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Strategies to Help with Math Fluency
Developing Fact Fluency and Quick Recall of Basic Facts is very similar to being on a successful dieting program. In order to lose weight, you need to eat healthy, exercise regularly and assess your progress through weighing yourself on the scale. The same is true for developing fact fluency! Extensive amount of time needs to be spent working with and applying basic fact strategies, as well as reasoning and mental strategies. In order to determine the effectiveness, assessment plays a key role. In contrast, assessing continuously without more time spent developing strategies is ineffective. That is like a person who knows about the dieting program, doesn’t eat healthy or exercise, but constantly weighs themselves and wonders why they are not losing weight.
Let’s Warm Up!A =
B =
C =
D =
E =
F =
Take 30 seconds to memorize this slide!
Which letter belongs in each box?
B + C =
D - B =
C x F =
EF E
Basic Fact Memorization What Does Research Show?
Children who have a strong conceptual understanding of addition, subtraction, multiplication and division are more successful at memorizing their facts.
When children have a firm conceptual foundation and can use fact strategies, memorizing facts becomes a matter of efficiency.
Learning with understanding is more powerful than simply
memorizing because the act of organizing improves retention
and promotes fluency.
EDThoughts 2001 p. 81
What does the research say?
Building Number Concepts
Concrete Manipulativ
es
Pictorial Representatio
n I I I I
I I I I
Abstract Symbols
4 + 4 = 8
2 x 4 = 8
*Significant time must be spentworking with concrete materials
and constructing pictorial representations
in order for abstract symbol and operational understanding to occur.
The National Council of Teachers of Mathematics (NCTM)
A mastery of lower-order skills instills confidence in students and facilitates higher-order thinking. The ability to automatically recall facts strengthens mathematical ability, mental mathematics, and higher-order mathematical learning. Without this automation, students have difficulty performing advanced operations.
Where do we begin?
Math Fluency*15 Minutes a Day
*Start by Teaching Strategies*Use Manipulatives
*Flashcards – Buddy/Individual Practice*Games
*1 Minute Drills*Fasst Math
*Facts in a Flash (oral practice)*Keep a Graph of Results
*Celebrate Growth(Individual, group, class, & grade
Rewards and or Clubs)
Building Numbers
Use Concrete Manipulatives
“Show me 5 with blocks.”
Number Recognition
Instant recognition of a quantity
4 6
Use Concrete Manipulatives
“Show me 2 more than 5 with your
cereal.”
Bullwinkle
Story of 4
Start with
beans
____and _____make_________and______make_________and______make_____
Use Concrete Manipulatives
“Let’s see how many other ways we can build 5.”
4 + 1 3 + 2 2 + 3 1 + 4
Story of 24
Move to
numbers____and____and ______ make_____
____and_____and______ make_________and______and_____make_____
24
____and _____make_________and______make_________and______make_____
*
Paper Plate Dot Cards
Front Back
7Seven
Paper Plate Dot Cards
Front Back
4Four
Use The Five Frame!
Allows children to see relationships to 5!
The Five Frame
“Make your five frame show three.”
The Five Frame
“We have three. How many more do we need to make five?”
“Two more.”
Use two different colors to represent the addends.
+ 2 = 53
- 2 = 13
“Remove two!” “How many are left?”
“What number do you see?How do you know?”
Five Frame Flash Cards
“What number do you see?How do you know?”
Five Frame Flash Cards
Use The Ten FrameAllows children to see relationships to 10!
“Make your ten frame show seven.”
Ten Frame Flash Cards
“Our ten frame is showing seven.
How many more do we need to have ten?”
Ten Frame Flash Cards
“We have six. Show three more than six.”2 different colors
Nine!6 + 3 = 9
7 - 2 = 5
What number do you see?How do you know?
Ten Frame Flash Cards
What number do you see?How do you know?
Ten Frame Flash Cards
Double Ten Frames
Connect The Ten Frame With A Number Line
1 2 3 4 5 6 7 8 9 10
Addition Strategies
*Counting On*Doubles*Doubles Plus One*Making Ten*Making Multiples of Ten*Front End Addition
*Zero’s & Ones*Two’s*Doubles*Doubles Plus or Minus One*Making Tens*Nine’s*Left over Three’s & Four’s*Left over Five’s & Sixes
0’s
Nothing to
something –
answer is the
other the addend
1’s-Counting On-One More
2’s
-Skip Counting
-Other addend is even than
the answer is odd…vice versa
(2+3 the other addend is 3 so
the answer will be odd)
-Count on
Doubles
*Count by 2’s
*All answers even
Doubles Plus OneUse your doubles, and
add one. Use the lowest addend.
