CMI2012 CCSS for Mathematics

Designing Common Core State Standards Systemic Mathema4cs Curriculum

Presented By Janet Hale www.CurriculumMapping101.com

Backchannel: todaysmeet.com/ccssm

Architects design. LEARN

Contractors build.

TEACH

Systemic Design - Interdependent 1 Grove…1 Root System

Aspen Grove Mentality

Designing Systemic K-12 CCSS Math Collaborative Maps

How long will it take for the K-12 Task

Force to complete Stage 1?

Part 1 Design / Part 2 Design Vertical Alignment

Design units that represent K-12 learning continuum

(e.g., Geometry, Measurement/Data) by single/mixed domains

across grade levels

Horizontal Alignment Design units of study that

integrate learning within and/or among strands in one grade level (e.g., intradisciplinary,

program-based, interdisciplinary)

Part 1 – Phase I

•  Unit Names

•  Enduring Understandings/ Essential Questions

•  Standards for Mathematical Practice

•  Vocabulary

Designing UNIT NAMES

Quickly locating learning

by reading electronic “binder” spine. (Pre-‐K) K through 12

Arizona http://www.azed.gov/standards-practices/mathematics-standards/

http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspxPage=3&TopicRelationID=1704&Content=123507 (Transitional Tools)

Ohio

High School Course Design

Determine Desired Pathway

Math CCSS Appendix A

Math CCSS Courses – Suggested Starting Points K-8 Math (K-8) GEOMETRY (K-2, 6-8) GEOMETRY/MEASURMENT (3-5)

DATA: MEASUREMENT/DATA (K-5) DATA: STATISTICS/PROBABILITY (6-8)

NUMBER/QUANTITATIVE: COUNTING/CARDINALITY (K) NUMBER/ALGEBRAIC: NUMBER BASE 10/OPERATIONS (K-5) NUMBER: NUMBER SYSTEM/EXPRESSIONS/EQUATIONS (6-8)

QUANTITATIVE: RATIOS/PROPORTIONAL RELATIONSHIPS (6-8) Coordinate Algebra (9) (Integrated Pathway) EXPRESSIONS/EQUATIONS LINEAR FUNCTIONS EXPOTENTIAL FUNCTIONS DATA ANALYSIS COORDINATE PLANE INEQUALITIES Analytic Geometry (10) Advanced Algebra (11) (Above examples based on work in Muscogee CSD, Columbus, GA)

Part 1 – Phase I

•  Unit Names



•  Vocabulary

K-12 CCSS Aligned/Designed

Enduring Understandings/ Essential Questions

Create CCSS-based EUs/EQs prior to Part 1 or… Create CCSS-based EUs/EQs prior to Part 2

Enduring Understandings/ Essential Questions

It usually takes a task force two full days (including initial training: “What are EUs/EQs/SQs?”)

to create K-12 CCSS-based Math EUs/EQs.

Part 1 – Phase I •  Unit Names

•  Understandings/ Essential Questions


•  Vocabulary

(CCSS, p. 5)

Domains, Cluster, Standard Statements

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.

Standards for Mathematical Practice are the same K-12…

Page 7-‐8, CCSSM

http://www.azed.gov/standards-practices/mathematics-standards/

Standards for Mathematical Practice

Choices… 1.  Embed SMP expectations as part of skill

statements by asking for justifying reasoning and provide examples (e.g., ____) for teachers to gain insight into higher level of expectation (students “owning” the learning)

2.  Create SMP-based skill statements that represent the essence of the eight practices to be included as a part of Part 2’s units of study.

3. Construct viable arguments and critique the reasoning of others.

Grade 1 GEOMETRY Content E. Geometrical Rela.onships: Composi.on -‐-‐2-‐Dimensional (Quarter Circle, Half Circle, Quarter Circle, Circle, Square, Rectangle, Triangle, Trapezoid, Hexagon) -‐-‐3-‐Dimensional (Cube)

Skill E. Compose manipula.vely, orally, and in wri.ng 1 two-‐dimensional shape/figure using appropriate 2-‐dimensional shapes (i.e., see Possible Composi/ons reference) and jus.fy reasoning (e.g., Ami has a cardstock square in front of her. She has various cardstock shapes nearby. Mr. Mar/n asks her to show him 3 ways she can compose a square with the various shapes. Ami makes 1 square first using 4 smaller squares; next using 2 rectangles; and then using 4 triangles. The teachers asks her to explain in wri/ng what she did and why. Ami shared, “I first composed 1 large square using 4 small squares…See 1, 2, 3, 4 equal shares. Then I took them off and used 2 equal shares; 2 rectangles. And last, I took off the rectangles and used 4 equal shares, but this /me they were triangles instead of squares, but the s/ll fit just right on the large square.”)

