Strategies to Help with Math Fluency Developing Fact

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= Take 30 seconds to memorize this slide! D= E= F=

Which letter belongs in each box? B+C= EF E D-B= Cx. F=

Basic Fact Memorization What Does Research Show? èChildren who have a strong conceptual understanding of addition, subtraction, multiplication and division are more successful at memorizing their facts. èWhen children have a firm conceptual foundation and can use fact strategies, memorizing facts becomes a matter of efficiency.

What does the research say? Learning with understanding is more powerful than simply memorizing because the act of organizing improves retention and promotes fluency. EDThoughts 2001 p. 81

Building Number Concepts Concrete Manipulatives Pictorial Representation Abstract Symbols IIII 4+4=8 IIII 2 x 4=8 *Significant time must be spent working 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 higherorder 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_____

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 24 * ____and ______ make_____and _____make_____ ____and______and_____make_____and______make_____

Paper Plate Dot Cards Front Back 7 Seven

Paper Plate Dot Cards Front Back 4 Four

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. 3 +2= 5

3 -2= 1 “Remove two!” “How many are left? ”

Five Frame Flash Cards “What number do you see? How do you know? ”

Five Frame Flash Cards “What number do you see? How do you know? ”

Use The Ten Frame Allows children to see relationships to 10!

Ten Frame Flash Cards “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? ”

“We have six. Show three more than six. ” 2 different colors 6+3=9 Nine!

7 - 2= 5

Ten Frame Flash Cards What number do you see? How do you know?

Ten Frame Flash Cards What number do you see? How do you know?

Double Ten Frames

1 2 3 4 5 6 7 8 9 10 Connect The Ten Frame With A Number Line

Addition Strategies *Counting On *Doubles Plus One *Making Ten *Making Multiples of Ten *Front End Addition *Zero’s & Ones *Two’s *Doubles Plus or Minus One *Making Tens *Nine’s *Left over Three’s & Four’s *Left over Five’s & Sixes

0’s s i r e w s n a – g n i h t e m o s o d t n g e n d i d h a e h Not t r e the oth 1’s -Coun ting O -One M n ore 2’s g n i t n u o C -Skip e h t n a h t n e v e s i d n e d a s -Other ad r e v e c i v … d d o s i r e e h t answ o s 3 s i d n e d d a r e h t o e h t 3 + (2 ) d d o e b l l answer wi -Count on

Doubles *Count by 2’s *All answers even Doubles Plus One Use your doubles, and add one. Use the lowest addend. 5 +6 Think 5+5=10 10+1=11 Doubles Minus One Use your doubles, and subtract one. Use the highest addend. 5 +6 Think 6+6=12 12 -1=11

Making Ten n e T e m w o h S / n e T f *Combo’s o Using ten frames s ie t r e p o r P e iv it n u *Comm t a h t s o b m o c e t a e r c o t d n e d d a n a g in *Decompos equal ten 10=15 + 5 = ) 8 + 2 ( + 5 7+8=(5+2)+8 so

9’s 4 1 = 5 d + d 9 a , n e t a e (mak ) a r t x e the 3’s&4’s Count o n Make a Ten 5’s & 6’s Mak ea. T en

Making Multiples of Ten n e t f o s o b m o c e z i n g o *rec 36 +4

Front End Addition Left to Right 7, 865+1987= 7000+1000=8000 800+900=1700 60+80=140 5+7+12 Add 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, Whole! ? 9 altogether

Flip Cards! ? 10 altogether Write an addition fact and a subtraction fact for each picture. ____ + ____ = ____ - ____ = ____

What’s On My Head? He has an 8…so I must have a 6. 6 The Sum is 14. He has a 6…so I must have an 8. 8

Show and discuss patterns! 1+2= 2+2= n+2= 4+n= 5+2= n+2= 7+n= 8+2= 9+2= 3 4 5 6 n 8 9 n 11

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

Fluency: 15 minutes every day! Review the strategies Flashcards Desk & set at home Play Games to Review Timings in class Oral Practice: Facts in a Flash Motivate 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 Plus or Minus One * Tens *Nine’s *Left over Three’s & Four’s *Left over Five’s & Sixes

0’s = e m a s e h t Numbers e m a g e h t s ’ o Zer ? -0=? Doubles s i r e w s n a e h T m e l b o r p e h t n i 1’s Count back Visualize on a number lin “I’m taking e e verything aw ay except__ 2’s Count back Number line How many apart?

