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Dr. Elizabeth Frangella January 2013

http://www.engageny.org/

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- A Story of UnitsO Each Unit tells the story of concepts

on their grade level.O Layout for each – Introduction

O Sequence of Grade- Modules Aligned to Standards

O Summary for the year O Key areas of FocusO Required Fluency O http://engageny.org/sites/default/files/

resource/attachments/a-story-of-ratios-a-curriculum-overview-for-grades-6-8.pdf

NEW!

http://engageny.org/sites/default/files/resource/attachments/a-story-of-ratios-a-curriculum-overview-for-grades-6-8.pdf




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To Find the Major, Supporting and Additional work of each grade

O http://engageny.org/sites/default/files/resource/attachments/nys-math-emphases-k-hs.pdf

http://engageny.org/sites/default/files/resource/attachments/nys-math-emphases-k-hs.pdf




© 2012 Common Core, Inc. All rights reserved. commoncore.org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

Instructional Shifts (went from 6 to 3)

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Curriculum Map

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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)



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.

Standards for Math Practice(part of the Common Core)

OLike the Instructional Shifts, each Standard for Mathematical Practice is integrated into the design of A Story of Units.

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Standards for Mathematical Practice

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“… describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.”



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.



Indicators of Quality in Instructional Materials and Tools for Mathematics

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• Problems in the materials are worth doing.

• Assignments aren’t haphazardly designed. Exercises are given to students in intentional sequences.

• The modules contain different types of problems that are presented in a simple to complex format. There is variety to what students produce in response to prompts.



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.



Key Point

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A Story of Units adheres to the guidelines established in the Publishers’ Criteria and benefits from on-going feedback from Student Achievement Partners throughout the writing process.



Three Types of PARCC AssessmentsPARCC Type I Tasks

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• Assess concepts, skills and procedures• Include a balance of conceptual understanding,

fluency, and application• Can involve any or all mathematical practice

standards• Are machine-scored including innovative, computer-

based formats



PARCC Type I Tasks

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PARCC Type II Tasks

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• Assess ability to express mathematical reasoning• Call for written arguments/justifications, critique of

reasoning, or precision in mathematical statements (MP.3, MP.6) and can involve other mathematical practice standards

• Are hand-scored, or machine-scored with innovative computer-based formats, or a combination



PARCC Type II Tasks

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PARCC Type III Tasks

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• Assess modeling/applications • Call for modeling/application in a real-world context

or scenario (MP.4) and can also involve other mathematical practice standards

• Are hand-scored, machine-scored with innovative computer-based formats, or a combination



PARCC Type III Tasks

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Sample Grade 4 ProblemJim has three times as much money as Sally. If Jim has$14 more than Sally, how much money do they havealtogether?

AssessmentsO PARCC?O New York State?O Computer based?O All unknown at this time

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Draft of CC Sample Questions

O Have you looked at the Draft of the New York State Testing Program documents?

O Let’s look at some other sample math questions the state has used in the Network Training. Please take them out now.

http://engageny.org/resource/new-york-state-common-core-sample-questions



Turn and Talk

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• How do the new PARCC assessments compare with previous assessments?

•Did you notice the SHIFTS•What did you notice about the RIGOR•? (anything else?)

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Sequence

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VOCABULARYO http://

www.graniteschools.org/depart/teachinglearning/curriculuminstruction/mathThe following slides are from the Granite School Math Department presentation on the Common Core.

http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math






Instructional Shifts

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Shift 1: Focus

O—“…focus deeply on only the concepts that are prioritized in the standards...”

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Shift 2: CoherenceO—“Principals and teachers carefully connect the learning within and across grades so that… students can build new understanding onto foundations built in previous years.”

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Shift 3: RigorO—“…pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications.”

4 consolidated

shifts

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FluencyO —“Students are expected to have

speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions...”

O One or two fluencies are required for each grade level and fluency suggestions are included in most lessons. Implementation of effective fluency practice is supported by the lesson structure.

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SPRINTS and CHORALS

O DO NOW-O Let’s take a minute to see what fluency is all about. SPRINT- written practice for speed and accuracy

CHORAL- Skip counting aloud This example is byfractions~ forward and backwardhttp://engageny.org/resource/nti-november-2012-rigor-breakdown-skip-counting-by-fractions#.UOjPB6s8YbU.email

http://www.engageny.org/sites/default/files/resource/attachments/gr-5-sprint-a.pdf

http://engageny.org/resource/nti-november-2012-rigor-breakdown-skip-counting-by-fractions




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Conceptual Understanding

O—“Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math.”

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Application—O“Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so.”

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Dual Intensity—O“Students are practicing and understanding. There is more than a balance between these two things in the classroom—both are occurring with intensity.”

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Rigor in the Assessments O Each assessment utilizes a

combination of problems that build from simple to complex

Oprocedural skill, Ofluency, and Oconceptual understanding.

OMultiple-choice questions will be representative of PARCC Type I and II tasks.

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RIGOR continuedO Application problems including

multi-step word problems are always part of the assessments.

O Constructed response questions, will typically involve more complex tasks that require students to explain their process for solving a problem—i.e., Type II and III tasks.

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Rigor continuedOFor these problems, answers

alone are insufficient. Students must be able to thoroughly explain their thought processes.

OHandout and discuss how to make questions more rigorous- Can you do it?

