A Story of Units Overview

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A Story of Units Overview


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


A Story of Units

Instructional Shifts

3


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)


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)


A Story of Units


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• 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


A Story of Units


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


A Story of Units

Key Points:

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• 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.


A Story of Units

AGENDA

9


A Story of Units

Standards for Mathematical Practice

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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.


A Story of Units

Focus Standards for Mathematical Practice

11


A Story of Units

Mathematical Practice in Lessons

12


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.


A Story of Units

AGENDA

14


A Story of Units

The Publishers’ Criteria

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I. Focus, Coherence, and Rigor in the CCSSM II. Criteria for Materials and Tools Aligned to the

StandardsIII. Appendix: “The Structure is the Standards”


A Story of Units

Focus, Coherence, and Rigor

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• 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.


A Story of Units

Indicators of Quality in Instructional Materials and Tools for Mathematics

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• 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.


A Story of UnitsModule Analysis Grade 2—Module 3


A Story of Units

AGENDA

19


A Story of Units

Walk Through and Analyze Module Components

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• Table of Contents• Overview• Topics including daily Lesson Plans• Module Assessments• Fluency Progression


A Story of Units


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•Module Overview •What is this module about?•What is the purpose of the Overview?


A Story of Units

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•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



A Story of Units


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•Fluency – New and Familiar•Fluency activities promote automaticity of skills, allowing students to reserve cognitive resources for higher level thinking.

•


A Story of Units

The Common Core Approach to Differentiating Instruction

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• 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


A Story of Units


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• Charts provide suggested scaffolds for:• English Language Learners• Students with Disabilities• Students Performing Above Grade Level• Students Performing Below Grade Level


A Story of Units


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• Marginal Notes to Teachers in Lessons


A Story of Units


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• Topic Opening:• Focus standard(s), instructional days, and coherence

links• Introductory paragraph• Concept chart (one lesson per concept)• Mathematical Practices Brought to Life


A Story of Units


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• Topic A - Suggested Lesson Structure


A Story of Units


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A Story of Units


30


A Story of Units


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• Rigor in Daily Lessons: Conceptual Development


A Story of Units


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A Story of Units

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• Each lesson contains daily assessments:• Activity Sheets• Exit tickets• Homework



A Story of Units

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• 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

•



A Story of Units

Key Points

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• 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.


A Story of Units

AGENDA

36


A Story of Units

Analyze Lesson Components of the Module

37


A Story of Units

Analyze Lesson Components of the Module

38


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.


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.

•


A Story of Units


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• Assessment Tasks• Mid-Module Assessments• End-of-Module Assessments• Cross-Modular Assessments

•


A Story of Units


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

•


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.


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

Documents

A Story of Units Overview