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Mathematics Educators to the Career and College Ready Conference A Quick Look at Critical Topics in Mathematics Reform from Past Academies

 R educe Side Chatter  I nvolve Yourself in the Process  G ive Your Thoughts & Ideas  O pen Your Mind on how You Can Change Instruction  R emember to Silence Electronic Devices

 Reflect on how the Standards for Mathematical Practice will be infused into daily instruction.  Become familiar with the Maryland's College and Career-Ready Standards.  Analyze the instructional SHIFTS

Standards for Mathematical Practice 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 reasoning Apply to every Mathematics Unit in every grade/course

SMP Placemat Activity Behavior Cards Placemat

Grade 7 Overview  Expressions and Equations ◦ Use properties of operations to generate equivalent expressions. ◦ Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Algebra Arithmetic with Polynomials and Rational Functions ◦ Perform arithmetic operations on polynomials ◦ Understand the relationship between zeros and factors of polynomials ◦ Use polynomial identities to solve problems ◦ Rewrite rational expressions Content Standards for Mathematics

 Focus  Coherence  Rigor SHIFTS in Mathematics Conceptual Understanding Procedural Skill Modeling/Application

FOCUS FOCUS is largely built into the CCSSM curriculum. The charge for the classroom teacher is to take opportunities to revisit major content frequently and make connections between the major and supporting and additional content.

New Learning Prior Learning COHERENCECOHERENCE Shift #2

Purposeful placement of standards to create logical sequences of content topics that bridge across the grades, as well as across standards within each grade. COHERENCE

GradeFrom Grade to Grade 5 th Understanding of fraction equivalence and the skill to generate equivalent fractions leads to the study of ratios. 6 th Skills with multiplication, division and fractions, contribute to the study of ratios and unit rates 7thAnalyze proportional relationships and solve problems involving unit rates associated with ratio fractions. 8thUnderstand the points (x,y) on a non-vertical line are solutions to the equation, y= mx + b, where m is the slope of the line as well as the unit rate of a proportional relationship.

Grade 7 - Within the Grade Analyze proportional relationships and solve problems involving unit rates associated with ratio fractions. Analyze proportional relationships in geometric figures.

Illustrative Mathematics – Overlapping Squares Alignment 1: 6.RP.A.3c Two congruent squares, ABCD and PQRS, have side length 15. They overlap to form the 15 by 25 rectangle AQRD, shown. What percent of the area of rectangle AQRD is shaded?

Group Presentations

“ Rigor is the goal of helping students develop the capacity to understand content that is complex, ambiguous, provocative, and personally or emotionally challenging.” Shift #3

Rigorous vs. NOT

Rigorous!Non-rigorous  Challenge students  Require effort and tenacity  Focus on quality  Have multiple paths  Not always “tidy”  Connect ideas in mathematics  Develop strategic, flexible thinking  Encourage reasoning and sense-making  Actively involve students  Has awkward, difficult values  Require minimal effort  Focus on quantity, repetition  Scripted, includes pathway to the solution  No links within mathematics  Routine, rote procedures  Memorize rules without understanding  Teachers do the work while students observe

PARCC Model Content Framework for Grade 6, includes:

DOMAIN: The Number System CLUSTER: Apply and extend previous understandings of numbers to the system of rational numbers. Standard 6.NS.C.7 7. Understand ordering and absolute value of rational numbers.

What does it mean to MODEL with mathematics?

PICTURES WORDS There were 3 frogs. 1 hopped away. There are 2 frogs. NUMBERS 3 – 1 = 2 OBJECTS

RIGOR MODELING/APPLICATION Learning experiences in mathematics classrooms should help students see, and make sense of, connections between mathematics, statistics, and everyday life.

Procedural Skill Modeling/Application Conceptual Understanding

Illustrative Math Bill McCullum, CCSS lead writer Sample Lessons that illustrate specific standards Achieve The Core Jason Zimba, CCSS lead writer Multiple Resources – e.g. Lesson Plans, Assessments, Professional Development courses, Grade-at-a-Glance PARCC Information about PARCC Assessments Sample Lessons Practice Tests

Noticing and Wondering Annie Fetter

The greatest danger for most of us is not that our aim is too high and we miss it…. But that it is too low and we reach it. -- Michelangelo