Region 11 Math and Science TEACHER PARTNERSHIP

Day 2: Number SenseAddition

AgendaReflections/IntroductionsGoals/StandardsVisualizing Numbers using Quick ImagesProblem Types and Strategies ReviewDefining Number SenseWhat is the Rekenrek?Number Talks using RekenreksTens FramesDecomposing/Composing NumbersNumber Talks Supporting Derived FactsMaking 10ClosurePLC Information

Reflect and Share

Be prepared to share out 1 insight and 1 question from each group.

What has happened with your students since our last session?

New insights?

What unanswered questions are there?

Housekeeping Details

● Timeframe

● Lunch

● Restrooms

● Wi-fi access

● “Misery is optional”

Goals

I can use ten-frames and Rekenreks to carry out number talks with my students

I can help my students compose and decompose numbers

I can describe several strategies that children use to derive addition facts

I can describe the pre-requisite strategies that children need to use a “make ten” strategy when adding whole numbers.

Pg. 1

Goals

Kindergarten Standards

K.1.2Use object and pictures to represent situations involving combining and

separating.K.1.2.1 Use objects and draw pictures to find the sums and differences of numbers between 0 and 10.

K.1.2.2 Compose and decompose numbers up to 10 with objects and pictures.

Pg. 1

Grade 1 Standards

1.1.2Use a variety of models and strategies to solve addition

and subtraction problems in real-world and mathematical

contexts.

1.1.2.1 Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations.

1.1.2.2 Compose and decompose numbers up to 12 with an emphasis on making ten.

1.2.2Use number sentences involving

addition and subtraction basic facts to represent and solve real-world

and mathematical problems; create real-world situations corresponding

to number sentences.

1.2.2.1 Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences.

1.2.2.2 Determine if equations involving addition and subtraction are true.

Pg. 1

Grade 2 Standards

2.1.2Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems

2.1.2.1 Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts.

2.1.2.2 Demonstrate fluency with basic addition facts and related subtraction facts.

2.2.2Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

2.2.2.1 Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences.

2.2.2.2 Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true.

Pg. 1

Reflection on MN Standards

What do you see developing across grade levels?What new ideas seem to appear at a particular grade level?

Pg. 1

Quick Image #1

Quick Image #2

Prep for Quick Image #3

Quick Image #3

Quick Image #4

Quick Image #5

Classification of Problem Types

JOIN JOIN (result unknown)

JOIN(change unknown)

JOIN(start unknown)

SEPARATE

SEPARATE(result unknown)

SEPARATE(change unknown)

SEPARATE(start unknown)

PART PART WHOLE

PART-PART WHOLE(whole unknown)

PART-PART WHOLE(part unknown)

PART-PART WHOLE(both parts unknown)

COMPARE

COMPARE(difference unknown)

COMPARE(quantity unknown)

COMPARE(referent unknown)

Problem Types and Strategies

What is the Problem Type?How many children are in the class? There are 7 boys and 8 girls in Ms. Weil’s class.

Write an example of how this could be solved using each strategy below.a)Direct Modeling

a)Counting On

a)Derived Facts (Number Sense)/Recall

Pg. 3

Problem Types and Strategies

What is the Problem Type?Monica has 7 carrots. Abdi gives her some more carrots, now Monica has 13 carrots.How many carrots did Abdi give Monica?

Write an example of how this could be solved using each strategy below.a)Direct Modeling

a)Counting On

a)Derived Facts (Number Sense)/Recall

Pg. 4

Problem Types & Strategies

Write a separate (result unknown) for the number sentence 14-8=?

Write an example of how this could be solved using each strategy below.a)Direct Modeling

a)Counting On

a)Derived Facts (Number Sense)/Recall

Pg. 5

10 Minute Break

Jo BoalerMath Professor, Stanford University

Jo Boaler video (How to Learn Math, session 5.1, YouTube)

Jo Boaler on Number Sense

So, what is Number Sense

anyway?

5 Minute Reflection on Video

At your table, define number sense.What did the video make you think more deeply about?What kinds of activities and experiences build number sense?

A few Key Ideas with Rekenreks

Show with “just one push” as students gain experience with the Rekenrek.

“Clear the space.”

Store on right. Show on left.

Rekenreks

Mathrack.com School PurchasingMath Learning Center Online Rekenrek

Pg. 6

5 Minute Number Talk

How many

beads did

you see?

