MATH GAMES THAT CONNECT UNDERSTANDING TO LEARNING JOHN FELLING ASCD ANAHEIM MARCH 25-27, 2017 [email protected] phone 1-866-342-3386 1-780-440-6284 boxcarsandoneeyedjacks.com BoxCarsEduc BoxcarsEducation For electronic copy send an email to: [email protected] Please include the conference/workshop title BETWEENERS LEVEL: Grade 3 - 4 CONCEPTS: ordering whole numbers and decimals, analytical thinking PLAYERS: 3 or 4 EQUIPMENT: 1 x 3-in-a-cube die per player, 1 recording sheet per player GOAL: to have a between number in each round GETTING STARTED: To begin, each player records the names of all the players in the round on their recording sheets. All players shake their 3-in-a-cube die. On STOP players peek at their die, mentally figure all possible 3-digit numbers they can make from their roll and then record one of the possibilities next to their name on their recording sheet. Players then announce their numbers and record every player's number next to that player's name on their gameboard. Players compare all the recorded numbers in the round. EXAMPLE: STRATEGIZING... math thinking Player John: "456 is the least I can make but has the best chance to be the between number for the round." math thinking Roll Number John 4,5,6 456 Jane 1,2,3 321 Norm 1,4,5 415 math thinking Jane: "321 is the greatest I can make but has the best chance to be the between number for the round." Norm: "541 is too large to win, 145 is too small to win, my best chance is either 451 or 415. 415 is closer to the middle and is my best chance to be the between number. t rule w ist "John's 456 is greatest. Jane's 321 is least. Norm's 415 is between 321 and 456." Players circle 415 and Norm earns a point for the round. 1. Four Player Version - Rules and scoring remain the same, however there can be two between numbers in a round, with two players earning points if their numbers fall between the greatest and least for the round. 2. Students must place a decimal point in their number (eg roll 4,6,1 - 46.1, 4.61, .461) Rules and scoring remain the same. ©Box Cars and One-Eyed Jacks 2 BETWEENERS primary 1. Players must make the largest number they can with their roll. They compare their numbers and the BETWEEN number wins a point. 2. Players roll one 10 sided double dice and play a 10's and 1's version. Players must decide which die (inside or outside) will represent the 10's and 1's place. Rules and scoring remain the same. middle years 1. Players use their three numbers in a math sentence with the goal of having their answer being between the answers of their opponents. EXAMPLE: Player math thinking Roll Number John 4,5,6 5 × (6 - 4) = 10 Jane 1,2,3 (2 + 1) × 3 = 9 Norm 1,4,5 5+4-1=8 John: "What makes a good BETWEEN answer? I'm thinking something between 8 and 15." math thinking scores 1 point Jane: "3, 2 and 1 are small numbers so I need to maximize the answer I can get with them." math thinking Norm: "Answers around 7 or 8 have been winners in the past few rounds so I want an answer close to those." math talk John: " I first subtracted 4 from 6 so I had to place that in parentheses. I then multiplied the difference of (6-4) by 5 to get an answer of 10." Jane: "I placed 2+1 in parentheses because I wanted to have that done first so I could multiply the sum of (2+1) by 3 to give me a product of 9 for an answer." Norm: "I added 5+4 to get 9 then subtracted the 1 to get a final answer of 8." Jane scores 1 point for having the "between answer". JOURNAL WORK & EXTENSIONS: 1. Explain what would be the ideal between number if you used two 10-sided double dice? ©Box Cars and One-Eyed Jacks 3 BETWEENERS & CUBIC MYSTERY PLAYER ROLL PLAYER RECORDING SHEET NUMBER PLAYER ROLL NUMBER ROLL NUMBER PLAYER ROLL NUMBER PLAYER ROLL NUMBER PLAYER ROLL NUMBER PLAYER ROLL NUMBER PLAYER ROLL NUMBER ©Box Cars and One-Eyed Jacks 4 Rounding Recording Sheet Turn Rolled Standard Rounded To 10's Rounded to 100's example 400 , 20 , 7 427 430 400 Notes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 © Box Cars And One Eyed Jacks 2014 5 10 SIDED DOUBLE DICE WARM UPS 1. ADDITION: SUMS TO 18 - each player rolls a 10-sided double dice and adds their sum. Both players verbalize their sum. The player with the greatest sum scores a point. 