Oklahoma Academic Standards for Mathematics Correlation to
Oklahoma Academic Standards for Mathematics Correlation to Eureka Math Grade 7 June 2016
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Grade 7 Mathematics Many of the Grade 7 Oklahoma Academic Standards for Mathematics (OAS) will require the use of Eureka Math™ content from another grade, or supplemental materials. A detailed analysis of alignment is provided in the table below. With strategic placement of supplemental materials, Eureka Math can ensure that students are successful in achieving the proficiencies of the Oklahoma Academic Standards for Mathematics while still benefiting from the coherence and rigor of Eureka Math. Indicators Green indicates that the OAS is fully addressed in Eureka Math. Yellow indicates that the OAS may not be completely addressed in Eureka Math. Red indicates that the OAS is not addressed in Eureka Math. Blue indicates that there is a discrepancy between the grade level at which the OAS and Eureka Math address the content.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Mathematical Actions and Processes Develop a Deep and Flexible Conceptual Understanding Demonstrate a deep and flexible conceptual understanding of mathematical concepts, operations, and relations while making mathematical and real‐world connections. Students will develop an understanding of how and when to apply and use the mathematics they know to solve problems.
Aligned Components of Eureka Math Lessons in every module engage students in developing a deep and flexible conceptual understanding as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 1 and 2, which are specifically addressed in the following modules: G7 M1: Ratios and Proportional Relationships G7 M2: Rational Numbers G7 M3: Expressions and Equations G7 M4: Percent and Proportional Relationships G7 M5: Statistics and Probability G7 M6: Geometry
Develop Accurate and Appropriate Procedural Fluency Learn efficient procedures and algorithms for computations and repeated processes based on a strong sense of numbers. Develop fluency in addition, subtraction, multiplication, and division of numbers and expressions. Students will generate a sophisticated understanding of the development and application of algorithms and procedures.
Lessons in every module engage students in developing accurate and appropriate procedural fluency as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 7 and 8, which are specifically addressed in the following modules: G7 M2: Rational Numbers G7 M3: Expressions and Equations G7 M4: Percent and Proportional Relationships G7 M6: Geometry
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Mathematical Actions and Processes
Aligned Components of Eureka Math
Develop Strategies for Problem Solving Analyze the parts of complex mathematical tasks and identify entry points to begin the search for a solution. Students will select from a variety of problem solving strategies and use corresponding multiple representations (verbal, physical, symbolic, pictorial, graphical, tabular) when appropriate. They will pursue solutions to various tasks from real‐ world situations and applications that are often interdisciplinary in nature. They will find methods to verify their answers in context and will always question the reasonableness of solutions.
Lessons in every module engage students in developing strategies for problem solving as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 1, 2, and 8, which are specifically addressed in the following modules: G7 M1: Ratios and Proportional Relationships G7 M2: Rational Numbers G7 M3: Expressions and Equations G7 M4: Percent and Proportional Relationships G7 M5: Statistics and Probability G7 M6: Geometry
Develop Mathematical Reasoning Explore and communicate a variety of reasoning strategies to think through problems. Students will apply their logic to critique the thinking and strategies of others to develop and evaluate mathematical arguments, including making arguments and counterarguments and making connections to other contexts.
Lessons in every module engage students in developing mathematical reasoning as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 3, which is specifically addressed in the following modules: G7 M5: Statistics and Probability G7 M6: Geometry
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Mathematical Actions and Processes
Aligned Components of Eureka Math
Develop a Productive Mathematical Disposition Hold the belief that mathematics is sensible, useful and worthwhile. Students will develop the habit of looking for and making use of patterns and mathematical structures. They will persevere and become resilient, effective problem solvers.
Lessons in every module engage students in developing a productive mathematical disposition as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 1, 7, and 8, which are specifically addressed in the following modules: G7 M1: Ratios and Proportional Relationships G7 M2: Rational Numbers G7 M3: Expressions and Equations G7 M4: Percent and Proportional Relationships G7 M6: Geometry
Develop the Ability to Make Conjectures, Model, and Generalize Make predictions and conjectures and draw conclusions throughout the problem solving process based on patterns and the repeated structures in mathematics. Students will create, identify, and extend patterns as a strategy for solving and making sense of problems.
