??????????????????

Did You Know?

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

Placemat Behavior Cards

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.

Content Standards for Mathematics

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

  

Focus

Coherence Rigor

Conceptual Understanding Procedural Skill Modeling/Application

Shift #1



FOCUS

MAJOR SUPPORTING

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.

C O H E R E N C E

Shift #2

Shift #2

COHERENCE

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

COHERENCE

Grade From 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 7th Analyze proportional relationships and solve problems involving unit rates associated with ratio fractions.

8th Understand 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.

COHERENCE

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

Analyze proportional relationships in geometric figures.

COHERENCE

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!

         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 Non-rigorous         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

.

OBJECTS NUMBERS 3 – 1 = 2

RIGOR MODELING/APPLICATION

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

Conceptual Understanding Procedural Skill Modeling/Application

• • Illustrative Math https://www.illustrativemathematics.org/ Bill McCullum, CCSS lead writer Sample Lessons that illustrate specific standards • • Achieve The Core https://achievethecore.org

Jason Zimba, CCSS lead writer Multiple Resources – e.g. Lesson Plans, Assessments, Professional Development courses, Grade-at-a-Glance • • • PARCC http://parcconline.org

Information about PARCC Assessments Sample Lessons Practice Tests

Annie Fetter

http://www.youtube.com/watch?v=WFvYZDR4OeY

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