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A Story of Units Overview. The Shape of Math in A+ Countries. Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states. Mathematics topics intended at each grade by at least two-thirds of A+ countries. Instructional Shifts. Curriculum Map. - PowerPoint PPT Presentation
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© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units Overview
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
The Shape of Math in A+ Countries
2
Mathematics
topics intende
d at each
grade by at least two-
thirds of A+
countries
Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Instructional Shifts
3
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Curriculum Map
4
Pre-Kindergarten Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5
Approx. test date
for grades 3-5
M1: Multiplication and Division with Factors of 2, 3,
4, 5, and 10(25 days)
M3: Multiplication and Division of up to a 4-Digit Number by up to a 1-Digit Number Using Place Value
(43 days)
*M2: Unit Conversions(7 days)
M1: Place Value, Rounding, Fluency with Addition and Subtraction Algorithms of
Whole Numbers(25 days)
M2: Problem Solving with Mass, Time, and Capacity
(25 days)
M6: Collecting and Displaying Data (10 days)
M1: Whole Number and Decimal Fraction Place Value
to the One-Thousandths(20 days)
M4: Addition and Subtraction of Angle
Measurements of Planar Figures
(20 days)
M5: Order and Operations with Fractions
(45 days)
M2: Multi-Digit Whole Number and Decimal Fraction Operations
(35 days)
M6: Decimal Fractions(20 days)
20 days
20 days
Test Date
9/6/12
10/10/12
M2: Addition and Subtraction with Length, Weight, Capacity, and Time
Measurements(20 days)
M3: Place Value, Counting, and Comparison of Numbers
to 1000(25 days)
M2: Analyze, Compare, Create, and Compose Shapes
(15 days)
M1: Analyze, Sort, Classify, and Count up to 5
(45 days)
M2: Identify and Describe Shapes (7 days)
M3: Comparison with Length, Weight, and Numbers to 10
(43 days)
M1: Addition and Subtraction of Numbers to 10 and Fluency
(45 days)
M3: Ordering and Expressing Length Measurements as
Numbers(15 days)
M2: Place Value, Comparison, Addition and
Subtraction of Numbers to 20(35 days)
11/8/12
12/11/12
*M1: Sums and Differences(10 days)
M3: Count and Answer "How Many" Questions up to 10
(50 days)
20 days
20 days
20 days
20 days
M1: Classify and Count Numbers to 10
(43 days)
M6: Graph Points on the Coordinate Plane to Solve
Problems(40 days)
M5: Addition and Multiplication with Volume
and Area(25 days)
M7: Exploring Multiplication(20 days)
M7: Word Problems with Geometry and Measurement
(40 days)
20 days
20 days
20 days
20 days
M5: Fractions as Numbers on the Number Line
(35 days)
M4: Multiplication and Area(20 days)
M3: Multiplication and Division with Factors of 6, 7,
8, and 9(25 days)
5/28/13
M4: Addition and Subtraction of Numbers to 1000
(35 days)
M5: Preparation for Multiplication and Division
Facts(40 days)
M5: Write Numerals to 5, Addition and Subtraction
Stories, Count to 20(35 days)
M6: Analyze, Compare, Create, and Compose Shapes
(10 days)
M4: Number Pairs, Addition and Subtraction of Numbers
to 10(47 days)
20 days
M4: Describe and Compare Length, Weight, and Capacity
(35 days)
20 days
1/17/13
2/15/13
3/22/13
4/29/13
M3: Addition and Subtraction of Fractions
(22 days)
M4: Multiplication and Division of Fractions
(38 days)
M5: Numbers 10-20, Counting to 100 by 1 and 10
(30 days)M6: Place Value,
Comparison, Addition and Subtraction of Numbers to
100(35 days)
M7: Recognizing Angles, Faces, and Vertices of
Shapes, Fractions of Shapes(20 days)
M6: Comparison, Addition and Subtraction with Length
and Money(30 days)
20 days
20 days
20 days
20 days
20 days
20 days
M5: Identify, Compose, and Partition Shapes
(15 days)
M4: Place Value, Comparison, Addition and
Subtraction of Numbers to 40(35 days)
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Story of Units Aligned to theLearning Progressions
5
• Coherence Across the Grades• Grade 2: 3 tens or 3 units of 10 • (Grade 2 OA Standards)• Grade 3: 3 fours or 3 units of/groups of four • (Grade 3 OA Standards)• Grade 4: 3 fourths or 3 units of one-fourth • (Grade 3 NF Standards)
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Story of Units Aligned to theLearning Progressions
6
• Coherence Across the Grades• Learning 12 tens = 120 12 tenths = 1.2• Learning 4 thirds 4/3 = 1 1/3• or even• 4 threes = 12
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Story of Units Aligned to theLearning Progressions
7
Grade 3 Grade 4 Grade 5
Number and Operations in Base Ten Standards (NBT)
Counting up and down by ones, tens and hundreds,
both with the number line and place value chart are
essential from Grade 3 forward to rounding and
mental math.
Meaningful understanding of all operations with base-ten
whole numbers
Understanding place value’s extension into decimal fractions and
operations
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Key Points:
8
• A Story of Units is being written in alignment with the Instructional Shifts required by the CCLS.
• All standards for each grade have been carefully included in the module sequence.
• The P-5 modules are designed with deliberate coherence to capitalize on the learning progressions that are embedded in the CCLS.
