A Guide to the K-8 and High School Publishers’ Criteria

for the CCSSMDana Cartier

ISBE Content Area Specialist

Slides adapted from the K-8 Publishers’ Criteria

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3.OA.9 Task #1

Fill in the blank below and explain.

2, 4, 6, ____

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3.OA.9 Task #2a) In each column and each

row of the table even and odd numbers alternate. Explain why.

b) Explain why the diagonal, from top left to bottom right, contains the even numbers 2,4,6,8, and 10.

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Compare the Tasks

What were the similarities and differences of the previous

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Objectives

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Introduce the K-8 & High School Publishers’ Criteria

Learn the why and how of using the criteria

Explore the math criteria

What is the Publishers’ Criteria?

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Supports faithful implementation of the CCSSMDeveloped by the three lead authors Phil Daro, Bill McCallum, Jason ZimbaTwo different documents- similiar

Why Do We Need This?

Standards cannot raise achievement.

Material should connect to assessment.

Educators complain about what is missing, but not about what has crept in.

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Wiggins, 2012

Because conventional textbook coverage is so fractured, unfocused, superficial, and unprioritized, there is no guarantee that most students will come out knowing the

essential concepts of algebra.

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How Can We Use This ToolInform purchase and adoption

Work with previously purchased materials

Review and guide teacher-developed materials

Plan professional development

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Part I: Major Shifts

Focus Coherence

Rigor Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Focus

Consider what is not said

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Math “needs to lose a few pounds” (p.3)

“Teach less, learn more”

“Cannot add “just one more thing”

Grade-level work begins during the first two to four weeks of instruction

Differentiation

Extensions

CoherencePractice-content coherence

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Math should make sense

A progression of learning

Use supporting material to teach major work

Coherence supports focus

RigorBalance with equal intensity

– Conceptual understanding– Procedural skill and fluency– Application

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Conceptual Understanding

“Understand”High-quality conceptual problemsElicit conversationIdentify relationshipsMultiple representations

Fluency“Fluently”

Methods are based on mathematical principles, not mnemonics or tricks

Quickly and accurate, to work with flow. It isn’t halting, stumbling, or reversing oneself.

Fluency

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1. Write a simplified expression for the following: 7r + 2(r + 3)

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2. Fill in the blanks below to make the equation true for every value of x. Explain the steps you took, as well as any math properties you used.

Fluency Example

ApplicationSingle-step and multi-step contextual problemsRequire students to make assumptions in order to model a situationModeling – a practice standard and a HS Conceptual Category

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Application ProblemMy phone beeps with a text from my friend who is an event coordinator:

My producer sent me only 50 feet of red velvet rope and 4 poles! I don’t know what he was thinking, how can I fit all of the VIPs in this section?“

What is the mathematical question?

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Application

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How many dinosaurs are standing in the lake?Explain how you know. Use words and mathematical language to explain your solution.

Part II: Criteria for Materials and Tools

10 criteria to analyze mathematics curricular materials

1 criterion to align mathematics to other disciplines

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K-8 Publishers’ Criteria

Part II: Criteria for Materials and Tools Aligned to the K-8 Standards

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1. Focus on Major WorkBetter to inadvertently leave something

out than to teach too much

65%-85%of time is spent on the major work

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5th Grade PARCC Model Content Framework

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2. Focus in Early Grades

Don’t cover material earlyDon’t assess material early

Patterns only within arithmetic

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3. Focus and Coherence through Supporting Work

Supporting work enhances major work

Supporting work does not detract from focus

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2nd Grade Examplefrom Measurement and Data Progression

4. Rigor and BalanceConceptual UnderstandingFluencyApplication

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Three aspects are not always together.

Three aspects are not always separate.

5. Consistent Progressions

Grade-by-gradeGrade-level problems

Relating to prior knowledge

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6. Coherent Connections

Curricular material makes connections between clusters and domains

CCSSM are more than a sum of their parts

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7. Practice-Content Connections

Not separate

Present throughout

Grounded in the content standards

Accompanying teacher-support

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8. Focus and Coherence via Practice Standards

Connect practice and content standards as specified

– Structure for structural themes (MP7)– Using repetition to find mathematical

regularity (MP8)

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9. Careful Attention to Each Practice Standard

Full meaning and spirit of the entire practice standard

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10. Emphasis on Mathematical Reasoning

Construct viable argumentsProblem-solving as argument

Specialized languageContent contained is licensed under a

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Construct Viable Argument25-50% of students’ time

Independent thinking, classroom discussion and written work

Critique arguments, error analysisMulti-step problems

Student-devised strategyCohesive arguments that can be verified and

critiqued Not a jumble of steps

Specialized Language

“The language of argument, problem-solving and mathematical explanations are taught rather than

assumed.”

Language of representations – Diagrams, tables, graphs, symbolic expressions, drawing,

images, text – Helpful for ELL students

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High School Publishers’ Criteria

Part II: Criteria for Materials and Tools Aligned to the High School

Standards

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1. Focus on Widely Applicable Prerequisites

Material should coherently include all of the standards in High School (without the + standards), with a majority of the time devoted to building the particular knowledge and skills that are most applicable and prerequisite to a wide range of college majors and postsecondary programs

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2. Rigor and BalanceConceptual UnderstandingFluencyApplication

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Three aspects are not always together.

Three aspects are not always separate.

3. Consistent Content

•Base course on content•Give students extensive work

with course-level problems•Explicitly relates course content

to prior knowledge

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4. Coherent Connections

Curricular material makes connections between clusters and domains

CCSSM are more than a sum of their parts

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5. Practice-Content Connections

Not separate

Present throughout

Grounded in the content standards

Accompanying teacher-support

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6. Focus and Coherence via Practice Standards

Connect practice and content standards as specified

– Structure for structural themes (MP7)– Using repetition to find mathematical

regularity (MP8)

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7. Careful Attention to Each Practice Standard

Full meaning and spirit of the entire practice standard

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8. Emphasis on Mathematical Reasoning

Construct viable argumentsProblem-solving as argument

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Connecting Criterion:Consistency with CCSSM

Materials for science and technical subjects are consistent with CCSSM

Grade-level appropriate mathematics in other disciplines

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Indicators of Quality

Variety in the pacing of each standard

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Problems are worth doing

Variety of student products

Separate teacher material

Best practices with manipulatives

Visual design is clear

Support for diverse learners

SHORT

Avoid crosswalks

Align to the letter and spirit of the standards

Don’t take the common out of COMMON core

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Dana CartierISBE Content Area Specialist Area 5&6

dcartier@stclair.k12.il.us

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