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Strategies to Help with Math Fluency

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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.

A =

B =

C =

D =

E =

F =

Take 30 seconds to memorize this slide!

E

F

E

B + C =

D - B =

C x F =

- 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.

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

Concrete Manipulatives

Pictorial Representation

Abstract Symbols

4 + 4 = 8

2 x 4 = 8

I I I I

I I I I

*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 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.

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)

Use Concrete Manipulatives

“Show me 5 with blocks.”

4

6

Use Concrete Manipulatives

“Show me 2 more than 5 with your cereal.”

Start

with

beans

____and _____make_____

____and______make_____

____and______make_____

Use Concrete Manipulatives

“Let’s see how many other ways we can build 5.”

4 + 13 + 2 2 + 31 + 4

Move

to numbers

24

*

____and____and ______ make_____

____and_____and______ make_____

____and______and_____make_____

____and _____make_____

____and______make_____

____and______make_____

Front Back

7

Seven

Front Back

4

Four

Use The Five Frame!

Allows children to see relationships to 5!

“Make your five frame show three.”

The Five Frame

“We have three. How many more do we need to make five?”

The Five Frame

“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

Nine!

6 + 3 = 9

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

*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 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

*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 on

Make a Ten

5’s & 6’s

Make 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=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

73

?

9 altogether

Write an addition fact and a subtraction fact for each picture.

____ + ____ = ___

____ - ____ = ____

?

10 altogether

What’s On My Head?

The Sum is 14.

He has a 6…so I must have an 8.

He has an 8…so I must have a 6.

6

8

Show and discuss patterns!

1 + 2 = 3

2 + 2 = 4

n + 2 = 5

4 + n = 6

5 + 2 = n

n + 2 = 8

7 + n = 9

8 + 2 = n

9 + 2 = 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

*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’s

Numbers the same=

Zero’s the game

?-0=?

1’s

Count back

Visualize on a number line

“I’m taking everything away except__

2’s

Count back

Number line

How many apart?

Doubles

The answer is in the problem

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 two digits for the answer

12-9=3

Add 1+2=3

*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!

141713

-9-9-9

4

5

8

4’s,5’s,6’s

BOO HOO!

No Trick

3’s

No Trick

Count back 3

How many apart?

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)

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

Write Fact Families!

(3, 8, 11)

3 + 8 = 1111 - 8 = 3

8 + 3 = 1111 - 3 = 8

*Skip Counting Songs & Chants

*Repeated Addition

*Draw Pictures

*Explore Patterns

*Arrays

*Factors & Product

*Hints & Tricks

- 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!

Use Concrete Manipulatives

“Show Me”

3 x 4

What fact is shown?

What is the area of each rectangle?

5 x 3 = 15

Have children draw arrays to show facts!

3 x 6 = 18

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?

The Product is 32.

He has a 4…so I must have an 8.

He has an 8…so I must have a 4.

4

8

I taught division

right along with multiplication

showing the Fact Family

Dividing By 3

Fair Share

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

3 x 6 = 18

18 6 = 3

18 3 = 6

18

3

6

Write Fact Families!

(3, 9, 27)

3 x 9 = 2727 /9 = 3

9 x 3 = 2727 /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 = 324 3 = 8

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!

- Addend
- Minuend
- Subtrahend
- Factor
- Product

Games

Use IF…Then Charts to show:

Order

IFI knowTHENI 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 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.

- 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.

122136

184533

564810

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”

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

A= 1F= 6

B= 2G=7

C= 3H= 8

D= 4I= 9

E=5J= 10

What’s The Value of …….

……your name?

……Mississippi?

…….your spelling words?

8 x 3

6 x 4

2 x 12

24

12 x 2

4 x 6

24 x 1

3 x 8

Fact Webs

Yes

No

4 + 6

2 + 5

3 + 2 + 1

3 + 9

6 + 6

3 + 7 + 2

The numbers on the Yes side have a sum of 12.

- 2

INOUT

42

9

7

5

X 2

INOUT

48

9

7

5

What

Happened

Here?

BeforeAfter

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

- Give timed fact tests regularly
- Set a regular schedule
- Give the same amount of problems each time
- 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.

Blue = Addition FactsRed = Subtraction Facts

Goalie Club

Give me 5 Club

Blog

Certificate

Stickers

Trophy

5 min extra Recess

Party

Bulletin Boards

Hip hip hooray

club

Any More Ideas?