A Games-based, Strategy-focused Fluency Plan

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1 A Games-based, Strategy-focused Fluency Plan To have with you for tonight s webinar: ü Deck of Cards ü 2 dice (6-sided or 10-sided) ü Games Recording Sheet ü This powerpoint with Game Boards Jennifer Bay-Williams University of

2 Revisiting the 5 Fundamentals

3 Procedural fluency is skill in carrying out procedures flexibly, accurately, efficiently and appropriately (CCSSO, 2010, NCTM, 2014, NRC, 2001)

4 Addition Facts Mastery Chart Flexible Learning Progression +/- 0,1,2 Foundational Fact Sets Doubles Combos of Near Doubles Making 10 Pretend-a-10 Derived Fact Strategies Bay-Williams, J. M. & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

5 Bay-Williams, J. M. & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

6 Mastering Basic Facts Based on Baroody, 2006

7 Use Quick Looks: A Progression Quick Looks Quick Looks + Equations Equation and Imagine a Quick Look Explicitly encourage selected strategies

8 ü Are engaging. ü Provide opportunities for strategy discussion and assessment. ü Should be sequenced developmentally (for example, playing combinations of ten games before exploring making ten strategies). ü Can be targeted practice or general practice. ü Lend to differentiation.

9 ü Are targeted toward a single strategy, fact group or set of reasoning strategy ü Do not have time-pressure as an element of the game. ü Have each student in the group solving different problems. ü Lend to talking about the possible strategies.

10 SQUARES Fill your game board with these squares: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 Yes, use a number more than once. One a turn, you can only cover ONE number.

11 Reflecting on the Game 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted? BINGO Free

12 Reflecting on the Game Lucky 13 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted? Materials: Deck of cards with numbers 0 10 (Ace = 1, Jack = 0), Players: 2-4 Players How to Play: 1. Each player turns over 5 cards. 2. Each player selects 2 cards which, when added together, produce a sum as close to Lucky 13 as possible. 3. Players find how far their total is from Lucky 13 and record that difference (e.g., if the two cards add to 11, the score is 2 because 11 is 2 away from 13). 4. Players discard the two cards that were used and draw two new cards. 5. Repeat for 5 rounds. 6. Lowest score wins!

13 Rectangle Fit (Tetris) Rectangle Fit Players: Whole Class How to Play: 1. The teacher (or selected student leader) rolls two dice. You need: q Empty Grid q 2 Dice 2. Each student decides where on their game board to shade a rectangle of the dimensions rolled. For example, if the leader rolls 4 and 6, each student decides where and in what orientation they can best fit a 4-by-6 rectangle on their grid paper. 3. Students record the related multiplication fact inside the rectangle. 4. The leader continues to roll, and students fill in a rectangle with those dimensions somewhere on their gameboard. 5. When a student cannot fit a rectangle with the dimensions rolled, they are out of the game. 6. The last students in the game are the winners. Possible Adaptations: Use 10-sided dice and a game board with more unit squares.

14 Reflecting on the Game Rectangle Fit (Tetris) Rectangle Fit Game Board (6-Sided Dice) 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

15 Double to Connect 4 You need: q Game board q 10 Sided Die or Deck of Cards q Optional: 2 colors of chips Players: Partners Rectangle Fit (Tetris) How to Play: 1. Each partner has a different colored chip to cover board, or partners decide who will be Xs and who will be Os. 2. Partners take turns. On their turn, they flip over a number card and doubles the value of the card. 3. Player places their color chip (or an X or O) on one the Game Board on that double value (e.g., if player turns up a 6, they choose which 12 they want to cover). 4. Players try to get four of their own color (mark) in a row. For each Connect 4 (column, row or diagonal), players score 5 points. 5. Optional: Winner is first player to score 20. Possible Adaptations: Use separate game boards; Connect 3 (or 5) rather than 4; Have players say the sum and/or the product. Game from Bay-Williams, J. M., & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

16 Reflecting on the Game Double to Connect 4 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

17 Rectangle Fit (Tetris) Fishing for 10s (adapted from Investigations in Number, Data, and Space, 2008) Materials: Ten frame cards or deck of cards with numbers 0 10 (Ace = 1, Jack = 0, remove other face cards), Players: 2-4 Players How to Play: 1. This is played like the card game Go Fish, only instead of looking for matching cards, a match is a combination of ten. 2. Deal 5 cards to each player. You need: q Deck of Cards 3. Take turns. On a players turn, ask for a card that makes a ten for a card in your hand. For example, if you have a 4, ask another player Do you have a 6? Ø If yes, the player gives you the card and you have a match. Ø If no, the player says Go Fish. 4. Draw a card from the deck and it is the next players turn. 5. Play until all cards are used. Optional: Players record equations for the pairs they got.

