Number Talks

Why Number Talks?

Clarify Their Own Thinking

Consider and Test Other Strategies

Investigate and Apply Math Relationships

Develop Multiple Strategies and Choose the Most Efficient One

Number Talks

Strings- Give students a series of smaller problems that build on each other to teach a particular strategy.

Focused Problem- 1 bigger problem that allows students to explore how to solve the problem in different ways- develops flexible and efficient thinking.

Number TalksCharacteristics

5-15 minutes

Think-Pair-Share

Wait Time- Emphasize Thinking Over SpeedWait until most students feel they have at least one strategy

Students who solve problem quickly are encouraged to solve problems in more than 1 way

Accept All IdeasDifferent Strategies develop flexible thinking and build on understanding of number relationships

Wrong answers lead discussion to focus on important strategies and clear up common misconceptions

Classroom DiscussionsEmphasize Talk!

Sample PromptsI agree with ____________ because__________.

I disagree with__________ because__________.

I do not understand____________. Can you please explain again?

Why did you decide to_________________?

Getting Started

Start with smaller problems

Offer strategies from former students

It’s ok to put an answer on the back burner

5-15 minutes

Be patient

Building Mathematical Relationships

Writing Problems Horizontally

199 + 199

+1 +1

200 + 200 = 400

-2

398

Vertical problems encourage standard algorithm

Building Mathematical Relationships

Anticipate Student Answers and Name Them:

28+29

Friendly Numbers or Landmarks

25+23=25+25-2= 50-2=48

7x5= 5x5+2x5Compensation

28+29 = (28-1) + (29+1)= 27+30

+10 +10 +10

27 37 47 57

Breaking Numbers Into Place Value

(20+8)+ (20+9) = (20+20) + (8+9) = 40+17 = 40 +10 + 7 = 50 +7 = 57

Strings- a series of smaller problems that teach a pattern, strategy, etc….

• 7+3

• 3+4

• 7+3+4

• 7+7

Strings- a series of smaller problems that teach a pattern, strategy, etc….

• 3x5•Clarify Their Own Thinking• Tyler realized his mistake and did the

2nd one correctly

•Consider and Test Other Strategies

•Investigate and Apply Math Relationships• Associative property

•Develop Multiple Strategies and Choose the Most Efficient One• 3x (5x2) is more efficient than (3x5)x2

• 2x6

• 3x5x2

• 5x2x6

1 Problem- Many Strategies

12+19

CompensationMake a 12 a friendly number by subtracting 2. Add 2 to 19

to compensate.

12+19= 10 + 21 (12-2) + (19+2)

1 Problem- Many Strategies

12+19

Place Value

Rewrite numbers in expanded form12+19=( 10+2) +(10+9)

Use associative property to add 10’s and 1’s

10+10=20 2+9=1120+11=31

1 Problem- Many Strategies

12+19

Friendly Landmarks

Adjust 12 and 19 to make the friendly landmarks of 10 and 19.12-2=10 and 19+1=20

10+20=30

Readjust numbers back 30+2=3232-1=31

1 Problem- Many Strategies12x15

Decomposing and The Associative Property

Decompose The Factors12=3x4 15=3x5

12x15=3x4x3x5

Rearrange to friendlier numbers 12x15=(4x5)x (3x3)

Recompose with friendlier numbers12x15=20x912x15=180

1 Problem- Many Strategies

12x15

Distributive Property

Distribute 12 Groups of 15 Into Friendly Groups- 10 Groups of 15 +2 Groups of 1512x15= (10 x 15) + (2 x 15) = 150+30=180

Or

Distribute 15 Groups of 12 Into Friendly Groups- 10 Groups of 12 + 5 Groups of 12

12x15= (12 x 10) + (12 x 5)= 120 +60=180

1 Problem- Many Strategies12x15

Doubling and Halving

Double 1 Factor and Halve The Other12x15=6x30

Decompose 30 Into 3x106x30= 6x3x10

Use associative property to multiply a basic fact and multiple of 10

6x3=1818x10=180

Accountability

Smaller Number Talks

Signal most efficient strategy

Posters of Strategies Used

Exit Problems

Weekly Computation Assessment

Day 1 – Problem TalkTed is saving money for a new bike. He deposits money at his bank three times a month. Each time he goes, he deposits $5. How much will he have saved in a year.

First we have to figure out how much he saves in a month- 3x5

Then we have to find out he saves in a year- (3x5) x12

Day 2 – Number Talk3x5

15x12

K-2 Classrooms: Big Ideas

Developing Number SenseRelationships

Magnitude

Effect of operations

Mental Math

Estimation

Conservation of #

Developing Fluency With Small NumbersMore than memorizing facts…understanding number relationships

Subitizing

Making 10’s

K-2 Classrooms: Tools

Dot Cards

Rekenreks (Bead models)

5 Frames and 10 Frames

Number Lines

Number Grids

K-2 Classrooms: Strategies

Counting on/ Counting Back

Counting chunks

Finding 10’s

Compose and Decompose

Place Value

Doubles/ Near Doubles

Compensation

3-5 ClassroomsDeveloping Number Sense

Relationships

Magnitude

Effect of operations

Mental Math

Estimation

Conservation of #

Place Value

Developing FluencyMore than memorizing facts…understanding number relationships

Properties

Connecting Mathematical Ideas

3-5 Classrooms: Addition And Subtraction Strategies

Counting on/ Counting Back

Counting chunks

Finding 10’s

Compose and Decompose

Place Value

Doubles/ Near Doubles

Compensation

3-5 Classrooms: Multiplication Strategies

Area Models

Repeated addition

Skip Counting

Doubling and Halving and related relationships5 x 4 = 10 x 2

Partial Products

Landmarks and Friendly Numbers

Decomposing Factors into Smaller Factors

3-5 Classrooms: Division Strategies

Area Models

Repeated subtraction

Sharing out (picture models)

Multiplying Up (Partial products)

Partial Quotients

Proportional Reasoning (halving and halving)200/4 = (200/2) / (4/2) = 100/2 = 50

Decomposing Factors into Smaller Factors40/8 = 40 / (4x2) = (40/4) / 2 = 10/2 = 5