 A 2 Player 1 draws Ace, 2, 3 and 6, builds 63 and 12 and scores. 5 and 2 are drawn and put in the middle as 52. A 2 Player 2 draws Ace, 2, 3 and 4, builds 43 and 12, both lower than 52. No points scored! 40 Betweeners © Box Cars And One-Eyed Jacks. 4 Player Version – Highest doesn't win. Lowest doesn't win. The two between numbers win. Betweeners Variation of Betweeners From Math Attack © Box Cars And One-Eyed Jacks Concepts: Number Sense, Ordering Numbers (whole and decimal) Equipment: One 3inCube die / player Goal/Object: record a number that is between the highest and lowest for the round Traditional- Each player shakes their own 3inCube die and secretly looks at it, mentally determining the possible answers they could use. Each player then secretly records one of their possible answers. Once all the players have recorded their answer, they reveal it to the other players. All players copy all other players' answers onto their own score sheet. The answers are compared, lowest doesn't win, highest doesn't win, between number (or numbers if 4 player game) wins. Variations: (1) Players are allowed to create numbers with decimals meaning answers can range from 0.111 to 666. (2) Players create multi-operation math sentences trying to have the between answer example 3+2x1=5 (3) Players create mixed fractions example 3 2 1 makes 3½ or 1⅔ or 2⅓ 2 1 1 can only make 1½ (4) For simpler version of the game, each player can use a 1-12 die ( or 1-20 die/player or 1-30 die/player ) (5) Division: Make 2-digit number, divide it by the remaining number. (Rolled 2, 3, 5 made 35 ÷ 2 = 17.5) 41 42 Rolls 17 X 23 X X X X X X X X X X X X Round Example 1 2 3 4 5 6 7 8 9 10 11 12 380 391 Actual Total Differences = Estimate 10 Difference Name: _______________________ Date: ________________ Multiplication Estimation – Recording Sheet 43 Rolled 30 and 12. 30÷12 = 2 R6 see pictures to right to see how to do this on a number line. 100 Board Wipe Out Level: Grade 3 and up Skills: Multi-operations ( + - x ÷ √ X2 ), Order of Operations Players: 2-3 players working together as a team Equipment: Dice Tray, pencil, recording sheet per player/team Objective/Goal: To make equations for 1-100 in fewest rolls Getting Started: Team One decides whether to roll 3, 4 or 5 dice and records the roll in the Roll 1 space on the recording sheet. Team One then creates math sentences using the numbers rolled that have the numbers 1-100 as answers. They record each math sentence on the recording sheet in the space for the answer. Each math sentence must use each number rolled. For example, if 4, 4, 2 and 6 are rolled then each math sentence must contain 4, another 4, 2 and 6. Once the team has exhausted all the possibilities for Roll 1, they can take Roll 2. At the beginning of each roll, the team can decide to roll 3, 4 or 5 dice. In other words, they don’t always have to roll the same number of dice for every roll. Example: The team rolled 4, 4, 2 and 6 and made the following math sentences, (utilizing the rules for Order of Operations where necessary - see examples with answers = 10 and = 12): 4 x 4 x 2 + 6 = 38 (6 – 4 + 4) x 2 = 12 6 – 4 + 4 x 2 = 10 42 x 4 + 6 = 70 etc In the examples, the team first rolled 4 dice and using those numbers, made equations for 30 answers before rolling a second time. For the second and third rolls, they rolled 5 dice and had written math sentences for 61 answer before the math period ended (they said they could have kept going). Variation: (1) Teams can use dice other than regular spotted dice, such as 10-sided 0-9, 12-sided 1-12, 20-sided 1-20 or 30-sided 1-30 dice. (2) Teachers may place restrictions on equations to make it more challenging such as “Every math sentence must include at least one multiplication component”. 