OREGON MATH STANDARDS (2021): [Focus Areas]
Overview
The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.
Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.
2021 Oregon Math Guidance: Grade K Focus
Grade K Math Standards and Guidance
Critical Areas of Focus
In Kindergarten, instructional time should focus on two critical areas: (1) representing and comparing whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.
(1) Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.
(2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.
Domains and Clusters
K.OA - Algebraic Reasoning: Operations
- K.OA.A Understand addition and subtraction
K.NCC - Numeric Reasoning: Counting and Cardinality
- K.NCC.A Know number names and the count sequence
- K.NCC.B Count to tell the number of objects.
- K.NCC.C Compare numbers.
K.NBT - Numeric Reasoning: Base Ten Arithmetic
- K.NBT.A Work with numbers 11-19 to gain foundations for place value
K.GM - Geometric Reasoning and Measurement
- K.GM.A Identify and describe shapes
- K.GM.B Analyze, compare, create, and compose shapes.
- K.GM.C Describe and compare measurable attributes
K.DR - Data Reasoning
- K.DR.A Pose investigative questions and collect/consider data
- K.DR.B Analyze, represent, and interpret data.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 1 Focus
Grade 1 Math Standards and Guidance
Critical Areas of Focus
In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.
(1) Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.
(2) Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
(3) Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.
(4) Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.
Domains and Clusters
1.OA - Algebraic Reasoning: Operations
- 1.OA.A Represent and solve problems involving addition and subtraction
- 1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.
- 1.OA.C Add and subtract within 20.
- 1.OA.D Work with addition and subtraction equations
1.NBT - Numeric Reasoning: Base Ten Arithmetic
- 1.NBT.A Extend the counting sequence
- 1.NBT.B Understand place value.
- 1.NBT.C Use place value understanding and properties of operations to add and subtract.
1.GM - Geometric Reasoning and Measurement
- 1.GM.A Reason with shapes and their attributes.
- 1.GM.B Describe and compare measurable attributes
- 1.GM.C Tell and write time.
1.DR - Data Reasoning
- 1.DR.A Pose investigative questions and collect/consider data.
- 1.DR.B Analyze, represent, and interpret data
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 2 Focus
Grade 2 Math Standards and Guidance
Critical Areas of Focus
In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.
(1) Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).
(2) Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.
(3) Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a given length.
(4) Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.
Domains and Clusters
2.OA - Algebraic Reasoning: Operations
- 2.OA.A Represent and solve problems involving addition and subtraction.
- 2.OA.B Add and subtract within 20.
- 2.OA.C Work with equal groups of objects to gain foundations for multiplication.
2.NBT - Numeric Reasoning: Base Ten Arithmetic
- 2.NBT.A Understand place value
- 2.NBT.B Use place value understanding and properties of operations to add and subtract.
2.GM - Geometric Reasoning and Measurement
- 2.GM.A Reason with shapes and their attributes.
- 2.GM.B Measure and estimate lengths in standard units.
- 2.GM.C Relate addition and subtraction to length.
- 2.GM.D Work with time and money.
2.DR - Data Reasoning
- 2.DR.A Pose investigative questions and collect/consider data.
- 2.DR.B Analyze, represent, and interpret data.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 3 Focus
Grade 3 Math Standards and Guidance
Critical Areas of Focus
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
(1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.
(2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
(3) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.
(4) Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.
NOTE: Links to Achievement Level Descriptors (ALDs) in the Content Explorer are provided for most clusters. ALDs describe the knowledge, skills, and processes that students demonstrate on state tests at pre-determined levels of achievement for each tested grade level. Explore more OSAS Math Test resources on ODE's Math Assessment webpage.
Domains and Clusters
3.OA - Algebraic Reasoning: Operations
- 3.OA.A Represent and solve problems involving multiplication and division. [LINK to ALDs]
- 3.OA.B Understand properties of multiplication and the relationship between multiplication and division. [LINK to ALDs]
- 3.OA.C Multiply and divide within 100. [LINK to ALDs]
- 3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic. [LINK to ALDs]
3.NBT - Numeric Reasoning: Base Ten Arithmetic
- 3.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic. [LINK to ALDs]
3.NF - Numeric Reasoning: Fractions
- 3.NF.A Develop understanding of fractions as numbers. [LINK to ALDs]
3.GM - Geometric Reasoning and Measurement
- 3.GM.A Reason with shapes and their attributes. [LINK to ALDs]
- 3.GM.B Solve problems involving measurement and estimation. [LINK to ALDs]
- 3.GM.C Geometric measurement: understand concepts of area and relate area to multiplication and to addition. [LINK to ALDs]
- 3.GM.D Geometric measurement: recognize perimeter. [LINK to ALDs]
3.DR - Data Reasoning (3.DR)
- 3.DR.A Pose investigative questions and collect/consider data.
