Meaningful Ways to Develop Math Facts

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1 NCTM 206 San Francisco, California Meaningful Ways to Develop Math Facts -5 Sandra Niemiera Elizabeth Cape

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8 Game Analysis Tool of Game Math Involved in the Game This game supports students development of (circle all that apply): models informal strategies counting strategies reasoning strategies flexibility connections recall. What strategies do you anticipate your students will use when playing the game? 2. Where do you anticipate your students will be successful?. Where do you anticipate they will be challenged? 4. What questions would you ask as the game progresses to promote conceptual development? 8

Floor Tiler The object of the game is to be the first player to fill his or her grid paper with rectangles. This game can be played by two to four players. DRAFT Copyright 202 TIMS Project, Inc.

9 Floor Tiler The object of the game is to be the first player to fill his or her grid paper with rectangles. This game can be played by two to four players. DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Materials Spinners 4 and 0 A clear plastic spinner or a paper clip and pencil 2 sheet of Floor Tiler Grid Paper Crayon or marker Scissors Directions. The first player makes two spins so that he or she has two numbers. The player may either spin one spinner twice or spin each spinner once The player must then find the product of the two numbers he or she spun. The product is the answer to a multiplication problem. For example, is the product Multiplication and Rectangles 9

10 . After finding the product, the player colors in a rectangle with that number of grid squares on the grid paper. He or she can use any two factors of the product to make a rectangle, not just the facts on the spinner. For example, the player might use the factors on the spinner and color in rows of 4 squares for a total of 2 squares. But the player can also think of other factors of 2, such as 2 rows of 6 squares or row of 2 squares. (Remember, the squares colored in must connect so that they form a rectangle.) 4. Once the player has made his or her rectangle, the player draws an outline around it and writes its number sentence inside. For example, a player who colored in rows of 4 squares would write 4 = 2. A player who used the factors 2 and 6 would write 2 6 = Players take turns spinning and filling in their grids. 6. If a player is unable to fill in a rectangle for his or her spin, that player loses the turn, and the next player takes a turn. 7. The first player to completely fill in his or her grid paper wins the game. DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Multiplication and Rectangles

11 Spinners 4 and DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Multiplication and Rectangles

12 Floor Tiler Grid Paper DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Multiplication and Rectangles 2

13 Four in a Row The object of the game is to cover four squares in a row vertically, horizontally, or diagonally. This is a game for two players. Materials Four in a Row Game Board 2 paper clips 2 different color game markers, color for each player DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Directions. Player chooses a number from the Factor List by placing a paper clip on the number. 2. Player 2 also chooses a number from the Factor List by placing the second paper clip on the number. Two paper clips can be placed on one factor, for example 5 x 5.. Player 2 finds the product of the two numbers marked by the paper clips and places one of his or her makers on that number on the Product List. 4. Player then moves either paper clip to another factor, and covers the new product with one of his or her markers. 5. Players take turns moving one paper clip and covering a product with their marker. If a product is already marked, the player does not get to mark a product in that turn. If the product the player tries to mark is not correct, the the correct product must be marked. 6. The winner is the first player to mark four products in a row with his or her markers. Variations Vary the game board by varying the list of factors and creating a board with all the related products. See the Four in Row Game Board 2. Change the number of products players have to get in a row to win (for example, five in a row). Workshop: Strategies for Multiplication Facts

14 Four in a Row Game Board Product List DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Factor List

15 Four in a Row Game Board 2 Product List Factor List DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE 5

16 DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Line Target Game This game is for two players. The object of the game is to be the player that covers the sum equal to or greater than the target number. I will cover an eight. Fifteen plus eight equals twenty-three. Hmm. The target number is = 0. If I cover a seven, I will win! Materials Line Target Game Boards game markers Directions. Player chooses a target number. Start with a small number, such as 20, and play on Game Board. 2. Player covers a number and then Player 2 covers a number. Players track the sum of the covered numbers using the number line.. Take turns covering numbers. The winner covers the number that makes the sum equal to or greater than the target number. Variation Play the game using Game Board 2 with a larger target number, such as 00. Line Target SAB Grade Unit Lesson 2 6

17 DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Line Target Game Boards Game Board Game Board SAB Grade Unit Lesson 2 Line Target 7