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Let’s try oneO Take a few minutes to do this

assessment task-

O The EVOO problem is a Grade 6 Problem

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Do Now- A problem with “teeth”

O Elaine bought 6 lbs 4oz of EVOO for 16.80. The container leaked and she lost some of the oil. She quickly sold the remaining oil to George, at a per ounce price 3/7 higher than she paid for it. Altogether she made a profit of $ 3.60. What percentage of oil was lost in the leak?

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A Lesson Structure(others on site)

Fluency Practice 15 minutes

Concept Development 20 minutes

Application Problems 15 minutes

Student Debrief 10 minutes

Total Time 60 minutes

O .

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Common LanguageAddition and Subtraction, Grade 1 Multiplication and Division, Grade 3

Represent and solve problems involving addition and subtraction.

Represent and solve problems involving multiplication and division.

Apply properties of operations as strategies to add and subtract.

Apply properties of operations as strategies to multiply and divide.

Understand subtraction as an unknown-addend problem.

Understand division as an unknown-factor problem.

Add and subtract within 20. Multiply and divide within 100.

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

Determine the unknown whole number in a multiplication or division problem relating three whole numbers.

Use place value understanding and properties of operations to add and subtract.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

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Student needsA student may not be able to meet this expectation:

Without being to meet these:

1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. K.OA.5. Fluently add and subtract within 5. 1.OA.3. Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. 1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

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Some ConnectionsSo much for the distinctions. Some of the connections between OA, NBT, and NF are

summarized in the diagram below. (This diagram only refers to whole numbers in NBT.)

4.NF 5.NF 6.NS

1.OA

1.NBT 2.NBT

3.OA

3.NBT 4.NBT 5.NBT

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MAPOLet’s take a few minutes to

look at the standards and how they progress

OROLLOUT- Standards Map

http://engageny.org/sites/default/files/resource/attachments/01_a_graph_of_the_content_standards.pdf

http://engageny.org/sites/default/files/resource/attachments/01_a_graph_of_the_content_standards.pdf

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Some good “stuff” inside

O http://engageny.org/sites/default/files/resource/attachments/grade-5-math-guide_0.pdf

OFrom: Educator Guide to the 2013

Grade 5 Common Core Mathematics Test(time frame for teaching- what is taught

AFTER the test)

http://engageny.org/sites/default/files/resource/attachments/grade-5-math-guide_0.pdf



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Emphasis and Sequencing

Teach after the test

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WHAT ABOUT TEACHERS?O I HAVE TO BE COMFORTABLE WITH

MATH!

O Let’s say that together-

O I HAVE TO BE COMFORTABLE WITH MATH!

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Cluster Emphases for Instruction and the 2013 Grade 8 Common Core

Mathematics Test 65–75% 70–80% 15–25% 10–20% 5–15% 5–10%

Cluster Emphasis Recommended Instructional Time

Approximate Number of Test Points

Major Supporting Additional

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Looking at how to use the mapped standards

O 6.NS.4- This standard refers to greatest common factor- a staple of in-class worksheets. Note the second sentence and the example given:

O Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor with a multiple as a sum of two whole numbers with no common factor. For example, express 36 +8 as 4(9 + 2)

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The example given is to express 36 + 8, a sum of two numbers with a common factor, as 4 (9 + 2), a multiple of a sum of two numbers with no common factor. This example sends a signal about how ―greatest common factor can be piped into the main flow of ideas leading to algebra. For example, consider what we do when we express ax + a as a(x + 1). We are using the distributive property to express a sum of terms with a common factor as a multiple of a sum of terms with no common factor (6.EE.3,4). Standard 6.NS.4 is a kind of rehearsal for this, with numbers instead of variables.

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Think about the student

mistakes that COULD

happen, and plan

appropriately.

Answer a question

with another question-make them think

DON’T TOUCH THE

MANIPULATIVES!

•For Teachers:Anticipate the Errors

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ResourcesO https://mathreasoninginventory.com/Home/Index

EXCELLENT FREE ASSESSMENT SITE from Scholastic magazine- TOO OLD TO LEARN?

O National Library of Virtual Manipulatives http://nlvm.usu.edu/

O Mathematics Assessment Project http://map.mathshell.org/materials/index.php

O Maths Dictionary for Kidshttp://amathsdictionaryforkids.com/

O Thinkingblocks.com http://thinkingblocks.com/O Laying the foundation- http://www.ltftraining.org/O Commoncore.pearson.ed.com/

http://commoncore.pearsoned.com/index.cfm?locator=PS1cO9

O Ilustrative Mathematics http://illustrativemathematics.org/standards/k8

https://mathreasoninginventory.com/Home/Index

http://nlvm.usu.edu/

http://map.mathshell.org/materials/index.php

http://amathsdictionaryforkids.com/

http://thinkingblocks.com/

http://www.ltftraining.org/



http://illustrativemathematics.org/standards/k8



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Don’t ForgetO Download the most recent PARRC model

frameworksO http://

www.parcconline.org/parcc-model-content-frameworks

O Check out the Network Training information for November on www.engageny.org

O Check out this link for math resources- especially for High School

O http://www.mrlsmath.com/20-free-resources-for-high-school-math-teachers/

http://www.parcconline.org/parcc-model-content-frameworks




http://www.engageny.org/

http://www.mrlsmath.com/20-free-resources-for-high-school-math-teachers/




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