6 8 = 15 9 "15 is a greater sum than 11" = 11 3 Students can explore the commutative property of addition: 6 + 9 = 15 or 9 + 6 = 15" 2. ADDITION: SUMS TO 36 WITH REGROUPING - each player rolls two 10-sided double dice and adds all four addends for the greatest sum. The player with the greatest sum scores a point. Player One: 6 2 + 9 5 Player Two: = 8 + 14 = 22 9 4 + 6 2 = 13 + 8 = 21 "22 is a greater sum than 21" This is a great activity for students to explore the associative property of addition. Addends from Player One above: 6 2 9 5 = 11 + 11 = 22 3. ADDITION: DOUBLES TO 36 - this is a two step mental math activity. Each player rolls a 10-sided double die, adds their sum, and then doubles it. The player with the greatest doubled sum scores a point. Player One: Player Two: 6 =6+4 10 x 2 = 20 4 9 =9+5 14 x 2 = 28 5 "28 is a greater sum than 20" 4. SUBTRACTION: FROM 9 - each player rolls a 10-sided double die, and subtracts the numbers for the least difference. The player with the least difference scores a point. Player One: 9 Player Two: =9-8=1 8 6 =6-2=4 2 "1 is a smaller difference than 4" ©Box Cars and One-Eyed Jacks 6 10 SIDED DOUBLE DICE WARM UPS 5. PLACE VALUE TO 99 - Outside number is 10's value, inside number is the unit or "one's". Students should play on a number line and place their die right down onto it to compare numbers. Play for greatest number, in later practice sessions work on least. Player One: 2 Player Two: "9 tens 2 ones = ninety-two" 92 9 4 6 "6 tens 4 ones = sixty-four" 64 "92 is greater than 64" As students mature, they can estimate and verbalize the difference between the two numbers: "92 is about 30 more than 64" =10 is ≈10 Add a third player and the between value scores a point. t w ist =10 rule 92 84 74 Player One: 1 8 Player Two: 81 1 1 Player Three: 11 11 Player Two 3 6 63 63 81 Player Three Player one "63 is between 11 and 81, Player Three scores a point" 6. DECIMAL PLACE VALUE ©Box Cars and One-Eyed Jacks 7 10 SIDED DOUBLE DICE WARM UPS 7. MULTIPLICATION: PRODUCTS TO 81 including practice with 0 - each player rolls a 10-sided double die and multiplies the two factors. The player with the greatest product scores a point. 6 2 6 x 9 = 54 9 2x0=0 0 Students can explore the commutative property of multiplication in this activity: "6 x 9 = 54 ; 9 x 6 = 54" 8. EQUIVALENT FRACTIONS - players roll one 10-sided double die between them and write down the fraction less than one that can be made. If 0 is rolled, it is used as "tenths" 10 . The players call out a simplified fraction (if possible) and one other fraction name. Play cooperatively. 3 6 = 3 6 = 1 2 and 6 12 ©Box Cars and One-Eyed Jacks 5 7 = 10 14 8 Multiplication Estimation – Recording Sheet Name: _______________________ Date: ________________ Round Rolls Estimate Actual Difference Example 17 X 23 380 391 10 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X 11 X 12 X Total Differences = ©Box Cars and One-Eyed Jacks 9 MATH SHAKERS ©Box Cars and One-Eyed Jacks 10 A H B FLUENCY PRACTICE + STRATEGIES + WHOLE BRAIN ENGAGEMENT = POWERFUL LEARNING A RE A E V M AT H S H A KE K Subitizing, recognizing numbers 1-6 Comparing > <, numbers 1-6, ODD/EVEN Recognition of doubles, doubles + 1 Plus 1, Plus 2, Minus 1, Minus 2 Making 10’s, 100’s, Rounding Addition to 12 Commutative; Adding to 18 Associative Addition with multi-digit numbers, estimation Multiplication to 36 Commutative, Multiplication Associative Place Value - reading numbers from ten’s ► 1,000,000 Reading decimals Comparing number > < 10’s ► 1,000,000 Fractions - less than one, greater than one and fractions = 1 ©Box Cars and One-Eyed Jacks 11 MAKE A TEN SHAKERS LEVEL: Kindergarten - Grade 2 SKILL: fact fluency, subitizing, making a sum of 10 SET UP: vertical or horizontal, 1 die in each slot, 1 shaker for 2 students PLAYERS: 2 (cooperative pair) or solitaire GOAL: call out number, immediately give missing addend to equal a sum of 10 GETTING STARTED: For solitaire or pair work have students shake a container, hold it still, then say out loud their numbers as they work down the slots: SEE SAY SEE math talk SAY “4” +6 “10” “3” +7 “10” +7 “10” “3” “6” Have students then go back through, working from the top, giving the missing addend to equal 10. math talk +4 “10” +9 “10” “2” +8 “10” “4” +6 “10” “1” Have students work toward full fluency, see say “4 + 6 = 10” Have students record their "ten facts" using the recording sheets when ready. ©Box Cars and One-Eyed Jacks 12 MAKE A TEN SHAKERS RECORDING SHEET SEE + SEE + ? ? SEE + ? + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 