44 100 Board Wipe Out – Recording Sheet Team Members _______________ _______________ Roll One: __________ Roll Two: __________ Roll Five: __________ Roll Six: __________ _______________ Date: __________ Roll Three: __________ Roll Seven: __________ Roll Four: __________ Roll Eight: _________ = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = 11 = 12 = 13 = 14 = 15 = 16 = 17 = 18 = 19 = 20 = 21 = 22 = 23 = 24 = 25 = 26 = 27 = 28 = 29 = 30 = 31 = 32 = 33 = 34 = 35 = 36 = 37 = 38 = 39 = 40 = 41 = 42 = 43 = 44 = 45 = 46 = 47 = 48 = 49 = 50 = 51 = 52 = 53 = 54 = 55 = 56 = 57 = 58 = 59 = 60 = 61 = 62 = 63 = 64 = 65 = 66 = 67 = 68 = 69 = 70 = 71 = 72 = 73 = 74 = 75 = 76 = 77 = 78 = 79 = 80 = 81 = 82 = 83 = 84 = 85 = 86 = 87 = 88 = 89 = 90 = 91 = 92 = 93 = 94 = 95 = 96 = 97 = 98 = 99 = 100 45 Place Value Patterns Students typically begin pattern work in the early primary grades and it often remains a challenge throughout their elementary years. Pattern counting is an excellent way to practice place value and explore number patterns. When doing this activity with students, it is best to go through several examples, and allow for plenty of practice. To Model: Roll a decade die (00-90) and a ones (0-9) die. Example : 60 + 8 = 68 Players now verbalize a plus (+) 1 pattern 68, 69, 70, 71. Players now verbalize a minus (-) 1 pattern 68, 67, 66, 65. Players now verbalize a plus (+) 2 pattern 68, 70, 72, 74. Players now verbalize a plus (+) 10 pattern 68, 78, 88, 98. Players now verbalize a plus (+) 5 pattern 68, 73, 78, 83. Any additional numeric patterns can be introduced once the students are ready. Using a hundreds board with this activity may be beneficial as students will begin to see and understand the patterns that appear. This will extend into addition and subtraction strategies once 2-digit concepts are introduced. Once players have mastered these patterns, more complex scenarios can be introduced and practiced. Roll a hundreds die (000-900), decade die (00-90) and a ones (0-9) die. Example 300 + 20 + 4 = 324 Players now verbalize a plus (+) 1 pattern 324, 325, 326, 327. Players now verbalize a plus (+) 10 pattern 324, 334, 344, 354. Players now verbalize a minus (-) 10 pattern 324, 314, 304, 294. Players now verbalize a plus (+) 50 pattern 324, 374, 424, 474. Players now verbalize a minus (-) 50 pattern 324, 274, 224, 174. The bonus to students rolling dice is that combinations will come up where they must make logical predictions and expand their knowledge of number sense. These place value activities can be explored using decimal dice as well. Teaching Tip: Players can record all of their patterns for future practice. 46 Hundred Board 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Hundred Board Tic Tac Toe Player one rolls 2 0-9 dice and builds a ten's/one's number. Covers the space on the board with a bingo chip. eg 62 and/or 26 Player two takes their turn6 BBuild Tic Tac Toe three in a row, horizontally, vertically or diagonally. One point per chip. Roll your partner's space and capture for 2 points per chip. 47 48 Ten For Me 49 50 Tens 20 200 30 300 Player One 10 00 Hundreds 100 000 Ones 40 400 50 500 70 700 Hundreds 60 600 FLIPPIN' OUT Tens 90 100 Ones 900 1000 Player Two 80 800 Two-Digit Scramble LEVEL: Kindergarten – Grade 2 SKILLS: Place value to 100, betweeness PLAYERS: 2 EQUIPMENT: 1 deck of cards Ace – 9 (Ace = 1), paper and pencil GETTING STARTED: Each player needs their own gameboard. Each player turns over two cards and makes a twodigit number. Players call their number out loud, then write the number down in the appropriate space on their gameboard. If a player draws a 2 and a 7, for example, they can put 27 in the space for 20 – 29 or 72 in the space for 70 – 79. The first player to fill all ten spaces is the winner. VARIATIONS: To increase the difficulty, have players fill in their gameboards in order from lowest to highest. For longer playing time, add more blanks to be filled in. The game can also be played as a solitaire, “3 strikes and you're out.” Each player needs to make 10 - 19 __________ their own game board 20 - 29 __________ 30 - 39 __________ 40 - 49 __________ 50 - 59 __________ 60 - 69 __________ 70 - 79 __________ 80 - 89 __________ 90 - 99 __________ 51 Star 99 / Two Digit Scramble 00 - 09 __________ 00 - 09 __________ 10 - 19 __________ 10 - 19 __________ 20 - 29 __________ 20 - 29 __________ 30 - 39 __________ 30 - 39 __________ 40 - 49 __________ 40 - 49 __________ 50 - 59 __________ 50 - 59 __________ 60 - 69 __________ 60 - 69 __________ 70 - 79 __________ 70 - 79 __________ 80 - 89 __________ 80 - 89 __________ 90 - 99 __________ 90 - 99 __________ Fill in Frenzy / Three Digit Scramble 000 - 099 __________ 000 - 099 __________ 100 - 199 __________ 100 - 199 __________ 200 - 299 __________ 200 - 299 __________ 300 - 399 __________ 300 - 399 __________ 400 - 499 __________ 400 - 499 __________ 500 - 599 __________ 500 - 599 __________ 600 - 699 __________ 600 - 699 __________ 700 - 799 __________ 700 - 799 __________ 800 - 899 __________ 800 - 899 __________ 900 - 999 __________ 900 - 999 __________ Draw 2 (or 3) cards or roll 2 (or 3) place value dice to make a two (or three) digit number. Player can choose how to set their number and then write the number in the appropriate space on gameboard. If a player cannot use their roll, it counts as a strike and play moves to the next player. The first player to fill all 10 spaces is the winner. 52 100’s, 10’s AND 1’s HORSE RACE PLAYER ONE HUNDREDS TENS PLAYER TWO ONES HUNDREDS TENS ONES 53 ROLL ON PLACE VALUE – PRIMARY ROLLS ROUND ONE PLAYER ONE ROUND TWO PLAYER ONE ROUND THREE HUNDREDS PLAYER ONE TENS STANDARD FORM ONES HUNDREDS TENS ONES PLAYER TWO PLAYER TWO PLAYER TWO 54 ROUND ONE PLAYER ONE ROUND TWO PLAYER ONE ROUND THREE ROLL ON PLACE VALUE PLAYER ONE PLAYER TWO PLAYER TWO PLAYER TWO Roll on Place Value (from Stratedice) The goal of the game is to create the largest number. Players take turns rolling a die, placing it into the tray and announcing its place value for that roll. After 6 rolls, players compare numbers. A point is earned by the player with the largest number. A Place Value Systems die is rolled to identify a specific place value (for example 100's) A second point is earned by the player with the highest value in that place. A third "upside down" bonus point is awarded to the player with the biggest number when the tray is turned upside down and the numbers are compared. 55 ROLL ON PLACE VALUE - DECIMALS 56 ROCK & ROLL ROLL REGULAR DICE TO BUILD PLACE VALUE AS FOLLOWS 2 DICE: TENS / ONES HUNDREDS / TENS / ONES THOUSANDS / HUNDREDS / TENS / ONES TEN THOUSANDS / THOUSANDS / HUNDREDS / TENS / ONES TEN THOUSANDS / THOUSANDS / HUNDREDS / TENS / ONES 3 DICE: 4 DICE: 5 DICE: 6 DICE: HUNDRED THOUSANDS / Roll dice, arrange for greatest possible number First to call ROCK & ROLL scores 5 POINTS All other players must freeze their dice when ROCK & ROLL is called. If a player's number is greater than the player who called ROCK & ROLL, they also get 5 POINTS ROLL NUMBER EXPANDED NUMBER 1 2 3 4 5 6 7 8 9 10 57 Batters Up! Skills: Place Value to 100 000s, Addition with Expanded Notation Equipment: Cards 0-9. Place Value System die, paper/pencil Goal: Greatest total sum after ten rounds wins Getting Started: Each player builds a number in the 100 000s with their cards Build in order from 100 000s place to 1s place (Example 230 516) Each player reads their number to the other players. One player rolls the PV System die and calls out the place value Players identify the value at that place value in their number (this is their score for the round) and record their score for that round. Example: ten thousands is rolled, 3 is in the 10 000s place, score for that round is 30 000 Play 10 rounds, (rotate roller) then total your score. BATTERS UP! Round Number Roll Value/Points/Score 1 2 3 4 5 6 7 8 9 10 Total Score = Copyright Box Cars and One Eyed Jacks Inc. 58 59 • • • • Ten Millions Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones My Number Use 0-9 Dice Roll and then record on sheet to build number. Compare numbers with opponent at end of round. Largest number wins. For 3 players, the between number wins (ie not largest or smallest) Randomly choose specific place value, compare with opponent. Largest number wins. Hundred Millions What's My Number 60 • • • • Ten Thousands Thousands Hundred Tens Ones Tenths Hundredths Thousandths My Number Use 0-9 Dice Roll and then record on sheet to build number. Compare numbers with opponent at end of round. Largest number wins. For 3 players, the between number wins (ie not largest or smallest) Randomly choose specific place value, compare with opponent. Largest number wins. Hundred