18 Reflecting on the Game Fishing for 10s 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

19 One More Cover It Players: Partners How to Play: 1. Each partner has a different colored chip to cover board. You need: q Game Board q Die q Chips to cover board. 2. Partners take turns. Each player rolls the number cube and covers a square that is one more than what was rolled on the number cube. 3. Players try to cover a complete column, row or diagonal. 4. Optional: The player who first gets a column, row or diagonal wins.

20 Reflecting on the Game One More Cover It 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

21 Crossed Wires Players: Partners How to Play: 1. Shuffle the cards and place them face down. 2. Each player takes one card from the deck. This tells them how many horizontal lines to draw on their paper. For example, player 1 may draw a 3, so draws three lines: You need: 3. Each player draws a second card and draws that many vertical lines, Creating crossed wires. For example, player 1 draws a 4 on their second draw: q Two Dice q Blank Paper 4. Each player determines how many crossed wires they have (points of intersection) and records the product on a recording page. [Note: A 0 on either draw leads to 0 points of intersection] Player 1 has 12 crossed wires: 5. Play 8 rounds. The winner is the one with the most total intersections. Game from Bay-Williams, J. M., & Kling, G. G. (in press). Math Fact Fluency: 60+ Games

22 Reflecting on the Game Crossed Wires 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

23 You need: q Cards Product Pile-Up Players: 3-4 Players How to Play: 1. Each player is dealt 8 cards. 2. The player to the left of the dealer begins by playing two cards and saying out loud the product of those two cards. 3. The next player (to the left) must play two cards that have a product higher than the product just shared. Play continues around the group in this manner. 4. If a player cannot top the product just played, he or she draws two cards from the deck and tries again to create a higher product. If he or she is still unable to create a higher product, the player says pass and play moves to the next player. 5. Once all players have to pass, the player who played the last set of cards (the highest product) gets to start a new round, selecting any two cards from their hand. 6. The first player to use all their cards is the winner.

24 Reflecting on the Game Product Pile Up 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

25 Fixed ADDEND WAR Players: Partners How to Play: 1. Identify an addend (e.g., 9) and place a card with that number face up in the middle. You need: q Cards 2. Deal the rest of the cards equally, face down. 3. At the same time, partners turn up their top card and say the sum. 4. Each partner takes turns saying their full addition equation, and how they added. Both decide if sums are correct. 5. The player with the larger (correct) sum gets the cards. 6. If there is a tie, it is a war and partners repeat steps Optional: Play for a set time; player with the most cards wins.

26 Reflecting on the Game 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted? Fixed Addend War 8

27 Fixed ADDEND WAR Players: Partners How to Play: 1. Identify an addend (e.g., 9) and place a card with that number face up in the middle. You need: q Cards 2. Deal the rest of the cards equally, face down. 3. At the same time, partners turn up their top card and say the sum. 4. Each partner takes turns saying their full addition equation, and how they added. Both decide if sums are correct. 5. The player with the larger (correct) sum gets the cards. 6. If there is a tie, it is a war and partners repeat steps Optional: Play for a set time; player with the most cards wins.

28 Reflecting on the Game 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted? Fixed Addend War 8

29 Finding 5s Players: Partners How to Play: 1. Spread the cards out face down (like concentration) 2. Each partner takes a turn. 3. On their turn, a partner turns over two cards and adds the numbers together, saying the equation (For example, if a 2 and a 5 are turned up, say 2 plus 5 equals 7. You need: q Cards (only 0 5) 4. If the two cards do not equal 5, they are turned back upside down. If the two cards do equal 5, the player keeps the pair, face up, as one combination that makes Play until all cards are gone. 6. The player with the most combinations is the winner. Possible Adaptations: Use numeral cards; Use dot cards; Change to Finding Ten (or other total).

30 Reflecting on the Game Finding 5s 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

Subtraction Stacks Players: 2-4 Players How to Play: 1. Each player counts out 10 counters. 2. Each player places the 10 counters on the Subtraction Stacks Play Card wherever they want to place them, as illustrated here.

31 Subtraction Stacks Players: 2-4 Players How to Play: 1. Each player counts out 10 counters. 2. Each player places the 10 counters on the Subtraction Stacks Play Card wherever they want to place them, as illustrated here. You need: q Game Board q 10 Counters q 2 Dice On a players turn, they roll both dice, and find the difference between the two numbers. Ø If the difference is 2, the player removes a counter from the 2 stack. Ø If the player has nothing in their 2 stack, no counter is removed. 4. The player who removes all of their counters first is the winner.

32 Subtraction Stacks Reflecting on the Game 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

33 Factor Game Players: Partners How to Play: 1. Player 1 chooses a number on the game board and marks it/covers it. This will be Partner 1 s score for Round 1. For example, if Player 1 selects 15, they get 15 points. You need: q Game Board q Optional: Counters to cover 2. Player 2 marks/covers all the proper factors of Player 1 s number. Partner 2 adds all of the factors they found. This is Player 2 s score for Round 1. For example, if Player 1 selects 15, Player 2 may take 1, 3, and 5, scoring 9 points. 3. Player 2 goes first for Round 2, selecting a value that has not been taken. Player 1 then gets all the factors of the selected number (that have not yet been crossed out). Note: If player 2 marks/covers a number that has no factors left on the board, player 1 gets 0 points. 4. Play continues in this manner, with players taking turns selecting values and the other playing collecting available factors. 5. The game ends when all numbers are taken. 6. Players sum their totals from each round; the player with the larger sum wins.

