Crossing the BridgeCrossing the Bridge

Training #3Horizontal Alignment

Secondary Mathematics

“In schools across the state, there has been a proliferation of course titles and they often fail to communicate their contents clearly. With the implementation of the Common Core State Standards for Mathematics, there should be one common system for naming courses to help parents understand, monitor, and advocate for the needs of their children.” (Confrey, Nguyen, and Lee, A Proposal for a Unified Common Core Mathematics in North Carolina, 2011)

3

Middle School Mathematics Sequence

Fifth Grade Math

Fifth Grade Math

Common Core Math 6

Common Core Math 6

Common Core Math 7

Common Core Math 7

Common Core Math 8

Common Core Math 8

Common Core

Math 6 PLUS

Common Core

Math 6 PLUS

Common Core

Math 7 PLUS

Common Core

Math 7 PLUS

CommonCore

Math I (High

School Credit)

CommonCore

Math I (High

School Credit)

Common Core

Math IIHonors

Common Core

Math IIHonors

Common Core

Math I

Common Core

Math I

Common Core

Math IIIHonors

Common Core

Math IIIHonors

Common Core

Math II

Common Core

Math II

Common Core

Math III

Common Core

Math III

Course Sequence (Phase-In Implementation) Course Sequence (Phase-In Implementation) for 2012-2013 and beyondfor 2012-2013 and beyond

2011-2012 2012-2013 2013-2014 2014-2015 2015-2016

SCOS Grade 8 (2003) Common Core Mathematics I

Common Core Mathematics II

Common Core Mathematics III

4th Mathematics Course

Assessment Grade 8 EOG NC Mathematics I ACT PLAN SBAC/ACT None

SCOS Algebra I (2003) Geometry (2003) Algebra II 4th Mathematics Course

5th Mathematics Course

Assessment Algebra I EOC Field Testing for NC

Mathematics I

None ACT PLAN SBAC/ACT None

SCOS Geometry (2003) Algebra II (2003) 4th Mathematics Course

5th Mathematics Course +

Univ/CC Course *+

Assessment None None ACT PLAN SBAC/ACT None

SCOS Algebra II (2003) 4th Mathematics Course

5th Mathematics Course +

Univ/CC Course*+ Univ/CC Course*+

Assessment None None ACT PLAN None None

4

*Univ/CC indicates courses taken at a university or community college.SBAC indicates national assessments developed by Smarter Balanced Assessment Consortium.The ACT PLAN is given to all 10th graders and the ACT is given to all 11th graders regardless of the course enrollment.Field testing of CCSS Mathematics I is only for samples of students across the state.+Optional

Course Sequence (Phase-In Implementation) Course Sequence (Phase-In Implementation) for 2012-2013 and beyondfor 2012-2013 and beyond

2011-2012 2012-2013 2013-2014 2014-2015 2015-2016

8th Grade Student Grade 8 (2003) Common Core Mathematics I

Common Core Mathematics II

Common Core Mathematics III

4th Mathematics Course

Assessment Grade 8 EOG NC Mathematics I ACT PLAN SBAC/ACT None

9th Grade Student Algebra I (2003) Geometry (2003) Algebra II 4th Mathematics Course

Assessment Algebra I EOC Field Testing for NC

Mathematics I

None ACT PLAN SBAC/ACT

10th Grade Student Geometry (2003) Algebra II (2003) 4th Mathematics Course

Assessment None None ACT PLAN

11th Grade Student Algebra II (2003) 4th Mathematics Course

Assessment None None

5

*Univ/CC indicates courses taken at a university or community college.SBAC indicates national assessments developed by Smarter Balanced Assessment Consortium.The ACT PLAN is given to all 10th graders and the ACT is given to all 11th graders regardless of the course enrollment.Field testing of CCSS Mathematics I is only for samples of students across the state.+Optional

Webb’s Webb’s Depth of Depth of KnowledgeKnowledge

Webb’s Depth of KnowledgeWebb’s Depth of Knowledge

Webb’s DOK …1. focuses on the cognitive demand required to

successfully complete an assessment/task.2. focuses on the context of the “verb” 3. focuses on the depth of thought required

Webb’s Depth of KnowledgeWebb’s Depth of KnowledgeLevel 1 RecallRecall of a fact, information or procedureLevel 2 Skill/ConceptUse information or conceptual knowledge, two or moresteps, etc.Level 3 Strategic ThinkingRequires reasoning, developing a plan or sequence ofsteps, some complexity, more than one possible answerLevel 4 Extended ThinkingRequires an investigation, time to think and processmultiple conditions of the problem

Webb’s Depth of KnowledgeWebb’s Depth of KnowledgeActivity #1- Pick a concept for your grade level and come up

with an activity for each level of DOK.

