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Common Core Mathematics Scope and Sequence State-wide Conference Christina Foran and Rebecca Candino, TSD

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Common Core Mathematics. Scope and Sequence State-wide Conference Christina Foran and Rebecca Candino , TSD. Introductions. Christina Foran [email protected] Website: metateacher.net Rebecca Candino [email protected] Blog: rcandino.edublogs.org - PowerPoint PPT Presentation

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Page 1: Common Core Mathematics

Common Core Mathematics

Scope and Sequence

State-wide Conference

Christina Foran and Rebecca Candino, TSD

Page 2: Common Core Mathematics

IntroductionsChristina Foran

[email protected]

Website: metateacher.net

Rebecca Candino

[email protected]

Blog: rcandino.edublogs.org

Core Math Wiki: metateacher.net/coremath

Page 3: Common Core Mathematics

AgendaOverview of the Content Standards

Using the Common Core Navigator to develop standards-based IEP and differentiated learning ladders

Overview of the Mathematical Practices

Selecting and modifying tasks for Constructed Response Assessment practice

Page 4: Common Core Mathematics

Domains across Grade LevelIllustrativeMathematics.org

Page 5: Common Core Mathematics

The Common Core Navigator

Standards organized by topics called Learning Pathways

Standards organized developmentally across grade levels

How to Use:

Select your topic from the table of contents.

Consider the grade-level standards.

Drill down to your student’s level.

Go even farther back with previous learning pathways.

Page 6: Common Core Mathematics

Standards-Based IEPs

Freshman algebra student with a 1.5 grade level equivalency

GRADE LEVEL STANDARD: A-CED.1

“Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.”

GOAL: The student will use equations in one variable to solve problems.

LEARNING PATHWAYS:

Concepts of Equality and Equations

Equations and Inequalities

Page 7: Common Core Mathematics

Standards-Based IEPsOBJECTIVES:

Determine the unknown whole number in an addition or subtraction equation (1.OA.8).

Determine the unknown whole number in a multiplication or division equation (3.OA.4)

Represent two-step word problems in four operations using equations with a letter standing for the unknown quantity (3.OA.8).

Apply properties of operations, including the distributive property, to generate equivalent expressions (6.EE.3)

Solve problems by writing and solving equations in the form of x+p=q and px=q with nonnegative rational numbers (6.EE.7).

Solve word problems leading to equations in the form of px+q=r and p(x+q)=r with rational numbers (7.EE.4).

Page 8: Common Core Mathematics

Standards-Based IEPs

Third-grade student on a 1st grade level

GRADE LEVEL STANDARD: 3.OA.8

“Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding.”

GOAL: The student will represent two-step word problems in four operations using equations with a letter standing for the unknown quantity.

LEARNING PATHWAYS:

Concepts of Equality and Equations

Page 9: Common Core Mathematics

Standards-Based IEPs

OBJECTIVES:• Apply commutative and associative

properties of operations as strategies to add and subtract (1.OA.3).

• Understand the meaning of the equal sign (1.OA.7).

• Determine if equations involving addition and subtraction are true or false (1.OA.7).

• Determine the unknown whole number in an addition or subtraction equation (1.OA.8).

• Determine the unknown whole number in a multiplication or division equation (3.OA.4)

Page 10: Common Core Mathematics

Standards-Based IEPs

Third-grade student on a 1st grade level

GRADE LEVEL STANDARD: 3.OA.3

“Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.”

GOAL: The student will multiply and divide within 100 to solve problems.

LEARNING PATHWAYS:

Basic Multiplication and Division

Counting

Page 11: Common Core Mathematics

Standards-Based IEPsOBJECTIVES:

• Count to 120, starting at any number less than 120 (1.NBT.1).

• Skip count by 5s, 10s, and 100s (2.NBT.2).• Use addition to find the total number of objects arranged in

a rectangular array with up to 5 rows and 5 columns (2.OA.4).

• Interpret products of whole numbers as groups of objects (3.OA.1)

• Interpret whole-number quotients of whole numbers as being partitioned into equal shares (3.OA.2).

• Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities by using drawings and equations (3.OA.3).

• Fluently multiply and divide within 100, using strategies such as the relationship between multiplication or division or the properties of operations (3.OA.7).

Page 12: Common Core Mathematics

Differentiated Learning LaddersWhat are learning ladders?

Lists of prerequisite skills to build up to a learning objective

Stated in positive, student-friendly language.

Sample questions from each learning level could be used to make a pre- and post-assessment.

Help teachers differentiate instruction.