I saw 7. How did you see them?

45 Minute Lunch

Video using a Rekenrek in a Number Talk

Number Talks K.2 Rekenreks

Pg. 7

• Composing & Decomposing Number multiple ways

• Guess My Way game

Video reflection

1. How does the Rekenrek warm-up with 4 and 6 provide the teacher with information to guide her instructional decisions?

1. When does the teacher tell or show information to students and when does she provide opportunities for them to make sense of the mathematics?

How is this similar to or different than your math instruction?

2. Are there number combinations that seem more accessible to the students? How does the teacher build on this foundation?

Pg. 7

Your Turn

Practicing with Rekenreks

1. Letter and number off.

2. Go off with “like letters” and plan your 5 Minute Rekenrek number talk.

5 Minute Number Talk Rotations

Return to your Number Group space.

Timer

Key Components of a Number Talk

Talk in your Groups. Write down a few key components you don’t want to forget.

Pg. 8

Be ready to

share out.

Four Procedures and Expectations Essential to Number Talks (from Number Talks by Sherry Parrish)

Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions.

Provide appropriate wait time for the majority of students to access the problem.

Accept, respect, and consider all answers.

Encourage student communication throughout the number talk.

Pg. 8

Some Large-Sized

Rekenreks

10 Rows of

10

Tens Frames

Math Learning Center Online Tens Frames

Pg. 9

Kindergarten Number Talk: A

Kindergarten Number Talk: B

Kindergarten Number Talk: C

Grade 1 Number Talk: A

Grade 1 Number Talk: B

Grade 1 Number Talk: C

Rekenreks or Ten-Frames?

Compare and Contrast these tools in how they support students learning to compose and

decompose numbers.

10 Minute Break

Grade 2 Number Talk: Making 10s Using Number Sentences

Teacher Goal: Making Tens

Anticipate what students will share.

Show sentences one at a time.

Plan how you will record their thinking.

8+2

8+5

8+4

8+7

Grade 2 Number Talk: Looking for Landmark or Friendly Numbers Using

Number Sentences

Teacher Goal: Looking for Landmark or Friendly Numbers

Anticipate what students will share.

Show sentences one at a time.

Plan how you will record their thinking.

40+4

39+4

39+15

39+39

Composing and Decomposing Using a Tens Frame

Pg. 12

Video: Number Talk

Number Talks 2.1 Adding NumbersWhat do you notice about the teacher’s recordings of student thinking?What else do you want to remember?

Pg. 14

Planning a 5 Minute Number Talk

Use the Critical Learning Phases on pp.43-71 for ideas.

What Math Talk would you craft for your students, using a single or double ten-frame, Rekenrek, or number sentences?

Bring each time

Pg. 15

Planning a 5 Minute Number Talk

Use the same groups as earlier.

Using pg. 13…Draw a picture of what you would show to your students.Brainstorm a series of questions you want to ask.Predict number sentences you think will come up.

Pg. 13

5 Minute Number Talk Rotations

Return to your Number Group space.

Timer

“Make-a-10” for Addition Strategy

3 Pre-requisites to use a make-a-ten strategy effectively

They must…1.Know what 2-digit number combinations equal 10 (e.g. 9+1, 8+2, etc.)2.Be able to break numbers apart into any of its two addends (e.g. 8=5+3 so that when they do 8+7 they can then do 5+3+7=5+10=15)3.Know 10+single digits and beyond (e.g. 10+7=17)

(from Fuson Ch. 6 in Research Companion pg. 74)

Pg. 16

Free Apps

2 Resources to Pick Up

1. CEU sheet

1. Classroom Conversation A Handout for PLC Meeting 1

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 PLCs

#1. Classroom Conversation A● Handout● Use dot cards or own word problems

#2. Interview● Will be posted online in Region 11 folder. Work with 2

students, individually or as a pair● You might want to interview the same 2 students from last

time if wanting to follow them all year.

#3. Classroom Conversation B● Will be posted online in Region 11 folder.

Bring Artifacts to PLCs

● Teacher 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

Goals

I can use ten-frames and Rekenreks to carry out number talks with my students

I can help my students compose and decompose numbers

I can describe several strategies that children use to derive addition facts

I can describe the pre-requisite strategies that children need to use a “make ten” strategy when adding whole numbers.

Pg. 1

Goals

See you in January.Have wonderful teaching days in November & December and a GREAT winter break!