MAA G3 D1 FNL - esc13.netjukebox.esc13.net/PSgateway/k3math/gr3_trainer/MAA_G3_D1_PPT_Handout.pdfeveryday life, estimation sk ills are valuable. Computational estimation is a higher-level

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MATHEMATICS ACHIEVEMENT ACADEMY, GRADE 3

Day 1: Addition and Subtraction

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

Rotating Trios

0

1

2

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 learning about mathematics.

Yackel & Cobb, 1996

Learning Progression

A learning progression is a sequenced set of subskills and bodies of enabling knowledge that, it is believed, students must master en route to mastering a more remote curricular aim.

In other words, it is composed of step-by-step building blocks students are presumed to need in order to successfully attain a more distant, designated instructional outcome.

Popham, 2008

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• Create a graphic organizer to show a learning progression from kindergarten to fourth grade for the concepts of addition and subtraction.

• Trade your poster with another table group.

o How are the big ideas of the other group’s poster similar to your group’s poster?

o How are they different?


• Where would you place the grade-level student expectations on your graphic organizer?

• Where would you place the 2015 STAAR® Released Items on your graphic organizer?


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How can a learning progression support planning for focused, targeted, and systematic instruction?

Whole Number Addition and Subtraction

• 3(4)(A) The student is expected to solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

• 3(5)(A) The student is expected to represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.

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Balanced Pre-Assessment

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

Balanced Pre-Assessment

MSTAR Math Academy, 2010

Target Knowledge and

Skills

Foundational Knowledge and

Skills

Bridging Knowledge and Skills

Connections Across the Knowledge Representations

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• What are the broad and deep ideas that students must master to be successful in grade 3 mathematics?

• What are the concepts and procedures from grade 2 that students must have mastered?

• What are the foundational knowledge and skills that students may use to build towards mastery?


Target Knowledge and Skills

Foundational Knowledge and Skills

Bridging Knowledge and Skills• What are the bridging knowledge

and skills that students may use to connect foundational understandings to target understandings?

• What are the target knowledge and skills mathematics that students must master?

Guiding Questions for Balanced Pre-Assessment

Guiding Questions for Examining Student Work

Guiding Questions for Examining Student Work

Models of Mathematics• What models do we see students using the most often?• With what models are students most successful?• What models are we not seeing students use?• With what models are students least successful?

Mathematical Processes and Procedures• What processes or procedures are students

using the most often?• With what processes or procedures are

students most successful?• What misconceptions are present in this work?• What steps are students taking most often?

Instructional Decisions

Where do we build from?

What do we need to develop?

What gaps do we need to address?

Connections Across Knowledge and Representations

Target Knowledge and Skills

Foundational Knowledge and Skills

Bridging Knowledge and Skills


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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?

Whole Class

Small Group

Best Practices: Guiding Questions for Balanced Pre-Assessment and Examining Student Work

Identifying Representations

• Mr. Hooper’s Purchase

• Representations Card Match

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• How did you determine which cards to use?

• Why does Card A not represent the first problem?

• Why would we ask students these questions?

Mr. Hooper’s Purchase

• How is the problem situation represented by a strip diagram?

• How is the problem situation represented by a number line?

• How is the problem situation represented by an equation?

Representations Card Match

Check Point: Identifying Representations

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Representing One-Step and Two-Step Problems

• Why might students choose different representations?

• What are the implications for later student work with addition and subtraction?

• Why might we ask students to pair a number line and an equation or a strip diagram and an equation?

Representations for Addition and Subtraction

Check Point: Representing One-Step and Two-Step Problems

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3(5)(A) What are the benefits of asking students to represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations?

Identify and Represent Problems

3(4)(B) The student is expected to round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems.

Estimation

The goal of computational estimation is to be able to flexibly and quickly produce an approximate result that will work for the situation and give a sense of reasonableness. In everyday life, estimation skills are valuable. Computational estimation is a higher-level thinking skill that requires decisions.

Van de Walle, Karp, & Bay-Williams, 2013

Estimation

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Solving Problems

Determining Sums and Differences

• How did Colin approach the problem?

• What steps did Colin use to move from one step to the next?

• How is Colin’s thinking reflected in your work?

• 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?

Mr. Jones’ Students

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Using Anchor Charts

Using Anchor Charts

Anchor Charts:Created with students as a summary of learning

• Why is it important for an anchor chart to be developed by the class rather than presented to the class?

• How and when might students refer to an anchor chart?

Using Anchor Charts

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Check Point: Solving Problems

Debriefing Mental Strategies

3(4)(A) The student is expected to solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.


3(4)(A) The student is expected to solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

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532 347532347

879

879

500 300 30 40 2 7

800 70 9

How does the use of mental strategies connect to the standard algorithm?

96 45 9645

51

90 40 6 5

50 151



532 349500 300 30 40 2 9

800 7010

11800 70 11

800 80 1881

10

1532349881



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1000 368

1000 300 60 8

1000 0 0 300 0 60 0 8

1000368



100

01 0 0368

0 1000

1000 368

1000 300 60 8

1000 0 0 300 0 60 0 8

0 300 0 60 0 81000 0



910 100

1 0 003 6 8

100

90010000

1000 368

1000 300 60 8

1000 0 0 300 0 60 0 8

1000 0 0 300 60 0 80



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900 901000 100 100

1000 368

1000 300 60 8

1000 0 0 300 0 60 0 8

1000 0 0 300 0 060 8

9 91010 100

01 0 03 6 8



9 910 10 100

1 0 0 0

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900 900 1000 100 10

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1000 0 0 300 0 60 0 8

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(1000 1)(368 1)

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9 910 10 100

1 0 0 03 6 86 3 2


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Solving Problems with Fluency

Solving Problems with Fluency

Scavenger Hunt

• When did you find yourself making a strip diagram or an equation to set up your process?

• How did all of the work with mental strategies facilitate your thinking during the scavenger hunt?

• When did you find yourself using the standard algorithm? Why?

• When did you find yourself using an alternate strategy? Why?

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Check Point: Solving Problems with Fluency

Whole Number Addition and Subtraction

Elements of Design

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Elements of Instructional Design

Concepts

Mental Strategies, Procedures, and Algorithms

Applications

Supporting Diverse Learners: ELL

Learning Progression Implications

#ideas

#SupportsforELLs


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ELPS Instructional Tool, TEA (2012)


Fair Festival

Order Purchase


Listening Speaking

Reading Writing

Language Domains


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Supporting Diverse Learners


Concepts

Mental Strategies, Procedures, and Algorithms

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 learning about mathematics.

AlgorithmAnchor ChartBalanced Pre-AssessmentFoundational–Bridging–Target Knowledge and SkillsLearning ProgressionRepresent

Equations Number Lines Pictorial Models

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

Academic Vocabulary

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Exit Slip

Learning ProgressionWhole Number Addition

and SubtractionDiverse Learners

What confirming/new ideas did you hear today?

How can you move new and intriguing ideas to action?

Documents

MAA G3 D1 FNL - esc13.netjukebox.esc13.net/PSgateway/k3math/gr3_trainer/MAA_G3_D1_PPT_Handout.pdfeveryday life, estimation sk ills are valuable. Computational estimation is a higher-level