Welcome toNumber Sense K-2Region 11Math and Science Center

Barb Abramson & Anne Bartel

Step In – Step Out Form a large circle around all the tables and

face each other.

Step to the inside of the circle if the statement is true for you.

Step In – Step Out I went to the MN Renaissance Fair this year.

I drove more than 30 miles this morning to get here.

I got up before 5 AM this morning.

I teach 1st grade / 2nd grade / 3rd grade

I know what CGI in math education stands for.

I like teaching math better than reading

Agenda & Parking Lot

Housekeeping DetailsTimeframe

Lunch

Restrooms

Wi-fi access

Sign-in

Norms

“Misery is optional”

Region 11 Math & ScienceFunded since 2007

Focus on 3-5 and 6-8

Focus this year on K-2: Number Sense with 450-500 teachers

Registration Concerns

Folder Contents

This Year’s Goal Give teachers the time and opportunity

to learn how students think about math…

…in an incremental, job-embedded, and ongoing structure…

…with support

Good news and good news

Teacher AssessmentAnonymous – we don’t want to

know who you are

Code: Birthdate and first letter of your last name

E.g., 0 4 1 5 4 8 B

Take a Break

Beloved ChildWork in groups of 3

Think – Pair – ShareWhat do you want for the child/children

who is/are most important to you?

In 20 years, what do you want these children to say about their memories of math?

Our GoalsAll children motivated to learn challenging

mathematics

All children expecting math to make sense – and expecting to understand it and use it

All children able to explain and defend their mathematical thinking

All children pattern-seekers & connection-makers

5 PracticesChoose the problem; then…

1.Anticipate

2.Monitor

3.Select

4.Sequence

5.Connect

Lunch – OK to bring it back

Cognitively Guided Instruction

Most children come to school with a rich store of informal mathematical knowledge.

We (and they) are more successful if we understand how they think about numbers and we can build on that knowledge.

Children do not always think about mathematics in the same way as adults do.

From a ‘13-’14 teacher“I have always known that it was

important to listen to kids, but I never knew what questions to ask or what to listen for before now.”

JOIN ProblemRiley has 5 cookies. Seth gives him 3 more

cookies.

START + CHANGE = RESULT

5 + 3 = ?

5 + ? = 8

? + 3 = 8

SEPARATE ProblemWes has some bagels. Stella eats three of the

bagels. Now Wes has five bagels.

START – CHANGE = RESULT

? – 3 = 5

8 – 3 = ?

8 – ? = 5

PART-PART WHOLEThere are five boys and three girls on the soccer

team. How many players are on the team?

PART + PART = WHOLE

5 + 3 = ?

? + 3 = 8 or 5 + ? = 8

COMPARE ProblemGracie has 5 bones. Veronica has three more

bones than Gracie. How many bones does Veronica have?

Gracie:

Veronica:

COMPARE ProblemsGracie has five bones. Veronica has three more

bones than Gracie. How many bones does Veronica have? (We don’t know the compare quantity.)

Gracie has five bones. Veronica has eight bones. How many more bones does Veronica have? (We don’t know the difference.)

• Gracie has some bones. Veronica has three more than Gracie. Veronica has eight bones. How many bones does Gracie have? (We don’t know the referent quantity.)

Classification

Problem Types Task

Categorize each word problem – What type of problem is it? Where would it fit in the template?Use any resource available in your

handout or at your table.THIS IS NOT A TEST

Handout, p. 5One way to write grade appropriate word

problems is to either…

Choose appropriate numbers

Have students choose appropriate numbers

Student StrategiesDirect Modeling

Counting

Derived Fact* / Recall

8 + 5 = ?Direct Modeling

Counts out 8

Counts out 5

Counts total from the beginning: “1, 2, ….13”

Direct ModelingYou can’t be a direct modeler unless you

can count

These students use fingers or cubes or some material to model exactly what they are hearing in the problem; then they go back and count all to get an answer.

8 + 5 = ?Counting

Says or thinks 8

Counts on: “8…9, 10, 11, 12, 13”

Counting If students are counting on their fingers, they might be

direct modelers or counters. It depends on how they use their fingers. In direct modeling, those fingers represent cookies and kids are more successful when the numbers are less than 10. In counting, those fingers represent numbers in the counting sequence.

