a story of units
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A Story of Units. Grade 2 – Module 5. Session Objectives. Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons. - PowerPoint PPT PresentationTRANSCRIPT
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NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Units
A Story of UnitsGrade 2 – Module 5
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Session Objectives
• Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.
• Introduction to mathematical models and instructional strategies to support implementation of A Story of Units.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Agenda
Introduction to the ModuleConcept DevelopmentModule Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Curriculum Overview of A Story of Units
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Building Towards the Algorithm: Base-Ten StructureConceptual understanding leading up to Module 5:5 groups
Ten frames Place Value disks
Make a ten strategy 8 + 6 /\ 2 4
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Module Overview
Read the narrative.
• *key concepts• models and tools• Important vocabulary
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Agenda
Introduction to the ModuleConcept DevelopmentModule Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Topic A
Strategies for Adding and Subtracting Within 1,000
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
What is the importance of place value language?
unit value tens place value hundreds digit ones
Lesson Objective: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 10 and 100.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 1
Lesson Objective: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 100.
Use your number disks to show me 157 on your place value chart.
What important connection did we make today?What are we actually doing when we talk about10 more or 100 less than a number?
Lesson 1, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
How does place value understanding lead to flexible thinking?
Lesson Objective: Add and subtract multiples of 100 including counting on to subtract.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 2
Lesson Objective: Add and subtract multiples of 100 including counting on to subtract.
Show 125 on your place value chart and say the number in unit form. What should you change to show 325.
Why is the arrow way a good choice when you have a missing addend?
Lesson 2, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
How is the make a ten strategy helpful when composing a new hundred?
Problem 5: 590 + 240
Lesson Objective: Add multiples of 100 and some tens within 1,000.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 3
Lesson 3, Student Debrief
Lesson Objective: Add multiples of 100 and some tens within 1,000.
Problem 5: 590 + 240
What was the most efficient way to add 280 + 640?Did you agree or disagree with your partner?Is there more than one way to solve?
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
How can we decompose numbers to make subtraction easier?
Lesson Objective: Subtract multiples of 100 and some tens within 1,000.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 4
Lesson Objective: Subtract multiples of 100 and some tens within 1,000.
Problem: 740 - 690
Terri solved the problem using an equal sign instead of arrows: 740 – 600 = 140 – 40 = 100 – 50 = 50.
Is her answer correct? Is her equation correct? Why can’t she use an equal sign to show the change?
Lesson 4, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
How do students look for and make use of structure?
Lesson Objective: Use the associative property to make a hundred in one addend.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 5Lesson Objective: Use the associative
property to make a hundred in one addend.
Problem 2: Add multiples of 10 by making a hundred.
In Problem 2(b), 260 + 190, how did you use a number bond to make a new, simpler addition problem? Which number did you break apart, or decompose? Why?
Lesson 5, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
What exactly is compensation?
Lesson Objective: Use the associate property to subtract from three-digit numbers and verify solutions with addition.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 6Lesson Objective: Use the associative
property to subtract from three-digit numbers and verify solutions with addition.
34 - 19
Explain what the compensation and number bond strategies have in common. What actions do you take to make solving easier?
Lesson 6, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
How does sharing strategies improve student learning?
Lesson Objective: Share and critique strategies for varied addition and subtraction problems within 1,000.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 7Lesson Objective: Share and critique
strategies for varied addition and subtraction problems within 1,000.
Study the strategy your partner used. Figure out and fix any mistakes.
Compare how your strategies are the same and how they are different.
Lesson 7, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Topic B
Strategies for Composing Tens and Hundreds Within 1,000
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Did we make a new ten? Did we make a new hundred?
Lesson Objective: Relate manipulative representations to the addition algorithm.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lessons 8-9Lesson Objective: Relate manipulative
representations to the addition algorithm.
Model 303 + 37Model 672 + 249
For Problem 1(c), how did your work with the numbers match the written addition? How did you show new groups below?
Lessons 8-9, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Why is it important to move from concrete to pictorial?
place value disks chip model
Lesson Objective: Use math drawings to represent additions with up to two compositions and relate drawings the the addition algorithm.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lessons 10-11Lesson Objective: Use math drawings to
represent additions with up to two compositions and relate drawings to the addition algorithm.
