transition from oaks to smarter balanced assessment...only ccss content is assessed by smarter...

from OAKS to Smarter Balanced Assessment

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Oregon Department of Education Office of Assessment & Accountability

Transition from OAKS to Smarter Balanced Assessment

Table of Contents (Click on the Part button to go directly to that section)

Movement of Content in Transition from Oregon Standards to CCSS These pages show how the content associated with the 2007/2009 Oregon Mathematics Content Standards will shift from each grade during the transition to the Common Core State Standards, by 2014‐2015.

Movement of Content in Transition from Oregon Standards to CCSS – All Grade Level Oregon Content after Transition to CCSS

These pages show the grades to which the 2007/2009 Oregon Mathematics Content Standards will shift in 2014‐2015, after the transition to the Common Core State Standards and the Smarter Balanced Assessment.

Math Content in the CCSS which is Substantially New to Oregon (No match or weak match to OR Standards at any grade)

For each grade, these pages show which CCSS standards introduce new content and/or rigor.

Overview of the Common Core State Standards and the Smarter Balanced Assessment System

Part 1

Part 2

Part 3

Part 4

Oregon Department of Education Office of Assessment & Accountability

1 Oregon Department of Education Office of Assessment & Accountability

Transition from OAKS to Smarter Balanced Assessment OAKS will be assessing the 2007/2009 Oregon Mathematics Content Standards through the 2013-2014 school year. Oregon will begin using the Smarter Balanced common assessment of the Common Core State Standards for Mathematics in school year 2014-2015. The Smarter Balanced assessment for mathematics will be designed to assess students’ knowledge and skills relative to four Claims; and each claim will be anchored in different subsets of the Mathematical Practices and specific Targets, which are clusters of the Common Core Standards. So, students must have the opportunity to learn the content necessary for success on the OAKS assessment in the school years through 2013-2014 and the content associated with the CCSS by school year 2014-2015. Schools must begin integrating content associated with both the Oregon standards and the Common Core State Standards in the new grades to which the content will shift for the common assessment in 2014-2015. That is, new content or new classroom strategies related to current content will be introduced through the Common Core State Standards, and districts must thoughtfully integrate this new material and new strategies over the next three school years to have it all in place by 2014-2015. This will set Oregon students up for success with both the OAKS test and the Smarter Balanced common assessment during the transition.

The documents on the following pages are intended to give a high-level visual of three things: (1) the grades at which content associated with 2007/2009 Oregon standards will be assessed by Smarter Balanced in 2014-2015, (2) the 2007/2009 Oregon Mathematics Content Standards which will shift to each grade in 2014-2015, and (3) content associated with the CCSS that was judged to be new content or requiring new pedagogy for instruction in each grade after the transition. All information is based on the Crosswalk document, which was prepared by a panel of Oregon mathematics content experts; for more detail see http://www.ode.state.or.us/search/page/?id=3403. An Overview of the Common Core State Standards and the Smarter Balanced Assessment system follows in part 4.

K: tan 1: lt blue 2: green 3: pink 4: lt green 5: lavender 6: peach 7: blue 8: olive green H S: orange

Grade-level documents illustrate:

Part 1: Movement of content between grades in the transition from Oregon Content Standards to CCSS -- highlighting the grades to which content will shift, with excellent or partial alignment. Shaded boxes show the grade for which content of the 2007/2009 Oregon content standard will be assessed beginning in 2014-2015, with a different color for each grade of origin. See Table 1 (followed by explanations) and Table 2 on following pages for suggestions on Impact of transition of content on instruction of Cohorts.

Part 2: Final destination of content associated with 2007/2009 Oregon Content Standards following the transition in 2014-2015, with colors helping to track the grades of origin for the content. See Table 1 (followed by explanations) and Table 2 on following pages for suggestions on Impact of transition of content on instruction of Cohorts.

Part 3: Math Content in the CCSS which is substantially new to Oregon — grade-level documents show the Common Core State Standards which have a weak or no match to the current Oregon standards. Either the actual content is new for Oregon classrooms, or different instructional/assessment approaches are demanded to reach the CCSS level of rigor that will be assessed.

Through the transition to the CCSS, educators must ensure that students have the opportunity to learn content for which they will be held responsible beginning in 2014-2015. Because the CCSS are generally written to higher levels of rigor than the 2007/2009 Oregon content standards, new classroom practices may be needed to facilitate students as they reach higher levels of cognition and fully experience the Mathematical Practices while learning the mathematics content.

Planning backward then, by 2014-2015, all classrooms must be fully implementing the CCSS, and accountability will be measured through the Smarter Balanced common assessment. In 2013-2014, schools should be ensuring that students are prepared for the OAKS assessment, while having the CCSS content in place and possibly prepared for participating in the Smarter Balanced common assessment field test. In 2012-2013, while continuing to ensure the OR standards have been adequately addressed for accountability for OAKS, schools could begin integrating new content and rigor for the CCSS in the grades where they appear in the CCSS. In 2011-2012, schools should have been fully aware of the CCSS and started their very thoughtful planning for a gradual transition. This is an opportunity for schools to truly become learning communities and to move through the shifts required for successfully transitioning to the CCSS. (See http://www.ode.state.or.us/wma/teachlearn/commoncore/common-core-shifts-math.pdf.)

School Year 2011-2012 2012-2013 2013-2014 2014-2015 Assessment for Accountability Purposes OAKS OAKS OAKS Smarter Balanced for CCSS


Interpreting the Charts

OREGON STANDARD

Shaded Cells Show Grades in Which Oregon Content Will Be Found in the CCSS with Excellent or Partial Alignment K 1 2 3 4 5 6 7 8 HS

OR.5.2.5 Develop fluency with efficient procedures for dividing whole numbers and justify why the procedures work on the basis of place value and number properties.

OR.5.2.6 Determine the most appropriate form of the quotient and interpret the remainder in a problem situation.

OR.5.3.1 Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).

OR.5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms.

OR.5.3.3 Describe three‐dimensional shapes (triangular and‐ rectangular prisms, cube, triangular‐ and square‐based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as types of faces.

OR.5.3.4 Recognize volume as an attribute of three‐dimensional space.

Some general suggestions:

I. When content is assessed in the same grade: study the CCSS to ensure students engage with all content and rigor by 2013-14.

II When content is to be assessed in later grades: consider teaching the content from the Oregon standard at the current grade and teaching the additional content and rigor from CCSS standards in the higher grade in the same year, in 2013-14, or sooner; then teach only CCSS standards in 2014-15.

III When content is to be assessed in earlier grades: consider teaching CCSS and OR content at both grades in 2012-13, or at least by 2013-14, then only teach CCSS in the earlier grade thereafter.

IV When CCSS content is new to OR, begin integrating into classroom curriculum in 2012-13, reaching full implementation by 2014-15.

Further explanation with specific examples follows:

Content from 5.2.5 will be assessed in grades 4, 5, and 6.

All content from 5.2.6 moves to grade 4.

All content from 5.3.2 moves to grade 6.

All content from 5.3.4 remains in grade 5.


Table 1 Example : Impact of transition of content on instruction of Cohorts (Content at higher grade in CCSS)

Oregon content standard 5.3.2 will be addressed by Smarter Balanced Assessments in grade 6.

Oregon content standard 5.3.2: Find and justify relationships among the formulas for the areas of triangles and parallelograms.

Shading Instruction Assessment Professional Development

The 5.3.2 content should have been taught in the student’s previous grades.

The assessment may still address this content. Keep in mind possible skipped content from CCSS in later grades beginning with 2014-15.

6th grade teachers begin integrating CCSS content related to OR 5.3.2 that students did not learn in 5th grade. (5th grade teachers continue to teach 5.3.2 content).

CCSS content related to OR 5.3.2 not yet being assessed at 5th grade. OR 5.3.2 is assessed in 5th grade by OAKS in 2011-12 through 2013-14.

6th grade teachers integrate new content from CCSS related to OR 5.3.2, preparing to teach all of CCSS content in 2014-15.

5th grade teachers teach all of Oregon 5.3.2 content. (6th grade teachers integrate additional content and rigor from related CCSS standards).

5.3.2 will be assessed in 5th grade by OAKS in 2011-12 through 2013-14. (Related CCSS content is assessed in 6th grade by Smarter Balanced in 2014-15).

6th grade teachers implement integration of additional CCSS content related to OR 5.3.2.

5th and 6th grade teachers teach only CCSS content for their grade in 2014-2015.

Only CCSS content is assessed by Smarter Balanced in 2014-15.

5th and 6th Grade: In 2014-15, teach full breadth and depth of CCSS.

The content related to OR 5.3.2 is not yet assessed by OAKS or Smarter Balanced. The content will be assessed at later grades.

2011-12 OAKS

2012-13 OAKS

2013-14 OAKS

2014-15 Smarter Balanced

Grade Level

7 7 7 7

6 6 6 6

5 5 5 5

4 4 4 4

3 3 3 3


Table 2 Example 2: Impact of transition of content on instruction of Cohorts (Content at lower grade in CCSS).

Oregon standard 5.2.6 content will be addressed by Smarter Balanced assessment in 4th grade in 2014-2015.

Oregon 2007 Content Standard 5.2.6: Determine the most appropriate form of the quotient and interpret the remainder in a problem situation.

2011-12 OAKS

2012-13 OAKS

2013-14 OAKS

2014-15 Smarter Balanced

Grade Level

6 6 6 6

5 5 5 5

4 4 4 4

3 3 3 3

Shading Instruction Assessment Professional Development

The 5.2.6 content should have been taught in the student’s previous grades.

The assessment may still address this content. Keep in mind that students may not have been taught the content/rigor of CCSS in earlier grades beginning with 2014-15.

5th grade teachers teach all of Oregon 5.2.6 content; or 4rd grade teachers teach all of 5.2.6 in 2012-13 through 2013-14.

5.2.6 assessed in 5th grade by OAKS in 2011-2012 through 2013-2014. (Related CCSS content is assessed in 4rd grade by Smarter Balanced in 2014-15).

4th and 5th grade teachers ensure implementation of 5.2.6 in either 4th or 5th grade and integration of additional CCSS content related to OR 5.2.6 into 4th grade.

4th grade teachers begin teaching all CCSS content related to OR 5.2.6.

OR 5.2.6 will be assessed in 5th grade by OAKS in 2012-2014 – could be taught in 4rd grade along with all related CCSS content.

Consider teaching CCSS content related to OR 5.32.6 in both 4th and 5th grade in either 2012-13 or 2013-14, then teaching in 4th grade thereafter.

4th and 5th grade teachers teach only CCSS content for their grade in 2014-15.

Only CCSS content is assessed by Smarter Balanced in 2014-15.

4th and 5th Grade: In 2014-15, teach full breadth and depth of CCSS

The content related to OR 5.2.6 is not yet assessed by OAKS or Smarter Balanced. The content will be assessed at later grades.


Part 1

Movement of Content in

Transition from Oregon Standards to CCSS

These pages show how the content associated with the 2007/2009 Oregon Mathematics Content Standards will shift from each grade during the transition to the

Common Core State Standards, by 2014-2015.


Movement of Content in Transition from Oregon Standards to CCSS – Grade K

OREGON STANDARD

Shaded Cells Show Grades in Which Oregon Content Will Be Found in the CCSS with Excellent or Partial Alignment

K 1 2 3 4 5 6 7 8 HS

OR.K.1.1 Read and write whole numbers to 10.

OR.K.1.2 Connect numbers, including written numerals, to the quantities they represent, using various physical models and representations.