Design Note … Use of parentheses in skill statements

Reduce complex frac.on (frac.on over frac.on) by mul.plying by common denominator (e.g., see complex frac/on example)

Describe orally and in wri.ng par..oned shares using 6 terms (halves, half of, thirds, third of, quarters, quarter of) (e.g., Carmen par//ons a circle into 2 equal shares. She writes: The circle has 2 equal shares or 2 halves.)

(e.g., _____________ ) =

(i.e., ______________) =

(______________) =

Algebra “Connec4ons” …. Use of “Baby a” Content S. Addi.on/Subtrac.on: Differen.a.on Between 1-‐Step/2-‐Step Word Problems Skills Sa. Differen.ate orally and in wri.ng between 1-‐step word problem having 1-‐event equa.on (1 sum/1 difference) versus 2-‐step problem where sum/difference of 1st-‐event equa.on must be used in 2nd-‐event equa.on to find final sum/difference and jus.fy reasoning (e.g., Mr. Bryan reads 2 displayed word problems to his class, "The first problem says: George collects coins. He has 32 coins. His uncle brought him 14 coins from Japan to add to the his collec/on. How many coins does George have now? The second problem says: A cafeteria has a basket of 25 oranges. The basket has 5 oranges leY in it at the end of lunch. The next morning a cafeteria worker adds 10 more oranges to the basket. How many oranges will be available for lunch today?" Mr. Bryan asks, "Which problem is a 1-‐step problem and which problem is a 2-‐step problem?" Jeb raises his hand. Mr. Bryan asks him to come to the board. Jeb comes up and shares his reasoning, "The problem about the coins is a 1-‐step problem because all you have to do is add the 2 sets of coins together so it is 1 event.” He writes on the board: 32 + 14 = 46. "The second problem is a 2-‐step problem because it has 2 events. For the 1st event you have to subtract to find the difference. Then you have to add 10 to the difference in the 2nd event." He writes: 25 – 20 = 5, 5 + 10 = 15).

Part 1 – Phase I

•  Unit Names



•  Vocabulary

Vocabulary

Choices… Embed vocabulary terms

and definitions within Content field? Skills field? Resources as an attachment?

Format… Agree on visual format so vocabulary will

be consistent for curriculum design not only for Math, but other disciplines as well. The more continuity among disciplines, the more accurate and useful the reporting features are within a mapping system.

Grade 6 QUANTITATIVE: RATIOS/PROPORTIONAL RELATIONSHIPS

A. Communicate concepts/explana.ons orally and in wri.ng using 3 terms:

Part 1 – Phase I

•  Unit Names



•  Vocabulary

Part 1 – Phase II

•  Breaking Apart (Translating, Unpacking) Standards (Design Influences – Key Shifts, Depth of Knowledge)

•  Systemic Content / Skills Development (Process: Format … Collaborative Agreement on Tight and Loose)

•  PreK-12 Vertical Reviews (Internal Alignment – Content/Skills & External Alignment to CCSS)

•  Horizontal Units of Study (Bridging Part 1 and Part 2 Design Work)

Implicit Influences

•  Breaking Apart (Translating, Unpacking) Standards

Teachers will, as architects-designers, spend extensive time studying the explicit and implicit intent of the codes, but need to first consider design influences.

•  Math CCSS - 3 Key Shifts

•  Depth of Knowledge (PARCC, SMARTER Balance)

CCSS Mathematics – 3 Key Shifts (www.achievethecore.org)

1.  FOCUS Focus Strongly Where the Standards Focus (narrow the scope of content to allow in-depth learning; no “but we have so much to cover”; need “inch wide, mile deep” mindset to ensure time necessary for students to explore, test, and reach personal conceptual understanding)

2. COHERENCE Think across grade levels (systemic design) (each new standard is not a “new event” … each new standard is an extension of previous distinct or linked learning) Link learning among domains within one grade level (leverage) (conceptual relationships across and among standards to aid in conceptual understanding and reasoning)

3. RIGOR Equitable, balanced curriculum (learning/teaching): –Conceptual Understanding –Procedural Skills and Fluencies –Application of Math Process using real-world/authentic problems/tasks (within/across disciplines)

Presenta.on Slide from CCSS for Mathema/cs: Key ShiYs -‐Sandra Alber., Student Achievement Partners

1.   FOCUS 2.   COHERENCE

www.achievethecore.org

Grade 7 (Content lis/ng in an Essen/al Map unit) Algebraic Representa.ons: Equa.on Fluency Involving 4 Opera.ons Mul.-‐Step Word Problems (Posi.ve/Nega.ve Ra.onal Numbers, Inequali.es, Complex Frac.ons)

High School Fluencies: Algebra, Func4ons, Geometry, Sta4s4cs & Probability, and Modeling

