MAA G2 D2 FNL - Education Service Center Region 13

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Day 2: Addition and Subtraction

MATHEMATICS ACHIEVEMENT ACADEMY, GRADE 2

Purpose and Outcomes

• What is the purpose of the mathematics academies?

• What are the outcomes of the mathematics academies?

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Materials

Texas Gatewayhttp://www.texasgateway.org/

• Mathematics TEKS: Supporting Information

• Vertical Alignment Charts for Mathematics TEKS

Participation Norms

• Be fully present.

• Minimize distractions.

• Minimize “air time.”

• Take a chance.

• Celebrate accomplishments.

Discourse Norms

• Listen.

• Be involved.

• Contribute ideas.

• Participate by asking questions.

• Develop understanding, if not at the beginning, by the end.

Krusi, 2009

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Mathematics Norms

• Look for patterns in order to make generalizations.

• Make connections among models, representations, and generalizations.

• Communicate using academic vocabulary.

• Use mistakes as opportunities to support new learning about mathematics.

(Yakel & Cobb, 1996)

Learning Progression

Learning Progression

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• Write a problem that can be solved using the Equation Card. o If needed, use Picture Card for the context for your

problem.

• What are the similarities and differences between the word problems?

• Solve the problem.

Generating an Addition or Subtraction Problem

• How does the equation represent the given word problem?

• How might the word problem change if the location of the unknown in the equation changes?

• How do you know if your answer to your colleagues’ problem is correct?

Debrief: Generating an Addition or Subtraction Problem

Check Point: Generating an Addition or Subtraction Problem

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2(4)(D) The student is expected to generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000.

• Why would we want students to generate their own problems after experiences with representing and solving problems?

• How might reminding students of common underlying structures of addition and subtraction word problems help support this student expectation?

Debrief: Generating an Addition or Subtraction Problem

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What Works Clearinghouse

Aligning TEKS using common underlying structures helps students:

• know when to apply specific solution methods; and• discriminate irrelevant from relevant information.

K(3)(A) The student is expected to model the action of joining to represent addition and the action of separating to represent subtraction.

1(3)(B) The student is expected to use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3.

Common Underlying Structures

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Solving Word Problems Using Common Underlying Structures

Modeling and Solving Multi-Step Problems

• Use your base-10 blocks to model and solve the problems individually.

• Share your models and solutions.• Record one participant at your table explaining

how he or she used the base-10 blocks to model and solve one of the problems.

Modeling and Solving Addition and Subtraction Problems

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Debrief: Modeling and Solving Addition and Subtraction Problems

• How were the processes you used to solve problem 1 and problem 2 similar? How were they different?

• Why would we ask students to compare word problems?

Problem Solving with Mental Strategies

Debrief: Problem Solving with Mental Strategies

• How is the problem situation represented in the model?

• What operation(s) can be used to solve the problem?• Could you have used a different sequence of

operations to solve the problem? Why or why not?• Why should we allow students to chose their own

solution process?

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Look at question 3 and the matching number line.

295 ?

–125

+325

What might a strip diagram look like for the sandwich problem? 125?

295 325

Debrief: Problem Solving with Mental Strategies

• How would you solve this problem?

• Which cards did you group together?

• What do the cards in this group have in common?

• How do solution strategies differ within this group?

Ms. Santana’s Students

Ms. Santana’s Students: Think-Aloud for Student E

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Ms. Santana’s Students: Think-Aloud for Student A

Ryan had some jellybeans. He ate 27 of the jellybeans. Then, he bought a new pack of 134 jellybeans. Now, Ryan has 465 jellybeans.

How many jellybeans did Ryan have at the beginning?

Ryan’s Jellybeans

Modeling the Think-Aloud: Betty’s Thinking

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Modeling the Think-Aloud: Nick’s Thinking

Concept Process Exemplar

A record of meaningful information and ideas about a concept or vocabulary of the mathematics being studied that may grow over multiple lessons

A record of complex mathematics skills broken down into a sequence of steps and may be extended to include additional solution strategies

An annotated example created by the teacher, student or teacher and students together that can be used as a guide

Example Example Example

Using Anchor Charts

ExemplarAn annotated example created by the teacher, student or teacher and students together that can be used as a guideExample

Using Anchor Charts

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• 4: Solve problem 1 using 4 different models

• 2: Solve problem 2 using 2 different models

• 1: Solve problem 3

4-2-1: Solving Addition and Subtraction Problems

Solving Multi-Step Addition and Subtraction Problems

Solving Multi-Step Addition and Subtraction Problems

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•When did you find yourself making a strip diagram, an open number line, or an equation? Why?

•What mental strategies did you use to solve the problems?•How did mental strategies facilitate your thinking during the scavenger hunt?

•What algorithms did you use to solve the problems?

2(4)(C) The student is expected to solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms.