OR.K.1.3 Count forward by ones beginning with any number less than 30; count backward by ones beginning with any number 10 or less.

OR.K.1.4 Recognize the number of objects in a small set (such as the arrangements of dots on a number cube) without counting.

OR.K.1.5 Count objects in a set using one‐to‐one correspondence and produce sets of given sizes.

OR.K.1.6 Compare and order sets or numerals by using both cardinal and ordinal meanings.

OR.K.1.7 Model simple joining and separating situations and represent them with objects, pictures, and/or numerals.

OR.K.1.8 Choose, combine, and apply effective strategies for solving joining and separating problems.

OR.K.1.9 Identify, duplicate, and extend simple number patterns and sequential and growing patterns (e.g., patterns made with shapes).

Weak or No Match to CCSS

OR.K.2.1 Identify, name, and describe basic two‐dimensional shapes (e.g., square, circle, triangle, rectangle, regular hexagon) presented in a variety of ways (e.g., with different sizes or orientations).

OR.K.2.2 Identify, name, and describe basic three‐dimensional shapes (e.g., sphere, cube, and cylinder).


Movement of Content in Transition from Oregon Standards to CCSS – Grade K

OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS

OR.K.2.3 Use basic shapes and spatial reasoning to describe and model objects in their environment, and to construct more complex shapes.

OR.K.3.1 Identify the measurable attributes (e.g., length, weight) and non‐measurable attributes (e.g., color) of an object.

OR.K.3.2 Compare, sort, and order objects according to measurable (e.g., longest to shortest, lightest to heaviest) and non‐measurable (e.g., color, texture) attributes.

OR.K.3.3 Compare the lengths of two objects both directly (by comparing them with each other) and indirectly (by comparing both with a third object).


Movement of Content in Transition from Oregon Standards to CCSS – Grade 1

OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS

OR.1.1.1 Compare and order whole numbers to 100.

OR.1.1.2 Represent whole numbers on a number line, demonstrating an understanding of the sequential order of the counting numbers and their relative magnitudes.

OR.1.1.3 Count and group objects in tens and ones.

OR.1.1.4 Identify the number of tens and ones in whole numbers between 10 and 100, especially recognizing the numbers 10 to 19 as 1 group of ten and a particular number of ones.

OR.1.1.5 Determine the value of collections of pennies, nickels, and dimes.

OR.1.2.1 Model 'part‐whole,' 'adding to,' 'taking away from,' and 'comparing' situations to develop an understanding of the meanings of addition and subtraction.

OR.1.2.2 Develop and use efficient strategies for adding and subtracting whole numbers using a variety of models, including discrete objects, length‐based models (e.g., lengths of connecting cubes) and number lines.

OR.1.2.3 Apply with fluency sums to 10 and related subtraction facts.

OR.1.2.4 Use the concept of commutative [4 + 2 = 2 + 4], associative [(4 + 3) + 7 = 4 + (3 + 7)], and identity [0 + 3 = 3] properties of addition to solve problems involving basic facts.

OR.1.2.5 Relate addition and subtraction as inverse operations.

OR.1.2.6 Identify, create, extend, and supply a missing element in number patterns involving addition or subtraction by a single‐digit number.




OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS

OR.1.3.1 Describe geometric attributes of shapes (e.g., round, corners, sides) to determine how they are alike and different.

OR.1.3.2 Recognize and create shapes that are congruent or have symmetry.


OR.1.3.3 Compose and decompose shapes (e.g., cut a square into two right triangles and put two cubes together to make a rectangular prism), thus building an understanding of part‐whole relationships as well as the properties of the original and composite shapes.

OR.1.3.4 Recognize shapes when viewed from different perspectives and orientations.



OREGON STANDARD


OR.2.1.1 Write, compare, and order whole numbers to 1000.

OR.2.1.2 Understand and apply base‐ten numeration, and count in multiples of one, two, five, ten, and one hundred.

OR.2.1.3 Compose and decompose whole numbers less than one thousand by place value (e.g., 426 as 4 hundreds + 2 tens + 6 ones and 400 + 20 + 6).

OR.2.1.4 Use place value and properties of operations to find and use equivalent representations of numbers (such as 35 represented by 35 ones, 3 tens and 5 ones, or 2 tens and 15 ones).


OR.2.2.1 Apply, with fluency, sums to 20 and related subtraction facts.

OR.2.2.2 Solve multi‐digit whole number problems by applying various meanings (e.g., taking away, and comparing) and models (e.g., combining or separating sets, using number lines, and hundreds charts) of addition and subtraction.

OR.2.2.3 Develop fluency with efficient procedures for adding and subtracting multi‐digit whole numbers and understand why the procedures work on the basis of place value and number properties.

OR.2.2.4 Select and apply efficient methods to estimate sums and differences or calculate them mentally depending on the numbers and context involved.


OR.2.2.5 Determine the value of mixed collections of coins to $1.00.

OR.2.3.1 Determine length by finding the total number of equal‐length units that are placed end‐to‐end without gaps or overlaps.

OR.2.3.2 Apply concepts of partitioning (the mental activity of slicing the length of an object into equal‐sized units) and transitivity (e.g., if object A is longer than object B and object B is longer than object C, then object A is longer than object C).




OREGON STANDARD


OR.2.3.3 Demonstrate an understanding that using different measurement units will result in different numerical measurements for the same object.

OR.2.3.4 Explain the need for equal length units and the use of standard units of measure.


OR.2.3.5 Use rulers and other measurement tools to estimate and measure length in common units (e.g., centimeter and inch).

OR.2.3.6 Use the measurement process: choose an appropriate measurement unit, compare that unit to the object, and report the number of units.

OR.2.3.7 Demonstrate an understanding of time and use of time relationships (e.g., how many minutes in an hour, days in a week, and months in a year).


OR.2.3.8 Tell time in increments of five minutes using analog and digital clocks.



OREGON STANDARD


OR.3.1.1 Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line.

OR.3.1.2 Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole.

OR.3.1.3 Use fractions to represent numbers that are equal to, less than, or greater than one.

OR.3.1.4 Solve problems that involve comparing and ordering fractions by using models, benchmarks (0, ½, 1), or common numerators or denominators.

OR.3.1.5 Identify equivalent fractions using models, including the number line.

OR.3.1.6 Add common fractions with like denominators.

OR.3.2.1 Represent and apply the concept of multiplication as repeated addition.

OR.3.2.2 Represent and apply the concept of division as repeated subtraction and forming equal groups.

OR.3.2.3 Apply models of multiplication (e.g., equal‐sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems.

OR.3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.

OR.3.2.5 Apply the inverse relationship between multiplication and division (e.g., 5 x 6 = 30, 30 ÷ 6 = 5) and the relationship between multiples and factors.

OR.3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12, ...}, {1, 2, 4, 8, ...} ).



OREGON STANDARD


OR.3.2.7 Analyze frequency tables, bar graphs, picture graphs, and line plots; and use them to solve problems involving addition, subtraction, multiplication, and division.

OR.3.3.1 Identify right angles in two‐dimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute).

OR.3.3.2 Identify, describe, compare, analyze, and informally classify triangles by their sides and angles.

OR.3.3.3 Identify, describe, compare, analyze, and classify quadrilaterals (square, rectangle, parallelogram, rhombus, and trapezoid) by their sides and angles.

OR.3.3.4 Identify, describe, and compare pentagons, hexagons, and octagons by the number of sides or angles.

OR.3.3.5 Investigate and describe the results of decomposing, combining, and transforming polygons to make other polygons. Weak or No Match to CCSS

OR.3.3.6 Build, draw, and analyze two‐dimensional shapes to understand attributes and properties of two‐dimensional space.

OR.3.3.7 Determine an appropriate unit, tool, or strategy to find the perimeter of polygons.

OR.3.3.8 Use attributes and properties of two‐dimensional shapes to solve problems including applications involving parallel and perpendicular lines, congruence, symmetry, and perimeter.



OREGON STANDARD


OR.4.1.1 Extend the base‐ten system to read, write, and represent decimal numbers (to the hundredths) between 0 and 1, between 1 and 2, etc.

OR.4.1.2 Use models to connect and compare equivalent fractions and decimals.

OR.4.1.3 Determine decimal equivalents or approximations of common fractions.


OR.4.1.4 Compare and order fractions and decimals.

OR.4.1.5 Estimate decimal or fractional amounts in problem solving. Weak or No Match to CCSS

OR.4.1.6 Represent money amounts to $10.00 in dollars and cents, and apply to situations involving purchasing ability and making change.

OR.4.2.1 Apply with fluency multiplication facts to 10 times 10 and related division facts.

OR.4.2.2 Apply understanding of models for multiplication (e.g., equal‐sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive).

OR.4.2.3 Select and use appropriate estimation strategies for multiplication (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers.

OR.4.2.4 Develop and use accurate, efficient, and generalizable methods to multiply multi‐digit whole numbers.

OR.4.2.5 Develop fluency with efficient procedures for multiplying multi‐digit whole numbers and justify why the procedures work on the basis of place value and number properties.

OR.4.3.1 Recognize area as an attribute of two‐dimensional regions.



OREGON STANDARD


OR.4.3.2 Determine area by finding the total number of same‐sized units of area that cover a shape without gaps or overlaps.

OR.4.3.3 Recognize a square that is one unit on a side as the standard unit for measuring area.

OR.4.3.4 Determine the appropriate units, strategies, and tools to solving problems that involve estimating or measuring area.


OR.4.3.5 Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle.

OR.4.3.6 Find the areas of complex shapes that can be subdivided into rectangles.

OR.4.3.7 Solve problems involving perimeters and areas of rectangles and squares.

OR.4.3.8 Recognize that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas.



OREGON STANDARD


OR.5.1.1 Use fraction models to represent the addition and subtraction of fractions with unlike denominators.

OR.5.1.2 Use decimal models, place value, and number properties to add and subtract decimals (to the thousandths).

OR.5.1.3 Select and use appropriate strategies to estimate fraction and decimal sums and differences.


OR.5.1.4 Develop fluency with efficient procedures for adding and subtracting fractions and decimals and justify why the procedures work.

OR.5.1.5 Solve problems involving the addition and subtraction of fractions and decimals.

OR.5.1.6 Use ordered pairs on coordinate graphs to specify locations and describe paths.

OR.5.1.7 Construct and analyze double bar, line, and circle graphs to solve problems involving fractions and decimals.


OR.5.2.1 Apply understanding of models for division (e.g., equal‐sized groups, arrays, area models, equal intervals on the number line) and the relationship of division to multiplication to solve problems.

OR.5.2.2 Apply concepts of place value and the properties of operations to solve problems involving division.

OR.5.2.3 Select and use appropriate estimation strategies for division (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers.

OR.5.2.4 Develop and use accurate, efficient, and generalizable methods to find quotients for multi‐digit division problems.

OR.5.2.5 Develop fluency with efficient procedures for dividing whole numbers and justify why the procedures work on the basis of place value and number properties.



OREGON STANDARD


OR.5.2.6 Determine the most appropriate form of the quotient and interpret the remainder in a problem situation.

OR.5.3.1 Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).

OR.5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms.

OR.5.3.3 Describe three‐dimensional shapes (triangular and‐ rectangular prisms, cube, triangular‐ and square‐based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as types of faces.


OR.5.3.5 Determine volume by finding the total number of same‐sized units of volume that fill a three‐dimensional shape without gaps or overlaps.

OR.5.3.6 Recognize a cube that is one unit on an edge as the standard unit for measuring volume.

OR.5.3.7 Determine the appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume.

OR.5.3.8 Decompose three‐dimensional shapes and find surface areas and volumes of triangular and rectangular prisms.