Doubles Plus One Use a double, add one on! 11 -5 Use 5+5=10 or 10 -5=5 Tens Think backwards to find the missing addend? 10 -2=? Think ? +2= 10

9’s Add the top or two digits f the answer 12 -9=3 Add 1+2=3 14 *Magic 9 12 -3=9 because 1+2=3 Subtracting 9 from a teenager! When subtracting nine from a teenager number, simply add the digits of the teenager! 17 13 -9 -9 5 8 -9 4

3’s No Trick 3 k c a b t n u Co ? t r a p a y n a How m 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 -34 65 -30 -4 65 -30=35 35 -4=31

Show and discuss patterns! 9 -8=1 8 -7=1 7 -6=1 6 -5=1 5 -4=1 4 -3=1 3 -2=1 2 -1=1

Strategies To Support Fact Learning Write Fact Families! (3, 8, 11) 3 + 8 = 11 11 - 8 = 3 8 + 3 = 11 11 - 3 = 8

Multiplication Strategies *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 during Calendar • 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 Posters Children make a poster that shows a fact 3 different ways. 3 x 6 = 18

Paper Plate Multiplication Cards Front Back 8 2 x 4 Eight

Stick Drawing! Count the dots! 4 x 3 = 12

Hints & Tricks Packet Lynette Grow West Haven Elementary

Show and discuss patterns! 1 x 9= 9 2 x 9 = 18 n x 9 = 27 4 x n = 36 5 x 9=n n x 9 = 54 7 x n = 63 8 x 9=n 9 x 9 = 81

What’s On My Head? He has an 8…so I must have a 4. 4 The Product is 32. He has a 4…so I must have an 8. 8

Division Strategies I taught division right along with multiplication showing 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

What does the research say? 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

Fact Families Strategy - Can be used with all division facts. 6 x 3 = 18 18 3 x 6 = 18 18 6 = 3 18 3 = 6 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 = 3 12 4 = 3 48 6 = 8 24 3 = 8

Show and discuss patterns! 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!

Use Correct Vocabulary • • • Addend Minuend Subtrahend Factor Product

Games

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

Strategies To Support Fact Learning Use Seesaws to show Balance! 7+3 = 5+?

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 Cards Split 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?

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

What’s The Value of ……. A= 1 F= 6 ……your name? B= 2 G=7 ……Mississippi? C= 3 H= 8 ……. your spelling words? D= 4 I= 9 E=5 J= 10

8 x 3 6 x 4 2 x 12 24 12 x 2 4 x 6 24 x 1 3 x 8 Fact Webs

What’s The Rule? Yes No 3+9 4+6 6+6 2+5 3+7+2 3+2+1 The numbers on the Yes side have a sum of 12.

Use Function Tables! -2 IN OUT 4 2 9 7 5

Use Function Tables! X 2 IN OUT 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 Paint and or Power Point

Strategies To Support Fact Learning q. Give timed fact tests regularly q. Set a regular schedule q. Give the same amount of problems each time q. Give the same amount of time each test.

Strategies To Support Fact Learning Have students keep an updated graph of their own results in their mathematics folders

Strategies To Support Fact Learning *Have students keep an updated graph of their own results in their mathematics folders. Blue = Addition Facts Red = Subtraction Facts

MOTIVATION is the key! e i l a Go b u l C Give me 5 Club Blog Certificate Stickers Trophy 5 min extra Recess Party Bulletin Boards

Any More Ideas?