Meaningful Ways to Develop Math Facts fileSpinners 1–4 and 1–10 2 4 1 3 1 2 8 3 4 9 7 5 10 6...

NCTM 2016 San Francisco, California

Meaningful Ways to Develop Math Facts

3-5 Sandra NiemieraElizabeth Cape

[email protected]

1

Game Analysis Tool Name 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 1. What strategies do you anticipate your students will use when playing the game? 2. Where do you anticipate your students will be successful? 3. Where do you anticipate they will be challenged? 4. What questions would you ask as the game progresses to promote conceptual

development?

8

Name Date

Multiplication and Rectangles

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Floor TilerThe object of the game is to be the first player to fill his or her grid paper withrectangles. This game can be played by two to four players.

Materials• Spinners 1–4 and 1–10• A clear plastic spinner or a paper clip and pencil• 1–2 sheet of Floor Tiler Grid Paper• Crayon or marker• Scissors

Directions1. 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.

2. 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,3 � 4 � 12. 12 is the product.

4 1

3 2

11023

456

789

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of grid squares on the grid paper. He or she can use any two factors of theproduct to make a rectangle, not just the facts on the spinner.

For example, the player might use the factors on the spinner and color in3 rows of 4 squares for a total of 12 squares. But the player can also thinkof other factors of 12, such as 2 rows of 6 squares or 1 row of 12 squares.(Remember, the squares colored in must connect so that they form arectangle.)

4. Once the player has made his or her rectangle, the player draws an outlinearound it and writes its number sentence inside. For example, a player whocolored in 3 rows of 4 squares would write “3 � 4 = 12.” A player who usedthe factors 2 and 6 would write “2 � 6 = 12.”

5. 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 losesthe turn, and the next player takes a turn.

7. The first player to completely fill in his or her grid paper wins the game.

3 � 4 = 122 � 6 = 12

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Multiplication and Rectangles272

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Spinners 1–4 and 1–10

2

4 1

3

1 2

3 8

4

9

7 5

10

6

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Floor Tiler Grid Paper

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Workshop: Strategies for Multiplication Facts

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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 1• 2 paper clips• 2 different color game markers, 1 color for each player

Directions

1. Player 1 chooses a number from the Factor List by placing a paper clip onthe number.

2. Player 2 also chooses a number from the Factor List by placing the secondpaper clip on the number. Two paper clips can be placed on one factor, forexample 5 x 5.

3. Player 2 finds the product of the two numbers marked by the paper clipsand places one of his or her makers on that number on the Product List.

4. Player 1 then moves either paper clip to another factor, and covers the newproduct with one of his or her markers.

5. Players take turns moving one paper clip and covering a product with theirmarker. If a product is already marked, the player does not get to mark aproduct in that turn. If the product the player tries to mark is not correct, thethe correct product must be marked.

6. The winner is the first player to mark four products in a row with his or hermarkers.

Variations

• Vary the game board by varying the list of factors and creating a board withall 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 (forexample, five in a row).

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Four in a Row Game Board 1

Product List

P

Factor List

0 1 2 3

4 5 6 9

10 15 18 20

25 27 30 45

50 81 90 100

1 2 3 5 9 100

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Four in a Row Game Board 2

Product List

F

Factor List

1 2 3 4

7 8 9 10

15 16 18 20

25 27 28 30

36 40 42 45

5 6

12 14

21 24

32 35

48 49

50 54 56 60

70 72 80 81

63 64

90 100

7 8 9 101 2 3 4 5 6

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Hm

m. T

he t

arge

tnu

mb

er is

30.

23

+ 7

= 3

0.If

I cov

er a

sev

en,

I will

win

!

I will

cov

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n ei

ght.

Fift

een

plu

s ei

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equa

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enty

-thr

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Number Line Target SAB • Grade 3 • Unit 1 • Lesson 2 11

0 1

2 3

4

5 6

7 8

9 1

0 11

12

13

14

15

16

17

18

19 2

0 21

22

23

24

25

26

27

28

29 3

0

+ 5

+ 6

+ 4

+ 8

Materials

Num

ber

Lin

e Ta

rget

Gam

e B

oard

sga

me markers

Direc

tions

1.Player 1 ch

ooses a target num

ber. S

tart with

a small num

ber, suc

h as 20, and

play on

Gam

e Boa

rd 1.