- 3.DR.B Analyze, represent, and interpret data. [LINK to ALDs]
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 4 Focus
Grade 4 Math Standards and Guidance
Critical Areas of Focus
In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
(1) Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.
(2) Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.
(3) Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.
NOTE: Links to Achievement Level Descriptors (ALDs) in the Content Explorer are provided for most clusters. ALDs describe the knowledge, skills, and processes that students demonstrate on state tests at pre-determined levels of achievement for each tested grade level. Explore more OSAS Math Test resources on ODE's Math Assessment webpage
Domains and Clusters
4.OA - Algebraic Reasoning: Operations
- 4.OA.A Use the four operations with whole numbers to solve problems. [Link to ALDs]
- 4.OA.B Gain familiarity with factors and multiples. [Link to ALDs]
- 4.OA.C Generate and analyze patterns. [Link to ALDs]
4.NBT - Numeric Reasoning: Base Ten Arithmetic
- 4.NBT.A Generalize place value understanding for multi-digit whole numbers. [Link to ALDs]
- 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic. [Link to ALDs]
4.NF - Numeric Reasoning: Fraction
- 4.NF.A Extend understanding of fraction equivalence and ordering. [Link to ALDs]
- 4.NF.B Build fractions from unit fractions. [Link to ALDs]
- 4.NF.C Understand decimal notation for fractions, and compare decimal fractions. [Link to ALDs]
4.GM - Geometric Reasoning and Measurement
- 4.GM.A Draw and identify lines and angles, and classify shapes by properties of their lines and angles. [Link to ALDs]
- 4.GM.B Solve problems involving measurement and conversion of measurements. [Link to ALDs]
- 4.GM.C Geometric measurement: understand concepts of angle and measure angles. [Link to ALDs]
4.DR - Data Reasoning
- 4.DR.A Pose investigative questions and collect/consider data.
- 4.DR.B Analyze, represent, and interpret data. [Link to ALDs]
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 5 Focus
Grade 5 Math Standards and Guidance
Critical Areas of Focus
In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
(1) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)
(2) Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.
(3) Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.
NOTE: Links to Achievement Level Descriptors (ALDs) in the Content Explorer are provided for most clusters. ALDs describe the knowledge, skills, and processes that students demonstrate on state tests at pre-determined levels of achievement for each tested grade level. Explore more OSAS Math Test resources on ODE's Math Assessment webpage.
Domains and Clusters
5.OA - Algebraic Reasoning: Operations
- 5.OA.A Write and interpret numerical expressions. [Link to ALDs]
- 5.OA.B Analyze patterns and relationships. [Link to ALDs]
5.NBT - Numeric Reasoning: Base Ten Arithmetic
- 5.NBT.A Understand the place value system. [Link to ALDs]
- 5.NBT.B Perform operations with multi-digit whole numbers and with decimals to hundredths. [Link to ALDs]
5.NF - Numeric Reasoning: Fractions
- 5.NF.A Use equivalent fractions as a strategy to add and subtract fractions. [Link to ALDs]
- 5.NF.B Apply and extend previous understandings of multiplication and division. [Link to ALDs]
5.GM - Geometric Reasoning and Measurement
- 5.GM.A Graph points on the coordinate plane to solve real-world and mathematical problems. [Link to ALDs]
- 5.GM.B Classify two-dimensional figures into categories based on their properties. [Link to ALDs]
- 5.GM.C Convert like measurement units within a given measurement system. [Link to ALDs]
- 5.GM.D Geometric measurement: understand concepts of volume. [Link to ALDs]
5.DR - Data Reasoning
- 5.DR.A Pose investigative questions and collect/consider data.
- 5.DR.B Analyze, represent, and interpret data. [Link to ALDs]
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 6 Focus
Grade 6 Math Standards and Guidance
Critical Areas of Focus
In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
(1) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
(2) Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
(3) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
(4) Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.