Lessons in every module engage students in developing the ability to make conjectures, model, and generalize as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 4, 7, and 8, which are specifically addressed in the following modules: G7 M2: Rational Numbers G7 M3: Expressions and Equations G7 M4: Percent and Proportional Relationships G7 M5: Statistics and Probability G7 M6: Geometry
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Mathematical Actions and Processes Develop the Ability to Communicate Mathematically Students will discuss, write, read, interpret and translate ideas and concepts mathematically. As they progress, students’ ability to communicate mathematically will include their increased use of mathematical language and terms and analysis of mathematical definitions.
Aligned Components of Eureka Math Lessons in every module engage students in developing the ability to communicate mathematically as required by this standard. This process standard is analogous to the CCSSM Standards for Mathematical Practice 3 and 6, which are specifically addressed in the following modules: G7 M2: Rational Numbers G7 M3: Expressions and Equations G7 M4: Percent and Proportional Relationships G7 M5: Statistics and Probability G7 M6: Geometry
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
Number & Operations (N) 7.N.1 Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals.
7.N.1.1 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.
G7 M2 Lesson 14: Converting Rational Numbers to Decimals Using Long Division G6 M3 Lesson 6: Rational Numbers on the Number Line Note: Students are introduced to writing rational numbers as the ratio of two integers in Grade 6. They extend this knowledge in Grade 7, where they recognize terminating and repeating decimals.
7.N.1.2 Compare and order rational numbers expressed in various forms using the symbols , , and .
G6 M3 Topic B: Order and Absolute Value
7.N.1.3 Recognize and generate equivalent representations of rational numbers, including equivalent fractions.
G7 M2 Lesson 13: Converting Between Fractions and Decimals Using Equivalent Fractions G7 M2 Lesson 14: Converting Rational Numbers to Decimals Using Long Division G5 M3 Topic A: Equivalent Fractions G5 M4 Lesson 21: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1. G4 M5: Fraction Equivalence, Ordering, and Operations G3 M5 Topic E: Equivalent Fractions
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Correlation to Eureka Math
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Standard 7.N.2 Calculate with integers and rational numbers, with and without positive integer exponents, to solve real‐world and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero.
Objective
Aligned Components of Eureka Math
7.N.2.1 Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results.
Although Eureka Math addresses estimation of whole numbers and there is extensive work with integers in Grade 7 Module 2, estimation involving integers is not explicitly taught.
7.N.2.2 Illustrate multiplication and division of integers using a variety of representations.
G7 M2 Topic B: Multiplication and Division of Integers and Rational Numbers
7.N.2.3 Solve real‐world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms.
G7 M2: Rational Numbers
7.N.2.4 Raise integers to positive integer exponents.
G8 M1 Lesson 1: Exponential Notation
Note: Supplemental materials for visual models and representations are required to completely fulfill the intent of the standard.
G7 M3: Expressions and Equations Note: In Modules 2 and 3, students work extensively with negative rational numbers. In addition, the entire Grade 7 curriculum offers students multiple opportunities to solve problems involving operations with rational numbers.
G6 M4 Lesson 5: Exponents Note: Grade 6 introduces exponential notation with positive integer bases, and Grade 8 expands this learning to explicitly address raising a rational number to a power.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
7.N.2.5 Solve real‐world and mathematical problems involving calculations with rational numbers and positive integer exponents.
G8 M1 Topic A: Exponential Notation and Properties of Integer Exponents G7 M2: Rational Numbers G6 M4 Lesson 6: The Order of Operations Note: Grade 8 extends learning to properties of exponents.
7.N.2.6 Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value.
G6 M3 Lesson 11: Absolute Value—Magnitude and Distance
Algebraic Reasoning & Algebra (A) 7.A.1 Understand the concept of proportionality in real‐world and mathematical situations, and distinguish between proportional and other relationships.