5+6
Think5+5=1010+1=11
Doubles Minus One
Use your doubles, and subtract one. Use the
highest addend. 5+6
Think 6+6=1212-1=11
Making Ten
*Combo’s of Ten/Show me Ten
Using ten frames
*Communitive Properties
*Decomposing an addend to
create combos that equal ten
7+8=(5+2)+8 so 5+(2+8) = 5+10=15
9’s
9+5=14
(make a ten,
add the extra)
3’s&4’s
Count onMake a
Ten
5’s & 6’sMake a Ten
Making Multiples of Ten
*recognize combos of ten
36 +4
Front End Addition
Left to Right
7,865+1987=7000+1000=8000
800+900=170060+80=140
5+7+12Add them all up!
Draw a picture that goes with the number
fact. 8 + 5 = ?
+My Addition Story Problem+
Written and Illustrated by -______________
____________________________________________________________________________________________________________________________________________________________________________________
Here is a picture of my problem.
Here is an addition number sentence that solves the problem.
______+ ______ = _______
Show me all the ways to make
Fact Triangles
10
7 3
Flip Cards!!…Part, Part, Whole!
9 altogether
?
Flip Cards!
10 altogether
?
Write an addition fact and a subtraction fact for each picture.
____ + ____ = ___
____ - ____ = ____
What’s On My Head?
6 8
The Sum is 14.He has an 8…so I must have
a 6.
He has a 6…so I must have an 8.
1 + 2 = 3 2 + 2 = 4 n + 2 = 5 4 + n = 6 5 + 2 = n n + 2 = 8 7 + n = 98 + 2 = n
9 + 2 = 11
Show and discuss patterns!
Which Fact Solves The Problem?
Nine chairs. Each had 4 legs. How many legs in all?
Nine frogs in the pond. 4 more jump in. How many frogs are in the pond?
9 + 4 = 13
9 x 4 = 36
FlashcardsDesk & set at home
Fluency: 15 minutes every day!
Review the strategies
Play Games to Review
Timings in class
Oral Practice: Facts in a FlashMotivate the kids and Reward
Subtraction Strategies
*Counting Back and Counting On*Thinking Addition*Doubles & Building*Using a Ten*Compensation*Expanding Subtraction
*Zero’s & Ones*Two’s*Doubles*Doubles Plus or Minus One* Tens*Nine’s*Left over Three’s & Four’s*Left over Five’s & Sixes
0’sNumbers the
same=
Zero’s the game
?-0=?
1’sCount back
Visualize on a number line“I’m taking everything away except__
2’sCount backNumber lineHow many
apart?
DoublesThe answer is
in the problem
Doubles Plus OneUse a double, add one on!11-5Use 5+5=10 or 10-5=5
TensThink
backwards to find
the missing addend?10-2=?Think ?+2=10
Subtracting 9 from a teenager!
When subtracting nine from a teenager number, simply add the digits of the teenager!
14 17 13
-9 -9 -9
5 8 4
*Magic 912-3=9 because 1+2=3
9’s
Add the top
two digits for
the answer
12-9=3
Add 1+2=3
3’sNo Trick
Count back 3
How many
apart?
4’s,5’s,6’s
BOO HOO!No Trick
Compensation
Use this strategy when your subtrahend is an 8 or 9
14-8 14-10=4 6 (+2)16-9 16-10=6 7 (+1)23-18 23-20=3 5 (+5)
Expanded Subtrahend
65-3465-30-4
65-30=3535-4=31
9 - 8 = 18 - 7 = 1 7 - 6 = 16 - 5 = 15 - 4 = 14 - 3 = 1 3 - 2 = 1 2 - 1 = 1
Show and discuss patterns!
Strategies To Support Fact Learning
Write Fact Families!
(3, 8, 11)
3 + 8 = 11 11 - 8 = 3
8 + 3 = 11 11 - 3 = 8
MultiplicationStrategies
*Skip Counting Songs & Chants*Repeated Addition*Draw Pictures*Explore Patterns*Arrays*Factors & Product*Hints & Tricks
Skip Counting Songs
• I would teach these throughout the year duringCalendar
•Review all “skip counting” the month before I started teaching Multiplication (had them pass each COUNT BY off)
• Songs are in your folder and on my blog!
Building Numbers
Use Concrete Manipulatives
“Show Me”
3 x 4
Repeated Addition
Rectangle Collages(Give children grid paper to cut.)
What fact is shown?
What is the area of each rectangle?
Have children draw arrays to show facts!
5 x 3 = 15
Fact PostersChildren make a poster that shows a fact 3 different ways.
3 x 6 = 18
Paper Plate Multiplication Cards
Front Back
8Eight 2
x 4
Stick Drawing! Count the dots!
4 x 3 = 12
Hints & Tricks
Packet
Lynette GrowWest Haven Elementary
1 x 9 = 9 2 x 9 = 18 n x 9 = 27 4 x n = 365 x 9 = n
n x 9 = 54 7 x n = 63
8 x 9 = n 9 x 9 = 81
Show and discuss patterns!
What’s On My Head?
4 8
The Product is 32.He has an 8…so I must have
a 4.