NOTE: Links to Achievement Level Descriptors (ALDs) in the Content Explorer are provided for most clusters. ALDs describe the knowledge, skills, and processes that students demonstrate on state tests at pre-determined levels of achievement for each tested grade level. Explore more OSAS Math Test resources on ODE's Math Assessment webpage.
Domains and Clusters
6.AEE - Algebraic Reasoning: Expressions and Equations
- 6.AEE.A Apply and extend previous understandings of arithmetic to algebraic expressions. [Link to ALDs]
- 6.AEE.B Reason about and solve one-variable equations and inequalities. [Link to ALDs]
- 6.AEE.C Represent and analyze quantitative relationships between dependent and independent variables. [Link to ALDs]
6.RP - Proportional Reasoning: Ratios and Proportions
- 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. [Link to ALDs]
6.NS - Numeric Reasoning: Number Systems
- 6.NS.A Apply and extend previous understandings of multiplication and division to divide fractions by fractions. [Link to ALDs]
- 6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples. [Link to ALDs]
- 6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers. [Link to ALDs]
6.GM - Geometric Reasoning and Measurement
- 6.GM.A Solve real-world and mathematical problems involving area, surface area, and volume. [Link to ALDs]
6.DR - Data Reasoning
- 6.DR.A Formulate Statistical Investigative Questions. [Link to ALDs]
- 6.DR.B Collect and Consider Data.
- 6.DR.C Analyze, summarize, and describe data. [Link to ALDs]
- 6.DR.D Interpret data and answer investigative questions.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 7 Focus
Grade 7 Math Standards and Guidance
Critical Areas of Focus
In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
(1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.
(2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.
(3) Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
(4) Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.
NOTE: Links to Achievement Level Descriptors (ALDs) in the Content Explorer are provided for most clusters. ALDs describe the knowledge, skills, and processes that students demonstrate on state tests at pre-determined levels of achievement for each tested grade level. Explore more OSAS Math Test resources on ODE's Math Assessment webpage.
Domains and Clusters
7.AEE - Algebraic Reasoning: Expressions and Equations
- 7.AEE.A Use properties of operations to generate equivalent expressions. [Link to ALDs]
- 7.AEE.B Solve mathematical problems in authentic contexts using numerical and algebraic expressions and equations. [Link to ALDs]
7.RP - Proportional Reasoning: Ratios and Proportions
- 7.RP.A Analyze proportional relationships and use them to solve mathematical problems in authentic contexts. [Link to ALDs]
- 7.RP.B Investigate chance processes and develop, use, and evaluate probability models. [Link to ALDs]
7.NS - Numeric Reasoning: Number Systems
- 7.NS.A Apply and extend previous understandings of operations with fractions. [Link to ALDs]
7.GM - Geometric Reasoning and Measurement
- 7.GM.A Draw, construct, and describe geometrical figures and describe the relationships between them. [Link to ALDs]
- 7.GM.B Solve mathematical problems in authentic contexts involving angle measure, area, surface area, and volume. [Link to ALDs]
7.DR - Data Reasoning
- 7.DR.A Formulate Statistical Investigative Questions.
- 7.DR.B Collect and Consider Data. [Link to ALDs]
- 7.DR.C Analyze, summarize, and describe data. [Link to ALDs]
- 7.DR.D Interpret data and answer investigative questions.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: Grade 8 Focus
Grade 8 Math Standards and Guidance
Critical Areas of Focus
In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
(1) Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m·A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.
Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.
(2) Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.
(3) Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.
NOTE: Links to Achievement Level Descriptors (ALDs) in the Content Explorer are provided for most clusters. ALDs describe the knowledge, skills, and processes that students demonstrate on state tests at pre-determined levels of achievement for each tested grade level. Explore more OSAS Math Test resources on ODE's Math Assessment webpage.
Domains and Clusters
8.AEE - Algebraic Reasoning: Expressions and Equations
- 8.AEE.A Expressions and Equations Work with radicals and integer exponents. [Link to ALDs]
- 8.AEE.B Understand the connections between proportional relationships, lines, and linear equations. [Link to ALDs]
- 8.AEE.C Analyze and solve linear equations and pairs of simultaneous linear equations. [Link to ALDs]
8.AFN - Algebraic Reasoning: Functions
- 8.AFN.A Define, evaluate, and compare functions. [Link to ALDs]
- 8.AFN.B Use functions to model relationships between quantities. [Link to ALDs]
8.NS - Numeric Reasoning: Number Systems
- 8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers. [Link to ALDs]
8.GM - Geometric Reasoning and Measurement
- 8.GM.A Understand congruence and similarity using physical models, transparencies, or geometry software. [Link to ALDs]
- 8.GM.B Understand and apply the Pythagorean Theorem. [Link to ALDs]
- 8.GM.C Solve mathematical problems in authentic contexts involving volume of cylinders, cones, and spheres. [Link to ALDs]
8.DR - Data Reasoning
- 8.DR.A Formulate Statistical Investigative Questions.