OR.5.3.9 Identify and measure necessary attributes of shapes to use area, surface area, and volume formulas to solve problems (e.g., to find which of two gift boxes needs the most wrapping paper or has the greater volume?).



OREGON STANDARD


OR.6.1.1 Select and use appropriate strategies to estimate fraction and decimal products and quotients.


OR.6.1.2 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of fractions.

OR.6.1.3 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of decimals.

OR.6.1.4 Develop fluency with efficient procedures for multiplying and dividing fractions and decimals and justify why the procedures work.

OR.6.1.5 Apply the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and justify why they work.

OR.6.1.6 Apply the properties of operations to simplify calculations.

OR.6.1.7 Use the relationship between common decimals and fractions to solve problems including problems involving measurement.

OR.6.2.1 Develop, analyze, and apply the meaning of ratio, rate, and percent to solve problems.

OR.6.2.2 Determine decimal and percent equivalents for common fractions, including approximations.

OR.6.2.3 Understand the meaning of probability and represent probabilities as ratios, decimals, and percents. Weak or No Match to CCSS

OR.6.2.4 Determine simple probabilities, both experimental and theoretical.Weak or No Match to CCSS

OR.6.2.5 Develop the concept of pi as the ratio of the circumference of a circle to its diameter.



OREGON STANDARD


OR.6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols.

OR.6.3.2 Develop the meanings and uses of variables.

OR.6.3.3 Write, evaluate, and use expressions and formulas to solve problems.

OR.6.3.4 Identify and represent equivalent expressions (e.g., different ways to see a pattern).

OR.6.3.5 Represent, analyze, and determine relationships and patterns using tables, graphs, words and when possible, symbols.

OR.6.3.6 Recognize that the solutions of an equation are the values of the variables that make the equation true.

OR.6.3.7 Solve one‐step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation.



OREGON STANDARD


OR.7.1.1 Develop, analyze, and apply models (including everyday contexts), strategies, and procedures to compute with integers, with an emphasis on negative integers.

OR.7.1.2 Extend knowledge of integers and positive rational numbers to solve problems involving negative rational numbers.

OR.7.1.3 Develop and use strategies to estimate the result of rational number computations and justify the reasonableness of results.

OR.7.1.4 Apply properties of rational numbers and algebra to write and solve linear equations in one variable.

OR.7.2.1 Represent proportional relationships with coordinate graphs and tables, and identify unit rate as the slope of the related line.

OR.7.2.2 Apply ratio and proportionality to solve problems, including percent and simple probability.

OR.7.2.3 Use coordinate graphs, tables, and equations to distinguish proportional relationships from other relationships, including inverse proportionality.

OR.7.2.4 Develop and use scale factors and proportional relationships to solve problems, including similarity and congruence.

OR.7.2.5 Convert among different units of measurement to solve problems, including rates.

OR.7.2.6 Apply scale factor to analyze how the change in one measure (e.g., length, area, volume) affects another.


OR.7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of circles.

OR.7.3.2 Know common estimates of pi and use these values to estimate and calculate the circumference and area of a circle.




OREGON STANDARD


OR.7.3.3 Solve problems involving areas and circumferences of circles.

OR.7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and cylinders, and volume of pyramids, cylinders, and cones.

OR.7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area.

OR.7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of pyramids, cylinders, and cones.

OR.7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing them into basic shapes.



OREGON STANDARD


OR.8.1.1 Translate among contextual, verbal, tabular, graphical, and algebraic representations of linear functions.

OR.8.1.2 Determine the slope of a line and understand that it is a constant rate of change.

OR.8.1.3 Identify and interpret the properties (i.e. slope, intercepts, continuity, and discreteness) of linear relationships as they are shown in the different representations and recognize proportional relationships (y/x = k or y = kx) as a special case.

OR.8.1.4 Use linear functions and equations to represent, analyze and solve problems, and to make predictions and inferences.

OR.8.1.5 Relate systems of two linear equations in two variables and their solutions to pairs of lines that are intersecting, parallel, or the same line.

OR.8.1.6 Use informal strategies (e.g., graphs or tables) to solve problems involving systems of linear equations in two variables.

OR.8.2.1 Organize and display data (e.g., histograms, box‐and‐whisker plots, scatter plots) to pose and answer questions; and justify the reasonableness of the choice of display.

OR.8.2.2 Use measures of center and spread to summarize and compare data sets.

OR.8.2.3 Interpret and analyze displays of data and descriptive statistics.

OR.8.2.4 Compare descriptive statistics and evaluate how changes in data affect those statistics.


OR.8.2.5 Describe the strengths and limitations of a particular statistical measure, and justify or critique its use in a given situation.


OR.8.2.6 Use sample data to make predictions regarding a population.



OREGON STANDARD


OR.8.2.7 Identify claims based on statistical data and evaluate the reasonableness of those claims.

OR.8.2.8 Use data to estimate the likelihood of future events and evaluate the reasonableness of predictions.

OR.8.3.1 Use properties of parallel lines, transversals, and angles to find missing sides and angles, and to solve problems including determining similarity or congruence of triangles.

OR.8.3.2 Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles.

OR.8.3.3 Use models and logical arguments to show that the sum of the angles of any quadrilateral is 360 degrees, and apply this fact to find unknown angles.


OR.8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths.

OR.8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2‐ and 3‐dimensional contexts, including distances on coordinate graphs.

OR.8.3.6 Use models and referents to explore and estimate square roots.


Movement of Content in Transition from Oregon Standards to CCSS – High School

OREGON STANDARD


OR.11.1A.1 Compare, order, and locate real numbers on a number line.

OR.11.1A.2 Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers and variables that may also include absolute value, integer exponents, square roots, pi, and/or scientific notation.

OR.11.1A.3 Express square roots in equivalent radical form and their decimal approximations when appropriate.

OR.11.1A.4 Develop, identify, and/or justify equivalent algebraic expressions, equations, and inequalities using the properties of exponents, equality and inequality, as well as the commutative, associative, inverse, identity, and distributive properties.

OR.11.1A.5 Factor quadratic expressions limited to factoring common monomial terms, perfect‐square trinomials, differences of squares, and quadratics of the form x^2 + bx + c that factor over the integers.

OR.11.2A.1 Identify, construct, extend, and analyze linear patterns and functional relationships that are expressed contextually, numerically, algebraically, graphically, in tables, or using geometric figures.

OR.11.2A.2 Given a rule, a context, two points, a table of values, a graph, or a linear equation in either slope intercept or standard form, identify the slope of the line, determine the x and/or y intercept(s), and interpret the meaning of each.

OR.11.2A.3 Determine the equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, determine an equation of a new line, parallel or perpendicular to a given line, through a given point.

OR.11.2A.4 Fluently convert among representations of linear relationships given in the form of a graph of a line, a table of values, or an equation of a line in slope‐intercept and standard form.

OR.11.2A.5 Given a linear function, interpret and analyze the relationship between the independent and dependent variables. Solve for x given f(x) or solve for f(x) given x.



OREGON STANDARD


OR.11.2A.6 Analyze how changing the parameters transforms the graph of f(x)=mx + b.

OR.11.2A.7 Write, use, and solve linear equations and inequalities using graphical and symbolic methods with one or two variables. Represent solutions on a coordinate graph or number line.

OR.11.2A.8 Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically.

OR.11.3A.1 Given a quadratic or exponential function, identify or determine a corresponding table or graph.

OR.11.3A.2 Given a table or graph that represents a quadratic or exponential function, extend the pattern to make predictions.


OR.11.3A.3 Compare the characteristics of and distinguish among linear, quadratic, and exponential functions that are expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and interpret the domain and range of each as it applies to a given context.

OR.11.3A.4 Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain.

OR.11.3A.5 Given a quadratic equation of the form x^2+ bx + c = 0 with integral roots, determine and interpret the roots, the vertex of the parabola that is the graph of y = x^2 + bx +c, and an equation of its axis of symmetry graphically and algebraically.

OR.11.1G.1 Identify, apply, and analyze angle relationships among two or more lines and a transversal to determine if lines are parallel, perpendicular, or neither.

OR.11.1G.2 Apply theorems, properties, and definitions to determine, identify, and justify congruency or similarity of triangles and to classify quadrilaterals.

OR.11.1G.3 Apply theorems of corresponding parts of congruent and similar figures to determine missing sides and angles of polygons.



OREGON STANDARD


OR.11.1G.4 Use trigonometric ratios (sine, cosine and tangent) and the Pythagorean Theorem to solve for unknown lengths in right triangles.

OR.11.1G.5 Determine the missing dimensions, angles, or area of regular polygons, quadrilaterals, triangles, circles, composite shapes, and shaded regions.

OR.11.1G.6 Determine if three given lengths form a triangle. If the given lengths form a triangle, classify it as acute, right, or obtuse.


OR.11.1G.7 In problems involving circles, apply theorems and properties of chords, tangents, and angles; and theorems and formulas of arcs and sectors.

OR.11.2G.1 Identify, classify, model, sketch, and label representations of three‐dimensional objects from nets and from different perspectives.

OR.11.2G.2 Identify and apply formulas for surface area and volume of spheres; right solids, including rectangular prisms and pyramids; cones; and cylinders; and compositions thereof. Solve related context‐based problems.

OR.11.2G.3 Identify and apply formulas to solve for the missing dimensions of spheres and right solids, including rectangular prisms and pyramids, cones, and cylinders, both numerically and symbolically.

OR.11.3G.1 Recognize and identify line and rotational symmetry of two‐dimensional figures.

OR.11.3G.2 Identify and perform single and composite transformations of geometric figures in a plane, including translations, origin‐centered dilations, reflections across either axis or y = ±x, and rotations about the origin in multiples of 90°.

OR.11.3G.3 Apply a scale factor to determine similar two‐ and three‐dimensional figures, are similar. Compare and compute their respective areas and volumes of similar figures.

OR.11.3G.4 Apply slope, distance, and midpoint formulas to solve problems in a coordinate plane.



OREGON STANDARD


OR.11.1S.1 Given a context, determine appropriate survey methods, analyze the strengths and limitations of a particular survey, observational study, experiment, or simulation, and the display of its data.

OR.11.1S.2 Evaluate data‐based reports by considering the source of the data, the design of the study, and the way the data was analyzed and displayed.

OR.11.1S.3 Compare and draw conclusions about two or more data sets using graphical displays or central tendencies and range.

OR.11.1S.4 Use or construct a scatter plot for a given data set, determine whether there is a (n) linear, quadratic, exponential, or no trend. If linear, determine if there is a positive or negative correlation among the data; and, if appropriate, sketch a line of best fit, and use it to make predictions.

OR.11.1S.5 Construct, analyze, and interpret tables, scatter plots, frequency distributions, and histograms of data sets.

OR.11.2S.1 Identify, analyze, and use experimental and theoretical probability to estimate and calculate the probability of simple events.

OR.11.2S.2 Determine the sample space of a probability experiment.

OR.11.2S.3 Compute and interpret probabilities for independent, dependent, complementary, and compound events using various methods (e.g., diagrams, tables, area models, and counting techniques).


Part 2

Movement of Content in Transition from Oregon Standards to CCSS – All Grade Level Oregon Content after Transition to CCSS

These pages show the grades to which the 2007/2009 Oregon Mathematics Content

Standards will shift in 2014-2015, after the transition to the Common Core State Standards and the Smarter Balanced Assessment


Movement of Content in Transition from Oregon Standards to CCSS – All Oregon Content Assigned to Kindergarten in CCSS

OREGON STANDARD Shaded Cells Show Grades in Which Oregon Content Will Be Found in the CCSS with Excellent or Partial Alignment K 1 2 3 4 5 6 7 8 HS

OR.K.1.1 Read and write whole numbers to 10.