Draw a chip model to solve 545 + 278
What important math vocabulary have we used recently to talk about making a new unit? (Compose, bundle, rename, change)
Lessons 10-11, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
The value of flexible thinking.
Lesson Objective: Choose and explain solution strategies and record with a written addition method.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 12
Lesson Objective: Choose and explain solution strategies and record with a written addition method.
Share with your partner: Which strategy was most efficient for Tracy to use? Why? Do you agree or disagree with your partner?
Lesson 12, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Topic C
Strategies for Decomposing Tens and Hundreds Within 1,000
Do we have enough ones to subtract? Do we have enough tens to subtract?
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
What is the purpose of the magnifying glass?
Lesson Objective: Relate manipulative representations to the subtraction algorithm, and use addition to explain why the subtraction method works.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 13
Lesson Objective: Relate manipulative representations to the subtraction algorithm, and use addition to explain why the subtraction method works.
How can you use addition to explain why the subtraction works? Use part-whole language to explain your thinking.
Lesson 13, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
How can we use addition to explain why a subtraction method works?
Lesson Objective: Use math drawings to represent subtraction with up to two decompositions, relate drawings to the algorithm, and use addition to explain why the subtraction method works.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lessons 14-15
Lesson Objective: Use math drawings to represent subtraction with up to two decompositions, relate drawings to the algorithm, and use addition to explain why the subtraction method works.
584 – 147
How can you prove that this statement is true:If 584 – 147 = 437, then 147 + 437 = 584.
Lessons 14-15, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
What is the most efficient way to subtract from a multiple of 100?
Lesson Objective: Subtract from multiples of 100 and from numbers with zero in the tens place.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lessons 16-17Lesson Objective: Subtract from multiples
of 100 and from numbers with zero in the tens place.
800 – 463
Think like a detective: When you are subtracting three-digit numbers, when do you choose to unbundle a hundred? When do you choose to solve mentally? What clues in the numbers help you to choose a solution strategy?
Lessons 16-17, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Is there one right strategy?
Lesson Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson 18Lesson Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.
• Use compensation to solve 300 - 159• Add to solve 400 – 278• Solve 605 – 498 using the algorithm and a chip model• Choose your favorite strategy to solve 500 – 195
Choose one of these strategies to explain to a partner.
Lesson 18, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Topic DStudent Explanations for
Choice of Solution Methods
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Which solution strategies are fastest and easiest for you?
Lesson Objective: Choose and explain solution strategies and record with a written addition or subtraction method.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lessons 19-20Lesson Objective: Choose and explain solution
strategies and record with a written addition or subtraction method.
Look at Problem 1(c). Compare your strategy to your partner’s. Which one was more efficient? Defend your reasoning.
Lessons 19-20, Student Debrief
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Lesson Preparation and DemonstrationAt your table, prepare to demonstrate the main section of the Concept Development.
Think about:• What is the most important understanding I
need my students to take from this lesson?• What is the key learning component in the
lesson that supports students learning this concept.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
FluencyFluency is fun and engaging!It can be used to:• maintain previously learned content.• prepare for the upcoming lesson.• anticipate content knowledge
students will need in the future.
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Application Problems
2.OA.1: Use addition and subtraction within 100 to solveone- and two-step word problems.
Lesson 10, Application Problem
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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Agenda
Introduction to the ModuleConcept DevelopmentModule Review
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Biggest Takeaway
Turn and Talk:• What insights do you have about the trajectory of learning, both leading
up to and throughout Module 5?• What can you share with others about the importance of place value
language, flexible thinking, the use of structure, and strategies such as make a ten?
• What is the value of a conceptual vs. proceduralapproach to learning the addition and subtractionalgorithms?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units
Key Points• Module 5 focuses on conceptual understanding of place value
as the foundation for learning the addition and subtraction algorithms.
• Students learn and are encouraged to use strategies such as compensation, arrow notation, and chip models.
• The Student Debrief is an essential element in probing, deepening, and assessing student understanding.
• All components of each lesson are valuable and contribute to the overall rigor.