- 8.DR.B Collect and Consider Data.
- 8.DR.C Analyze, summarize, and describe data. [Link to ALDs]
- 8.DR.D Interpret data and answer investigative questions.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work ( ) and, where appropriate, additional work ( ) can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade. For more information, see the K-8 major work of the grade developed by Student Achievement Partners.
2021 Oregon Math Guidance: HS Algebra Focus
HS Algebra Standards and Guidance
Critical Areas of Focus
Expressions
An expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels, the operation of evaluating a function. Conventions about the use of parentheses and the order of operations assure that each expression is unambiguous. Creating an expression that describes a computation involving a general quantity requires the ability to express the computation in general terms, abstracting from specific instances.
Reading an expression with comprehension involves analysis of its underlying structure. This may suggest a different but equivalent way of writing the expression that exhibits some different aspect of its meaning. For example, p + 0.05p can be interpreted as the addition of a 5% tax to a price p. Rewriting p + 0.05p as 1.05p shows that adding a tax is the same as multiplying the price by a constant factor.
Algebraic manipulations are governed by the properties of operations and exponents, and the conventions of algebraic notation. At times, an expression is the result of applying operations to simpler expressions. For example, p + 0.05p is the sum of the simpler expressions p and 0.05p. Viewing an expression as the result of operation on simpler expressions can sometimes clarify its underlying structure.
A spreadsheet or a computer algebra system (CAS) can be used to experiment with algebraic expressions, perform complicated algebraic manipulations, and understand how algebraic manipulations behave.
Equations and inequalities
An equation is a statement of equality between two expressions, often viewed as a question asking for which values of the variables the expressions on either side are in fact equal. These values are the solutions to the equation. An identity, in contrast, is true for all values of the variables; identities are often developed by rewriting an expression in an equivalent form.
The solutions of an equation in one variable form a set of numbers; the solutions of an equation in two variables form a set of ordered pairs of numbers, which can be plotted in the coordinate plane. Two or more equations and/or inequalities form a system. A solution for such a system must satisfy every equation and inequality in the system.
An equation can often be solved by successively deducing from it one or more simpler equations. For example, one can add the same constant to both sides without changing the solutions, but squaring both sides might lead to extraneous solutions. Strategic competence in solving includes looking ahead for productive manipulations and anticipating the nature and number of solutions.
Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of x + 1 = 0 is an integer, not a whole number; the solution of 2x + 1 = 0 is a rational number, not an integer; the solutions of x2 – 2 = 0 are real numbers, not rational numbers; and the solutions of x2 + 2 = 0 are complex numbers, not real numbers.
The same solution techniques used to solve equations can be used to rearrange formulas. For example, the formula for the area of a trapezoid, A = ((b1+b2)/2)h, can be solved for h using the same deductive process.
Inequalities can be solved by reasoning about the properties of inequality. Many, but not all, of the properties of equality continue to hold for inequalities and can be useful in solving them.
Connections to Functions and Modeling
Expressions can define functions, and equivalent expressions define the same function. Asking when two functions have the same value for the same input leads to an equation; graphing the two functions allows for finding approximate solutions of the equation. Converting a verbal description to an equation, inequality, or system of these is an essential skill in modeling.
Numbers and Number Systems
During the years from kindergarten to eighth grade, students must repeatedly extend their conception of number. At first, “number” means “counting number”: 1, 2, 3... Soon after that, 0 is used to represent “none” and the whole numbers are formed by the counting numbers together with zero. The next extension is fractions. At first, fractions are barely numbers and tied strongly to pictorial representations. Yet by the time students understand division of fractions, they have a strong concept of fractions as numbers and have connected them, via their decimal representations, with the base-ten system used to represent the whole numbers. During middle school, fractions are augmented by negative fractions to form the rational numbers. In Grade 8, students extend this system once more, augmenting the rational numbers with the irrational numbers to form the real numbers. In high school, students will be exposed to yet another extension of number, when the real numbers are augmented by the imaginary numbers to form the complex numbers.