OR.K.1.2 Connect numbers, including written numerals, to the quantities they represent, using various physical models and representations.

OR.K.1.3 Count forward by ones beginning with any number less than 30; count backward by ones beginning with any number 10 or less.

OR.K.1.4 Recognize the number of objects in a small set (such as the arrangements of dots on a number cube) without counting.

OR.K.1.5 Count objects in a set using one‐to‐one correspondence and produce sets of given sizes.

OR.K.1.6 Compare and order sets or numerals by using both cardinal and ordinal meanings.

OR.K.1.7 Model simple joining and separating situations and represent them with objects, pictures, and/or numerals.

OR.K.1.8 Choose, combine, and apply effective strategies for solving joining and separating problems.

OR.K.2.1 Identify, name, and describe basic two‐dimensional shapes (e.g., square, circle, triangle, rectangle, regular hexagon) presented in a variety of ways (e.g., with different sizes or orientations).

OR.K.2.2 Identify, name, and describe basic three‐dimensional shapes (e.g., sphere, cube, and cylinder).

OR.K.2.3 Use basic shapes and spatial reasoning to describe and model objects in their environment, and to construct more complex shapes.




OR.K.3.1 Identify the measurable attributes (e.g., length, weight) and non‐measurable attributes (e.g., color) of an object.

OR.K.3.2 Compare, sort, and order objects according to measurable (e.g., longest to shortest, lightest to heaviest) and non‐measurable (e.g., color, texture) attributes.

OR.K.3.3 Compare the lengths of two objects both directly (by comparing them with each other) and indirectly (by comparing both with a third object).



OR.1.1.4 Identify the number of tens and ones in whole numbers between 10 and 100, especially recognizing the numbers 10 to 19 as 1 group of ten and a particular number of ones.

OR.1.2.1 Model 'part‐whole,' 'adding to,' 'taking away from,' and 'comparing' situations to develop an understanding of the meanings of addition and subtraction.



OR.1.3.4 Recognize shapes when viewed from different perspectives and orientations.

OR.3.3.4 Identify, describe, and compare pentagons, hexagons, and octagons by the number of sides or angles.




OR.5.3.3 Describe three‐dimensional shapes (triangular and‐ rectangular

prisms, cube, triangular‐ and square‐based pyramids, cylinder, cone, and

sphere) by the number of edges, faces, and/or vertices as well as types of

faces.


Movement of Content in Transition from Oregon Standards to CCSS – All Oregon Content Assigned to Grade 1 in CCSS

OREGON STANDARD

Colors in Shaded Cells Show Grades from which Oregon Content Originated with Excellent or Partial Alignment to CCSS Content for This Grade

K 1 2 3 4 5 6 7 8 HS OR.K.3.3 Compare the lengths of two objects both directly (by comparing

them with each other) and indirectly (by comparing both with a third object).



OR.1.1.4 Identify the number of tens and ones in whole numbers between 10 and 100, especially recognizing the numbers 10 to 19 as 1 group of ten and a

particular number of ones.

OR.1.2.1 Model 'part‐whole,' 'adding to,' 'taking away from,' and 'comparing' situations to develop an understanding of the meanings of addition and

subtraction.


OR.1.2.3 Apply with fluency sums to 10 and related subtraction facts.

OR.1.2.4 Use the concept of commutative [4 + 2 = 2 + 4], associative [(4 + 3) +

7 = 4 + (3 + 7)], and identity [0 + 3 = 3] properties of addition to solve

problems involving basic facts.

OR.1.2.5 Relate addition and subtraction as inverse operations.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS


OR.1.3.3 Compose and decompose shapes (e.g., cut a square into two right

triangles and put two cubes together to make a rectangular prism), thus

building an understanding of part‐whole relationships as well as the

properties of the original and composite shapes.

OR.2.3.1 Determine length by finding the total number of equal‐length units

that are placed end‐to‐end without gaps or overlaps.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.1.1.2 Represent whole numbers on a number line, demonstrating an understanding of the sequential order of the counting numbers and their relative magnitudes.

OR.2.1.1 Write, compare, and order whole numbers to 1000.

OR.2.1.2 Understand and apply base‐ten numeration, and count in

multiples of one, two, five, ten, and one hundred.

OR.2.1.3 Compose and decompose whole numbers less than one thousand

by place value (e.g., 426 as 4 hundreds + 2 tens + 6 ones and 400 + 20 + 6).

OR.2.2.1 Apply, with fluency, sums to 20 and related subtraction facts.

OR.2.2.2 Solve multi‐digit whole number problems by applying various

meanings (e.g., taking away, and comparing) and models (e.g., combining

or separating sets, using number lines, and hundreds charts) of addition

and subtraction.

OR.2.2.3 Develop fluency with efficient procedures for adding and

subtracting multi‐digit whole numbers and understand why the procedures

work on the basis of place value and number properties.

OR.2.2.5 Determine the value of mixed collections of coins to $1.00.

OR.2.3.3 Demonstrate an understanding that using different measurement

units will result in different numerical measurements for the same object.

OR.2.3.5 Use rulers and other measurement tools to estimate and measure

length in common units (e.g., centimeter and inch).



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.2.3.6 Use the measurement process: choose an appropriate

measurement unit, compare that unit to the object, and report the number

of units.

OR.2.3.8 Tell time in increments of five minutes using analog and digital

clocks.

OR.3.2.1 Represent and apply the concept of multiplication as repeated

addition.

OR.3.3.3 Identify, describe, compare, analyze, and classify quadrilaterals

(square, rectangle, parallelogram, rhombus, and trapezoid) by their sides

and angles.

OR.3.3.4 Identify, describe, and compare pentagons, hexagons, and

octagons by the number of sides or angles.

OR.4.1.6 Represent money amounts to $10.00 in dollars and cents, and

apply to situations involving purchasing ability and making change.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS

OR.1.1.5 Determine the value of collections of pennies, nickels, and dimes.

OR.3.1.1 Represent common fractions (e.g., halves, thirds, fourths, tenths)

as equal parts of a whole, parts of a set, or points or distances on a number

line.

OR.3.1.2 Recognize and demonstrate that sizes of fractional parts are

relative to the size of the whole.

OR.3.1.3 Use fractions to represent numbers that are equal to, less than, or

greater than one.

OR.3.1.4 Solve problems that involve comparing and ordering fractions by

using models, benchmarks (0, ½, 1), or common numerators or

denominators.

OR.3.1.5 Identify equivalent fractions using models, including the number

line.

OR.3.2.1 Represent and apply the concept of multiplication as repeated

addition.

OR.3.2.2 Represent and apply the concept of division as repeated

subtraction and forming equal groups.

OR.3.2.3 Apply models of multiplication (e.g., equal‐sized groups, arrays,

area models, equal 'jumps' on number lines and hundreds charts) and

division (e.g., repeated subtraction, partitioning, and sharing) to solve

problems.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.3.2.4 Apply increasingly sophisticated strategies based on the number

properties (e.g., place value, commutative, associative, distributive,

identity, and zero) to solve multiplication and division problems involving

basic facts.

OR.3.2.5 Apply the inverse relationship between multiplication and division

(e.g., 5 x 6 = 30, 30 ÷ 6 = 5) and the relationship between multiples and

factors.

OR.3.2.6 Represent, analyze and extend number patterns using rules that

involve multiplication and/or addition (e.g., {3, 6, 9, 12, ...}, {1, 2, 4, 8, ...} ).

OR.3.2.7 Analyze frequency tables, bar graphs, picture graphs, and line

plots; and use them to solve problems involving addition, subtraction,

multiplication, and division.

OR.3.3.3 Identify, describe, compare, analyze, and classify quadrilaterals

(square, rectangle, parallelogram, rhombus, and trapezoid) by their sides

and angles.

OR.3.3.7 Determine an appropriate unit, tool, or strategy to find the

perimeter of polygons.

OR.4.1.2 Use models to connect and compare equivalent fractions and

decimals.


OR.4.2.1 Apply with fluency multiplication facts to 10 times 10 and related

division facts.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.4.2.2 Apply understanding of models for multiplication (e.g., equal‐sized

groups, arrays, area models, equal intervals on the number line), place

value, and properties of operations (commutative, associative, and

distributive).

OR.4.2.3 Select and use appropriate estimation strategies for multiplication

(e.g., use benchmarks, overestimate, underestimate, round) to calculate

mentally based on the problem situation when computing with whole

numbers.

OR.4.3.1 Recognize area as an attribute of two‐dimensional regions.

OR.4.3.2 Determine area by finding the total number of same‐sized units of

area that cover a shape without gaps or overlaps.

OR.4.3.3 Recognize a square that is one unit on a side as the standard unit

for measuring area.

OR.4.3.5 Connect area measure to the area model used to represent

multiplication and use this to justify the formula for area of a rectangle.

OR.4.3.6 Find the areas of complex shapes that can be subdivided into

rectangles.

OR.4.3.7 Solve problems involving perimeters and areas of rectangles and

squares.

OR.4.3.8 Recognize that rectangles with the same area can have different

perimeters and that rectangles with the same perimeter can have different

areas.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.5.2.1 Apply understanding of models for division (e.g., equal‐sized

groups, arrays, area models, equal intervals on the number line) and the

relationship of division to multiplication to solve problems.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS

OR.3.1.6 Add common fractions with like denominators.

OR.3.3.1 Identify right angles in two‐dimensional shapes and determine if

angles are greater than or less than a right angle (obtuse and acute).

OR.3.3.2 Identify, describe, compare, analyze, and informally classify

triangles by their sides and angles.

OR.3.3.6 Build, draw, and analyze two‐dimensional shapes to understand

attributes and properties of two‐dimensional space.

OR.3.3.8 Use attributes and properties of two‐dimensional shapes to solve

problems including applications involving parallel and perpendicular lines,

congruence, symmetry, and perimeter.

OR.4.1.1 Extend the base‐ten system to read, write, and represent decimal

numbers (to the hundredths) between 0 and 1, between 1 and 2, etc.

OR.4.1.2 Use models to connect and compare equivalent fractions and

decimals.


OR.4.1.6 Represent money amounts to $10.00 in dollars and cents, and

apply to situations involving purchasing ability and making change.

OR.4.2.2 Apply understanding of models for multiplication (e.g., equal‐sized

groups, arrays, area models, equal intervals on the number line), place

value, and properties of operations (commutative, associative, and

distributive).



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.4.2.5 Develop fluency with efficient procedures for multiplying multi‐

digit whole numbers and justify why the procedures work on the basis of

place value and number properties.

OR.4.3.7 Solve problems involving perimeters and areas of rectangles and

squares.

OR.5.2.1 Apply understanding of models for division (e.g., equal‐sized



OR.5.2.2 Apply concepts of place value and the properties of operations to

solve problems involving division.

OR.5.2.3 Select and use appropriate estimation strategies for division (e.g.,

use benchmarks, overestimate, underestimate, round) to calculate

mentally based on the problem situation when computing with whole

numbers.

OR.5.2.4 Develop and use accurate, efficient, and generalizable methods to

find quotients for multi‐digit division problems.

OR.5.2.5 Develop fluency with efficient procedures for dividing whole

numbers and justify why the procedures work on the basis of place value

and number properties.

OR.5.2.6 Determine the most appropriate form of the quotient and

interpret the remainder in a problem situation.