34 Reflecting on the Game Factor Game V1 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

35 Right-Price Game You need: q Cards q 2 Dice Players: 2-4 Players How to Play: 1. Deal six cards to each player and place the rest face down in a draw pile. 2. The first player rolls the two dice and uses the two numbers to decide a price. (For example, a 2 and a 5 can be $25 or $52.) 3. The other players use the cards in their hand to form a multiplication fact that comes as close to the price as possible without going over. 4. The player with the closest product scores 12 points. If there is a tie, the players divide the points evenly. 5. Used cards are discarded, and new cards are drawn. Continue play until the deck is gone. 6. The player with the highest score wins.

36 Reflecting on the Game Right-Price Game 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

37 TRIOS Players: Partners How to Play: 1. Give each player a set of counters (one person has one color, the You need: q Game Board q Optional: 2 colors of counters to cover other the other color). 2. Take turns rolling the die (or choosing a card), 3. On your turn, multiply your number by 5, and place one of your counters on any square with that product. 4. The object is to cover three spaces in a row (horizontally, vertically, or diagonally) with the same color. And, your object is to try to block your partner from getting three spaces in a row! 5. Each successful trio is five points. The person with the highest score wins.

38 Reflecting on the Game TRIOS 1 Which fact sets are 2 Which strategies are 3 Is it aimed at fundamental facts? Derived fact strategies? Or both? 4 How might the game be adapted?

Salute! Form a Group of 3 and Identify a Leader The other two players, without looking at your card, place it on their forehead facing outward (so the others can see it).

39 Salute! Form a Group of 3 and Identify a Leader The other two players, without looking at your card, place it on their forehead facing outward (so the others can see it). The leader says the product (sum) of the two cards. The other two players determine the value of the card on their forehead. Both players share how they determined their number. The player who was fastest, keeps the cards. Rotate so that one of the players is now the leader.

40 Strategy Games Addition Games: Lucky 13 Finding 5s One More Cover It Fishing for 10s Double to Connect 4 Fixed Addend War Subtraction Stacks Salute Multiplication Games: Squares Bingo Trios Rectangle Fit Crossed Wires Product Pile-Up The Factor Game Right Price Game Salute

41 Strategy Games Addition Games: Lucky 13 Finding 5s One More Cover It Fishing for 10s Double to Connect 4 Fixed Addend War Subtraction Stacks Salute Multiplication Games: Squares Bingo Trios Rectangle Fit Crossed Wires Product Pile-Up The Factor Game Right Price Game Salute Addition Facts Mastery Chart Flexible Learning Progression +/- 0,1,2 Foundational Fact Sets Doubles Combos of Near Doubles Making 10 Pretend-a-10 Derived Fact Strategies

42 Strategy Games Addition Games: Lucky 13 Finding 5s One More Cover It Fishing for 10s Double to Connect 4 Fixed Addend War Subtraction Stacks Salute Multiplication Games: Squares Bingo Trios Rectangle Fit Crossed Wires Product Pile-Up The Factor Game Right Price Game Salute

43 Strategy-Focused Game Play: Aligning strategies with games Fact Set: Multiply by 4s Strategy: Double and Double Again Game(s): Bingo, Trios, Connect 4, and/or Fixed-Factor War PreTeach/Number Talk: Quick Looks with double and double again combinations

44 Questions to Ask While Playing Basic Facts Games : How did you figure it out? Can you share how you thought about it in your head? Is there another way you could figure it out? What is another fact that could be solved with that strategy? Questioning During Game Play: Focus on Strategies! If someone didn t know the answer to, how would you tell them to figure it out?

46 Reflecting on the Game 1 How might the game be adapted? Bowl-a-Fact st Roll (for Strike): 2 How might you use this game? 2 nd Roll (for Spare): 3 rd Roll (for Score): Equations: Scoring: Strike: 100 points Spare: 75 points Score: Sum of all taken facts My Score:

47 Which game(s) will you use (and for which fact sets/strategies)?

48 ASCD NCTM Articles

Roll & Make. Represent It a Different Way. Show Your Number as a Number Bond. Show Your Number on a Number Line. Show Your Number as a Strip Diagram

Roll & Make. Represent It a Different Way. Show Your Number as a Number Bond. Show Your Number on a Number Line. Show Your Number as a Strip Diagram Roll & Make My In Picture Form In Word Form In Expanded Form With Money Represent It a Different Way Make a Comparison Statement with a Greater than Your Make a Comparison Statement with a Less than Your