7.A.1.1 Describe that the relationship between two variables, and , is proportional if it can be expressed in the form or ; distinguish proportional relationships from other relationships, including inversely proportional relationships ( or ).
G7 M1 Topic B: Unit Rate and the Constant of Proportionality
7.A.1.2 Recognize that the graph of a proportional relationship is a line through the origin and the coordinate 1, , where both and the slope are the unit rate (constant of proportionality, ).
G7 M1 Lesson 10: Interpreting Graphs of Proportional Relationships
Note: Supplemental materials are needed to address inversely proportional relationships.
G7 M1 Lesson 15: Equations of Graphs of Proportional Relationships Involving Fractions
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
7.A.2 Recognize proportional relationships in real‐world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols, and graphs; solve problems involving proportional relationships and interpret results in the original context.
7.A.2.1 Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.
G7 M1: Ratios and Proportional Relationships
7.A.2.2 Solve multi‐step problems involving proportional relationships involving distance‐time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real‐world and mathematical situations.
G7 M1: Ratios and Proportional Relationships
7.A.2.3 Use proportional reasoning to solve real‐world and mathematical problems involving ratios.
G7 M1: Ratios and Proportional Relationships
7.A.2.4 Use proportional reasoning to assess the reasonableness of solutions.
G7 M1: Ratios and Proportional Relationships
7.A.3.1 Write and solve problems leading to linear equations with one variable in the form and , where , , and are rational numbers.
G7 M2 Lesson 17: Comparing Tape Diagram Solutions to Algebraic Solutions
7.A.3 Represent and solve linear equations and inequalities.
Aligned Components of Eureka Math
G7 M4: Percent and Proportional Relationships
G7 M4: Percent and Proportional Relationships
G7 M2 Lessons 22–23: Solving Equations Using Algebra G7 M3 Topic B: Solve Problems Using Expressions, Equations, and Inequalities
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective 7.A.3.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form and where and are nonnegative rational numbers.
Aligned Components of Eureka Math G7 M3 Lesson 12: Properties of Inequalities ,
G7 M3 Lesson 13: Inequalities G7 M3 Lesson 14: Solving Inequalities G7 M3 Lesson 15: Graphing Solutions to Inequalities G6 M4 Lesson 33: From Equations to Inequalities G6 M4 Lesson 34: Writing and Graphing Inequalities in Real‐World Problems Note: The foundational work with inequalities begins in Grade 6. This work is extended in Grade 7 and includes instances where and are negative rational numbers, and inequalities are in the form and .
7.A.3.3 Represent real‐world or mathematical situations using equations and inequalities involving variables and rational numbers.
G7 M2 Lesson 17: Comparing Tape Diagram Solutions to Algebraic Solutions G7 M2 Lessons 22–23: Solving Equations Using Algebra G7 M3 Topic B: Solve Problems Using Expressions, Equations, and Inequalities
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Correlation to Eureka Math
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Standard 7.A.4 Use order of operations and properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols; evaluate such expressions.
Objective
Aligned Components of Eureka Math
7.A.4.1 Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.
G8 M1 Topic A: Exponential Notation and Properties of Integer Exponents G7 M2 Lessons 18–19: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers G7 M3 Topic A: Use Properties of Operations to Generate Equivalent Expressions Note: The use of properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols is addressed in Grade 7. It is extended in Grade 8, which addresses whole number exponents.
7.A.4.2 Apply understanding of order of operations and grouping symbols when using calculators and other technologies.
Using calculators and other technologies to apply understanding of the order of operations and grouping symbols requires the use of supplemental materials.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
Geometry & Measurement (GM) 7.GM.1 Develop and understand the concept of surface area and volume of rectangular prisms.
7.GM.1.1 Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism with rational‐valued edge lengths can be found by wrapping the figure with same‐sized square units without gaps or overlap. Use appropriate measurements such as cm .