OR.5.3.1 Identify and classify triangles by their angles (acute, right, obtuse)

and sides (scalene, isosceles, equilateral).

OR.6.1.2 Use and analyze a variety of strategies, including models, for

solving problems with multiplication and division of fractions.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS

OR.6.1.7 Use the relationship between common decimals and fractions to

solve problems including problems involving measurement.

OR.11.3G.1 Recognize and identify line and rotational symmetry of two‐

dimensional figures.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.3.3.6 Build, draw, and analyze two‐dimensional shapes to understand

attributes and properties of two‐dimensional space.

OR.4.1.1 Extend the base‐ten system to read, write, and represent decimal

numbers (to the hundredths) between 0 and 1, between 1 and 2, etc.



multiply multi‐digit whole numbers.

OR.4.2.5 Develop fluency with efficient procedures for multiplying multi‐

digit whole numbers and justify why the procedures work on the basis of

place value and number properties.

OR.5.1.1 Use fraction models to represent the addition and subtraction of

fractions with unlike denominators.

OR.5.1.2 Use decimal models, place value, and number properties to add

and subtract decimals (to the thousandths).

OR.5.1.4 Develop fluency with efficient procedures for adding and

subtracting fractions and decimals and justify why the procedures work.

OR.5.1.5 Solve problems involving the addition and subtraction of fractions

and decimals.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.5.1.6 Use ordered pairs on coordinate graphs to specify locations and

describe paths.

OR.5.2.1 Apply understanding of models for division (e.g., equal‐sized



OR.5.2.2 Apply concepts of place value and the properties of operations to

solve problems involving division.







OR.5.3.5 Determine volume by finding the total number of same‐sized units

of volume that fill a three‐dimensional shape without gaps or overlaps.

OR.5.3.6 Recognize a cube that is one unit on an edge as the standard unit

for measuring volume.

OR.5.3.7 Determine the appropriate units, strategies, and tools for solving

problems that involve estimating or measuring volume.

OR.5.3.8 Decompose three‐dimensional shapes and find surface areas and

volumes of triangular and rectangular prisms.



OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.5.3.9 Identify and measure necessary attributes of shapes to use area,

surface area, and volume formulas to solve problems (e.g., to find which of

two gift boxes needs the most wrapping paper or has the greater volume?).




solving problems with multiplication and division of decimals.

OR.6.1.4 Develop fluency with efficient procedures for multiplying and

dividing fractions and decimals and justify why the procedures work.

OR.6.1.5 Apply the inverse relationship between multiplication and division

to make sense of procedures for multiplying and dividing fractions and

justify why they work.

OR.6.1.7 Use the relationship between common decimals and fractions to

solve problems including problems involving measurement.

OR.6.3.1 Use order of operations to simplify expressions that may include

exponents and grouping symbols.

OR.6.3.5 Represent, analyze, and determine relationships and patterns

using tables, graphs, words and when possible, symbols.

OR.7.2.5 Convert among different units of measurement to solve problems,

including rates.


Movement of Content in Transition from Oregon Standards to CCSS –

All Oregon Content Assigned to Grade 6 in CCSS

OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.5.1.4 Develop fluency with efficient procedures for adding and

subtracting fractions and decimals and justify why the procedures work.






OR.5.3.2 Find and justify relationships among the formulas for the areas of

triangles and parallelograms.

OR.5.3.8 Decompose three‐dimensional shapes and find surface areas and

volumes of triangular and rectangular prisms.

OR.5.3.9 Identify and measure necessary attributes of shapes to use area,

surface area, and volume formulas to solve problems (e.g., to find which of

two gift boxes needs the most wrapping paper or has the greater volume?).




solving problems with multiplication and division of decimals.

OR.6.1.4 Develop fluency with efficient procedures for multiplying and

dividing fractions and decimals and justify why the procedures work.




OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS


OR.6.2.1 Develop, analyze, and apply the meaning of ratio, rate, and

percent to solve problems.

OR.6.2.2 Determine decimal and percent equivalents for common fractions,

including approximations.

OR.6.2.5 Develop the concept of pi as the ratio of the circumference of a

circle to its diameter.

OR.6.3.1 Use order of operations to simplify expressions that may include

exponents and grouping symbols.

OR.6.3.2 Develop the meanings and uses of variables.

OR.6.3.3 Write, evaluate, and use expressions and formulas to solve

problems.

OR.6.3.4 Identify and represent equivalent expressions (e.g., different ways

to see a pattern).

OR.6.3.5 Represent, analyze, and determine relationships and patterns

using tables, graphs, words and when possible, symbols.

OR.6.3.6 Recognize that the solutions of an equation are the values of the

variables that make the equation true.




OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS OR.6.3.7 Solve one‐step equations by using number sense, properties of

operations, and the idea of maintaining equality on both sides of an

equation.

OR.7.1.4 Apply properties of rational numbers and algebra to write and

solve linear equations in one variable.


including rates.

OR.7.3.4 Use models to explain the reasonableness of formulas for the

surface area of pyramids and cylinders, and volume of pyramids, cylinders,

and cones.


different polygons when determining surface area.

OR.7.3.7 Estimate and compute the area and volume of complex or

irregular shapes by dividing them into basic shapes.

OR.8.1.4 Use linear functions and equations to represent, analyze and solve

problems, and to make predictions and inferences.

OR.8.1.6 Use informal strategies (e.g., graphs or tables) to solve problems

involving systems of linear equations in two variables.

OR.8.2.1 Organize and display data (e.g., histograms, box‐and‐whisker

plots, scatter plots) to pose and answer questions; and justify the

reasonableness of the choice of display.

OR.8.2.2 Use measures of center and spread to summarize and compare

data sets.




OREGON STANDARD


K 1 2 3 4 5 6 7 8 HS


OR.11.1A.4 Develop, identify, and/or justify equivalent algebraic

expressions, equations, and inequalities using the properties of exponents,

equality and inequality, as well as the commutative, associative, inverse,

identity, and distributive properties.

OR.11.2A.4 Fluently convert among representations of linear relationships

given in the form of a graph of a line, a table of values, or an equation of a

line in slope‐intercept and standard form.

OR.11.2A.5 Given a linear function, interpret and analyze the relationship

between the independent and dependent variables. Solve for x given f(x) or

solve for f(x) given x.

OR.11.1G.5 Determine the missing dimensions, angles, or area of regular

polygons, quadrilaterals, triangles, circles, composite shapes, and shaded

regions.

OR.11.2G.1 Identify, classify, model, sketch, and label representations of

three‐dimensional objects from nets and from different perspectives.

OR.11.2G.2 Identify and apply formulas for surface area and volume of

spheres; right solids, including rectangular prisms and pyramids; cones; and

cylinders; and compositions thereof. Solve related context‐based problems.



OREGON STANDARD

Colors in Shaded Cells Show Grades from which Oregon Content Originated with Excellent or Partial Alignment to CCSS Content for This Grade K 1 2 3 4 5 6 7 8 HS


OR.6.2.2 Determine decimal and percent equivalents for common fractions,

including approximations.

OR.6.2.5 Develop the concept of pi as the ratio of the circumference of a

circle to its diameter.

OR.7.1.1 Develop, analyze, and apply models (including everyday contexts),

strategies, and procedures to compute with integers, with an emphasis on

negative integers.

OR.7.1.2 Extend knowledge of integers and positive rational numbers to

solve problems involving negative rational numbers.

OR.7.1.3 Develop and use strategies to estimate the result of rational

number computations and justify the reasonableness of results.

OR.7.1.4 Apply properties of rational numbers and algebra to write and solve

linear equations in one variable.

OR.7.2.1 Represent proportional relationships with coordinate graphs and

tables, and identify unit rate as the slope of the related line.

OR.7.2.2 Apply ratio and proportionality to solve problems, including percent

and simple probability.



OREGON STANDARD


OR.7.2.3 Use coordinate graphs, tables, and equations to distinguish

proportional relationships from other relationships, including inverse

proportionality.

OR.7.2.4 Develop and use scale factors and proportional relationships to

solve problems, including similarity and congruence.


including rates.


circumference and area of circles.

OR.7.3.3 Solve problems involving areas and circumferences of circles.



and cones.


different polygons when determining surface area.

OR.7.3.6 Solve problems involving surface areas of pyramids and cylinders

and volumes of pyramids, cylinders, and cones.

OR.7.3.7 Estimate and compute the area and volume of complex or irregular

shapes by dividing them into basic shapes.

OR.8.1.2 Determine the slope of a line and understand that it is a constant

rate of change.



OREGON STANDARD


OR.8.1.3 Identify and interpret the properties (i.e. slope, intercepts,

continuity, and discreteness) of linear relationships as they are shown in the

different representations and recognize proportional relationships (y/x = k or

y = kx) as a special case.

OR.8.2.2 Use measures of center and spread to summarize and compare

data sets.

OR.8.2.6 Use sample data to make predictions regarding a population.

OR.8.2.7 Identify claims based on statistical data and evaluate the

reasonableness of those claims.

OR.8.2.8 Use data to estimate the likelihood of future events and evaluate

the reasonableness of predictions.





OR.11.2A.7 Write, use, and solve linear equations and inequalities using

graphical and symbolic methods with one or two variables. Represent

solutions on a coordinate graph or number line.

OR.11.1G.5 Determine the missing dimensions, angles, or area of regular

polygons, quadrilaterals, triangles, circles, composite shapes, and shaded

regions.






OREGON STANDARD


OR.11.3G.3 Apply a scale factor to determine similar two‐ and three‐

dimensional figures, are similar. Compare and compute their respective

areas and volumes of similar figures.

OR.11.1S.3 Compare and draw conclusions about two or more data sets

using graphical displays or central tendencies and range.

OR.11.2S.1 Identify, analyze, and use experimental and theoretical

probability to estimate and calculate the probability of simple events.

OR.11.2S.2 Determine the sample space of a probability experiment.

OR.11.2S.3 Compute and interpret probabilities for independent,

dependent, complementary, and compound events using various methods

(e.g., diagrams, tables, area models, and counting techniques).



2007/2009 OREGON STANDARD


OR.7.1.4 Apply properties of rational numbers and algebra to write and solve

linear equations in one variable.

OR.7.2.1 Represent proportional relationships with coordinate graphs and

tables, and identify unit rate as the slope of the related line.

OR.7.2.3 Use coordinate graphs, tables, and equations to distinguish

proportional relationships from other relationships, including inverse

proportionality.

OR.7.2.4 Develop and use scale factors and proportional relationships to

solve problems, including similarity and congruence.



and cones.

OR.7.3.6 Solve problems involving surface areas of pyramids and cylinders

and volumes of pyramids, cylinders, and cones.

OR.8.1.1 Translate among contextual, verbal, tabular, graphical, and

algebraic representations of linear functions.

OR.8.1.2 Determine the slope of a line and understand that it is a constant

rate of change.









OR.8.1.4 Use linear functions and equations to represent, analyze and solve

problems, and to make predictions and inferences.

OR.8.1.5 Relate systems of two linear equations in two variables and their

solutions to pairs of lines that are intersecting, parallel, or the same line.

OR.8.1.6 Use informal strategies (e.g., graphs or tables) to solve problems

involving systems of linear equations in two variables.

OR.8.2.1 Organize and display data (e.g., histograms, box‐and‐whisker plots,

scatter plots) to pose and answer questions; and justify the reasonableness

of the choice of display.

OR.8.2.3 Interpret and analyze displays of data and descriptive statistics.

OR.8.3.1 Use properties of parallel lines, transversals, and angles to find

missing sides and angles, and to solve problems including determining

similarity or congruence of triangles.