18 Fraction Order The object of the game is to fill the game board by placing six fractions in order from smallest to largest. This game is for one to four players. Materials Fraction Order Game Board for each player One set of Fraction Cards and 2 for two players. Mix the cards and place them face down between the players. Mix together two sets for or 4 players. Fraction Chart or fraction circle pieces DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Directions. Players take turns. On your turn, draw a card from the pile and decide where to place it on your game board. 2. If you draw a card that you cannot place because of the numbers already on your game board, keep the card and lose a turn.. If you draw a card with a fraction equivalent to one already placed on your game board, place the card to the right or left of the equivalent fraction, if a space is open. 4. When one player fills his or her game board, all players use a Fraction Chart or fraction circle pieces to check that the order is correct. 5. The winner is the player who correctly fills his or her game board first. Variations Partners play with one game board and take turns placing fraction cards on the game board. The winner is the player who fills the last space on the game board. Order the fractions from largest to smallest. Include fraction cards that are not easily represented with circle pieces or the Fraction Chart: 7, 20, 99 00, 99, 48 50, 2 22 Comparing Fractions Using 2 SAB Grade 4 Unit 8 Lesson

19 DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Fraction Order Game Board Smallest Largest 298 SAB Grade 4 Unit 8 Lesson 9 Comparing Fractions Using 2 9

20 Fraction Cards DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE 299 Comparing Fractions Using 2 SAB Grade 4 Unit 8 Lesson 9 20

21 Fraction Cards DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Comparing Fractions Using 2 SAB Grade 4 Unit 8 Lesson 9 0 2

22 Quotient Quest Game Rules The object of this game is to have the lowest sum of digits on your remaining digit cards at the ends of the game. This is a game for two players. Materials one Quotient Quest Game Board from the Student Activity Book two sets of 20 Quotient Quest Digit Cards cut out from the Student Activity Book two sets of Quotient Quest Game Cards cut out from the Student Activity Book calculator envelopes for storing cards Directions DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE. One player shuffles all 40 digit cards and deals 20 cards face up to each player. (To shorten the game, deal 0 cards to each player.) 2. Each player shuffles one set of game cards and places them face down in a stack.. Each player draws a game card from his or her stack. 4. Each player places digit cards in the boxes on his or her game board to make a quotient between the two numbers shown on the game card. 5. Players check each other s quotients to make sure they are between (but do not include) the numbers on the game card. A calculator may be used to double check. 6. Digit cards of correct quotients are placed face down in one discard pile. 7. Digit cards of incorrect quotients are returned to the player. 8. Both players draw another question card and play continues. 9. If a player cannot make a quotient to match the game card, he or she draws digit cards from the discard pile until a quotient can be made. 0. The game ends when a player has two or fewer digit cards left at the end of a turn.. At the end of the game, players add the numbers on their remaining digit cards. 2. The player with the lowest sum of digits on his or her remaining digit cards wins the game. Workshop: Division Concepts SAB Grade 4 Unit 2 Lesson

23 Quotient Quest Game Board DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Workshop: Division Concepts SAB Grade 4 Unit 2 Lesson

24 Quotient Quest Digit Cards DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Workshop: Division Concepts SAB Grade 4 Unit 2 Lesson

25 Quotient Quest Game Cards Divide to get a quotient between 0 and 0. Divide to get a quotient between 20 and 0. Divide to get a quotient between 40 and 50. Divide to get a quotient between 0 and 20. Divide to get a quotient between 0 and 40. Divide to get a quotient between 50 and 60. DRAFT Copyright 202 TIMS Project, Inc. DO NOT DISTRIBUTE Divide to get a quotient between 60 and 70. Divide to get a quotient between 80 and 90. Divide to get a quotient between 00 and 50. Divide to get a quotient between 70 and 80. Divide to get a quotient between 90 and 00. Divide to get a quotient between 50 and 200. Workshop: Division Concepts SAB Grade 4 Unit 2 Lesson