G7 M3 Lessons 21–22: Surface Area G7 M3 Lessons 25–26: Volume and Surface Area G7 M6 Lessons 23–24: Surface Area G6 M5 Topic D: Nets and Surface Area Note: In Grade 6, students use nets to visualize the surface area of a rectangular prism and develop the formula for surface area. This learning is extended in Grade 7 as students explore surface area in more complex contexts.
7.GM.1.2 Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms with rational‐valued edge lengths can be found by counting the total number of same‐sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements such as cm .
G6 M5 Topic C: Volume of Right Rectangular Prisms G5 M5 Topic A: Concepts of Volume G5 M5 Topic B: Volume and the Operations of Multiplication and Addition Note: Volume is introduced in Grade 5 through concrete exploration and, ultimately, the development of the formula for right rectangular prisms. This learning continues in Grade 6, where students find the volume of right rectangular prisms with fractional edge lengths, and is extended in Grade 7, where students use the formula to solve problems.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
7.GM.2 Determine the area of trapezoids and area and perimeter of composite figures.
7.GM.2.1 Develop and use the formula to determine the area of a trapezoid to solve problems.
G7 M3 Lesson 19: Unknown Area Problems on the Coordinate Plane G6 M5 Lesson 5: The Area of Polygons Through Composition and Decomposition Note: Area of a trapezoid is introduced in Grade 6 as composite areas and then extended in Grade 7 as students find the area of various polygons in the coordinate plane. Supplemental materials are needed to address the development of the formula.
7.GM.2.2 Find the area and perimeter of composite figures to solve real‐world and mathematical problems.
G7 M3 Lesson 18: More Problems on Area and Circumference G7 M3 Lesson 20: Composite Area Problems G7 M6 Lesson 20: Real‐World Area Problems G6 M5 Lesson 6: Area in the Real World Note: In Grade 6, students find the area of composite figures and extend this learning in Grade 7. Supplemental materials are necessary for calculating the perimeter of composite figures.
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Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
7.GM.3 Use reasoning with proportions and ratios to determine measurements, justify formulas, and solve real‐ world and mathematical problems involving circles and related geometric figures.
7.GM.3.1 Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is and can be approximated by rational numbers such as and 3.14.
G7 M3 Lesson 16: The Most Famous Ratio of All
7.GM.3.2 Calculate the circumference and area of circles to solve problems in various contexts, in terms of and using approximations for .
G7 M3 Lesson 16: The Most Famous Ratio of All G7 M3 Lesson 17: The Area of a Circle G7 M3 Lesson 18: More Problems on Area and Circumference G7 M3 Lesson 20: Composite Area Problems G7 M6 Lesson 22: Area Problems with Circular Regions
7.GM.4 Analyze the effect of dilations, translations, and reflections on the attributes of two‐ dimensional figures on and off the coordinate plane.
7.GM.4.1 Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.
G8 M3: Similarity
7.GM.4.2 Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar triangles and rectangles.
G8 M3 Lesson 11: More About Similar Triangles G8 M3 Lesson 12: Modeling Using Similarity G7 M1 Topic D: Ratios of Scale Drawings Note: Students solve problems involving scale drawings in Grade 7 but do not determine side lengths of similar triangles until Grade 8.
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Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
7.GM.4.3 Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation.
G8 M2 Topic A: Definitions and Properties of the Basic Rigid Motions G8 M2 Topic B: Sequencing the Basic Rigid Motions Note: Most transformations in Eureka Math are described as in a plane, not just the coordinate plane. The lessons listed above include instruction in both contexts.
Data & Probability (D) 7.D.1 Display and analyze data in a variety of ways.
7.D.1.1 Design simple experiments, collect data and calculate measures of central tendency (mean, median, and mode) and spread (range). Use these quantities to draw conclusions about the data collected and make predictions.
G6 M6: Statistics
7.D.1.2 Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.