OR.8.3.2 Use models to show that the sum of the angles of any triangle is

180 degrees and apply this fact to find unknown angles.

OR.8.3.4 Use models to explore the validity of the Pythagorean Theorem,

and use it to find missing lengths.

OR.8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2‐

and 3‐dimensional contexts, including distances on coordinate graphs.

OR.8.3.6 Use models and referents to explore and estimate square roots.






OR.11.1A.2 Evaluate, compute with, and determine equivalent numeric and

algebraic expressions with real numbers and variables that may also include

absolute value, integer exponents, square roots, pi, and/or scientific

notation.

OR.11.1A.3 Express square roots in equivalent radical form and their decimal

approximations when appropriate.

OR.11.2A.1 Identify, construct, extend, and analyze linear patterns and

functional relationships that are expressed contextually, numerically,

algebraically, graphically, in tables, or using geometric figures.

OR.11.2A.2 Given a rule, a context, two points, a table of values, a graph, or

a linear equation in either slope intercept or standard form, identify the

slope of the line, determine the x and/or y intercept(s), and interpret the

meaning of each.







OR.11.2A.8 Solve systems of two linear equations graphically and

algebraically, and solve systems of two linear inequalities graphically.





OR.11.3A.3 Compare the characteristics of and distinguish among linear,

quadratic, and exponential functions that are expressed in a table of values,

a sequence, a context, algebraically, and/or graphically, and interpret the

domain and range of each as it applies to a given context.

OR.11.1G.1 Identify, apply, and analyze angle relationships among two or

more lines and a transversal to determine if lines are parallel, perpendicular,

or neither.

OR.11.1G.3 Apply theorems of corresponding parts of congruent and similar

figures to determine missing sides and angles of polygons.

OR.11.1G.4 Use trigonometric ratios (sine, cosine and tangent) and the

Pythagorean Theorem to solve for unknown lengths in right triangles.




OR.11.2G.3 Identify and apply formulas to solve for the missing dimensions

of spheres and right solids, including rectangular prisms and pyramids,

cones, and cylinders, both numerically and symbolically.

OR.11.3G.4 Apply slope, distance, and midpoint formulas to solve problems

in a coordinate plane.

OR.11.1S.4 Use or construct a scatter plot for a given data set, determine

whether there is a (n) linear, quadratic, exponential, or no trend. If linear,

determine if there is a positive or negative correlation among the data; and,

if appropriate, sketch a line of best fit, and use it to make predictions.


Movement of Content in Transition from Oregon Standards to CCSS – All Oregon Content Assigned to High School in CCSS


Colors in Shaded Cells Show Grades from which Oregon Content Originated with Excellent or Complete Alignment to CCSS Content for This Grade K 1 2 3 4 5 6 7 8 HS



and cones.





OR.8.2.1 Organize and display data (e.g., histograms, box‐and‐whisker plots,

scatter plots) to pose and answer questions; and justify the reasonableness

of the choice of display.

OR.8.2.7 Identify claims based on statistical data and evaluate the

reasonableness of those claims.

OR.11.1A.2 Evaluate, compute with, and determine equivalent numeric and

algebraic expressions with real numbers and variables that may also include

absolute value, integer exponents, square roots, pi, and/or scientific

notation.

OR.11.1A.3 Express square roots in equivalent radical form and their decimal

approximations when appropriate.





OR.11.1A.5 Factor quadratic expressions limited to factoring common

monomial terms, perfect‐square trinomials, differences of squares, and

quadratics of the form x^2 + bx + c that factor over the integers.





OR.11.2A.3 Determine the equation of a line given any of the following

information: two points on the line, its slope and one point on the line, or its

graph. Also, determine an equation of a new line, parallel or perpendicular

to a given line, through a given point.




OR.11.2A.5 Given a linear function, interpret and analyze the relationship

between the independent and dependent variables. Solve for x given f(x) or

solve for f(x) given x.

OR.11.2A.6 Analyze how changing the parameters transforms the graph of

f(x)=mx + b.




OR.11.2A.8 Solve systems of two linear equations graphically and

algebraically, and solve systems of two linear inequalities graphically.

OR.11.3A.1 Given a quadratic or exponential function, identify or determine

a corresponding table or graph.

OR.11.3A.3 Compare the characteristics of and distinguish among linear,

quadratic, and exponential functions that are expressed in a table of values,

a sequence, a context, algebraically, and/or graphically, and interpret the

domain and range of each as it applies to a given context.

OR.11.3A.4 Given a quadratic or exponential function, interpret and analyze

the relationship between the independent and dependent variables, and

evaluate the function for specific values of the domain.





OR.11.3A.5 Given a quadratic equation of the form x^2+ bx + c = 0 with

integral roots, determine and interpret the roots, the vertex of the parabola

that is the graph of y = x^2 + bx +c, and an equation of its axis of symmetry

graphically and algebraically.

OR.11.1G.1 Identify, apply, and analyze angle relationships among two or

more lines and a transversal to determine if lines are parallel, perpendicular,

or neither.

OR.11.1G.2 Apply theorems, properties, and definitions to determine,

identify, and justify congruency or similarity of triangles and to classify

quadrilaterals.

OR.11.1G.3 Apply theorems of corresponding parts of congruent and similar

figures to determine missing sides and angles of polygons.

OR.11.1G.4 Use trigonometric ratios (sine, cosine and tangent) and the

Pythagorean Theorem to solve for unknown lengths in right triangles.

OR.11.1G.7 In problems involving circles, apply theorems and properties of

chords, tangents, and angles; and theorems and formulas of arcs and

sectors.




OR.11.2G.3 Identify and apply formulas to solve for the missing dimensions

of spheres and right solids, including rectangular prisms and pyramids,

cones, and cylinders, both numerically and symbolically.

OR.11.3G.1 Recognize and identify line and rotational symmetry of two‐

dimensional figures.





OR.11.3G.2 Identify and perform single and composite transformations of

geometric figures in a plane, including translations, origin‐centered dilations,

reflections across either axis or y = ±x, and rotations about the origin in

multiples of 90°.

OR.11.3G.3 Apply a scale factor to determine similar two‐ and three‐

dimensional figures, are similar. Compare and compute their respective

areas and volumes of similar figures.

OR.11.3G.4 Apply slope, distance, and midpoint formulas to solve problems

in a coordinate plane.

OR.11.1S.1 Given a context, determine appropriate survey methods, analyze

the strengths and limitations of a particular survey, observational study,

experiment, or simulation, and the display of its data.

OR.11.1S.2 Evaluate data‐based reports by considering the source of the

data, the design of the study, and the way the data was analyzed and

displayed.

OR.11.1S.3 Compare and draw conclusions about two or more data sets

using graphical displays or central tendencies and range.

OR.11.1S.4 Use or construct a scatter plot for a given data set, determine

whether there is a (n) linear, quadratic, exponential, or no trend. If linear,

determine if there is a positive or negative correlation among the data; and,

if appropriate, sketch a line of best fit, and use it to make predictions.

OR.11.1S.5 Construct, analyze, and interpret tables, scatter plots, frequency

distributions, and histograms of data sets.

OR.11.2S.3 Compute and interpret probabilities for independent,

dependent, complementary, and compound events using various methods

(e.g., diagrams, tables, area models, and counting techniques).

62

Part 3

Math Content in the CCSS which is Substantially New to Oregon

(No match or weak match to OR Standards at any grade)

For each grade, these pages show which CCSS standards introduce new content and/or rigor.

Oregon Department of Education Office of Assessment & Accountabililty

63

Math Content in the CCSS Which is Substantially New to Oregon – Kindergarten (No match or weak match to OR Standards at any grade)

Common Core Standards – Kindergarten

CC.K.OA.5 Fluently add and subtract within 5.


64

Math Content in the CCSS Which is Substantially New to Oregon – Grade 1 (No match or weak match to OR Standards at any grade)

Common Core Standards – Grade 1 CC.1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words

halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two

of, or four of the shares. Understand for these examples that decomposing into more equal shares creates

smaller shares.

CC.1.MD.3 Tell and write time in hours and half‐hours using analog and digital clocks.

CC.1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions

about the total number of data points, how many in each category, and how many more or less are in one

category than in another.

CC.1.NBT.4 Add within 100, including adding a two‐digit number and a one‐digit number, and adding a two‐

digit number and a multiple of 10, using concrete models or drawings and strategies based on place value,

properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a

written method and explain the reasoning used. Understand that in adding two‐digit numbers, one adds tens

and tens, ones and ones; and sometimes it is necessary to compose a ten.

CC.1.NBT.5 Given a two‐digit number, mentally find 10 more or 10 less than the number, without having to

count; explain the reasoning used.

CC.1.NBT.6 Subtract multiples of 10 in the range 10‐90 from multiples of 10 in the range 10‐90 (positive or

zero differences), using concrete models or drawings and strategies based on place value, properties of

operations, and/or the relationship between addition and subtraction; relate the strategy to a written method

and explain the reasoning used.

CC.1.OA.5 Relate counting to addition and subtraction.

CC.1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and

subtraction are true or false.

CC.1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole

numbers.


65


Common Core Standards – Grade 2 CC.2.G.2 Partition a rectangle into rows and columns of same‐size squares and count to find the total

number of them.

CC.2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the

words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths.

Recognize that equal shares of identical wholes need not have the same shape.

CC.2.MD.4 Measure to determine how much longer one object is than another, expressing the length

difference in terms of a standard length unit.

CC.2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given

in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the

unknown number to represent the problem.

CC.2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit,

or by making repeated measurements of the same object. Show the measurements by making a line plot,

where the horizontal scale is marked off in whole‐number units.=

CC.2.MD.10 Draw a picture graph and a bar graph (with single‐unit scale) to represent a data set with up to

four categories. Solve simple put‐together, take‐apart, and compare problems using information presented

in a bar graph.

CC.2.NBT.6 Add up to four two‐digit numbers using strategies based on place value and properties of

operations.

CC.2.NBT.8 Mentally add 10 or 100 to a given number 100‐900, and mentally subtract 10 or 100 from a

given number 100‐900.

CC.2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of

operations. (Explanations may be supported by drawings or objects.)

CC.2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g.,

by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two

equal addends.


66


Common Core Standards – Grade 3 CC.3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the

whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4

of the area of the shape.

CC.3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

CC.3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one‐step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

CC.3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths

of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate

units—whole numbers, halves, or quarters.

CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

CC.3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

CC.3.NBT.3 Multiply one‐digit whole numbers by multiples of 10 in the range 10‐90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.


67


Common Core Standards – Grade 4

CC.4.NBT.3 Use place value understanding to round multi‐digit whole numbers to any place.

CC.4.NBT.4 Fluently add and subtract multi‐digit whole numbers using the standard algorithm.

CC.4.MD.6 Measure angles in whole‐number degrees using a protractor. Sketch angles of specified measure.

CC.4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve

problems involving addition and subtraction of fractions by using information presented in line plots.

CC.4.MD.5Recognize angles as geometric shapes that are formed wherever two rays share a common

endpoint, and understand concepts of angle measurement:

‐‐ a. An angle is measured with reference to a circle with its center at the common endpoint of the rays,

by considering the fraction of the circular arc between the points where the two rays intersect the circle.

An angle that turns through 1/360 of a circle is called a “one‐degree angle,” and can be used to measure

angles.

‐‐ b. An angle that turns through n one‐degree angles is said to have an angle measure of n degrees.

CC.4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non‐overlapping parts, the

angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems

to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a

symbol for the unknown angle measure.