Debrief: Scavenger Hunt

Check Point: Solving Multi-Step Addition and Subtraction Problems

Addition and Subtraction of Whole Numbers

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Elements of Design

Elements of Instructional Design

Concepts

Mental Strategies, Procedures, and Algorithms

Applications

Supporting Diverse Learners: ELL

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Learning Progression Implications

#ideas#SupportsforELLs


ELPS Instructional Tool, TEA (2012)


Fair Festival

Order Purchase


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Listening Speaking

Reading Writing

Language Domains



Supporting Diverse Learners: English Language Learners

Concepts


Applications

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• 2(4)(A) The student is expected to recall basic facts to add and subtract within 20 with automaticity.

• 1(3)(D) The student is expected to apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10.

Pre-Assessment of Addition and Subtraction Facts

Where do we start with this year’s students?

What gaps do my students have?

Which adjustments are needed for the whole group?

Which adjustments are needed for a small group?

The Role of Pre-Assessment

Pre-Assessment: Guiding Questions

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Pre-Assessment Instructional Decisions

Where do we build from?

What do we need to develop?

What gaps do we need to address?

Addition and Subtraction Facts

At each station, complete the following:• Activity or game• Practice problems• Check point


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Description Examples

+/– 1+/– 2+/– 0

Students build on their understanding of counting by exploring one‐ or two‐more‐than, and one‐ or two‐less‐than relationships. Students build on the concept of adding or subtracting nothing from a quantity.

2 + 1 = 3 3 – 1 = 23 + 1 = 4 4 – 1 = 32 + 0 = 2 2 – 0 = 2

Debrief: Addition and Subtraction Facts


+/– 10Students build on their understanding of adding ten to a one‐digit number results in a two‐digit number, and subtracting ten from a two‐digit number results in a one‐digit number.

1 + 10 = 11 11 – 10 = 12 + 10 = 12 12 – 10 = 2


Description ExamplesDoubles and

HalvesStudents build on their understanding of doubling.

2 + 2 = 4 4 – 2 = 23 + 3 = 6 6 – 3 = 3


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Make 10Student build on their understanding of addition by exploring the relationship between two addends that result in a sum of ten.

1 + 9 = 102 + 8 = 103 + 7 = 10



Last FactsStudents use number sense and mental strategies to explore unknown facts.

7 + 57 + 3 = 1010 + 2 = 12

13‐413‐3=1010‐1=9


Visual Models for Facts

14 5

14 4 1

109

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Number Sense Practice

String A

8 + 28 + 5 + 28 + 6 + 27 + 6 + 3

String B

1 + 9 + 8 + 5 + 23 + 8 + 4 + 2 + 74 + 8 + 6 + 2 + 7

String C

18 + 1218 + 15 + 12

18 + 15 + 12 + 1517 + 16 + 13 + 15

String D

38 + 2238 + 15 + 22

38 + 15 + 42 + 1527 + 36 + 23 + 35

Number Sense Practice


• Head Facts• Four in a Row• Who Has More?• Technology Exploration

• Did you use any fact strategies to help you solve the fact?

• Why is it important to provide time for students to build understanding through strategy development before requiring automaticity?

1‐2‐3‐4

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Supporting Diverse Learners:Students with Special Needs

Expert Groups: Memory Challenges

0 1 2

Short‐termmemory

Workingmemory

Long‐term memory

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Blended Groups: Memory Challenges

0 1 2

Short‐termmemory

Workingmemory

Long‐term memory

Supporting Diverse Learners: Students with Special Needs

Concepts


Applications

Participation Norms

• Be fully present.

• Minimize distractions.

• Minimize “air time.”

• Take a chance.

• Celebrate accomplishments.

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Discourse Norms

• Listen.

• Be involved.

• Contribute ideas.

• Participate by asking questions.

• Develop understanding, if not at the beginning, by the end.

Krusi, 2009

Mathematics Norms

• Look for patterns in order to make generalizations.

• Make connections among models, representations, and algorithms.

• Communicate using academic vocabulary.

• Use mistakes as opportunities to support new learnings about mathematics.

Yackel & Cobb, 1996

Academic Vocabulary

• Algorithm• Anchor Chart• Balanced Pre-Assessment• Foundational–Bridging–Target Knowledge and Skills• Learning Progression• Mathematics

• Addend• Equation• Minuend• Subtrahend

• Represent• Equation• Number Line• Pictorial Model

• Strategies/Mental Strategies/Solution Strategies• Place Value• Properties of Operations• Relationship Between Addition and Subtraction

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Exit Slip

Learning ProgressionWhole Number Addition and Subtraction

Diverse Learners

What confirming/new ideas did you hear today?

How can you move new and intriguing ideas to action?

MAA G2 D2 FNL - Education Service Center Region 13

Documents

Transcript of MAA G2 D2 FNL - Education Service Center Region 13