26 Factor Games Factor 20 and Factor 40 are games about factors. The factors of a number are the whole numbers that can be multiplied together to get the number. For example, and 4 are factors of 2 since 4 2. All the factors of 2 are, 2,, 4, 6, and 2. Factor 20 or Factor 40 The goal is to mark the most factors and earn the most points. This is a game for two players. Materials one Factor 20 Game Board and Score Box or Factor 40 Game Board and Score Box from the Student Activity Book one pencil per player calculator, optional Directions Before Play Begins Players will alternate who uses an X and who uses an O for each round. Player X always takes the first turn. First Turn Player X chooses any number except on the game board and draws an X on it. Player X writes that number in Column X of the score box. Player X earns that number of points for this turn. Player O circles all the factors of Player X s number that are not marked. Player O writes all of those factors in Column O of the score box. Player O earns points equal to the sum of the factors for this turn. Second Turn Player O chooses any unmarked number on the board. (An unmarked number is one that has not yet been circled or marked with an X.) The number must have at least one factor that is unmarked. Player O circles the number and records it in Column O. Player X draws an X on all the unmarked factors of that number and records them in Column X. Play Continues Players take turns choosing numbers, marking factors, and recording scores in the score box for each turn. Players may choose only numbers that still have unmarked factors. The game ends when there are no numbers left with unmarked factors. Players total their points at the end of the game. The player with more points wins. 422 Factor Games DRAFT Copyright 204 TIMS Project, Inc. DO NOT DISTRIBUTE 26

27 DRAFT Copyright 204 TIMS Project, Inc. DO NOT DISTRIBUTE Factor 20 Game Board Score Box Running Total TOTAL TOTAL Running Total Factor Games SAB Grade 5 Unit 9 Lesson 59 27

28 Factor 40 Game Board Score Box TOTAL TOTAL DRAFT Copyright 204 TIMS Project, Inc. DO NOT DISTRIBUTE 62 Factor Games 28

29 Closest to This is a game for two to four players. The object is to estimate differences accurately and have the most points at the end of the game. Materials recording sheet per player prepared set of four Squares per player prepared deck from Closest to Game Cards Master scissors DRAFT Copyright 204 TIMS Project, Inc. DO NOT DISTRIBUTE Directions. Players hold their Squares in their hands. The deck of game cards are placed face down in the middle of the players. 2. For each round, one game card is turned over to display a mixed number. In Game, each player estimates the difference that results from subtracting this mixed number from 4. In Game 2, players will subtract from 4 2. Each player places one of their number cards face down, indicating whether they think the difference is closest to 0,, 2, or.. Players record the number sentence on their recording sheet and find the difference using mental math or paper and pencil. They also record whether the difference is closest to 0,, 2 or. 4. Players reveal their number cards. If their estimate was correct, they record one point on their recording sheet. 5. Players collect their number cards and begin another round. 6. The player with the most points at the end of the game wins. Squares Subtract Mixed s SAB Grade 5 Unit 0 Lesson

30 Recording Sheet: Game Sentence Closest to 0,, 2, Points Example: DRAFT Copyright 204 TIMS Project, Inc. DO NOT DISTRIBUTE Total Points Subtract Mixed s SAB Grade 5 Unit 0 Lesson

31 Recording Sheet: Game 2 Sentence Closest to 0,, 2, Points Example: Total Points DRAFT Copyright 204 TIMS Project, Inc. DO NOT DISTRIBUTE 408 SAB Grade 5 Unit 0 Lesson 5 Subtract Mixed s

32 Games in Digital Environments Multiplication and Division Bojagi gotmath.rhcloud.com/list Players solve this puzzle by building arrays around a given product. Students can also be challenged to create their own puzzles. (Modeling, Flexibility) Product Game The player can play against the computer or against another player. This is a fluency and flexibility game. (Flexibility, Fluency) Factor Game The player can play against the computer or against another player. This is a fluency and flexibility game. (Flexibility, Fluency) Factorize This is an interactive that focuses in finding the factors of a number by building arrays. This activity is for one player. (Modeling, Flexibility) Multiplication Blocks This is single player game where students are asked to find factors for a given product. This game progresses in difficulty. (Fluency, Flexibility) Sortify Multiplication This is a single player game that involves multiplication, division, factors, and multiples. Players classify and group products. (Modeling, Reasoning, Flexibility) Primary Krypto This puzzle game involves arithmetic and order of operations. (Flexibility, Reasoning) Visual Multiplication Table multiplication- table/id457862?mt=8 This is an ipad app designed to help students visualize multiplication. This would classify as a tool rather than a game. 2

High-Impact Games and Meaningful Mathematical Dialog Grades 3-5

NCTM 2017 San Antonio, Texas High-Impact Games and Meaningful Mathematical Dialog Grades 3-5 Elizabeth Cape Jennifer Leimberer Sandra Niemiera mathtrailblazers@uic.edu Teaching Integrated Math and Science