CC.4.NBT.1 Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents

in the place to its right.

CC.4.NBT.2 Read and write multi‐digit whole numbers using base‐ten numerals, number names, and expanded form.

Compare two multi‐digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record

the results of comparisons.

CC.4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this

technique to add two fractions with respective denominators 10 and 100.

CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5

times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as

multiplication equations.

CC.4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and

equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative

comparison from additive comparison.

CC.4.OA.4 Find all factor pairs for a whole number in the range 1‐100. Recognize that a whole number is a multiple

of each of its factors. Determine whether a given whole number in the range 1‐100 is a multiple of a given one‐digit

number. Determine whether a given whole number in the range 1‐100 is prime or composite.

CC.4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern

that were not explicit in the rule itself.


68



CC.5.G.4 Classify two‐dimensional figures in a hierarchy based on properties.

CC.5.MD.2 . Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

CC.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and

mathematical problems involving volume.

CC.5.NBT.1 Recognize that in a multi‐digit number, a digit in one place represents 10 times as much as

it represents in the place to its right and 1/10 of what it represents in the place to its left.

CC.5.NBT.4 Use place value understanding to round decimals to any place.

CC.5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

CC.5.NF.5 Interpret multiplication as scaling (resizing) by: ‐‐ a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. ‐‐ b. Explaning why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a) / (n×b) to the effect of multiplying a/b by 1.

CC.5.NF.7a Interpret division of a unit fraction by a non‐zero whole number, and compute such

quotients.

CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients.

CC.5.NF.7c Solve real‐world problems involving division of unit fractions by non‐zero whole numbers

and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to

represent the problem.

CC.5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical

expressions without evaluating them.


69


Common Core Standards – Grade 6 CC.6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real‐world or

mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent

solutions of such inequalities on number line diagrams.

CC.6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length

of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the

context of solving real‐world and mathematical problems.

CC.6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common

multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole

numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

CC.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite

directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits,

positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts,

explaining the meaning of 0 in each situation.

CC.6.NS.7 Understand ordering and absolute value of rational numbers.

CC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number

line diagram.

CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real‐world contexts.

CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret

absolute value as magnitude for a positive or negative quantity in a real‐world situation.

CC.6.NS.7d Distinguish comparisons of absolute value from statements about order.

CC.6.NS.8 Solve real‐world and mathematical problems by graphing points in all four quadrants of the coordinate

plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or

the same second coordinate.

CC.6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and

accounts for it in the answers.

CC.6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be

described by its center, spread, and overall shape.

CC.6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single

number, while a measure of variation describes how its values vary with a single number.

CC.6.SP.5 Summarize numerical data sets in relation to their context, such as by:

‐‐ a. Reporting the number of observations.

‐‐ b. Describing the nature of the attribute under investigation, including how it was measured and its units of

measurement.

‐‐ c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean

absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with

reference to the context in which the data was gathered.

‐‐ d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in

which the data was gathered.


70



CC.7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the

problem and how the quantities in it are related.

CC.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are

specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

CC.7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given

conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions

determine a unique triangle, more than one triangle, or no triangle.

CC.7.G.3 Describe the two‐dimensional figures that result from slicing three‐dimensional figures, as in plane

sections of right rectangular prisms and right rectangular pyramids.

CC.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi‐step problem

to write and solve simple equations for an unknown angle in a figure.

CC.7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample

of the population; generalizations about a population from a sample are valid only if the sample is representative

of that population. Understand that random sampling tends to produce representative samples and support

valid inferences.

CC.7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the

likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an

unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability

near 1 indicates a likely event.

CC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated

from a chance process.


71



CC.8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate

very large or very small quantities, and to express how many times as much one is than the other.

CC.8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of

a function is the set of ordered pairs consisting of an input and the corresponding output. *(Aligns to an

Oregon Advanced Mathematics Standard)

CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line;

give examples of functions that are not linear.

CC.8.G.2 Understand that a two‐dimensional figure is congruent to another if the second can be

obtained from the first by a sequence of rotations, reflections, and translations; given two congruent

figures, describe a sequence that exhibits the congruence between them.

CC.8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that

every number has a decimal expansion; for rational numbers show that the decimal expansion repeats

eventually, and convert a decimal expansion which repeats eventually into a rational number.

CC.8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by

displaying frequencies and relative frequencies in a two‐way table. Construct and interpret a two‐way

table summarizing data on two categorical variables collected from the same subjects. Use relative

frequencies calculated for rows or columns to describe possible association between the two variables.


72

Math Content in the CCSS Which is Substantially New to Oregon – High School (No match or weak match to OR Standards at any grade)

Common Core Standards – High School CC.9‐12.A.APR.1 . Understand that polynomials form a system analogous to the integers, namely, they are

closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply

polynomials. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.APR.2Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder

on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). *(Aligns to an Oregon Advanced

Mathematics Standard)

CC.9‐12.A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to

construct a rough graph of the function defined by the polynomial. *(Aligns to an Oregon Advanced


CC.9‐12.A.APR.4 Prove polynomial identities and use them to describe numerical relationships. For example,

the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

CC.9‐12.A.APR.6 Rewrite rational expressions. Rewrite simple rational expressions in different forms; write

a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less

than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer

algebra system. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or

inequalities, and interpret solutions as viable or non‐viable options in a modeling context. *(Aligns to an Oregon

Advanced Mathematics Standard)

CC.9‐12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving

equations.

CC.9‐12.A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers

asserted at the previous step, starting from the assumption that the original equation has a solution. Construct

a viable argument to justify a solution method.

CC.9‐12.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how

extraneous solutions may arise. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients

represented by letters. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an

equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

*(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the

sum of that equation and a multiple of the other produces a system with the same solutions.

CC.9‐12.A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on

pairs of linear equations in two variables. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.REI.7 . Solve a simple system consisting of a linear equation and a quadratic equation in two variables

algebraically and graphically. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.REI.11 Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y =

g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using

technology to graph the functions, make tables of values, or find successive approximations. Include cases

where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.



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CC.9‐12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

CC.9‐12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.

CC.9‐12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.

CC.9‐12.A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

CC.9‐12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of

the function it defines. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. *(Aligns

to an Oregon Advanced Mathematics Standard)

CC.9‐12.A.SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1),

and use the formula to solve problems. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.


CC.9‐12.F.BF.1b Combine standard function types using arithmetic operations. *(Aligns to an Oregon Advanced


CC.9‐12.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and

geometric sequences both recursively and with an explicit formula, use them to model situations, and translate

between the two forms. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by

f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the

graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Include recognizing even and odd functions from their graphs and algebraic expressions for them. *(Aligns to an


CC.9‐12.F.BF.4 Find inverse functions. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an

expression for the inverse. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.IF.3 . Recognize that sequences are functions, sometimes defined recursively, whose domain is a

subset of the integers. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a

table) over a specified interval. Estimate the rate of change from a graph.

CC.9‐12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple

cases and using technology for more complicated cases. *(Aligns to an Oregon Advanced Mathematics

Standard)

CC.9‐12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. *(Aligns to an


CC.9‐12.F.IF.7b Graph square root, cube root, and piecewise‐defined functions, including step functions and

absolute value functions. *(Aligns to an Oregon Advanced Mathematics Standard)


74


CC.9‐12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and

showing end behavior. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and

trigonometric functions, showing period, midline, and amplitude. *(Aligns to an Oregon Advanced Mathematics

Standard)

CC.9‐12.F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. *(Aligns to

an Oregon Advanced Mathematics Standard)

CC.9‐12.F.IF.9 Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions). *(Aligns to an Oregon Advanced Mathematics

Standard)

CC.9‐12.F.LE.4 For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are

numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. *(Aligns to an Oregon Advanced


CC.9‐12.F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by

the angle. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric

functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the

unit circle. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude,

frequency, and midline. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.F.TF.8 Prove the Pythagorean identity (sin A)^2 + (cos A)^2 = 1 and use it to find sin A, cos A, or tan A,

given sin A, cos A, or tan A, and the quadrant of the angle. *(Aligns to an Oregon Advanced Mathematics

Standard)

CC.9‐12.G.C.1 Prove that all circles are similar.

CC.9‐12.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for

a quadrilateral inscribed in a circle.

CC.9‐12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,

based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

CC.9‐12.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles,

perpendicular lines, parallel lines, and line segments.

CC.9‐12.G.CO.10 Prove theorems about triangles.

CC.9‐12.G.CO.11 . Prove theorems about parallelograms.

CC.9‐12.G.CO.12. Make formal geometric constructions with a variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

CC.9‐12.G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

CC.9‐12.G.GMD.4 Identify the shapes of two‐dimensional cross‐sections of three‐dimensional objects, and

identify three‐dimensional objects generated by rotations of two‐dimensional objects.


75


CC.9‐12.G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem;

complete the square to find the center and radius of a circle given by an equation. *(Aligns to an Oregon


CC.9‐12.G.GPE.2 Derive the equation of a parabola given a focus and directrix. *(Aligns to an Oregon Advanced


CC.9‐12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.

CC.9‐12.G.GPE.6 Find the point on a directed line segment between two given points that partitions the

segment in a given ratio. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling

a tree trunk or a human torso as a cylinder).

CC.9‐12.G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per

square mile, BTUs per cubic foot).

CC.9‐12.G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to

satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

CC.9‐12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles

to be similar.

CC.9‐12.G.SRT.4 Prove theorems about triangles.

CC.9‐12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the

triangle, leading to definitions of trigonometric ratios for acute angles. *(Aligns to an Oregon Advanced


CC.9‐12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.

CC.9‐12.N.CN.1 Know there is a complex number i such that i^2 = −1, and every complex number has the form a

+ bi with a and b real. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.N.CN.2 Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add,

subtract, and multiply complex numbers. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.

CC.9‐12.N.Q.1 Use units as a way to understand problems and to guide the solution of multi‐step problems;

choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and

data displays.

CC.9‐12.N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.

CC.9‐12.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting

quantities.

CC.9‐12.N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the

properties of integer exponents to those values, allowing for a notation for radicals in terms of rational

exponents. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.N.RN.3 . Explain why the sum or product of rational numbers is rational; that the sum of a rational

number and an irrational number is irrational; and that the product of a nonzero rational number and an

irrational number is irrational.


76


CC.9‐12.S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or

categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

CC.9‐12.S.CP.4 Construct and interpret two‐way frequency tables of data when two categories are associated

with each object being classified. Use the two‐way table as a sample space to decide if events are independent

and to approximate conditional probabilities.

CC.9‐12.S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday

language and everyday situations. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to

A, and interpret the answer in terms of the model. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of

the model. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.IC.1 Understand statistics as a process for making inferences about population parameters based on

a random sample from that population. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin

of error through the use of simulation models for random sampling. *(Aligns to an Oregon Advanced


CC.9‐12.S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide

if differences between parameters are significant. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for

possible effects of extreme data points (outliers). *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to

estimate population percentages. Recognize that there are data sets for which such a procedure is not

appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. *(Aligns to an


CC.9‐12.S.ID.5 Summarize categorical data for two categories in two‐way frequency tables. Interpret relative

frequencies in the context of the data (including joint, marginal, and conditional relative frequencies).

Recognize possible associations and trends in the data. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals. *(Aligns to an Oregon


CC.9‐12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association. *(Aligns to an Oregon


CC.9‐12.S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the

context of the data. *(Aligns to an Oregon Advanced Mathematics Standard)

CC.9‐12.S.ID.9 Distinguish between correlation and causation.



