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

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Strategies to Help with Math Fluency

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Strategies to help with math fluency

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

Let’s Warm Up!

A = 

B =   

C =  

D =       

E =      

F =   

Take 30 seconds to memorize this slide!


Which letter belongs in each box

Which letter belongs in each box?

E

F

E

B + C =

D - B =

C x F =


Basic fact memorization what does research show

Basic Fact MemorizationWhat 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.


Strategies to help with math fluency

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

Building Number Concepts

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.


Strategies to help with math fluency

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

Where do we begin?


Strategies to help with math fluency

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

Building Numbers

Use Concrete Manipulatives

“Show me 5 with blocks.”


Number recognition instant recognition of a quantity

Number RecognitionInstant recognition of a quantity

4

6


Strategies to help with math fluency

Use Concrete Manipulatives

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


Bullwinkle

Bullwinkle


Story of 4

Story of 4

Start

with

beans

____and _____make_____

____and______make_____

____and______make_____


Strategies to help with math fluency

Use Concrete Manipulatives

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

4 + 13 + 2 2 + 31 + 4


Story of 24

Story of 24

Move

to numbers

24

*

____and____and ______ make_____

____and_____and______ make_____

____and______and_____make_____

____and _____make_____

____and______make_____

____and______make_____


Paper plate dot cards

Paper Plate Dot Cards

Front Back

7

Seven


Paper plate dot cards1

Paper Plate Dot Cards

Front Back

4

Four


Strategies to help with math fluency

Use The Five Frame!

Allows children to see relationships to 5!


Strategies to help with math fluency

“Make your five frame show three.”

The Five Frame


Strategies to help with math fluency

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

The Five Frame

“Two more.”


Strategies to help with math fluency

Use two different colors to represent the addends.

3

+ 2 =

5


Strategies to help with math fluency

3

- 2 =

1

“Remove two!”

“How many are left?”


Strategies to help with math fluency

Five Frame Flash Cards

“What number do you see?

How do you know?”


Strategies to help with math fluency

Five Frame Flash Cards

“What number do you see?

How do you know?”


Strategies to help with math fluency

Use The Ten Frame

Allows children to see relationships to 10!


Strategies to help with math fluency

Ten Frame Flash Cards

“Make your ten frame show seven.”


Strategies to help with math fluency

Ten Frame Flash Cards

“Our ten frame is showing seven.

How many more do we need to have ten?”


Strategies to help with math fluency

“We have six. Show three more than six.”

2 different colors

Nine!

6 + 3 = 9


Strategies to help with math fluency

7 -

2 =

5


Strategies to help with math fluency

Ten Frame Flash Cards

What number do you see?

How do you know?


Strategies to help with math fluency

Ten Frame Flash Cards

What number do you see?

How do you know?


Strategies to help with math fluency

Double Ten Frames


Connect the ten frame with a number line

Connect The Ten Frame With A Number Line

1 2 3 4 5 6 7 8 9 10


Addition strategies

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

Making Multiples of Ten

*recognize combos of ten

36

+4


Strategies to help with math fluency

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!


Strategies to help with math fluency

Draw a picture that goes with the number fact. 8 + 5 = ?


Strategies to help with math fluency

+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.

______+ ______ = _______


Strategies to help with math fluency

Show me all the ways to make


Strategies to help with math fluency

Fact Triangles

10

73


Flip cards part part whole

Flip Cards!!…Part, Part, Whole!

?

9 altogether


Flip cards

Flip Cards!

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

____ + ____ = ___

____ - ____ = ____

?

10 altogether


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to help with math fluency

4’s,5’s,6’s

BOO HOO!

No Trick

3’s

No Trick

Count back 3

How many apart?


Compensation

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

Expanded Subtrahend

65-34

65-30-4

65-30=35

35-4=31


Strategies to help with math fluency

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

Strategies To Support Fact Learning

Write Fact Families!

(3, 8, 11)

3 + 8 = 1111 - 8 = 3

8 + 3 = 1111 - 3 = 8


Multiplication strategies

MultiplicationStrategies

*Skip Counting Songs & Chants

*Repeated Addition

*Draw Pictures

*Explore Patterns

*Arrays

*Factors & Product

*Hints & Tricks


Skip counting songs

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 numbers1

Building Numbers

Use Concrete Manipulatives

“Show Me”

3 x 4


Repeated addition

Repeated Addition


Rectangle collages give children grid paper to cut

Rectangle Collages(Give children grid paper to cut.)

What fact is shown?

What is the area of each rectangle?


Strategies to help with math fluency

5 x 3 = 15

Have children draw arrays to show facts!


Fact posters children make a poster that shows a fact 3 different ways

Fact PostersChildren make a poster that shows a fact 3 different ways.

3 x 6 = 18


Paper plate multiplication cards

Paper Plate Multiplication Cards

Front Back

8

2

x 4

Eight


Strategies to help with math fluency

Stick Drawing! Count the dots!

4 x 3 = 12


Strategies to help with math fluency

Hints & Tricks

Packet

Lynette Grow

West Haven Elementary


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Division strategies

DivisionStrategies

I taught division

right along with multiplication

showing the Fact Family


Strategies to help with math fluency

Dividing By 3

Fair Share


Strategies to help with math fluency

Make Connections Between Multiplication and Division

What facts do you see?

3 x 5 = 15

15  3 = 5


Strategies to help with math fluency

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


Strategies to help with math fluency

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


Strategies to support fact learning1

Strategies To Support Fact Learning

Write Fact Families!

(3, 9, 27)

3 x 9 = 2727 /9 = 3

9 x 3 = 2727 /3 = 9


Strategies to help with math fluency

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


Strategies to help with math fluency

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

Use Correct Vocabulary

  • Addend

  • Minuend

  • Subtrahend

  • Factor

  • Product


Strategies to help with math fluency

Games


Strategies to support fact learning2

Strategies To Support Fact Learning

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 help with math fluency

Strategies To Support Fact Learning

Use Seesaws to show Balance!

7 + 3 = 5 + ?


Strategies to help with math fluency

Play Fact Games That Include All Students

“Let’s Play

Pig!”


Cross out

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.


Strategies to help with math fluency

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

Smack A Fact!

122136

184533

564810

2 x 5 = ?


Strategies to help with math fluency

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…..Who Has?


Strategies to help with math fluency

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

?


Strategies to help with math fluency

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


Strategies to help with math fluency

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?


Strategies to help with math fluency

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

What’s The Rule?

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.


Use function tables

Use Function Tables!

- 2

INOUT

42

9

7

5


Use function tables1

Use Function Tables!

X 2

INOUT

48

9

7

5


Strategies to help with math fluency

What

Happened

Here?

BeforeAfter

7 30

12 50

50 202

Multiply by 4, then add 2


Strategies to help with math fluency

Smart Board Games

Don’t forget to get games from exchange.smarttech.com


Strategies to help with math fluency

Digital Math Stories

Using Microsoft Paint

and or Power Point


Strategies to support fact learning3

Strategies To Support Fact Learning

  • 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.


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


Strategies to support fact learning4

Strategies To Support Fact Learning

*Have students keep an updated graph of their own results in their mathematics folders.

Blue = Addition FactsRed = Subtraction Facts


Motivation is the key

MOTIVATION is the key!

Goalie Club

Give me 5 Club

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Stickers

Trophy

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Hip hip hooray

club


Strategies to help with math fluency

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