G6 M6 Lesson 4: Creating a Histogram
Note: Grade 6 Module 6 provides students with opportunities to collect and describe data using measures of center (mean and median) and variability (mean absolute deviation and interquartile range). Grade 7 provides an extension where students explore sampling methods and variability and use sample data to compare populations, using statistical measures of center and variability. Teachers need to supplement to address mode and range, as well as use statistical measures to make predictions.
G6 M6 Lesson 5: Describing a Distribution Displayed in a Histogram Note: Supplemental materials are needed to address circle graphs, spreadsheets, and other graphing technology.
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Correlation to Eureka Math
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Standard 7.D.2 Calculate probabilities and reason about probabilities using proportions to solve real‐world and mathematical problems.
Objective
Aligned Components of Eureka Math
7.D.2.1 Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1.
G7 M5 Lesson 1: Chance Experiments G7 M5 Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes G7 M5 Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities G7 M5 Lesson 9: Comparing Estimated Probabilities to Probabilities Predicted by a Model
7.D.2.2 Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.
G7 M5 Topic A: Calculating and Interpreting Probabilities G7 M5 Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities G7 M5 Lesson 9: Comparing Estimated Probabilities to Probabilities Predicted by a Model Note: Supplemental materials are needed to address geometric probability and to determine the fraction of area.
7.D.2.3 Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.
G7 M5 Topic A: Calculating and Interpreting Probabilities G7 M5 Topic B: Estimating Probabilities
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Correlation to Eureka Math
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Critical Gaps for 2016–2017 G6 M5 Lesson 15: Representing Three‐Dimensional Figures Using Nets
5.GM.1 Describe, classify, and draw representations of two‐ and three‐ dimensional figures.
5.GM.1.3 Recognize and draw a net for a three‐dimensional figure (e.g., cubes, rectangular prisms, pyramids).
5.GM.2 Understand how the volume of rectangular prisms and surface area of shapes with polygonal faces are determined by the dimensions of the object and that shapes with varying dimensions can have equivalent values of surface area or volume.
5.GM.2.1 Recognize that the volume of rectangular prisms can be determined by the number of cubes ( ) and by the product of the dimensions of the prism ( ). Know that rectangular prisms of different dimensions ( , , and ) can have the same volume if .
G5 M5 Lesson 7: Solve word problems involving the volume of rectangular prisms with whole number edge lengths.
5.GM.2.2 Recognize that the surface area of a three‐dimensional figure with rectangular faces with whole numbered edges can be found by finding the area of each component of the net of that figure. Know that three‐dimensional shapes of different dimensions can have the same surface area.
G6 M5 Lesson 17: From Nets to Surface Area
G6 M5 Lesson 16: Constructing Nets G6 M5 Lesson 17: From Nets to Surface Area
Note: In order to meet the standard, extend lessons to include three‐dimensional shapes of different dimensions with the same surface area.
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Correlation to Eureka Math
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6.N.3 Understand the concept of ratio and its relationship to fractions and percents and to the multiplication and division of whole numbers. Use ratios to solve real‐world and mathematical problems.
6.N.3.3 Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.
G7 M4: Percent and Proportional Relationships
6.GM.1 Calculate area of squares, parallelograms, and triangles to solve real‐world and mathematical problems.
6.GM.1.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm.
G6 M5 Lesson 1: The Area of Parallelograms Through Rectangle Facts
6.GM.1.2 Develop and use formulas to determine the area of triangles.
G6 M5 Topic A: Area of Triangles, Quadrilaterals, and Polygons
6.GM.1.3 Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real‐world and mathematical problems.
G6 M5 Topic A: Area of Triangles, Quadrilaterals, and Polygons
G6 M1: Ratios and Unit Rates Note: Students start working with percentages in Grade 6 but extend their knowledge in Grade 7. This extension also includes working with mixtures and concentrations.
G4 M3 Topic A: Multiplicative Comparison Word Problems
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Correlation to Eureka Math
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6.GM.4 Use translations, reflections, and rotations to establish congruency and understand symmetries.
6.GM.4.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two‐dimensional figure.
G8 M2: The Concept of Congruence
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Correlation to Eureka Math
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