Computational Fluency
What is it?
Fluency has 3 components: 1) Efficiency-a quick way to obtain the answer
2) Accuracy-get the right answer
3) Flexibility-if a problem can’t be figured out, have another way to approach the problem
What does the research tell us?
“The best way to develop fluency with numbers is to develop number sense and to work with
numbers in different ways, not to blindly memorize without number sense.” Jo Boaler, Professor
of Mathematics Education at Stanford.
“Brain research has shown that those who learned through strategies achieved ‘superior
performance’ over those who memorized; they solved problems at the same speed and showed
better transfer to new problems. The brain researchers concluded that automaticity should be
reached through understanding of numerical relations, achieved through thinking about number
strategies” (Delazar et al, 2005).
What happens at school?
During the school day, students are instructed in strategies during Number Corner and Bridges
lessons through direct instruction and with peers as part of their mathematical discourse. Later,
students have opportunities to practice those strategies during small group, guided instruction or
with peers during Work Places.
How can we connect home and school?
According to Johnny Lott, former NCTM president, “it takes a family, a community, and a
teacher to educate a student in mathematics” (NCTM, 2003). Family involvement can be a
powerful way to learn about how math is being taught today. Involvement can take many forms,
large and small. We invite and encourage families to play math games, use transition times as a
time to talk with students about what is happening during math instruction, read math stories,
and look for math opportunities is everyday life. If families feel they lack access to “just right”
games for children, reaching out to the child’s classroom teacher is a wonderful way to acquire
the necessary materials to support the home/school connection.
Computational Fluency Card and Dice Games Addition
Subtraction
Addition Number Battle- Split the deck in half.
Players pick two cards from their deck and find the
sum of their two cards. The player with the greater
sum wins the cards.
Advanced Addition Number Battle- Split the deck
in half. Players pick three cards from their deck and
find the sum of their three cards. The player with the
greater sum wins the cards.
Reading Addition Minds- Pick a target number.
Remove cards greater than the target number. Player
1 puts a card on his/her forehead without looking.
Player 2 says the number that goes with that number
to make the target number. Player 1 wins the card if
he/she can determine the number on the card.
Reverse roles.
Addition Toss-up- Each player draws 3 cards from
the deck and tosses them in the air. Players find the
total sum of the cards that land face up. Players keep
a running total to reach a designated amount of
points (50 or 100). First player to 50/100 wins. Subtraction Number Battle- Split the deck in half.
Players pick two cards from their deck and subtract
the smaller number from the larger number. The
player with the greater difference wins the cards.
Multi-Digit Subtraction Number Battle- Split the
deck in half. Players pick three cards and make a 2digit number using two cards. Subtract the third card
from the 2-digit number. The player with the greatest
difference wins the cards.
Take 100- Each player starts with 100 points.
Players take turns rolling a regular dice and
subtracting the number from his/her 100 points. The
first player to reach zero wins.
*** Variation- roll two dice and add or multiply the
two numbers before subtracting from the total
Multiplication
Division Multiplication Number Battle- Split the deck in
half. Players pick two cards from their deck and find
the product of their two cards. The player with the
higher product wins the cards.
Advanced Multiplication Number Battle- Split the
deck in half. Players pick three or four cards from
their deck and find the product of their cards. The
player with the higher product wins the cards.
Multi-Digit Multiplication Number Battle-Split
the deck in half. Players pick three cards and make a
2-digit number using two cards. Multiply the 2-digit
number by the third card. The player with the higher
product wins the cards.
Multiplication Toss-up- Each player draws 3 cards
from the deck and tosses them in the air. Players
find the product of the cards that land face up.
Players keep a running total to reach a designated
amount of points (100 or 200). First player to
100/200 wins.
Throw the Dice- Players take turns rolling three
dice. Add the first two dice together and divide by
the third. Record your equations and your
remainders. The player with the lowest remainder
after 5 rounds is the winner.
***Variation-roll 4 dice, add the first 3 together
and divide by the 4th.
Division Go Fish- Deal six cards to each player and
place the rest of the deck in the middle as a draw
pile. Each player is trying to find a match for a card
he/she has. For example, a player who wants to find
a match for his 8 could say, "Do you have any 16s
divided by 2s?" or "I’m looking for a card that is a
24 divided by 3." Play ends when the first player gets
rid of all cards or when the draw pile is gone.
Divide Conquer-Remove face cards. Deal each
player 4 cards, put the rest of the cards in the middle
as your draw pile. Player 1 takes a card from the
draw pile. Player 1 looks for a pair where 1 card can
divide into another card. Ex: 6/2 or 4/2. Pairs are
placed in a discard pile. Player 2 takes a turn.
Continue play until the first player gets rid of all
cards.
*When cards are used, face cards can be removed or given a value like 10, 11, and/or 12.