number talks. hally third grade student describe hally’s understandings and misunderstandings....

NUMBER TALKS

HallyThird Grade

Student

Describe Hally’s understandings

and misunderstandin

gs.

VIDEO

Second Grade Student: I couldn’t take seven

from three so I borrowed ten. I made the one a

zero and the three became a thirteen, and thirteen minus seven is

six. That’s just how you do it when the bottom number is bigger than

the top.

0 13

13- 7 6

NEED FOR NUMBER TALKS

Traditional View of Mathematics:

A discrete set of rules and procedures to be memorized and implemented with speed and accuracy……but without understanding the mathematical logic or numerical relationships that provide the foundation for these rules.

VIEW OF MATHEMATICS

Accuracy – ability to produce an accurate answerEfficiency – ability to choose an appropriate, expedient strategy for a specific computation problemFlexibility – ability to use number

relationships with ease in computation

MATHEMATICALLY PROFICIENT STUDENTS

Our math classrooms must provide opportunities for students:To grapple with number relationshipsApply numerical relationships to computation strategies

Discuss and analyze their reasoning

CREATING MATHEMATICALLY PROFICIENT STUDENTS

Number Talks

DIRECTIONS

1. When the problem is put up, solve in your head.

2. When you have solved, put your thumb up in front of your chest.

3. Try to solve in a different way. For each different way you solve, put up another finger.

HOW MANY OBJECTS DO YOU SEE?

HOW MANY OBJECTS DO YOU SEE?

26 + 58 = ?

What is a number talk? What is the role of the teacher?

What is the role of the students?

Describe the classroom community and environment.

VIDEOThird Grade

38 + 37

Number

Talks

Characteristics of Number

Talks

Classroom Community & Environment

Role of the Teacher

Role of the Students

Classroom conversations and discussions around a few purposefully crafted computation problems

Short, ongoing daily routine (5 – 15 minutes)

Provides students with meaningful ongoing practice with computation

Intended to help students develop computational fluency

Problems are designed to elicit specific strategies that focus on number relationships

NUMBER TALKS

Teacher presents problem

Students figure it

out

Students share their

answers

Students share their

thinking

Class agrees on

the answer

FORMAT

1.Classroom environment & community

2.Classroom discussion3.The role of mental math4.The teacher’s role5.Purposeful computation problems

KEY COMPONENTS

CLASSROOM ENVIRONMENT

saferisk-freecomfortableacceptingrespectfulclear

expectations

Encourages students:To build on number relationships to solve problems instead of relying on memorized procedures

To develop efficient, flexible strategies with accuracy

To strengthen students’ understanding of place value

Ways to encourage mental math:Students solve problems without paper and pencil

Write problems in a horizontal format

MENTAL MATH

199 + 199 11

199+199 398

TEACHER’S ROLE

Read “What is the Teacher’s Role during Number Talks?”

What should the teacher do during Number Talks?

What should the teacher not do during Number Talks?

Teacher

Facilitator

Listener

Questioner

Learner

TEACHER’S ROLE

Select a designated location Give students time to think by

providing appropriate wait timeEncourage student communication

and equitable participationTurn & TalkThink/Pair/Share

Accept and record all responses without judgment

Ask students to test new strategiesCapture and record strategies so it is accessible

to others (notation should be mathematically correct)

PROCEDURES

Provide access to tools and manipulativesNumber lines, hundred boards, cubes, counters, ten frames, place value blocks, fraction tiles, etc.

Model how to ask questions & make comments I agree with _____ because….. I do not understand ____________. Can you explain this again?

I disagree with ___ because…..How did you decide to ______?

ROLE OF THE TEACHER

Ask students to use finger signals Number of strategies Agree/Disagree Effi cient strategy

Keep records of problems posed and the corresponding student strategies Record student’s name next to the strategy Document student participation and strategies

Smartboard fi le Notebook/Document Camera Camera

Hold small-group number talks throughout the week Pull groups based on common needs Select students who need to be challenged Work with students who are shy or reluctant to share in the

whole group

DEVELOPING ACCOUNTABILITY

Require students to solve an exit problem using the discussed strategiesSpecific types of problems or strategies

Occasionally give a computation assessmentConsists of a few related problems Requires students to solve each problem in two ways

Create and post class strategy charts

DEVELOPING ACCOUNTABILITY

Start with smaller problems to elicit thinking from multiple perspectives

Offer strategies from a previous student

Put a student’s strategy on the back burner

Limit number talks to 5 - 15 minutesBe patient with yourself and your students

Handout: “Tips for Implementing Number Talks”

HELPFUL TIPS & HINTS

K-2 NUMBER TALKS

How does the teacher build student fluency with small numbers?