3. RIGOR --Conceptual Understanding --Procedural Skills and Fluencies --Application of Math Process

CCSS Fluency ≠ Rote Memoriza4on

CCSS Fluency = Speed and Accuracy using self-‐selected strategies

Implicit Influences





Cognitive Complexity New

BLOOM’S

DOK

Evaluate Predict Hypothesize

Output E/C

Generate Speculate Forecast

Imagine If/then Create

Judge Apply Speculate

Compare Distinguish Analyze

Process A/A

Contrast Explain Synthesize

Classify Discriminate Reason

Infer Sequence Interpret

Duplicate Identify Paraphrase

Input R/U

Count List Recite

Define Memorize Locate

Describe Name Reproduce

Understanding/Remembering

Analyzing/Applying

Creating/Evaluating

New Bloom’s

Cognitive Complexity

R/U Input

A/A Process

E/C Output

New BLOOM’S

DOK

Several things are involved, including the content, the ac4vity and/or thinking processes, and the complexity of both the content and ac4vity/thinking processes. -‐-‐Debbie Baughman, The Standards Company

Norman Webb’s

Depths of Knowledge DOK Model (1997) created to analyze the cogni.ve expecta.on

demanded by standards, curricular ac.vi.es, and assessment tasks. redesign.rcu.msstate.edu

DOK Four Levels

Level 1 Recall/Reproduc4on Recall facts, informa.on, procedures, basic concept founda.ons (minor comprehension involved at this level, no depth, no complexity)

Level 2 Skill/Concept Apply/process facts, informa.on, procedures, conceptual understanding involving at least two steps that require reasoning (a need to interpret material and make simple decisions about how to approach a problem, but does not yet have a deep complexity)

DOK Four Levels

Level 3 Strategic Thinking Requires deeper reasoning, developing a plan or sequence of steps to complete a task; more than one possible solu.on/answer (deal with abstrac/ons and open-‐ended conclusions and able to support one’s reasoning; wrestle with complex concepts, tasks, material)

Level 4 Extended Thinking Process mul.ple condi.ons and solu.ons for the problem; extend thinking by comple.ng much deeper and complex tasks (according to Webb, higher-‐level thinking is absolutely central; interac/on with concepts, tasks, material is in-‐depth and purposeful)

CAUTION!

Bloom’s Verbs cannot be applied with the same mindset for what students must cogni9vely do when applying Webb’s Depth Of Knowledge (DOK) to student learning, teaching, and assessment items/tasks.

DOK 2 – Describe number/shape paberns that follow determined term/rule and jus.fy reasoning (e.g., Look at the bowling pins pafern. What will the next two rows look like in this pafern? Explain the increase using textual, visual, and number representa/ons. Without drawing, what would be the number of pins in the 15th row? Explain your reasoning. )

DOK 1 – Describe shape-‐pabern term/number-‐pabern rule using real-‐world examples (e.g., Pretend you are walking outside. Draw and explain a natural or man-‐made pafern’s term.)

The “cau4on” influences wri4ng skills…

Measurable Verb + Descriptor

Cognitive Complexity

1 Recall/

Reproduction

2 Skill/

Concept

4 Extended Thinking

3 Strategic Thinking

New BLOOM’S

DOK PARCC www.parcconline.org/parcc-content-frameworks

Smarter Balanced www.smarterbalanced.org/wordpress/wp-content/uploads/2012/03/

DRAFTMathItemSpecsShowcase2.pdf

R/U Input

A/A Process

E/C Output

www.illustrativemathematics.org

Implicit Influences





Part 1 – Phase II





Step 1: Code hard-‐copy of each Part 1 “full-‐year” UNIT’s Content/Skill statements to aligned standards.

Part 2 – Phase II K-‐8 Process For “Pla4ng” Quartered Learning Expecta4ons

Step 2 (Quartered Units): Cut out Content/Skills Sets and create graphic organizers that represent full year of “quartered” UNIT learning.

Step 3: Create quartered UNITS in mapping system (ensure newly created UNITS include aligned standards for each quarter’s learning).

Part 2 – Phase II K-‐8 Process For “Pla4ng” the Learning Expecta4ons

Step 4: Ensure abachments are included properly in each quartered UNIT (preferably as .pdf files).

Step 1: Code hard-‐copy of each UNIT’s Content/Skill statements to aligned standards.

Part 2 – Phase II Process For “Pla4ng” Sequen4al Learning Expecta4ons

Step 2 (Sequen.al Units): Cut out Content/Skills Sets and create graphic organizers that represent full year of learning.

Step 3: Create sequen.al UNITS in mapping system (ensure newly created UNITS include aligned standards for each UNIT’s learning).

Step 4: Ensure abachments are included properly in each UNIT (preferably as .pdf files).

Part 1 – Phase II





Wearing the right design gear, dive on in! (Even though it may feel a liple unnerving at first…)

Janet Hale www.CurriculumMapping101.com

[email protected] 520-‐241-‐8797

Education

CMI2012 CCSS for Mathematics