Ideas to build math computation from the county
News and Notes
December 10, 2007
Debby Kramb Area 4 ALT
Applying research to instruction: Computational fluency
Computational fluency and number sense go hand in hand: they develop together and one cannot exist without the other. (Griffin and Case, 1997)
Standard: Number and Operations
Students will further develop their understanding of computation of whole numbers and compute in problem-solving situations without calculators.
Element: Know facts with understanding and fluency
Bloom: Application (Apply an abstract idea in a concrete situation to solve a problem or relate it to prior experience.)
Fluency refers to having efficient, accurate, and generalizable methods (algorithms) for computing that are based on well-understood properties and number relations (NCTM, 2000).
Computation is a particular form of mathematical problem solving. Computation engages a significant amount of problem solving skills.
Computational Capers
The activities involve a standard deck of playing cards (without the face cards) or number cards. As a bonus, these activities incorporate not only various content standards but Process Standards as well!
K-2
Hit the Target. Have your partner close his or her eyes and choose one card from the deck of cards. The number on the card is your target. Place the remaining cards face up on the playing surface. With your partner, take turns looking for two cards that you can add or subtract to get the number on your target card. Keep playing until you cannot find any more combinations that equal the target number. Repeat the game with a different target number.
Five Alive. Have your partner pick a card or call out a number between 5 and 10. You respond by saying “5 and ---“,” for example, if your partner says “9”, you respond “5 and 4.” Take turns calling out the number.
The DoubleMaker. Turn your calculator into a ‘double maker’ by pressing 2 X or x 2, depending on the calculator. Now press any digit followed by = and you will get double that number. Work with a partner to find the double before using the calculator to check the answer.
3-5
Hit the target II. Select five cards from a shuffled deck and arrange them in a row. Place a sixth card, known as the target card, below the row of cards. Can you add or subtract any combination of the five cards to equal the number on the target card? Challenge a friend to find the greatest number of combinations that equal the target card.
Face off. Start with a deck of cards facedown. You and a friend each draw one card from the deck and turn it face up so that both players can see it. The first player to call out the correct product of the two cards wins both cards. If both players call out incorrect answers, place the cards in a discard pile. When no cards remain in the deck pile, the game ends. The player with the most cards is the winner.
What’s the difference? Choose four cards and arrange them to make the least possible four digit number. Have your partner choose three cards and make the greatest possible number. If either of you draw a 10, discard the card and draw again. The player with the four cards subtracts the three the three –digit number, or subtrahend, from the four-digit number, or the minuend. If the answer is odd, the player with four cards wins the point. If the answer is even, the partner with three cards wins. Switch roles and repeat. When you have drawn all the cards in the deck, the player with the most points wins.
Fast Facts You and a partner choose two cards from a deck placed facedown. Place the two cards faceup next to each other, making a two digit number. This number is your som. Challenge each other to find two numbers, or factors, that you can add to get your sum. Take turns calling out pairs of factors. Pick two more cards and continue finding factors.
3 by 3 magic Use or draw a 3 x 3 grid. Place the numbers 1 – 9 in the squares so that none of the rows, columns, or diagonals have the same sum. Use each number only once. Compare your solution to other classmates’ solutions. Challenge yourself to try again, using a 4 x 4 square grid and the numbers 1 -16.
Those fabulous fives. Can you make five 2’s equal 5? On a piece of paper write a horizontal row of five 2s, leaving enough space between each number for one of the operational symbols (+, -, x, or ÷)
2 2 2 2 2 = 5
Insert symbols to make the equation equal 5. You do not have to use every symbol, and you may use a symbol mre than once. You may need to use parentheses to show the order of operations. Try to use five 3s, five 4s, and five 5s to write equations that equal 5.
High/Low. Do this activity with a partner or a group of three or four students. Using a deck of cards with the face cards and 10’s removed; the dealer deals six cards to each player. The remaining cards become a stockpile. Before the players look at their cards, the dealer announced where they are playing for either the high or the low sum. Players then turn their cards faceup and form two three digit numbers that add up to either the high or the low sum. Beginning with the dealer, the players draw once from the stockpile and may choose to exchange the card they draw for a card in their hand. Each player then must discard one card. The player who gets the highest or lowest sum is awarded one point. Play continues until a player has ten points. Change the game to subtraction and play for the highest or lowest difference, or deal four cards and play a multiplication version of the game.
Games provide the motivation to practice ‘facts’! Use them often and change partners often.
Teach one game at a time and then allow students to pick a game to play when they arrive in the morning, during transition times, inside recess or when they are finished with their work. Research says this format is very reliable in teaching automaticity. Do instead of or in combination with speed drills on paper and pencil and math games on the computer.
