CONNECTIONS 2012

Mathematics for College Success/Readiness Courses

Jennifer WinchesterFlorida Department of Education

Teaching Channel video explains key features of the Common Core

Math Standards

The Teaching Channel has developed a 14-minute video about the key features and differences of the Common Core math standards: https://www.teachingchannel.org/videos/common-core-state-standards-for-math?fd=1  The video discusses the purpose of the standards for mathematical practice and how these should be integrated with the content; how teaching fewer topics in each grade changes planning; and, how the standards can help in closing the achievement gap. It is an easy-to-understand introduction that can be used to explain the new Math Common Core Standards to a general audience.

Features of the Standards

• Standards for Mathematical Practice– Outline the expertise and habits of mind that should be

developed in all students

• Standards for Mathematical Content– K-8 standards presented by grade level– High school standards presented by conceptual theme– Aligned with college and work expectations– Focused and coherent

• Focus: doing fewer things at any given grade so that students have time to internalize, practice, and learn what is being done in that grade

3

Standards for Mathematical Practice

“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.”- Common Core State Standards for Mathematics,

page 6

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

6

Pairs of PracticesReasoning and Explaining2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others

Modeling and Using Tools4. Model with mathematics5. Use appropriate tools strategically

Seeing Structure and Generalizing7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Overarching Habits of Mind of a Productive Mathematical Thinker1. Make sense of problems and persevere in solving them6. Attend to precision

Adapted from (McCallum, 2011)

The Standards for Mathematical Practice

• Turn to page 6 of the Common Core State Standards for Mathematics

• Take a moment to examine the first three words of the narrative description for each of the 8 mathematical practices.

• What do you notice?

Mathematically Proficient Students…

8

• Read Mathematical Practices 1 and 6.

• Identify the verbs that illustrate the student actions for this practice.

Common Core StandardsInterpret the Structure of Expressions

MACC.912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context.*

MACC.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

Mathematics Postsecondary Readiness Competencies

• MPRCC1– Understand that to solve certain problems and equations,

number systems need to be extended from whole numbers to the set of all integers (positive, negative and zero), from integers to rational numbers, and from rational numbers to real numbers (rational and irrational numbers); define and give examples of each of these types of numbers

• MPRCC6– Locate the position of a number on the number line, know that its

distance from the origin is its absolute value, and know that the distance between two numbers on the number line is the absolute value of their difference

• MPRCC9– Use estimation and approximation to solve problems

(Include evaluating answers for their reasonableness, detecting errors, and giving answers to an appropriate level of precision)

Student Goals

Goal: The student will be able to demonstrate understanding of an expression in terms of its context and value.

Learning Scale:

4:

3: Proficient

2:

1:

Number Line Activity

• White cards

• Tan cards

• Blue cards

Middle Grades to High School Progression

• MACC.7.NS.1.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

• MACC.8.NS.1.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

• MACC.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

• MACC.912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context.*

– MACC.912.A-SSE.1.1a Interpret parts of an expression, such as terms, factors, and coefficients.*

– MACC.912.A-SSE.1.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.*

• MACC.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

Note on courses and transitions

Some of the highest priority content for college and career readiness comes from Grades 6-8.

Because important standards for college and career readiness are distributed across grades and courses, systems for evaluating college and career readiness should reach as far back in the standards as Grades 6-8.

Planning Reflection

1. How will you use the Common Core Standards for Mathematical Practices to inform instruction and lesson planning?

2. Identify the benefits of integrating the Common Core Standards for Mathematical Practices.

Digital Resources

• Common Core App• http://itunes.apple.com/us/app/common-co

re-standards/id439424555?mt=8

• www.masteryconnect.com

Resources• Common Core homepage( http://www.corestandards.org/)

• Progressions(http://ime.math.arizona.edu/progressions/)

• Illustrative Mathematics Project(http://illustrativemathematics.org)

• William McCallum’s blog, Tools for the Common Core,(http://commoncoretools.wordpress.com)

• Institute for Mathematics & Education(http://ime.math.arizona.edu/commoncore/)

• Mathematics Practices and includes video clips of the practices(http://www.insidemathematics.org/index.php/common-core-standards)

• video clips that align with the common core(https://www.teachingchannel.org/)