Part 4

Overview of the Common Core State Standards

and the Smarter Balanced Assessment System


Part 4:

Overview of the Common Core State Standards and Smarter Balanced Common Assessment Standards-based education is the process of teaching, learning, and assessment that focuses on national, state, and local educational standards. Academic content standards are statements of what students are expected to know and be able to do at specified grade levels. Content standards serve several important functions and roles: Content standards focus on essential concepts, knowledge, skills and behaviors necessary for students to succeed in the 21st century. As such, they are designed to increase achievement. Because content standards clearly address what all students should learn and each school’s responsibility in that effort, standards can be used as a means of preventing school failure and reducing the number of students dropping out of school. Content standards serve as beginning points for teachers when they make decisions about what to teach. Development of Content Standards in Oregon Content standards were first introduced in Oregon at grades 3, 5, 8, and 10 in 1991 through the Educational Act for the 21st Century. With the passage of No Child Left Behind in 2001, Oregon moved to grade level content standards in English language arts and mathematics. In 2007 Oregon began to transition to a core standards structure designed to create fewer standards that are more focused and coherent. This continual commitment to standards revision effectively positioned Oregon for the adoption of the Common Core State Standards in October 2010. In a recent communication with Oregon educators, State Superintendent of Public Instruction Susan Castillo wrote, “By joining other states in the Common Core movement, we better position our students to compete nationally and internationally with their peers for jobs in the 21st century workplace.” The Common Core State Standards (CCSS) for English language arts and mathematics are content standards shared among participating states. They are designed to help ensure that all students are college and career ready in literacy and mathematics no later than the end of high school. Developed as part of the Common Core State Standards Initiative, a voluntary state-led effort, this common set of standards describes what students in our nation should know and be able to do. Parents, teachers, school administrators, and experts from across the country, together with state leaders through their membership in the Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practices (NGA Center), led the effort to develop the standards. The Common Core State Standards were released by CCSSO and the NGA Center on June 2, 2010. These content standards are

Aligned with expectations for college and career success; Built upon strengths and lessons of current state content standards and standards of top performing nations; Informed by other top performing countries, so that all students are prepared to succeed in our global economy and society; and Evidence- and research-based.

For more information on the Common Core State Standards, please visit http://www.corestandards.org./


Oregon’s role in the CCSS initiative Oregon has been engaged in CCSS work since the initiative’s inception in spring 2009. A total of 48 states including Oregon signed a memorandum of understanding to participate in the Common Core State Standards Initiative. Oregon Department of Education staff reviewed each draft of the standards and provided feedback throughout the development process. Oregon educators and interested stakeholders reviewed the draft standards regionally and in an online survey. On October 28, 2010, the State Board of Education adopted the two sets of standards:

The Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects The Common Core State Standards for Mathematics

Smarter Balanced Common Assessment for the Common Core State Standards The Smarter Balanced Assessment Consortium is one of two multistate consortia awarded funding from the U.S. Department of Education to develop an assessment system based on the new Common Core State Standards (CCSS). To achieve the goal that all students leave high school ready for college and career, SBAC is committed to ensuring that assessment and instruction embody the CCSS and that all students, regardless of disability, language, or subgroup status, have the opportunity to learn this valued content and show what they know and can do. The assessment system will be field tested in the 2013-2014 school year and administered live for the first time during the 2014-2015 school year.

With strong support from member states, institutions of higher education, and industry, Smarter Balanced will develop a balanced set of measures and tools, each designed to serve specific purposes. Together, these components will provide student data throughout the academic year that will inform instruction, guide interventions, help target professional development, and ensure an accurate measure of each student’s progress toward career and college readiness.

The state of Oregon is a Governing State in the Smarter Balanced Assessment Consortium. As defined in the Governance Document, each state is required to take an active role in supporting the work of the Consortium, thus Oregon’s participation includes:

Co-chairs on three work groups, and Members of other work groups.

A Summary of Core Components

Summative Assessments Mandatory comprehensive accountability measures that include computer adaptive assessments and performance tasks, administered in the last 12 weeks

of the school year in grades 3–8 and high school for English Language Arts (ELA) and mathematics; Designed to provide valid, reliable, and fair measures of students’ progress toward and attainment of the knowledge and skills required to be college and

career ready; Capitalize on the strengths of computer adaptive testing, i.e., efficient and precise measurement across the full range of achievement and quick turnaround

of results; Produce composite content area scores, based on the computer-adaptive items and performance tasks.


Interim Assessments Optional comprehensive and content-cluster measures that include computer adaptive assessments and performance tasks, administered at locally

determined intervals; Designed as item sets that can provide actionable information about student progress; Serve as the source for interpretive guides that use publicly released items and tasks; Grounded in cognitive development theory about how learning progresses across grades and how college- and career-readiness emerge over time; Afford teachers and administrators the flexibility to:

select item sets that provide deep, focused measurement of specific content clusters embedded in the CCSS; administer these assessments at strategic points in the instructional year; use results to better understand students’ strengths and limitations in relation to the standards; support state-level accountability systems using end-of-course assessments.

Formative tools and processes: Provides resources for teachers on how to collect and use information about student success in acquisition of the CCSS; Will be used by teachers and students to diagnose a student’s learning needs, check for misconceptions, and/or to provide evidence of progress toward

learning goals.

Accountability: Fully committed to providing each member state reliable, valid, and comparable achievement and growth information for each student; Enables each state to implement its own approved state accountability system. Establishes achievement standards in 2014 following the administration of the field test in the 2013-2014 school year;

System Features Ensures coverage of the full range of ELA and mathematics standards and breadth of achievement levels by combining a variety of item types (i.e.,

selected-response, constructed response, and technology-enhanced) and performance tasks, which require application of knowledge and skills; Provides comprehensive, research-based support, technical assistance, and professional development so that teachers can use assessment data to improve

teaching and learning in line with the standards; Provides online, tailored reports that link to instructional and professional development resources.

For more information on the SMARTER Balanced Assessment Consortium, please visit http://www.smarterbalanced.org/


Development of the Smarter Balanced Common Assessment of the Common Core State Standards for Mathematics

Smarter Balanced has developed a set of Content Specifications for English language arts and mathematics, which describe the Consortium’s current specification of critically important claims about student learning that are derived from the Common Core State Standards. These claims will serve as the basis for the Consortium’s system of summative and interim assessments and its formative assessment support for teachers. Open and transparent decision-making is one of the Consortium’s central principles. Each draft of the mathematics content specifications was made available for comment consistent with that principle, and all responses to this work are considered as it continues to be refined. Developed in partnership with member states, leading researchers, content experts, and the authors of the Common Core State Standards, content specifications are intended to ensure that the assessment system accurately assesses the full range the standards. This content specification of the Common Core mathematics standards provides clear and rigorous focused assessment targets that will be used to translate the grade-level Common Core standards into content frameworks along a learning continuum, from which test blueprints and item/task specifications will be established. Assessment evidence at each grade level provides item and task specificity and clarifies the connections between instructional processes and assessment outcomes. Four claims have been proposed for the summative mathematics assessment. The Content Specifications include a detailed treatment of each claim. Each claim is a summary statement describing the knowledge and skill students will be expected to demonstrate on the assessment related to a particular aspect of the CCSS for mathematics. The level of the knowledge and skills necessary for a student to be proclaimed “Proficient” will be established through the development of Achievement Level Descriptors and during the setting of performance standards on the assessments. The claims will be finalized in spring 2012. The four claims in draft form are below:

Claims for Mathematics Summative Assessment -- DRAFT Claim #1

Concepts & Procedures: “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”

Claim #2

Problem Solving: “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”

Claim #3

Communicating Reasoning: “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”

Claim #4

Modeling and Data Analysis: “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”

Each claim is accompanied by a set of assessment targets that provide more detail about the range of content and Depth of Knowledge levels. The targets are intended to support the development of high-quality items and tasks that contribute evidence to the claims. The targets are identified by the cluster level headings of the standards in the Common Core State Standards for Mathematics in order to allow for the creation and use of assessment tasks that require proficiency in a broad range of content and practices.


Clearly the Smarter Balanced Common Assessment will assess students’ knowledge and skills with a higher degree of rigor than in any current assessment in any of the states. Transition to this assessment system will provide both opportunities and challenges for the entire education community. Rethinking scope and sequence of curriculum, classroom practices, and professional development will be highly important. However, we can rest assured that the Smarter Balanced mathematics assessments and the assessment system are being shaped by a set of characteristics shared by the systems of high-achieving nations and states, and include the following principles: 1) Assessments are grounded in a thoughtful, standards-based curriculum and are managed as part of an integrated system of standards, curriculum, assessment, instruction, and teacher development. Curriculum and assessments are organized around a set of learning progressions along multiple dimensions within subject areas. These guide teaching decisions, classroom-based assessment, and external assessment. 2) Assessments include evidence of student performance on challenging tasks that evaluate Common Core Standards of 21st century learning. Instruction and assessments seek to teach and evaluate knowledge and skills that generalize and can transfer to higher education and multiple work domains. They emphasize deep knowledge of core concepts and ideas within and across the disciplines, along with analysis, synthesis, problem solving, communication, and critical thinking. This kind of learning and teaching requires a focus on complex performances as well as the testing of specific concepts, facts, and skills. 3) Teachers are integrally involved in the development and scoring of assessments. While many assessment components can and will be efficiently and effectively scored with computer assistance, teachers will also be involved in the interim/benchmark, formative, and summative assessment systems so that they deeply understand and can teach to the standards. 4) Assessments are structured to continuously improve teaching and learning. Assessment as, of, and for learning is designed to develop understanding of what learning standards are, what high-quality work looks like, what growth is occurring, and what is needed for student learning. This includes:

Developing assessments around learning progressions that allow teachers to see what students know and can do on multiple dimensions of learning and to strategically support their progress;

Using computer-based technologies to adapt assessments to student levels to more effectively measure what they know, so that teachers can target instruction more carefully and can evaluate growth over time;

Creating opportunities for students and teachers to get feedback on student learning throughout the school year, in forms that are actionable for improving success;

Providing curriculum-embedded assessments that offer models of good curriculum and assessment practice, enhance curriculum equity within and across schools, and allow teachers to see and evaluate student learning in ways that can feed back into instructional and curriculum decisions; and

Allowing close examination of student work and moderated teacher scoring as sources of ongoing professional development.


5) Assessment, reporting, and accountability systems provide useful information on multiple measures that is educative for all stakeholders. Reporting of assessment results is timely, specific, and vivid—offering specific information about areas of performance and examples of student responses along with illustrative benchmarks, so that teachers and students can follow up with targeted instruction. Multiple assessment opportunities (formative and interim/benchmark, as well as summative) offer ongoing information about learning and improvement. Reports to stakeholders beyond the school provide specific data, examples, and illustrations so that administrators and policymakers can more fully understand what students know in order to guide curriculum and professional development decisions. Accessibility to Content Standards and Assessments: In addition to these five principles, SMARTER Balanced is committed to ensuring that the content standards, summative assessments, teacher-developed performance tasks, and interim assessments adhere to the principles of accessibility for students with disabilities and English Language Learners.3 It is important to understand that the purpose of accessibility is not to reduce the rigor of the Common Core State Standards, but rather to avoid the creation of barriers for students who may need to demonstrate their knowledge and skills at the same level of rigor in different ways. Toward this end, each of the claims for the CCSS in Mathematics is briefly clarified in terms of accessibility considerations. Information on what this means for content specifications and mapping will be developed further during the test and item development phases.

Oregon Department of Education

255 Capitol St NE, Salem, Oregon 97310 (503) 947-5600

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