Level 1 Recall- Draw, identify, list, recall, use, memorize, calculate, define, state, label, quote, match, measure, illustrate

Level 2 Skill/Concept- compare, make observations, predict, estimate, graph, sketch, solve, show, interpret, modify

Level 3 Strategic Thinking- develop a logical argument, assess, investigate, hypothesize, use concepts to solve non-routine problems, formulate, appraise, differentiate, draw conclusions

Level 4 Extended Thinking- analyze, apply concepts, compose, connect, create, critique, defend, design, evaluate, judge, propose, prove, support, synthesize

Common Core FormatCommon Core FormatHigh School

Conceptual Category

Domain

Cluster

Standards

K-8

Grade

Domain

Cluster

Standards

(No pre-K Common Core Standards)

Grade Level/Course OverviewGrade Level/Course Overview

Accessing Common Core DocumentsAccessing Common Core DocumentsActivity #2- Scavenger HuntActivity #2- Scavenger Hunt

Common Core State Standards http://www.corestandards.org/Home Page• Background and research availableThe Standards (upper right hand corner)• Appendices• Standards PDF documents

Mathematics | Grade 6Mathematics | Grade 6In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and

using concepts of ratio and rate to solve problems

(2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers

(3) writing, interpreting, and using expressions and equations (4)developing understanding of statistical thinking.

Mathematics | Grade 7Mathematics | Grade 7In Grade 7, instructional time should focus on four critical areas:

(1)developing understanding of and applying proportional relationships

(2) developing understanding of operations with rational numbers and working with expressions and linear equations

(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume

(4) drawing inferences about populations based on samples

Mathematics | Grade 8Mathematics | Grade 8In Grade 8, instructional time should focus on three critical areas:

(1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations

(2) grasping the concept of a function and using functions to describe quantitative relationships

(3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the

Pythagorean Theorem.

ACRE Website AccessACRE Website AccessACRE- NC Common Core Instructional

Support Tools

http://www.ncpublicschools.org/acre/standards/common-core-tools/#crela

• Unpacking Standards

• Crosswalks

Activity #3- Crosswalks

Steps:1. Examine your grade level crosswalk document2. On the outline in your e-packet list the following:

• What is new to my curriculum• What is no longer in my curriculum• How do I plan to gather resources for new

material

New to 6th Grade:• Unit rate (6.RP.3b)• Measurement unit conversions (6.RP 3d)• Number line – opposites and absolute value (6.NS.6a, 6.NS.7c)• Vertical and horizontal distances on the coordinate plane (6.NS.8)• Distributive property and factoring (6.EE.3)• Introduction of independent and dependent variables (6.NS.9)• Volume of right rectangular prisms with fractional edges (6.G.2)• Surface area with nets (only triangle and rectangle faces) (6.G.4)• Dot plots, histograms, box plots (6.SP.4)• Statistical variability (M.A.D. and Interquartile Range) (6.G.5c)Moved from 6th Grade:• Multiplication of fractions (moved to 5th grade)• Scientific notation (moved to 8th grade)• Transformations (moved to 8th grade)• Area and circumference of circles (moved to 7th grade)• Probability (moved to 7th grade)• Two-step equations (moved to 7th grade)• Solving one- and two-step inequalities (moved to 7th grade)

6th Grade Notes:• Topics may appear to be similar between the CCSS and the 2003 NCSCOS; however, the CCSSmay be presented at a higher cognitive demand.• Equivalent fractions, decimals and percents are in 6th grade but as conceptual

representations (see 6.RP.2c). Use of the number line (building on elementary foundations) is also encouraged.

• For more detailed information, see the crosswalks.• 6.NS. 2 is the final check for student understanding of place value.