SEE + SEE + ? ? SEE + ? + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 + = 10 ©Box Cars and One-Eyed Jacks 13 FRACTION ACTION LEVEL: Grade 3-6 SKILL: identifying and naming proper fractions, improper fractions, fractions equal to 1 SET UP: horizontal, 1 die in each slot (preferably 2 different colors of dice), 2 shakers PLAYERS: 3 GOAL: to have the most points after nine rounds GETTING STARTED: Players will play 3 sets of 3 rounds each. In the first round, Player One will be assigned to look for proper fractions, Player Two will be assigned to look for improper fractions, and Player Three will look for fractions that equal 1. Players shake the two containers until STOP is called and the containers are then lined up to create 7 fractions. EXAMPLE: (Round One) Numerator Denominator 3 =1 3 1 4 2 =1 2 4 =2 2 1 5 2 3 5 2 =1 3 3 Players now analyze the types of fractions rolled and score 1 point for each falling within their category. 1 1 2 3 points Player One scores 1 point for each proper fraction: 4 5 3 Player Two scores 1 point for each improper fraction: 4 =2 2 5 2 =1 3 3 Player Three scores 1 point for each fraction that equals 1: 3 = 1 3 2 =1 2 2 points 2 points Player One wins this Shaking Round! ©Box Cars and One-Eyed Jacks 14 FRACTION ACTION For the second round, players will rotate the type of fraction they are looking for (ie Player Two will be assigned to look for proper fractions, Player Three will be assigned to look for improper fractions, and Player One will look for fractions that equal 1) and then shake the containers again to create seven new fractions. Students analyze this new shake and score accordingly. For the final round in the set, players once again rotate the type of fractions they are looking for, (ie Player Three will be assigned to look for proper fractions, Player One will be assigned to look for improper fractions, and Player Two will look for fractions that equal 1) and shake for a third round, creating new fractions and scoring accordingly. Continue play with 2 more sets of 3 rounds, rotating the type of fractions as per the first set. The player with the most points after 9 rounds is the winner. FOLLOW UP ACTIVITIES: 1. Have students record each round and arrange their fractions from least to greatest on the recording sheet. 1 5 1 4 2 3 2 2 3 3 2. Have students circle all proper fractions, box cloud all fractions that equal one. 5 3 4 2 all improper fractions and 3. Have students see which improper fractions can be simplified to mixed fractions. For example 5 3 2 simplifies to 1 3 . 4. Have students plot every other round on an open number line. math thinking 5. Have students explore if the game would be fair if the type of fraction they were looking for did not change with each round. Have students explain their thinking by drawing all possible outcomes. ©Box Cars and One-Eyed Jacks 15 FRACTION ACTION RECORDING SHEET SET ONE ROUND 1 ROUND 2 ROUND 3 numerator denominator numerator denominator numerator denominator SET TWO ROUND 4 ROUND 5 ROUND 6 numerator denominator numerator denominator numerator denominator SET THREE ROUND 7 ROUND 8 ROUND 9 numerator denominator numerator denominator numerator denominator ©Box Cars and One-Eyed Jacks 16 FRACTION ACTION RECORDING SHEET SHAKE 1 SHAKE 2 SHAKE 3 SHAKE 4 SHAKE 5 SHAKE 6 SHAKE 7 SHAKE 8 SHAKE 9 SHAKE 10 numerator denominator numerator denominator numerator denominator numerator denominator numerator denominator numerator denominator numerator denominator numerator denominator numerator denominator numerator denominator ©Box Cars and One-Eyed Jacks 17 ROCK AND ROLL LEVEL: 3-6 SKILLS: comparing place value, expanding numbers PLAYERS: 2 – 4 (1 player as referee) EQUIPMENT: GOAL: 2 – 6 dice per player (# of dice determines size of number), recording sheet to be the first player to order their dice and to create the greatest number possible GETTING STARTED: The referee calls players to “Rock and Roll”. All players shake their dice and hide the roll with their hands until the referee calls “Reveal”. Players then begin arranging their dice to make the largest number possible. The first player to finish calls out “Rock and Roll”. All other players must immediately freeze their work in their current order and pull their hands off their dice. The first player verbalizes their number to the other players. If the first player to finish has correctly ordered and read their number, they earn 5 points. If they are also the largest number of the group they earn another 5 points for a total of 10 points. All other players earn zero. If any player in the group has a number greater than the first to call “Rock and Roll” they earn 5 points for the round as well. MATH TALK Don’t let students use AND when reading their numbers. AND is the decimal. EXAMPLE: Playing to ten thousands ROLL: ARRANGE: 5 READ: 5 , 4 2 1 Fifty-five thousand, four hundred twenty-one ©Box Cars and One-Eyed Jacks 18 ROCK AND ROLL VARIATIONS: 1. Students play for the least possible number. 