Mapping to the Core Professional Learning Community Day 5 Math

We do not want anyone to be a casualty of the standards.

1 CCSS, 2010, p. 5 2 PARCC – Draft Content Framework

Math PLC Norms  Practice the “P” word (Perseverance)  Think, Talk, and Write about mathematics  Manage your electronic devices respectfully  Track your progress toward learning targets

Big/Ideas for this course Day 1-Laying the Foundation- Phase 1 Day 2-Consensus Mapping using Comparatives-Phase 2 Day 3- Draft Unit/Lesson Plan Development and align assessments- Phase 3 Day 4-Training on Mapping Software and entering units/plans in the system. Day 5-Read-throughs for SMP’s, Critical Areas of Focus and upgrading with web 2.0 tools-Phase 4

Day 5 Phase 4 of Curriculum Mapping What are 21 st Century Skills? Investigate web 2.0 tools to use with K-2 for Math Lunch11:30-12:30 What about Assessments? Team time to work further on plans Track your progress toward learning goals for this training Evaluation

Check for understanding Back to Back Partner 3 min What are the 8 Standards of Mathematical Practices? Write them on an index card When cued, get with a back to back partner, turn and share. Add to your card When cued, get with another back to back partner, turn and share. Add to your card

CCSS Mathematical Practices 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

Change of Emphasis K- Grade 5 K-2 Greater development of how numbers work Data analysis is just a tool for working with numbers and shapes Grades 3-5 Fractions then decimals Multiplication with inverse division Operation strategies and relationships developed BEFORE algorithm procedures

What does literacy look like in the mathematics classroom? Learning to read mathematical text Communicating using correct mathematical terminology Reading, discussing and applying the mathematics found in literature Researching mathematics topics or related problems Reading appropriate text providing explanations for mathematical concepts, reasoning or procedures Applying readings as citing for mathematical reasoning Listening and critiquing peer explanations Justifying orally and in writing mathematical reasoning Representing and interpreting data

CCSS Domain Progression K HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability

Standards Progression: Number and Operations in Base Ten

Use Place Value Understanding Grade 1Grade 2Grade 3 Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 6. Subtract multiples of 10 in the range from multiples of 10 in the range (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding and properties of operations to add and subtract. 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100– Explain why addition and subtraction strategies work, using place value and the properties of operations. Use place value understanding and properties of operations to perform multi-digit arithmetic. 1. Use place value understanding to round whole numbers to the nearest 10 or Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Grade Level Comparative Analysis Content that is new to Grade 8 Content that is still included at Grade 8, but may be modified or at a greater depth Content that is no longer a focus at Grade 8  The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. (8.NS.1-2)  Functions Define, evaluate, and compare functions. (8.F.1-3)  Functions Use functions to model relationships between quantities. (8.F.4-5)  Geometry Understand congruence and similarity using physical models, transparencies, or geometry software.[initial introduction] (8.G.1-2)  Geometry Understand and apply the Pythagorean Theorem. [initial introduction] (8.G.6-8)  Statistics and Probability Investigate patterns of association in bivariate data. (8.SP.4)  Expressions and Equations Work with radicals and integer exponents. (8.EE.1-4)  Expressions and Equations Understand the connections between proportional relationships, lines, and linear equations. [derive y=mx] (8.EE.5-6)  Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations. (8.EE.7-8)  Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. (8.G.3-5)  Geometry Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. (8.G.9)  Statistics and Probability Draw informal comparative inferences about two populations. (7.SP.3-4)  Statistics and Probability Investigate patterns of association in bivariate data. (8.SP.1-3)  Number, Number Sense and Operations Ratio, proportion percent problems (See Grade 7.RP)  Measurement Order and conversion of units of measure (See Grade 6.G)  Measurement Rates (See Grade 7.RP)  Geometry Geometric figures on coordinate plane (See Grades 6-7.G)  Geometry Nets (See 6.G.4)  Patterns, Functions and Algebra Algebraic expressions (See Grades 6-7.EE)  Patterns, Functions and Algebra Grade 8 learning is limited to linear equations  Patterns, Functions and Algebra Quadratic equations (See HS)  Data Analysis Graphical representation analysis (See Grade 6.SP)  Data Analysis Measures of center and spread; sampling (See Grade 7.SP)  Probability (See Grade 7.SP)

MP + CAF + Standards = Instruction In order to design instruction that meets the rigor and expectations of the CCSSM, understanding the Mathematical Practices and Critical Areas of Focus are essential.

Activity 1: K-2 Critical Areas of Focus Read your grade level’s Critical Areas of Focus –What are the concepts? –What are the skills and procedures? –What relationships are students to make?

Concepts, Skills and Procedures Concepts Big ideas Understandings or meanings Strategies Relationships Understanding concepts underlies the development and usage of skills and procedures and leads to connections and transfer. Skills and Procedures Rules Routines Algorithms Skills and procedures evolve from the understanding and usage of concepts.

Concepts, Skills and Procedures Grade 4 Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700  70 = 10 by applying concepts of place value and division. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place.

What Makes a Problem Rich? Significant mathematics Mathematical Practices Multiple layers of complexity Multiple entry points Multiple solutions and/or strategies Leads to discussion or other questions Students are the workers and the decision makers

How will you embed Web 2.0 tools in your Math Classroom? 1.Investigate resources listed on wikispace 20 minutes 2.Get into Grade Level Groups 3.Frayer Model Define Web. 2.0 in Math Classroom at your grade level 45 min

Break- 10 minutes

Wikispace…

Team Time Use this time to continue with your Unit Plans, Daily Plans How can you embed Web 2.0 tools and rich problems into your daily plans?

Lunch-on your own 1 HOUR

Team Time Use this time to continue with your Unit Plans, Daily Plans How can you embed Web 2.0 tools and rich problems into your daily plans?

Shift HAPPENS… - NCTM FromToward Assessing students knowledge of specific facts and isolated skills Assessing students full mathematical power Developing assessments by oneselfDeveloping a shared vision of what to assess Treating assessments as separate from curriculum and instruction Aligning assessments with curriculum and instruction Viewing students as objects of assessmentsViewing students as active participants in the assessment process Using assessments to filter students out of select opportunities to learn math Using assessments to ensure that all students have the opportunity to achieve their potential Regarding assessments as sporadic and conclusive Regarding assessment as continual and recursive

Break- 10 minutes

How to teach Math as a Social Activity How can you make this work in your classroom?

Rich Task Sources Ohio Resource Center Inside Mathematics Balanced Assessment (MARS tasks) NCTM Illuminations

External Resources for CCSSM CCSSO – Achieve – NCTM – Center for K-12 Assessment & Performance Management at ETS – YouTube Video Vignettes explaining the CCSS –

Learning Targets.. Track your progress and turn in to me I Can… Access the Common Core Standards, Model Curriculum, Comparatives and Crosswalks online Review the Crosswalks and Comparative documents for Math Common Core standards to identify the non-negotiables and targeted levels of instruction Collaborate with peers to develop scaffolded curriculum units/lessons that emphasize coherence, focus, and rigor

Next Steps

What Should Districts Do Now? Deepen your understanding of the CCSSM in Professional Learning Communities through: –the Standards for Mathematical Practice –the Critical Areas –the Model Curriculum –the Standards Progressions –the Comparative Analysis Begin focusing instruction around: – the Mathematical Practices –The Critical Areas Develop support structures for reaching all students –Use previous mathematics in service of new ideas –Provide all students access to the regular curriculum; RtI

Wikispace…

ODE Mathematics Consultants Brian Roget Ann Carlson Yelena Palayeva