Kids who are counters are able to hold onto the fact that 8 ones are also one group of 8 at the same time; this is what allows them to hold onto the 8 in their minds.

This is much more complicated because you have to hold onto two counting sequences (e.g., I’m seeing one finger but counting “9”)

8 + 5 = ?Derived Fact / Recall

Says “13” or uses relationships between the numbers to find the solution

Example: 8 + 5 8 + (2 + 3) (8 + 2) + 3 10 + 3 13• How else might you solve this using a

derived fact?

Derived Facts / RecallFact Recall is our ultimate goal, but we don’t

want to get their by sacrificing understanding.

If students can derive the answers to facts fluently, they have a good beginning number sense.

Elbow PartnersPerson A: Teacher

Person B: Student

Use handout pages 7-9

The teacher selects one of the problems, creates a word problem, and asks the student to solve it;

The student solves it, using one of the strategies;

The teacher identifies the strategy used;

Discuss, especially if there is a difference of opinion.

Debrief StrategiesThese strategies are not always distinct.

Some kids waver as they move from direct modeling to counting.

Some kids move back to less sophisticated strategies when the numbers increase in size.

Some kids might look less sophisticated because they think you want to see their work, but when you ask them to tell you what they really did, they use a more sophisticated strategy.

Teaching IssuesHow do we encourage students to use

more sophisticated strategies?

How do we help students who are stuck at counting?

How Children Learn Number Concepts

Form groups of 3

Read pages 43-47

Find 3 statements that speak to your experience or make you wonder about something.

Discuss: Take turns sharing your statements and general reactions to the author’s comments.

Why do Number Talks?

Reinforces number sense

Reinforces fluency

Reinforces composing and decomposing numbers

Reinforces subitizing

Discourages counting

Communicates that math is about ‘making sense’

What is a Number Talk?Short, daily routine

Teacher presents intentionally selected problems

Students are not pressured to see things they don’t see or use language they don’t understand

Students learn from others, but only if the explanations of other students make sense to them

Elements of a Number Talk

A safe environment

Problems of various levels of difficulty

Concrete Models

Interaction

Self-correction

Problems can Include…Dot Cards

Ten Frames

Other Visual Images

Towers of Unifix Cubes

Written problems

Teacher’s RoleSet a goal; select appropriate problems

Facilitate the discussion

Listen carefully to student thinking; record it if appropriate

Build connections among student strategies

Limit time (5-10 minutes)

Adult Number Talk

Adult Number Talk

197 + 395

ResourcesNumber Talks by Sherry Parrish

(See your PLC Facilitator)

Math Perspectives Websitehttp://www.mathperspectives.com/

Search the Internet for Number Talks

PLC Calendar Day 1: Number Sense 3 PLC Meetings

Day 2: Addition 3 PLC Meetings

Day 3: Subtraction 3 PLC Meetings

Day 4: Multiplication/Division 3 PLC Meetings

Day 5: Place Value

3 PLCsClassroom Conversation #1

Use Region 11 word problem setsUse dot cards, strings of related

equations, own word problems

InterviewWork with 2 students, individually

or as a pairPossibly follow same 2 students

all year

Classroom Conversation #2Use Region 11 word problem setsUse dot cards, strings of related

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ArtifactsTeacher notes, photos, or videos from a

verbal discussion, students acting out problems, or using manipulatives

Chart paper, photo or video showing a record of student thinking & strategies

Written student work

Adults learn best not merely by listening, reading or doing but by reflecting on what they hear, read or do.   York-Barr, Sommers, Ghere, Montie. Reflective Practice to Improve Schools: An Action Guide for Educators. Thousand Oaks, CA: Corwin Press. 2001.

Thank You!For leaving your students

For participating in today’s work

For cooperating with your tablemates

For asking questions

For following the norms

For all the work you do for students

CAPS Exit SlipC: Something that CONFIRMS my

thinking . . .

A: A question that was ANSWERED . . .

P: I am still PONDERING . . .

S: Something that SURPRISED me . . .

And…any other feedback you would be willing to share with us.