With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system—integers, rational numbers, and real numbers—the four operations stay the same in two important ways: They have the commutative, associative, and distributive properties and their new meanings are consistent with their previous meanings.
Extending the properties of whole-number exponents leads to new and productive notation. For example, properties of whole-number exponents suggest that (51/3)3 should be 5(1/3)3 = 51 = 5 and that 51/3 should be the cube root of 5.
Calculators, spreadsheets, and computer algebra systems can provide ways for students to become better acquainted with these new number systems and their notation. They can be used to generate data for numerical experiments, to help understand the workings of matrix, vector, and complex number algebra, and to experiment with non-integer exponents.
Quantities
In real world problems, the answers are usually not numbers but quantities: numbers with units, which involves measurement. In their work in measurement up through Grade 8, students primarily measure commonly used attributes such as length, area, and volume. In high school, students encounter a wider variety of units in modeling, e.g., acceleration, currency conversions, derived quantities such as person-hours and heating degree days, social science rates such as per-capita income, and rates in everyday life such as points scored per game or batting averages. They also encounter novel situations in which they themselves must conceive the attributes of interest. For example, to find a good measure of overall highway safety, they might propose measures such as fatalities per year, fatalities per year per driver, or fatalities per vehicle-mile traveled. Such a conceptual process is sometimes called quantification. Quantification is important for science, as when surface area suddenly “stands out” as an important variable in evaporation. Quantification is also important for companies, which must conceptualize relevant attributes and create or choose suitable measures for them.
Domains and Clusters
HS.AEE - Algebraic Reasoning: Expressions and Equations
- HS.AEE.A Use algebraic reasoning to rewrite expressions in equivalent forms.
- HS.AEE.B Use algebraic reasoning to find solutions to an equation, inequality, and systems of equations or inequalities.
- HS.AEE.C Analyze the structure of an equation or inequality to determine an efficient strategy to find and justify a solution.
- HS.AEE.D Make predictions in different applications using expressions, equations, and inequalities to analyze authentic contexts.
HS.AFN - Algebraic Reasoning: Functions
- HS.AFN.A Describe functions by using both symbolic and graphical representations.
- HS.AFN.B Compare and relate functions using common attributes.
- HS.AFN.C Represent functions graphically and interpret key features in terms of the equivalent symbolic representation.
- HS.AFN.D Model a wide variety of authentic situations using functions through the process of making and changing assumptions, assigning variables, and finding solutions to contextual problems.
HS.NQ - Numeric Reasoning: Number and Quantity
- HS.NQ.A Understand and apply the real number system.
- HS.NQ.B Attend to units of measurement needed to solve problems through quantitative reasoning and mathematical modeling.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work () and, where appropriate, additional work () can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time
2021 Oregon Math Guidance: HS Geometry Focus
HS Geometry Standards and Guidance
Critical Areas of Focus
Geometric Reasoning
An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most efficient use of material.
Although there are many types of geometry, school mathematics is devoted primarily to plane Euclidean geometry, studied both synthetically (without coordinates) and analytically (with coordinates). During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions and developing careful proofs. Later in college some students develop Euclidean and other geometries carefully from a small set of axioms.
Congruence, similarity, and symmetry
The concepts of congruence, similarity, and symmetry can be understood from the perspective of geometric transformation. Fundamental are the rigid motions: translations, rotations, reflections, and combinations of these, all of which are here assumed to preserve distance and angles (and therefore shapes generally). Reflections and rotations each explain a particular type of symmetry, and the symmetries of an object offer insight into its attributes—as when the reflective symmetry of an isosceles triangle assures that its base angles are congruent.
In the approach taken here, two geometric figures are defined to be congruent if there is a sequence of rigid motions that carries one onto the other. This is the principle of superposition. For triangles, congruence means the equality of all corresponding pairs of sides and all corresponding pairs of angles. During the middle grades, through experiences drawing triangles from given conditions, students notice ways to specify enough measures in a triangle to ensure that all triangles drawn with those measures are congruent. Once these triangle congruence criteria (ASA, SAS, and SSS) are established using rigid motions, they can be used to prove theorems about triangles, quadrilaterals, and other geometric figures.
Similarity transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence, thereby formalizing the similarity ideas of "same shape" and "scale factor" developed in the middle grades. These transformations lead to the criterion for triangle similarity that two pairs of corresponding angles are congruent.
