Strategies to Help with Math Fluency

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


“Show me 2 more than 5 with your

cereal.”

Bullwinkle

Story of 4

Start with

beans

____and _____make_________and______make_________and______make_____


“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?”


“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?


What number do you see?How do you know?


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


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!

http://www.qacblogs.org/nicki.slaugh

Building Numbers


“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


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


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!


Use Correct Vocabulary

• Addend• Minuend• Subtrahend• Factor• Product

Games

http://qacblogs.org/candokids/?s=multiplication+madness


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 + ?


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=?



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


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



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

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Any More Ideas?

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Strategies to Help with Math Fluency