Instructional considerations for CCSS implementation in 2012 – 2013:

• Multiplication of fractions (reference 5.NF.3, 5.NF.4a, 5.NF.4b, 5.NF.5a, 5.NF.5b, 5.NF.6)• Division of whole number by unit fractions and division of unit fractions by whole numbers (reference 5.NF.7a, 5.NF.7b, 5.NF.7c)• Multiplication and division of decimals (reference 5.NBT.7)• Volume with whole number (reference 5.MD.3, 5.MD.4, 5.MD.5)• Classification of two-dimensional figures based on their properties (reference 5.G.3, 5,G.4

New to 7th Grade:• Constant of proportionality (7.RP.2b)• Percent of error (7.RP.3)• Factoring to create equivalent expressions (7.EE.1)• Triangle side lengths (7.G.2)• Area and circumference of circles (7.G.4)• Angles (supplementary, complementary, vertical) (7. G.5)• Surface area and volume of pyramids (7.G.6)• Probability (7.SP.5 – 7.SP.8)

Moved from 7th Grade:• Similar and congruent polygons (moved to 8th grade)• Surface area and volume of cylinders (moved to 8th grade – volume only)• Creation of box plots and histograms (moved to 6th grade – 7th grade continues to

compare)• Linear relations and functions (y-intercept moved to 8th grade)• Views from 3-Dimensional figures (removed from CCSS)• Statistical measures (moved to 6th grade)

7th Grade Notes:• Topics may appear to be similar between the CCSS and the 2003 NCSCOS; however, the

CCSS may be presented at a higher cognitive demand.• Proportionality in 7th grade now includes identifying proportional relationships from

tables and graphs; writing equations to represent proportional relationships.• Using a number line for rational number operations is emphasized in CCSS.

Instructional considerations for CCSS implementation in 2012 – 2013:• Work with ratio tables and relationships between tables, graphs and equations; focus on

the multiplicative relationship between and within ratios (6.RP.3a, 6.RP.3b)• Unit conversions within systems (6.RP.3d)• Opposites and absolute value (6.NS.6a, 6.NS.7c)• Distributive property with area models and factoring (6.EE.3) – prerequisite to 7.EE.1• Volume of rectangular prisms (6.G.2) and surface area (6.G.4) – prerequisite to 7.G.6• Mean Absolute Deviation (6.SP.5c) – prerequisite to 7.SP.3 and foundational to standard

deviation in Math One

New to 8th Grade:• Integer exponents with numerical bases (8.EE.1)• Scientific notation, including multiplication and division (8.EE.3 and 8.EE.4)• Unit rate as slope (8.EE.5)• Qualitative graphing (8.F.5)• Transformations (8.G.1 and 8.G.3)• Congruent and similar figures (characterized through transformations) (8.G.2 and 8.G.4)• Angles (exterior angles, parallel cut by transversal, angle-angle criterion) (8.G.5)• Finding diagonal distances on a coordinate plane using the Pythagorean Theorem (8.G.8)• Volume of cones, cylinders and spheres (8.G.9)• Two-way tables (8.SP.4)Moved from 8th Grade:• Indirect measurement (embedded throughout)• Linear inequalities (moved to high school)• Effect of dimension changes (moved to high school)• Misuses of data (embedded throughout)• Function notation (moved to high school)• Point-slope form (moved to high school) and standard form of a linear equation (not in

CCSS)

8th Grade Notes:• Topics may appear to be similar between the CCSS and the 2003 NCSCOS; however, the

CCSS may be presented at a higher cognitive demand.

Instructional considerations for CCSS implementation in 2012 – 2013:• Solving proportions with tables, graphs, equations (7.RP.2a, 7.RP.2b, 7.RP.2c, 7.RP.2d) prerequisite to 8.EE.5• Mean Absolute Deviation (6.SP.5c) – foundational to standard deviation in Math One• Identifying the conditions for lengths to make a triangle (7.G.2)• Supplementary, complementary, vertical and adjacent angles (7.G.5) – prerequisite to

8.G.5• Finding vertical and horizontal distances on the coordinate plane (6.NS.3) – foundational

to 8.G.8)

ResourcesResources

• Webb, Norman L. “Alignment, Depth of Knowledge, & Change.”,Wisconsin Center for Education Research, 2005.

Contact InformationContact InformationDawn Perks

Grayling B. Williams,

Secondary Mathematics Specialist

dawn.perks@dpsnc.net

grayling.williams@dpsnc.net (919) 560-2000

(Ext. 21314-Grayling)

(Ext. 21315-Dawn)