2. Students play on the decimal game sheet. 3. Arrange and write all your numbers in ascending order. MATH JOURNAL WORK AND EXTENSIONS: 1. Why is it important to see place value represented in many different ways? 2. What is the largest possible number that can be rolled? The least? How close were you on any roll to either of these possibilities? 3. What strategy did you use to tell which number is greatest in the round? Do you use the same strategy when the numbers are very close? 4. This game is excellent for teaching expanded notation. After each round have players slot their dice into the black tray on top of the Stratedice place value chart. This provides the language for the students. After the dice are slotted in, have players expand them out as follows: <<SAMPLE>> The blank spaces in the trays represent zeroes. Students can put their fingers right into the empty slots. From this physical expanding of the number we then have students record on their math journal recording sheet. ©Box Cars and One-Eyed Jacks 19 ROCK AND ROLL RECORDING SHEET ROLL NUMBER EXPANDED NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ©Box Cars and One-Eyed Jacks 20 ©Box Cars and One-Eyed Jacks ONES TENS HUNDREDS THOUSANDS TEN THOUSANDS HUNDRED THOUSANDS ROCK AND ROLL 21 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: + = PLAYER ONE MATH TALK 8 + = 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. MATH JOURNAL WORK AND EXTENSIONS: This game is full of opportunities to teach basic addition concepts, adding to 12. 1. Have players record a full game on the recording sheet. See example on page 56. 2. Have players highlight or color in examples of doubles, near doubles. Count how many were rolled in your game, and compare with the rest of the class. 3. As students are playing, observe the following: • Which students are identifying sums immediately? • Which students are counting on from the greatest addend? Least addend? • Which students are recognizing the doubles and doubles +1 and using these to add quickly or with immediate recall? ©Box Cars and One-Eyed Jacks 22 HORSE RACE – PRIMARY ADDITION • Which students are still at a concrete level of touching the pips on the dice, and will need more practice with immediate recognition of patterns to 6? 4. As a class you can analyze the types of games that happened. When a game is complete, we have students determine if their Horse Race was: (see example on bottom corner of p. 56) • Dead Heat – both players have the exact same amount of dice on their trays • Wipe Out – one player has at least 3 or more pairs greater in their side of the racetrack • Too Close to Call – basically the game is close throughout the play and is typically won by one or two pairs, right near the end of the game 5. You can also analyze as a class the following questions: • How many doubles were rolled in the game? Keep track by tallying or taking counters each time doubles are rolled. • How many tie sums were rolled in your game? Compare your total with the rest of the class. How many of your tie sums were identical rolls? For example: • tie sums 4+4=8 6+2=8 tie sums with identical rolls 3+3=6 3+3=6 PLAYER ONE PLAYER TWO This analysis helps students understand fact families, and that some sums have more than one roll or pair of addends that equal it. Which sums often had ties? 6. Have students work with the commutative property of addition which states: “The sum stays the same when the order of the addends is changed.” 