Oklahoma Academic Standards for Mathematics Correlation to ...
Oklahoma Academic Standards for Mathematics Correlation to Eureka Math Pre‐Algebra June 2016
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Pre‐Algebra Mathematics Many of the Pre‐Algebra Oklahoma Academic Standards for Mathematics (OAS) will require the use of Eureka Math™ content from another grade or course, or supplemental materials. Please note that the majority of the Pre‐Algebra standards are included in the Grade 8 Eureka Math curriculum. 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 addresses aspects of the CCSSM Standards for Mathematical Practice 1 and 2, which are specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M2: The Concept of Congruence G8 M4: Linear Equations G8 M5: Examples of Functions from Geometry G8 M6: Linear Functions
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 addresses aspects of the CCSSM Standards for Mathematical Practice 7 and 8, which are specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M3: Similarity G8 M4: Linear Equations G8 M5: Examples of Functions from Geometry G8 M6: Linear Functions G8 M7: Introduction to Irrational Numbers Using Geometry
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Mathematical Actions and Processes 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.
Aligned Components of Eureka Math Lessons in every module engage students in developing strategies for problem solving as required by this standard. This process standard addresses aspects of the CCSSM Standards for Mathematical Practice 1, 2, and 8, which are specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M2: The Concept of Congruence G8 M3: Similarity G8 M4: Linear Equations G8 M5: Examples of Functions from Geometry G8 M6: Linear Functions G8 M7: Introduction to Irrational Numbers Using 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 addresses aspects of the CCSSM Standards for Mathematical Practice 3, which is specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M2: The Concept of Congruence G8 M3: Similarity G8 M4: Linear Equations
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Mathematical Actions and Processes 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.
Aligned Components of Eureka Math Lessons in every module engage students in developing a productive mathematical disposition as required by this standard. This process standard addresses aspects of the CCSSM Standards for Mathematical Practice 1, 7, and 8, which are specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M4: Linear Equations G8 M5: Examples of Functions from Geometry G8 M6: Linear Functions G8 M7: Introduction to Irrational Numbers Using 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 addresses aspects of the CCSSM Standards for Mathematical Practice 4, 7, and 8, which are specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M3: Similarity G8 M4: Linear Equations G8 M5: Examples of Functions from Geometry G8 M6: Linear Functions G8 M7: Introduction to Irrational Numbers Using 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 addresses aspects of the CCSSM Standards for Mathematical Practice 3 and 6, which are specifically addressed in the following modules: G8 M1: Integer Exponents and Scientific Notation G8 M2: The Concept of Congruence G8 M3: Similarity G8 M4: Linear Equations G8 M5: Examples of Functions in Geometry G8 M6: Linear Functions G8 M7: Introduction to Irrational Numbers Using Geometry
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
Number & Operations (N) PA.N.1 Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts.
PA.N.1.1 Develop and apply the properties of integer exponents, including 1 (with 0), to generate equivalent numerical and algebraic expressions.
G8 M1 Topic A: Exponential Notation and Properties of Integer Exponents
PA.N.1.2 Express and compare approximations of very large and very small numbers using scientific notation.
G8 M1 Lesson 7: Magnitude G8 M1 Lesson 8: Estimating Quantities G8 M1 Lesson 13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology
PA.N.1.3 Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.
G8 M1 Topic B: Magnitude and Scientific Notation
PA.N.1.4 Classify real numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational number and an irrational number is irrational; and the product of a non‐zero rational number and an irrational number is irrational.
Algebra I M1 Topic B: The Structure of Expressions
Note: Eureka Math lessons include all four operations. These lessons exceed the standard, and modifications may need to be made.
Algebra I M4 Lesson 13: Solving Quadratic Equations by Completing the Square G8 M7 Topic B: Decimal Expansions of Numbers Note: Algebra I includes sum and product references. Supplemental materials will be needed to address closure.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
PA.N.1.5 Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.
G8 M7 Topic A: Square and Cube Roots G8 M7 Lesson 10: Converting Repeating Decimals to Fractions G8 M7 Lesson 11: The Decimal Expansion of Some Irrational Numbers G8 M7 Lesson 13: Comparing Irrational Numbers G8 M7 Lesson 14: Decimal Expansion of
Algebraic Reasoning & Algebra (A) PA.A.1 Understand the concept of function in real‐ world and mathematical situations, and distinguish between linear and nonlinear functions.
PA.A.1.1 Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable.
G8 M5 Lesson 1: The Concept of a Function
PA.A.1.2 Use linear functions to represent and explain real‐world and mathematical situations.