The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and similarity, and, with the Pythagorean Theorem, are fundamental in many real-world and theoretical situations.
Dynamic geometry environments provide students with experimental and modeling tools that allow them to investigate geometric phenomena in much the same way as computer algebra systems allow them to experiment with algebraic phenomena.
Connections to Equations.
The correspondence between numerical coordinates and geometric points allows methods from algebra to be applied to geometry and vice versa. The solution set of an equation becomes a geometric curve, making visualization a tool for doing and understanding algebra. Geometric shapes can be described by equations, making algebraic manipulation into a tool for geometric understanding, modeling, and proof.
Domains and Clusters
Geometric Reasoning and Measurement (HS.GM)
- HS.GM.A Apply geometric transformations to figures through analysis of graphs and understanding of functions.
- HS.GM.B Construct and communicate geometric arguments through use of proofs, logical reasoning, and geometric technology.
- HS.GM.C Solve problems and interpret solutions of area and volume of shapes by applying concepts of congruence, similarity, symmetry in authentic contexts.
- HS.GM.D Apply concepts of right triangle trigonometry in authentic contexts to solve problems and interpret solutions.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work () and, where appropriate, additional work () can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time
2021 Oregon Math Guidance: HS Data & Statistics Focus
HS Data & Statistics Standards and Guidance
Critical Areas of Focus
Decisions or predictions are often based on data—numbers in context. These decisions or predictions would be easy if the data always sent a clear message, but the message is often obscured by variability. Statistics provides tools for describing variability in data and for making informed decisions that take it into account.
Questioning in Statistics
The statistical problem-solving process typically starts with a statistical investigative question, followed by a study designed to collect data that aligns with answering the question. Analysis of the data is also guided by questioning. Constant questioning and interrogation of the data throughout the statistical problem-solving process can lead to the posing of new statistical investigative questions.
Often when considering secondary data, the data need to first be interrogated – how were measurements made, what type of data were selected, what is the meaning of the data, and what was the study design to collect the data. Once a better understanding of the data has been gained, then one can judge whether the data set is appropriate for exploring the original statistical investigative question or one can pose statistical investigative questions that can be explored with the secondary data set.
Analyze, summarize, and describe data
Data are gathered, displayed, summarized, examined, and interpreted to discover patterns and deviations from patterns. Quantitative data can be described in terms of key characteristics: measures of shape, center, and spread. The shape of a data distribution might be described as symmetric, skewed, flat, or bell shaped, and it might be summarized by a statistic measuring center (such as mean or median) and a statistic measuring spread (such as standard deviation or interquartile range). Different distributions can be compared numerically using these statistics or compared visually using plots. Knowledge of center and spread are not enough to describe a distribution. Which statistics to compare, which plots to use, and what the results of a comparison might mean, depend on the question to be investigated and the real-life actions to be taken.
Technology in Statistics
The teaching of statistics has been greatly enhanced, moving from teaching with no technology to teaching with integrated technology. The field has evolved from using programming languages in the 1980s to hand-held statistical calculators in the 1990s to online statistical calculators, powerful statistical software packages, and amazing data visualization tools. Simulation is now as easy as accessing a public applet where point-and-click options provide the ability to perform thousands of trials. Computer labs are not necessary – just internet access. Moving to web-based technology allows more access to data visualization, exploration of data, and simulation. However, access to technology varies across school districts. Not all classrooms are equipped with internet access or technology hardware and software. Modern statistical practice is intertwined with technology; thus, it is recommended that technology be embraced to the greatest extent possible within a given circumstance.
Connections to Functions and Modeling.
Functions may be used to describe data; if the data suggest a linear relationship, the relationship can be modeled with a regression line, and its strength and direction can be expressed through a correlation coefficient.
Domains and Clusters
Data Reasoning and Probability (HS.DR)
- HS.DR.A Formulate Statistical Investigative Questions.
- HS.DR.B Collect and Consider Data.
- HS.DR.C Analyze, summarize, and describe data.
- HS.DR.D Interpret data and answer investigative questions.
- HS.DR.E Understand independence and conditional probability and use them to interpret data.
Students should spend the large majority1 of their time on the major work of the grade ( ). Supporting work () and, where appropriate, additional work () can engage students in the major work of the grade.
1At least 65% and up to approximately 85% of class time