Help the students understand what they should be learning and lets them keep track of their progress toward the learning goal.

Page 13: Common Core Mathematics

Differentiated Learning Ladders

Lesson Topic: Dividing Fractions by Fractions

Class: 6th grade with most students on 3rd-5th grade level and a couple on a first grade level

Learning Pathways:

Dividing Fractions

Multiplying Fractions

Representing Fractions

Page 14: Common Core Mathematics

Differentiated Learning Ladders

I can divide fractions by fractions (6.NS.1).I can divide whole numbers by fractions and fractions by whole numbers

(5.NF.7).

I can multiply fractions by fractions (5.NS.4).

I can draw rectangular arrays to model multiplication of fractions (5.NF.4).

I can draw rectangular arrays to model multiplication problems (4.NBT.5).

I can multiply fractions by whole numbers (4.NS.4).

I can represent fractions as copies of the unit fraction (3.NF.1)

I can draw unit fractions by dividing a shape into equal parts (3.G.2).

I can draw thirds, fourths, and halves (2.G.3, 1.G.3).

Page 15: Common Core Mathematics

Task and Assessment Resources

TNCore.org

parcconline.org

MasteryConnect.com

IllustrativeMathematics.org by Bill McCallum

InsideMathematics.org

Mathematics Assessment Project - map.mathshell.org

teachingchannel.org

Page 16: Common Core Mathematics

MasteryConnect.com

Page 17: Common Core Mathematics

InsideMathematics.org

Page 18: Common Core Mathematics

map.mathshell.org

Page 19: Common Core Mathematics

IllustrativeMathematics.org

Page 20: Common Core Mathematics

CCSS for Mathematical Practice

• Based on NCTM Process Standards and the National Research Council Adding it Up: Helping

Children Learn Mathematics

• Equal emphasis on conceptual understanding and procedural fluency

• Seeing mathematics as “sensible, useful, and worthwhile” while believing in one’s own skill and abilities

• The “8 habits of highly successful problem solvers”

Common Core State Standards, NGA Center/CCSS), 2010

Page 21: Common Core Mathematics

CCSS for 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.

Common Core State Standards for Mathematics, 2010, NGA Center/CCSSO

Page 22: Common Core Mathematics

Selecting and Modifying

High Level Math Tasks

Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it… [Tasks] are central to students’ learning, shaping not only their opportunity to learn, but their view of the subject matter.

Adding it Up, National Research Council, 2001, p. 335

Page 23: Common Core Mathematics

The Importance of High Level Instructional Tasks:

“The Hook”

Page 24: Common Core Mathematics

How Are Math Tasks Categorized?

…all tasks are not created equal−different tasksrequire different levels and kinds of student thinking.

The Mathematical Task Analysis Guide

Stein M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematicsinstruction: A casebook for professional development, p. 3. New York: Teachers College Press

Low –level Tasks High-Level Tasks

•Memorization

•Procedures without Connections

•Procedures with Connections

•Doing Mathematics

Page 25: Common Core Mathematics

Examples of Different Levels of Tasks

Memorization Procedures With Connections

Procedures Without Connections

Doing Mathematics

Page 26: Common Core Mathematics

Instructional Task Modification• Students create real-world stories for “naked number”

problems.

• Include a prompt that asks students to represent the information another way and to write about any “noticings” or “wonderings” about a math concept.

• Eliminate too much scaffolding.

• Include a prompt that asks students to notice a pattern or make a conjecture and test that conjecture.

• Select numbers carefully to prevent use of rote memorization in responses.

• Begin instruction of a new concept with a high level task before students have memorized rules and/or procedures.

Learning Research and Development Center, University of Pittsburgh, 2012

Page 27: Common Core Mathematics

Differentiating the Instructional Task

• Use the Common Core Navigator to “drill down”

Grade Level Standard: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (A-SSE.3).

HSA-SSE.B.3 HSA-SSE.B.3 A-SSE.3

“Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement

quantities by using drawings and equations (3.OA.3).”

• Questioning techniquesAssessing and Advancing Questions

Page 28: Common Core Mathematics

Growth Occurs in the Struggle

• Allow students to “grapple” with high level tasks

• The role of the teacher is to facilitate thinking and discussion

• Be prepared to pull out of the task to teach prerequisite skills, then dive back in.

• Practice, practice, practice

Page 29: Common Core Mathematics

Intertwined Strands of Proficiency

Conceptual Understanding Procedural Fluency

Common Core Content Standards

Common Core Mathematical Practices

Adding It Up, National Research Council, 2001

Page 30: Common Core Mathematics

Thank You!!