He has a 4…so I must have an 8.
DivisionStrategies
I taught divisionright along with multiplicationshowing the Fact Family
Fair Share
Dividing By 3
Make Connections Between Multiplication and Division
What facts do you see?
3 x 5 = 15
15 3 = 5
Teachers and parents should help children recognize that solving one kind of problem is related to solving another
kind.
Principles and Standards for School Mathematics, NCTM 2000
What does the research say?
Fact Families Strategy - Can be used with all division facts.
18
3 6
6 x 3 = 18
3 x 6 = 18
18 6 = 3
18 3 = 6
Strategies To Support Fact Learning
Write Fact Families!
(3, 9, 27)
3 x 9 = 27 27 / 9 = 3
9 x 3 = 27 27 / 3 = 9
Halves Strategy - Use halves to find quotients when dividing by 4, 6 or 8. First halve the dividend and the divisor. Then find the quotient of the smaller fact.
24 8 = 48 6 =
12 4 = 3 24 3 = 8
3 8
72 / 9 = 8……………..(7+1=8)
63 / 9 = 7……………..(6+1=7)
54 / 9 = 6……………..(5+1=6)
45 / 9 = 5……………..(4+1=5)
When dividing by 9, just add 1 to the first digit of the dividend!
Show and discuss patterns!
Use Correct Vocabulary
• Addend• Minuend• Subtrahend• Factor• Product
Strategies To Support Fact Learning
Use IF…Then Charts to show:
Order
IF I know THEN I also know
3 x 2 = 6 2 x 3 = 6
4 + 5 = 9 5 + 4 = 9
15 / 3 = 5 15 / 5 = 3
12 - 7 = 5 12 - 5 = 7
Use Seesaws to show Balance!
7 + 3 = 5 + ?
Strategies To Support Fact Learning
Play Fact Games That Include All Students
“Let’s Play
Pig!”
Cross Out• Cross Out Board• Dice• Beans or some kind of Marker
Taking turns rolling the dice…Player either adds, subtracts or multiplies the 2 dice. Use the counter, covers the sum, or product on the board. Play continues until the board is covered. If they roll the same number, turn is skipped.
WAR
• Deck of CardsSplit the deck in half between 2
players.Both players turn 2 cards over. The
player with the higher sum or product is the winner and collects the cards. They can either add or mulitply to get the largest answer. Other than that twist, it is played just as regular WAR.
Smack A Fact!12 21 36
18 45 33
56 48 10
2 x 5 = ?
Buzz!!
Practicing The Seven’s Table “1,2,3,4,5,6,Buzz,8,9,10,11,12,13,Buzz,15,16,17,18,
19,20,Buzz”
I Have…..Who Has?
I have 56. Who has 9 x 4=?
I have 77 Who has 3 x 5 x 3=?
I have 36. Who has 7 x 11=?
I have 45. Who has 8 x 7=?
The product is 36. Name the facts.
4 x 9
9 x 4
12 x 3
3 x 12
18 x 2
2 x 18
?
Find and Fix The Mistakes!
3 x 6 = 18
8 x 7 = 56
4 + 3 = 12
8 + 3 = 10
12 - 5 = 5
4 + 7 = 11
What’s The Value of …….A= 1 F= 6
B= 2 G=7
C= 3 H= 8
D= 4 I= 9
E=5 J= 10
……your name?
……Mississippi?
…….your spelling words?
24
6 x 4
8 x 3
2 x 12
12 x 2
3 x 8 24 x 1
4 x 6
Fact Webs
What’s The Rule?
Yes No
3 + 9
6 + 6
3 + 7 + 2
4 + 6
2 + 5
3 + 2 + 1
The numbers on the Yes side have a sum of 12.
Use Function Tables!
IN OUT
- 2
4 2
9
7
5
Use Function Tables!
IN OUT
X 2
4 8
9
7
5
What
Happened
Here?
Before After
7 30
12 50
50 202
Multiply by 4, then add 2
Smart Board Games
Don’t forget to get games from exchange.smarttech.com
Digital Math Stories
Using Microsoft Paintand or Power Point
Strategies To Support Fact Learning
Give timed fact tests regularlySet a regular scheduleGive the same amount of problems each timeGive the same amount of time each test.
Have students keep an updated graph of their own results in their mathematics folders
0
10
20
30
40
50
Date Date Date Date
My Fact Progress
Strategies To Support Fact Learning
Strategies To Support Fact Learning
My Fact Progress
0
10
20
30
40
50
60
70
Week 1 Week 2 Week 3 Week 4
Blue = Addition Facts Red = Subtraction Facts
*Have students keep an updated graph of their own results in their mathematics folders.
MOTIVATION is the key!
Goalie
ClubGive me 5 Club
HIP HIP HOORAY
CLUB
BlogCertificateStickersTrophy5 min extra RecessPartyBulletin Boards
Any More Ideas?
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