6 +4 = 4+6 + = + We have the students cover up one addend with their hand and verbalize: 4 + 6 = 10 6 ©Box Cars and One-Eyed Jacks + 4 = 10 23 HORSE RACE – PRIMARY ADDITION PLAYER ONE BOTH PLAYERS START PLAYER TWO START ©Box Cars and One-Eyed Jacks 24 Horse Race - Graphing, Interpreting, Inferring Box Cars and One-Eyed Jacks ©2015 Set Up Play the game Horse Race (one player uses white dice, one player uses blue dice), it is extremely important that the players place the dice properly in the tray or lid. In other words, if a player rolls a 2 and a 3, then they must put 2 and 3 into the tray or lid (not just toss them in so any value faces up). Versions of Horse Race for this activity include: 2 addend addition (largest sum wins), 3 addend addition (largest sum wins), single digit subtraction (smallest difference wins), 2 factor multiplication (largest product wins), 3 factor multiplication (largest product wins), comparing proper fractions (smallest value wins). Once the players have completed their game, they evaluate their game to determine whether it was a tie or who won (blue or white). Also, for win/loss games, they evaluate whether the win was close or a "blow out" (one player won by a lot). Players can also quickly estimate (ie not count exactly) what dice values (regardless of color) were rolled the most/least. Graphing, Interpreting and Inferring Players take all of the dice from both the tray and the lid and create a bar graph by lining up the dice according to their value. From this graph they can easily see which number(s) were rolled the most/least and may be able to determine the likely winner (white or blue). STEP 2: Reorganize Dice to Create a Double Bar Graph STEP 1: Create Single Bar Graph As a further extension, students can alter the graph by lining up the blue and white dice for each value next to each other to create a double-bar graph. Students can then write on a sticky note which color won and whether the win was close or a blow out. Students visit other games and with only looking at the doublebar graph try to figure by discussing the graphs with their own partners, whether the game was won by blue or white and whether it was close or a blow out. Math Journal Questions 1. How did you infer which color won or if the game ended in a tie? 2. How did you infer whether win/loss games ended as a close race or blow out? 3. Were your inferences always correct? 4. What types of games were easiest to infer correctly, hardest to infer correctly and explain why you think they were easy or hard to infer correctly. ©Box Cars and One-Eyed Jacks 25 Let The Games Begin All the Box Cars games are written using the same format. As a sample, we've chosen one of our basic games to familiarize you with our style. LEVEL: SKILLS: PLAYERS: EQUIPMENT: GETTING STARTED: Cards 1 - 5 Cards 1 - 9 Grade 1 - 7 addition facts 1 - 10, 1 - 18 combinations 2 Cards (Ace = 1) - 5, or (Ace = 1) - 9 Players divide cards evenly between themselves. Each player turns over two cards and adds them together. The highest sum gets all the cards. In the event of a tie; (ie: each player has the same sum), WAR is declared. Each player deals out three more cards face down and then turns over two more cards. These two cards are added together. The highest sum wins all of the cars. Play continues until one player has collected all of the cards. Grade 1 - 2 Sums to 10 Grade 2 - 3 Sums to 18 Player 1 Player 2 2+3 4+1 War is declared 2+3 4+1 Concepts: Missing Addend, Factor Equipment: Cards 0-12 (J=11 Q=12 K=0) Goal/Object: Figure Out value of the card on your head 3 cards are turned upside down. 4+3 Salute Box Cars "All Hands On Deck" Mystery Number (adapted) 6+2 Player 2 collects all of the cards Try These Variations Place Usually 3 players with one player taking the role of "General". The General says "salute". The other two players take the card from the top of their deck and WITHOUT LOOKING AT IT place it on their forehead so everyone else can see what the card on their forehead is. The General Adds the two cards together and says "The sum of your two cards is...." The two players then Value War Subtraction War 3 Addend War Multiplication War Integer War Fraction War Mixed Operations use the sum and the card they can see on their opponent's forehead to try and figure out their own card. Variations: (1) Multiplication (take out 0s) (2) 4 Players (one General, 3 soldiers) (3) Red = neg integers / Black = pos integers Remember: War is a traditional game. However, due to the negative connotation you may want to change the term "war'' to one of your own choice. We often call these our Buzz Games (ie. Three Card Buzz). ©Box Cars and One-Eyed Jacks 26

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