What questions does the teacher pose to build understanding?

What strategies are the students using to build meaning of the numbers?

How does the teacher support student communication during the number talk?

VIDEOKindergarten

1.Developing number sense2.Developing fluency with

small numbers3.Subitizing4.Making tens

GOALS OF K-2 NUMBER TALKS

Describe each goal. What does it mean?

“Number sense is an awareness and understanding about what

numbers are, their relationships, their magnitude, the relative

effect of operating on numbers, including the use of mental

mathematics and estimation”

~Fennell & Landis, 1994, p. 187

NUMBER SENSE

Conservation of numberOne-to-one correspondenceCompose and decompose numbersFact fluencySubitizingMaking tens

Place ValueTen ones is one group of 10How many more to make tenCompose and decompose 10

GOALS OF K-2 NUMBER TALKS

Dot ImagesFive/Ten FramesNumber LinesHundred ChartStory Problems

K-2 NUMBER TALK TOOLS

What strategies are the students using to build meaning of the numbers?

How does the teacher build student fluency with small numbers using ten-frames?

What questions does the teacher use to build understanding about decomposing and composing numbers?

VIDEOSecond Grade

8 + 6

3-5 NUMBER TALKS

1.Number sense2.Place value3.Fluency4.Properties5.Connecting mathematical

ideas

GOALS FOR GRADES 3-5

How do the students’ strategies exhibit number sense?

How do the teacher and students connect math ideas throughout the number talk?

How does the progression of problems help students to apply the associative property?

VIDEOFifth Grade

12 x 15

Carefully, purposefully select problemsBased on student needsProgression of number skills

Anticipate how students will solve the problemsSolve the problem yourself in multiple ways

Use resources to anticipate strategiesTrailblazer’s Teacher’s GuidesTeaching Student-Centered Mathematics

PLANNING

Fluency with Dot ImagesFluency using Five- and Ten-FramesAddition:

Counting All/Counting On with Dot Images Counting All/Counting On with Double Ten-Frames Counting All/Counting On with Number Sentences 3 + 9 Doubles/Near-Doubles with Double Ten-Frames Doubles/Near-Doubles with Number Sentences 7 + 8; 16 +

15 Making Tens with Double Ten-Frames 5 + 6 Making Tens with Number Sentences 6 + 5 + 4 Making Landmark or Friendly Numbers 48 + 13 Breaking Each Number into Its Place Value 16 + 26 Compensation 19 + 26 Adding Up in Chunks 44 + 35

NUMBER & ADDITION

Addition: Making Tens 2 + 6 + 8 + 3 + 4Making Landmark or Friendly Numbers 49 + 23Doubles/Near Doubles 24 + 26Breaking Each Number into Its Place Value 35 + 26

Adding Up in Chunks 28 + 24Subtraction:

Adding Up 60 – 49Removal/Counting Back 50 – 17Place Value and Negative Numbers 48 – 29Adjusting One Number to Create an Easier Problem 50 – 24 (49 – 24 = 25; 25 + 1 = 26)

Keeping a Constant Difference 51 – 26

ADDITION & SUBTRACTION

Multiplication:Repeated Addition or Skip CountingMaking Landmark or Friendly Numbers 25 x 9 Partial Products 8 x 16Doubling and Halving 15 x 16 (30 x 8)Breaking Factors into Smaller Factors 4 x 9 (4 x 3 x 3)

Division:Repeated Subtraction or Sharing/Dealing OutPartial QuotientsMultiplying UpProportional Reasoning

MULTIPLICATION & DIVISION

Number Talks: Helping Children Build Mental Math and Computation Strategies

Mental Math

Marcy Cook ResourcesNumber SENSE Books

RESOURCES

Math Perspectives by Kathy Richardsonhttp://www.mathperspectives.com/num_talks.html

Video: 4th grade Area/Perimeter

Inside Mathematics: Number Talkshttp://www.insidemathematics.org/index.php/classroom-video-visits/number-talks

Videos: 2nd grade, 4th grade, 5th grade

get2MATH K-5: Number Talks https://sites.google.com/site/get2mathk5/home/number-talks 

ONLINE RESOURCES

Discuss with your grade level:How can we incorporate Number Talks into our daily instruction?

What practices are we currently doing well and how can we improve?

What types of number talks will we incorporate during the first quarter?

REFLECTION

Number

Talks

Characteristics of Number

Talks

Classroom Community & Environment

Role of the Teacher

Role of the Students