Thousands What's My Number Decimals Rainbow Fraction 61 Fraction Horse Race Middle Muddle Box Cars Stratedice Book page 34 (Adapted) Box Cars "Piece It Together With Fractions" page 28 Concepts: Comparing Fractions Equipment: Stratedice Tray, Chart, Fraction Pieces Goal/Object: To have the smallest fraction, have most dice in the racetrack at the end Each player has their own color of dice. Players roll 2 dice and create a proper fraction. Players build their fraction with fraction pieces (or find their fraction on the chart) and compare. Player with the SMALLEST fraction wins the round and places their dice in the "racetrack" (black grid). Losing player places their dice into the lid (clear grid). In the case of a tie or equivalent fraction, both players put their dice into the black tray. Play continues until all of the dice have been used. Player with the most dice in the black tray at the end wins. Variation: Each player rolls 3 dice and creates a mixed fraction (whole number and fraction) like 2¾. Concepts: Comparing & Ordering Fractions Equipment: Stratedice Tray / Player Goal/Object: to be the between fraction, have the most dice in the racetrack at the end. Players roll 2 dice and create a proper fraction. Players build their fraction with fraction pieces (or find their fraction on the chart) and compare. Player with the SMALLEST fraction DOES NOT WIN. Player with the LARGETS fraction DOES NOT WIN. Player with the IN-BETWEEN FRACTION WINS THE ROUND. Winner places their dice into their black tray, losers place their dice into their lids. In the case of a tie of 2 or 3 players or equivalent fractions for 2 or 3 players, all players put their dice into their lids (they all lose because no one is "between"). Play continues until all of the dice have been used. Player with the most dice in the black tray at the end wins. Variation: Each player rolls 3 dice and creates a mixed fraction (whole number and fraction) like 2¾. Rainbow Fractions Order In The Court Box Cars "Piece It Together With Fractions" page 49 Box Cars "Double Dare You" page 15 (Adapted) Concepts: Fraction Number Sense, Equivalent Fractions Equipment: Fraction Pieces (circles) Goal/Object: Find as many ways as possible of creating the whole (1) using at least two different kinds of fraction piece sizes. Players create a circle using at least two different colored fraction pieces. They then color in a circle on their page showing the different color pieces used and record the size of fraction pieces used (ie keep track of what sizes are used on the sheet). EACH "Rainbow" must be different for other "Rainbows" on the answer page. Concepts: Comparing and Ordering Fractions Equipment: 1 double regular die & gameboard per player Goal/Object: To place all 5 fractions in order in 7 or less rolls. Each player has a gameboard showing 5 places (left to right) to place fractions and 2 places for rejected fractions. Player one rolls a double die and makes a proper fraction from the roll. Player one records the fraction on their gameboard. Player two rolls their double die, makes a proper fraction and records it on their gameboard. Player one rolls again and makes another proper fraction and records it on their gameboard. Player two rolls again and records their second fraction as well. Players continue to roll and record fractions IN ORDER FROM LEAST to GREATEST on their gameboards until one player wins in even turns or both players bust. Player One 1/6 1/4 1/2 ___ 3/3 rolls 3/4 "OK" Previous Rejects = 1/5 Player Two 1/5 2/5 ___ 3/6 5/6 rolls 1/3 "Reject" Previous Rejects = 4/4 Player One wins the game, Player two can't play 1/3 between 2/5 and 3/6 (it's smaller than 2/5) 62 BASIC FRACTION HORSE RACE BASIC FRACTIONS WORK AND SCORE SHEET RECORD AND CIRCLE WHICH GAME NUMBER MY ROLLED FRACTION MY REDUCED FRACTION (if necessary) MY MY PLAYER HAS THE PARTNER'S FRACTION PARTNER'S REDUCED FRACTION LEAST FRACTION ME MY PARTNER (if necessary) 1 2 3 4 5 6 7 8 9 10 POINT TOTAL 63 ORDER IN THE COURT Reject Rolls Reject Rolls Reject Rolls Reject Rolls Reject Rolls Reject Rolls Use Double Sided Dice, 6-sided Dice, or 1-12 Dice Goal: To get as many fractions in a row as possible Roll one die at a time. (Variation: You may roll all the dice at once and race your partner to line them up) Write the fraction into the chain or put into the reject boxes. Points are awarded at the end of 7 rolls. 