• The activities promote a careful balance of fluency practice, conceptual understanding, and application, which aligns with the instructional shift, rigor.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
AGENDA
9
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Standards for Mathematical Practice
10
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning
of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Focus Standards for Mathematical Practice
11
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Mathematical Practice in Lessons
12
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Key Point
13
•A Story of Units brings the Standards for Mathematical Practice to life. Although all practices are integrated throughout the curriculum, individual lessons may highlight one or two practices specifically to facilitate educators in developing these habits of mind in their students.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
AGENDA
14
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
The Publishers’ Criteria
15
I. Focus, Coherence, and Rigor in the CCSSM II. Criteria for Materials and Tools Aligned to the
StandardsIII. Appendix: “The Structure is the Standards”
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Focus, Coherence, and Rigor
16
• At any given grade level 75% of the year should be spent on major areas of work.
• The first half of the year should predominantly cover major areas of work.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Indicators of Quality in Instructional Materials and Tools for Mathematics
17
• There are separate teacher materials that support and reward teacher study.
• The use of manipulatives follows best-practices.
• The visual design isn’t distracting or chaotic.
• Support for English language learners and members of other special populations is provided.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of UnitsModule Analysis Grade 2—Module 3
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
AGENDA
19
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
20
• Table of Contents• Overview• Topics including daily Lesson Plans• Module Assessments• Fluency Progression
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
21
•Module Overview •What is this module about?•What is the purpose of the Overview?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
22
•The Overview of Module Topics and Focus Lessons chart lists the teaching sequence towards attaining mastery of the standards highlighted in each lesson.
•Teaching sequences are the appropriate sequentialorder for developing mathematics skills. Teachers “build a ladder” to help students:•develop conceptual understanding•synthesize and apply knowledge from earlier concepts
Walk Through and Analyze Module Components
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
23
•Fluency – New and Familiar•Fluency activities promote automaticity of skills, allowing students to reserve cognitive resources for higher level thinking.
•
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
The Common Core Approach to Differentiating Instruction
24
• Structure provided by Universal Design for Learning (UDL)
• Asks teachers to consider:• multiple means of representation• multiple means of action and expression• multiple means of engagement
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
The Common Core Approach to Differentiating Instruction
25
• Charts provide suggested scaffolds for:• English Language Learners• Students with Disabilities• Students Performing Above Grade Level• Students Performing Below Grade Level
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
The Common Core Approach to Differentiating Instruction
26
• Marginal Notes to Teachers in Lessons
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
27
• Topic Opening:• Focus standard(s), instructional days, and coherence
links• Introductory paragraph• Concept chart (one lesson per concept)• Mathematical Practices Brought to Life
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
28
• Topic A - Suggested Lesson Structure
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
29
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
30
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Walk Through and Analyze Module Components
31
• Rigor in Daily Lessons: Conceptual Development
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A Story of Units
Walk Through and Analyze Module Components
32
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
33
• Each lesson contains daily assessments:• Activity Sheets• Exit tickets• Homework
Walk Through and Analyze Module Components
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
34
• Each module has an accompanying section for Supplementary Materials:• Assessment Tasks
• Exit Tickets for each lesson• Mid-Module Assessment Task• End-of-Module Assessment Task• Cross Modular Assessment Task
• Fluency Progressions• Bank of activities to assist with planning• Intentionally organized to revisit previously learned skills to develop
automaticity, to build for the day’s concept or to anticipate future concepts
•
Walk Through and Analyze Module Components
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Key Points
35
• A Story of Units includes 5-7 modules for each grade level. A curriculum map and grade level overviews are provided in A Story of Units: A Curriculum Overview for Grades P-5.
• Topics break into concepts and concepts become lessons. The concepts may be displayed in the classroom as the learning objectives for the lessons.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
AGENDA
36
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Analyze Lesson Components of the Module
37
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Analyze Lesson Components of the Module
38
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Key Points
39
• The Distribution of Instructional Minutes diagram displays the 3 components of rigor.
• The Suggested Lesson Structure pie chart shows the breakdown of a lesson based upon a 60 minute class.
• The Publishers’ Criteria emphasize that materials must reflect the Standards’ balanced approach to mathematics, stressing both conceptual understanding as well as procedural skill and fluency. There is a balance of activities and tasks and a balance of how time is spent.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Look At Rigorous Problems in the Module
40
• Daily Assessments• Worksheets• Exit Tickets• Homework Assignments
• Daily assessments provide valuable data to inform teachers and direct instruction.
• Students have daily opportunities to apply conceptual understanding learned during lessons and are held accountable for independent work.
•
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Look At Rigorous Problems in the Module
41
• Assessment Tasks• Mid-Module Assessments• End-of-Module Assessments• Cross-Modular Assessments
•
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
A Look At Rigorous Problems in the Module
42
• Homework Sheets• Build upon what students learn in the lesson for the day• Provide opportunities for students to check their
understanding and confirm they can solve problems independently
•
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Key Points
43
• Rigorous problems that produce a variety of student responses are embedded throughout the module.
• For these problems, answers alone are insufficient. Students must be able to thoroughly explain their thought processes. Possible student work may include bar diagrams, number sentences, area models, paragraphs, etc.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Units
Engageny.org
• 1 module for 2nd and 5th grade• Videos of teachers actually using strategies with
students• Presentations• Rigor Breakdown- with videos
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