G8 M6 Topic A: Linear Functions
G8 M5 Lesson 2: Formal Definition of a Function Note: Throughout Module 5 Topic A, the terms input and output are used instead of independent variable and dependent variable.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math G8 M5 Lesson 3: Linear Functions and Proportionality
PA.A.1.3 Identify a function as linear if it can be expressed in the form or if its graph is a straight line.
G8 M5 Lesson 5: Graphs of Functions and Equations G8 M5 Lesson 6: Graphs of Linear Functions and Rate of Change G8 M6 Topic A: Linear Functions
PA.A.2 Recognize linear functions in real‐ world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret results in the original context.
PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.
G8 M5 Topic A: Functions
PA.A.2.2 Identify, describe, and analyze linear relationships between two variables.
G8 M6 Topic A: Linear Functions
PA.A.2.3 Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the ‐intercept is zero when the function represents a proportional relationship.
G8 M4 Topic B: Linear Equations in Two Variables and Their Graphs
G8 M6 Topic A: Linear Functions
G8 M4 Topic C: Slope and Equations of Lines G8 M6 Topic A: Linear Functions Notes: Grade 7 Module 1 Topics A and B lay the groundwork for students in Grade 8/Pre‐Algebra by representing proportional relationships with equations and interpreting graphs of proportional relationships.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
PA.A.2.4 Predict the effect on the graph of a linear function when the slope or ‐intercept changes. Use appropriate tools to examine these effects.
G8 M4 Topic B: Linear Equations in Two Variables and Their Graphs G8 M4 Topic C: Slope and Equations of Lines G8 M5 Lesson 7: Comparing Linear Functions and Graphs G8 M6 Topic A: Linear Functions Note: Cited lessons and topics provide the foundation for understanding slope and intercepts in general. Supplemental tools that examine the effects of these changes will need to be added to meet the standard.
PA.A.2.5 Solve problems involving linear functions and interpret results in the original context.
G8 M4 Topic B: Linear Equations in Two Variables and Their Graphs G8 M5 Lesson 7: Comparing Linear Functions and Graphs G8 M6 Topic A: Linear Functions
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard PA.A.3 Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.
Objective
Aligned Components of Eureka Math G8 M4 Topic A: Writing and Solving Linear Equations
PA.A.3.1 Use substitution to simplify and evaluate algebraic expressions.
G6 M4 Topic C: Replacing Letters and Numbers G6 M4 Topic F: Writing and Evaluating Expressions and Formulas Note: Students begin formally replacing letters with numbers in Grade 6 Module 4 and continue throughout Grades 6 and 7. In Grade 8/Pre‐Algebra, students evaluate algebraic expressions in the context of checking the solution to a linear equation.
PA.A.3.2 Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations, including grouping symbols.
G8 M4 Topic A: Writing and Solving Linear Equations Note: In Grades 6 and 7, students learn skills involving symbolic notation, expressions, and properties of equality. They use these skills in Grade 8/Pre‐Algebra to transcribe and solve equations in one and two variables.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard PA.A.4 Represent real‐ world and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context.
Objective
Aligned Components of Eureka Math
PA.A.4.1 Illustrate, write, and solve mathematical and real‐world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret solutions in the original context.
G8 M4 Topic A: Writing and Solving Linear Equations
PA.A.4.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form and , where , , and are rational numbers.
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
PA.A.4.3 Represent real‐world situations using equations and inequalities involving one variable.
G8 M4 Topic A: Writing and Solving Linear Equations 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 G7 M4 Lesson 10: Simple Interest G7 M4 Lesson 11: Tax, Commissions, Fees, and Other Real‐World Percent Applications G7 M4 Lesson 17: Mixture Problems Note: Grade 7 lessons also include two‐variable equations.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
Geometry & Measurement (GM) PA.GM.1 Solve problems involving right triangles using the Pythagorean Theorem.
PA.GM.1.1 Informally justify the Pythagorean Theorem using measurements, diagrams or dynamic software and use the Pythagorean Theorem to solve problems in two and three dimensions involving right triangles.
G8 M2 Topic D: The Pythagorean Theorem G8 M3 Topic C: The Pythagorean Theorem G8 M7 Topic A: Square and Cube Roots G8 M7 Topic C: The Pythagorean Theorem G8 M7 Lesson 19: Cones and Spheres G8 M7 Lesson 23: Nonlinear Motion
PA.GM.2 Calculate surface area and volume of three‐ dimensional figures.
PA.GM.1.2 Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.