1 point for each fraction in the chain. Use Fraction Circles or Fraction Bars to check accuracy. Copyright Box Cars and One Eyed Jacks Inc. 64 BASIC FRACTION HORSE RACE 1 1 2 1 2 1 3 1 3 1 4 1 4 1 5 1 6 1 3 1 4 1 5 1 6 1 5 1 6 1 4 1 5 1 6 1 5 1 6 1 6 65 66 One Twelfth 1/12 0.083 8% One Eleventh 1/11 0.091 9% One Tenth 1/10 0.10 10% Two Elevenths 2/11 0.182 18% Seven Twelfths 7/12 0.583 58% Ten Twelfths 10/12 0.83 83% Eleven Twelfths 11/12 0.92 92% Twelve Twelfths 12/12 1.00 100% Eleven Elevenths 11/11 1.00 100% Ten Tenths 10/10 1.00 100% Nine Ninths 9/9 1.00 100% Eight Eighths 8/8 1.00 100% Ten Elevenths 10/11 0.909 91% Nine Tenths 9/10 0.90 90% Eight Ninths 8/9 0.888 89% Nine Elevenths 9/11 0.818 82% Nine Twelfths 9/12 0.75 75% Eight Elevenths 8/11 0.727 73% Eight Twelfths 8/12 0.667 67% Seven Elevenths 7/11 0.636 64% Eight Tenths 8/10 0.80 80% Seven Ninths 7/9 0.777 78% Seven Tenths 7/10 0.70 70% Six Ninths 6/9 0.666 67% Six Tenths 6/10 0.60 60% Six Elevenths 6/11 0.545 55% Six Twelfths 6/12 0.50 50% Five Elevenths 5/11 0.454 45% Five Twelfths 5/12 0.417 42% Four Elevenths 4/11 0.364 36% Five Tenths 5/10 0.50 50% Five Ninths 5/9 0.555 56% Seven Eighths 7/8 0.875 87.5% Seven Sevenths 7/7 1.00 100% Six Sixths 6/6 1.00 100% Five Fifths 5/5 1.00 100% Four Fourths 4/4 1.00 100% Three Thirds 3/3 1.00 100 Six Sevenths 6/7 0.857 86% Five Sixths 5/6 0.833 83% Six Eighths 6/8 0.75 75% Five Sevenths 5/7 0.714 71% Four Sixths 4/6 0.666 67% Two Halves 2/2 1.00 100% Four Fifths 4/5 0.80 80% Three Fourths 3/4 0.75 75% Five Eighths 5/8 0.625 62.5% Four Sevenths 4/7 0.571 57% Three Fifths 3/5 0.60 60% Two Thirds 2/3 0.666 67% Four Eighths 4/8 0.50 50% Four Ninths 4/9 0.444 44% Four Tenths 4/10 0.40 40% Four Twelfths 4/12 0.33 33% Three Elevenths 3/11 0.273 27% Three Tenths 3/10 0.30 30% Three Twelfths 3/12 0.25 25% Two Tenths 2/10 0.20 20% Two Ninths 2/9 0.222 22% Three Eighths 3/8 0.375 37.5% Three Sevenths 3/7 0.429 43% Three Ninths 3/9 0.333 33% Two Sevenths 2/7 0.286 29% Three Sixths 3/6 0.50 50% Two Fourths 2/4 0.50 50% Two Fifths 2/5 0.40 40% Two Sixths 2/6 0.333 33% Two Eighths 2/8 0.25 25% Two Twelfths 2/12 0.166 17% One Ninth 1/9 0.111 11% One Eighth 1/8 0.125 12.5% One Seventh 1/7 0.143 14% One Sixth 1/6 0.166 17% One Fifth 1/5 0.20 20% One Fourth 1/4 0.25 25% One Third 1/3 0.333 33% One Half 1/2 0.50 50% One Whole 1/1 1.00 100% Copyright Box Cars And One-Eyed Jacks Inc. Fractions Decimals Percents Fractions “Cents” copyright 2014 Box Cars And One-Eyed Jacks Grade 5 and up Converting fractions to equivalent percent or decimal, mental math, division, estimation 1 vs 1 Cards 1 to 12, Number Line 0-100, fraction/decimal/percent chart Earn points by having the most accurate answer when converting a fraction to its decimal or percent equivalent. Grades: Concept: Players: Equipment: Object / Goal: Set Up and Play: Each player begins with a deck of about half the cards in the game. Play begins with each player turning turn over the top card of their deck at the same time. Players count out loud “1, 2, 3 point”. While they are counting, they are mentally arranging the cards into a “Proper Fraction (numerator/top smaller than or equal to denominator/bottom), and calculating the percent equivalent. When they say “point” each player places one finger on the number line at the percent equivalent they think is correct (it is possible for both players to be on the same point) and says what their answer is. They check their accuracy by referring to the Fraction/Decimal/Percent chart or by using a calculator to divide the numerator by the denominator. If a player is exactly correct, they collect the cards from that round and place them into their point pile. In the case of a tie both players place the card they turned over into their point pile. If neither player is exactly correct, the player closest to the correct answer wins the round and places the cards into their point pile. Example: Player One turned over a 5 and Player Two turned over an 8. When they said “point” Player One pointed to 63 and said “five eighths of 100 is 63”. Player Two pointed to 65 and said “five eighths of 100 is 65. 