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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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Learning Progression
• 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?
Learning Progression
• 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?
Learning Progression
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Learning Progression
Learning Progression
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?
MSTAR Math Academy, 2010
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
MSTAR Math Academy, 2010
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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.
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.
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Debriefing Mental Strategies
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
Debriefing Mental Strategies
How does the use of mental strategies connect to the standard algorithm?
532 349500 300 30 40 2 9
800 7010
11800 70 11
800 80 1881
10
1532349881
How does the use of mental strategies connect to the standard algorithm?
Debriefing Mental Strategies
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1000 368
1000 300 60 8
1000 0 0 300 0 60 0 8
1000368
How does the use of mental strategies connect to the standard algorithm?
Debriefing Mental Strategies
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
How does the use of mental strategies connect to the standard algorithm?
Debriefing Mental Strategies
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
How does the use of mental strategies connect to the standard algorithm?
Debriefing Mental Strategies
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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
How does the use of mental strategies connect to the standard algorithm?
Debriefing Mental Strategies
9 910 10 100
1 0 0 0
23 6 86 3
900 900 1000 100 10
1000 368
1000 300 60 8
1000 0 0 300 0 60 0 8
1000 0 0 300 0 60 0 8
600 30 2632
How does the use of mental strategies connect to the standard algorithm?
Debriefing Mental Strategies
Debriefing Mental Strategies
(1000 1)(368 1)
999367632
9 910 10 100
1 0 0 03 6 86 3 2
How does the use of mental strategies connect to the standard algorithm?
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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
Supporting Diverse Learners: ELL
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ELPS Instructional Tool, TEA (2012)
Supporting Diverse Learners: ELL
Fair Festival
Order Purchase
Supporting Diverse Learners: ELL
Listening Speaking
Reading Writing
Language Domains
Supporting Diverse Learners: ELL
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Supporting Diverse Learners
Supporting Diverse Learners: ELL
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?