G8 M2 Lesson 16: Applications of the Pythagorean Theorem
PA.GM.2.1 Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as cm .
G7 M3 Lessons 21–22: Surface Area
G8 M7 Lesson 17: Distance on the Coordinate Plane
G7 M6 Lessons 23–24: Surface Area G6 M5 Topic D: Nets and Surface Area
PA.GM.2.2 Calculate the surface area of a cylinder, in terms of and using approximations for , using decomposition or nets. Use appropriate measurements such as cm .
G7 M3 Lessons 21–22: Surface Area Note: Foundational knowledge for surface area can be found in Grade 7 Module 3. Grade 8 materials deal only with the volume of a cylinder. Supplemental material will be needed to address the surface area of a cylinder.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
PA.GM.2.3 Develop and use the formulas and to determine the volume of rectangular prisms. Justify why base area ( ) and height ( ) are multiplied to find the volume of a rectangular prism. Use appropriate measurements such as cm .
G8 M5 Lesson 9: Examples of Functions from Geometry G8 M5 Lesson 10: Volumes of Familiar Solids—Cones and Cylinders G7 M3 Lessons 23–24: The Volume of a Right Prism G7 M3 Lessons 25–26: Volume and Surface Area G7 M6 Topic E: Problems Involving Volume
PA.GM.2.4 Develop and use the formulas and to determine the volume of right cylinders, in terms of and using approximations for . Justify why base area ( ) and height ( ) are multiplied to find the volume of a right cylinder. Use appropriate measurements such as cm .
G8 M5 Lesson 10: Volumes of Familiar Solids—Cones and Cylinders G8 M5 Lesson 11: Volume of a Sphere G8 M7 Lesson 21: Volume of Composite Solids Note: Module 5 Lesson 11 and Module 7 Lesson 21 use the volume of cylinders to compare to and determine the volume of spheres.
Oklahoma Academic Standards for Mathematics
Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
Data & Probability (D) PA.D.1 Display and interpret data in a variety of ways, including using scatterplots and approximate lines of best fit. Use line of best fit and average rate of change to make predictions and draw conclusions about data.
PA.D.1.1 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact.
Algebra I M2 Lesson 3: Estimating Centers and Interpreting the Mean as a Balance Point Algebra I M2 Topic B: Describing Variability and Comparing Distributions Note: Supplemental materials will be needed for the technology component of this standard. Algebra I M2 Lesson 3: Estimating Centers and Interpreting the Mean as a Balance Point
PA.D.1.2 Explain how outliers affect measures of central tendency.
Algebra I M2 Lesson 7: Measuring Variability for Skewed Distributions (Interquartile Range) Algebra I M2 Lesson 8: Comparing Distributions
PA.D.1.3 Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units.
G8 M6 Topic B: Bivariate Numerical Data G8 M6 Topic C: Linear and Nonlinear Models
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Correlation to Eureka Math
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Standard
Objective
Aligned Components of Eureka Math
PA.D.2 Calculate experimental probabilities and reason about probabilities to solve real‐world and mathematical problems.
PA.D.2.1 Calculate experimental probabilities and represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.
G7 M5 Topic A: Calculating and Interpreting Probabilities
PA.D.2.2 Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.
G7 M5 Topic C: Random Sampling and Estimating Population Characteristics
PA.D.2.3 Compare and contrast dependent and independent events.
G7 M5 Lesson 6: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities
G7 M5 Topic B: Estimating Probabilities
G7 M5 Lesson 7: Calculating Probabilities of Compound Events G7 M5 Lessons 10–11: Conducting a Simulation to Estimate the Probability of an Event Note: The formal vocabulary terms independent event and dependent event are introduced in Algebra II Module 4 Topic A. Consider modifying the Grade 7 lessons listed above to incorporate this vocabulary while maintaining appropriate rigor.
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Correlation to Eureka Math
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Critical Gaps for 2016–2017 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.
7.N.2.5 Solve real‐world and mathematical problems involving calculations with rational numbers and positive integer exponents.
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).
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/Pre‐Algebra extends learning to properties of exponents.
G6 M5 Lesson 15: Representing Three‐Dimensional Figures Using Nets G6 M5 Lesson 16: Constructing Nets G6 M5 Lesson 17: From Nets to Surface Area
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Correlation to Eureka Math
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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
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
Note: To meet the standard, consider extending lessons to show that three‐dimensional shapes of different dimensions can have the same 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.
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Correlation to Eureka Math
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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. This is further extended in Grade 7, where students use the formula to solve problems.
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/Pre‐Algebra.
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Correlation to Eureka Math
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