5 divided by 8 is 62.5. Player One was the closest and wins, placing both cards into their point pile. Variation: 1. The number line is considered “1”. Players say the decimal equivalent when they voice their answer. In the example, Player One would have pointed to 63 and said “Five eighths of one is 0.63”. Player Two would have pointed to 65 and voiced “Five eighths of one is 0.65”. Exact answer is 0.625, Player One wins. 2. The number line is considered 100%. Players say the percent equivalent when they Voice their answer. In the example, Player One would have pointed to 63 and said “Five eighths of 100% is 63%.” Player Two would have pointed to 65 and voiced “Five eighths of 100% is 65%.””. Exact answer is 62.5%, Player One wins. Round Fraction Equivalent Example 5 8 62.5 Player 1 Player 2 63 65 Observations / Comments Both of us were close! 1 2 3 4 5 6 7 8 9 67 Balanced Equations © Box Cars And One-Eyed Jacks Inc. Concepts: Problem Solving, Linear Equations Equipment: Two 3-in-a-Cube Dice / Game Goal/Object: Be the first player to create a balanced equation. A player shakes both 3-in-a-Cube dice and places them on the table so all players can see them. Each player (or team of two - if that is the way the teacher has set them up) races to create a balanced equation with the numbers from one die on one side of the equation and the numbers from the other die on the other side of the equation. A player says "Balanced" when they have a balanced equation. Other players verify the "Balanced" player's equation. If correct, that player earns a point. In the case of a tie, if both players have a balanced equation (they could be different but still correct) they both earn a point The player with the most points at the end of the time wins. All players record all the winning answers for each round. Example: 3, 2, and 6 as well as 1, 2, and 5 2 3 - 6 = 5 - (1 x 2) OR 6 - 2 + 3 = 1 x 5 + 2 Betweeners (Traditional) Concepts: Number Sense, Ordering Numbers (whole and decimal) Equipment: One 3inCube die / player Goal/Object: record a number that is between the highest and lowest for the round Each player shakes their own 3inCube die and secretly look at it, mentally determining the possible answers they could use. Each player then secretly records one of their possible answers. Once all the players have recorded their answer, they reveal it to the other players. All players copy all other players' answers onto their own score sheet. The answers are compared, lowest doesn't win, highest doesn't win, between number (or numbers if 4 player game) wins. Variations: (1) Three addend addition. The between sum (add all 3 numbers) wins. (2) Use 12-sided die on a ruler, 30-sided die on a yardstick, 10s 1's on a meter stick (1-100) Variation of Betweeners From Math Attack © Box Cars And One-Eyed Jacks (unpublished) 68 TIC TAC OH NO! Box Cars And One-Eyed Jacks 2014 © 6 (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) 5 (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) 4 (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) 3 (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) 2 (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) 1 (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) 5 6 Y Use The Clear Lid X 1 2 Dice are placed on the X and Y to the right to verify which will represent the X coordinate and Y coordinate 3 4 (X,Y) Roll 2 dice Place "Y" coordinate into clear lid. "X" goes back into pile. Game ends when one player has less than 2 dice remaining. st If you land on a space already occupied, pull out the 1 die and discard into black tray. Put your "Y" in clear lid in its place. Scoring dice in play = 1 point each. Dice in Tic Tac Toes also count 2 points each. 69 TIC TAC OH NO! Player One Type of Tic Tac Toe Game ________ Game ________ Score 1 2 3 4 5 6 7 8 Total Dice (1 point/die) Total Score Player Two Type of Tic Tac Toe Score 1 2 3 4 5 6 7 8 Total Dice (1 point/die) Total Score 70

Download PDF

advertisement