2.Player 1 co

vers a num

ber and

the

n Player 2 co

vers a num

ber. P

layers track the

sum

of the

cov

ered

numbers using the nu

mber line

.

3.Take turns covering nu

mbers. The

winne

r co

vers the

num

ber tha

t makes the

sum

equa

l to or

grea

ter than

the

targe

t nu

mber.

Variation

Play the ga

me using Gam

e Boa

rd 2 with

a larger targe

t nu

mber, suc

h as 100

.

This gam

e is for tw

o players. T

he object of the gam

e is to be the player that covers the

sum

eq

ual to or greater tha

n the target num

ber.

Number Line Target Game

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SAB • Grade 3 • Unit 1 • Lesson 2 Number Line Target12

Nam

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Number Lin

e Target G

ame Boards

0 10

15 25

35 45

55 65

75 85

95 5

20 30

40 50

60 70

80 90

100

Gam

e Bo

ard 1

Gam

e Bo

ard 2

0 1

2 3

4 5

6 7

8 9

0 0

5 5

10 10

20 20

30 30

0 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

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Name Date

Fraction OrderThe object of the game is to fill the game board by placing six fractionsin 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 1 and 2 for two players. Mix the cards and placethem face down between the players. Mix together two sets for 3 or 4players.

• Fraction Chart or fraction circle pieces

Directions

1. Players take turns. On your turn, draw a card from the pile and decidewhere to place it on your game board.

2. If you draw a card that you cannot place because of the numbersalready on your game board, keep the card and lose a turn.

3. If you draw a card with a fraction equivalent to one already placed onyour game board, place the card to the right or left of the equivalentfraction, if a space is open.

4. When one player fills his or her game board, all players use a FractionChart 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 fractioncards on the game board. The winner is the player who fills the lastspace on the game board.

• Order the fractions from largest to smallest.

• Include fraction cards that are not easily represented with circle piecesor the Fraction Chart:

3�7 ,3�20,

99��100 ,1�99 ,

48�50,21�22

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297Comparing Fractions Using 1�2 SAB • Grade 4 • Unit 8 • Lesson 9

18

Nam

eDate

Smallest

Largest

Fraction Order Game Board

SAB • Grade 4 • Unit 8 • Lesson 9 Comparing Fractions Using 1�2

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Fraction Cards 1

0–31–2

1–3

1–42–3

3–44–4

3–51–5

4–51–6

3–62–6

5–61–8

3–82–8

4–87–8

0

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299Comparing Fractions Using 1�2 SAB • Grade 4 • Unit 8 • Lesson 9

Name Date

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Fraction Cards 2

1

1––102––10

3––105––10

7––109––10

0––121––12

2––123––12

5––129––12

10––1211––12

12––12

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301Comparing Fractions Using 1–2

SAB • Grade 4 • Unit 8 • Lesson 9

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Quotient Quest

Game Rules

The object of this game is to have the lowest sum of digits on your remainingdigit 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

1. One player shuffles all 40 digit cards and deals 20 cards face up to eachplayer. (To shorten the game, deal 10 cards to each player.)

2. Each player shuffles one set of game cards and places them face down in a stack.

3. 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 todouble 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. 10. The game ends when a player has two or fewer digit cards left at the end

of a turn.11. At the end of the game, players add the numbers on their remaining

digit cards.12. The player with the lowest sum of digits on his or her remaining digit

cards wins the game.

Name Date

Workshop: Division Concepts SAB • Grade 4 • Unit 12 • Lesson 5 513

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Quotient Quest Game Board

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Quotient Quest Digit Cards

0 1 2 435 6 7 980 1 2 435 6 7 98

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Quotient Quest Game Cards

Divide to get a quotient between

0 and 10.


10 and 20.


20 and 30.


30 and 40.


40 and 50.


50 and 60.


60 and 70.


70 and 80.


80 and 90.


90 and 100.


100 and 150.


150 and 200.

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Factor GamesFactor 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, 3 and 4 are factors of 12 since 3 � 4 � 12. All the factors of 12 are 1, 2, 3, 4, 6, and 12.

Factor 20 or Factor 40The goal is to mark the most factors and earn the most points. This is agame for two players.

Materials

• one Factor 20 Game Board and Score Box or Factor 40 Game Board andScore 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 1 on the game board and draws an“X” on it. Player X writes that number in Column X of the score box. PlayerX 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 Oearns points equal to the sum of the factors for this turn.

Second Turn• Player O chooses any unmarked number on the board. (An unmarkednumber is one that has not yet been circled or marked with an X.) Thenumber must have at least one factor that is unmarked. Player O circles thenumber and records it in Column O.

• Player X draws an X on all the unmarked factors of that number andrecords them in Column X.

Play Continues• Players take turns choosing numbers, marking factors, and recordingscores 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 morepoints wins.

1 Factor Games422

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Factor Games SAB • Grade 5 • Unit 9 • Lesson 1 359

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12

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10

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1314

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ors

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ors

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1 Factor Games362

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Factor 40

Game Board Score Box

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

TOTAL

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

Factors

Number

TOTAL

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

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Closest toThis is a game for two to four players. The object is to estimate differencesaccurately and have the most points at the end of the game.

Materials

• 1 recording sheet per player• 1 prepared set of four Number Squares per player• 1 prepared deck from Closest to Game Cards Master• scissors

Directions

1. Players hold their Number Squares in their hands. The deck of game cardsare placed face down in the middle of the players.

2. For each round, one game card is turned over to display a mixed number. InGame 1, each player estimates the difference that results from subtractingthis mixed number from 3 3�4 . In Game 2, players will subtract from 4

1�2 . Eachplayer places one of their number cards face down, indicating whether theythink the difference is closest to 0, 1, 2, or 3.

3. Players record the number sentence on their recording sheet and find thedifference using mental math or paper and pencil. They also record whetherthe difference is closest to 0, 1, 2 or 3.

4. Players reveal their number cards. If their estimate was correct, they recordone 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.

Number Squares

0 1 2 3

Name Date

Subtract Mixed Numbers SAB • Grade 5 • Unit 10 • Lesson 5 405

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Recording Sheet: Game 1

Example: 3 � 2 � 13�41�8

5�8

Number SentenceClosest to0, 1, 2, 3

Points

Total Points

3�43 �

3�43 �

3�43 �

3�43 �

3�43 �

3�43 �

3�43 �

3�43 �

Name Date

Subtract Mixed Numbers SAB • Grade 5 • Unit 10 • Lesson 5 407

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Recording Sheet: Game 2

1�24 �

1�24 �

1�24 �

1�24 �

1�24 �

1�24 �

1�24 �

1�24 �

Number SentenceClosest to0, 1, 2, 3

Points

Total Points

Example: 4 � 2 � 21�21�8

3�8

Name Date

SAB • Grade 5 • Unit 10 • Lesson 5 Subtract Mixed Numbers408

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Games in Digital EnvironmentsMultiplication and Division

Bojagi http://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 http://illuminations.nctm.org/Activity.aspx?id=4213 The player can play against the computer or against another player. This is a fluency and flexibility game. (Flexibility, Fluency)

Factor Game http://illuminations.nctm.org/Activity.aspx?id=4134 The player can play against the computer or against another player. This is a fluency and flexibility game. (Flexibility, Fluency)

Factorize http://illuminations.nctm.org/Activity.aspx?id=3511 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 https://www.brainpop.com/games/multiplicationblocks/ 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 https://www.brainpop.com/games/sortifymultiplication/ This is a single player game that involves multiplication, division, factors, and multiples. Players classify and group products. (Modeling, Reasoning, Flexibility)

Primary Krypto http://illuminations.nctm.org/Activity.aspx?id=3569 This puzzle game involves arithmetic and order of operations. (Flexibility, Reasoning)

Visual Multiplication Table https://itunes.apple.com/us/app/visual-‐multiplication-‐table/id457381162?mt=8 This is an iPad app designed to help students visualize multiplication. This would classify as a tool rather than a game.

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Meaningful Ways to Develop Math Facts fileSpinners 1–4 and 1–10 2 4 1 3 1 2 8 3 4 9 7 5 10 6...

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