Middle School Math Curriculum
Math Grade 6
Math Grade 6 Pacing and Unit Guides
Students in Math 6 will continue to build upon their understanding of the four operations from elementary school through work with integers and fractions, including contextual problems. They will develop proportional reasoning in various contexts through the exploration of ratios, tables, and the coordinate plane. Students add percents to the list of rational numbers they can consider in comparing and ordering values. They will develop a deeper understanding of formulas, expressions, equations, and inequalities using models, variables, and problem solving. Students will engage in the data cycle throughout the year then end the year with a focus on circle graphs.
Quarter 1
Unit 1: Let’s Meet Each Other and The Data Cycle
As the year begins, students learn about each other, their teacher, and the mathematics that will occur during the year. This is accomplished through the introduction of the data cycle. Students will practice formulating good statistical questions, consider different ways to gather data, and learn about how to ensure their sample will be representative of the population. Students will return to the data cycle at multiple points in the year to continue to build on this initial work. During this initial experience with the data cycle, students will consider a variety of graphs they learned in elementary school and how different types of questioning and data collection might result in different graphical representations.
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs. [a, b, c, f]
Unit 2: Integers and Inequalities
Students learn about integers, representing them in multiple ways, and using the concept of absolute value to further understand their meaning. An exploration of integers naturally leads to comparing and ordering in both abstract and contextual situations. Once students have a firm grasp of both the value of integers and inequality symbols, students will graph linear inequalities using a number line and consider possible solutions.
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order integers.
6.PFA.4 The student will represent a contextual situation using a linear inequality in one
variable with symbols and graphs on a number line.
Unit 3: The Coordinate Plane and Congruence
A second dimension is added to locating a point as students apply what they have learned by locating integers on a number line to plotting a point on a coordinate plane. Students will identify and label coordinate plane parts, plot and identify points, determine distances and draw polygons on
the coordinate plane. This work with polygons allows the coordinate plane to serve as a tool for exploring congruence of line segments and polygons.
6.MG.3 The student will describe the characteristics of the coordinate plane and graph ordered pairs.
6.MG.4 The student will determine congruence of segments, angles, and polygons.
Targeted Review
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order
integers.
Quarter 2
Unit 4: Operations with Integers and One-Step Linear Equations
Unit 4 allows students to work with representing integers in a variety of ways, leading to computation. Students will learn to add, subtract, multiply, and divide integers, including absolute value and contextual problems. This allows for revisiting plotting ordered pairs on a coordinate plane and applying integer computation to find the distance between two points with the same first or second coordinate. Then, students will apply their knowledge of integer operations to equations, starting with algebraic vocabulary and ending with creating and solving one-step linear equations.
6.CE.2 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context.
6.PFA.3 The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equation in one variable.
Targeted Review
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order
integers.
Begin Unit 5: Operations and Applications of Fractions, Decimals, Percents
In Unit 5, student experiences with integers widen to experiences with positive rational numbers. Students use multiple strategies to express equivalence and compare and order fractions, decimals, and percents, justifying their reasoning. The work with rational numbers expands into multiplying and dividing fractions and solving contextual problems that involve all operations with fractions and mixed numbers. The introduction of percents leads back to the data cycle, where students will continue to build on their data cycle knowledge by collecting, organizing, and representing data in circle graphs. They will use their new knowledge of percent to support both the creation and analysis of circle graphs.
Exploration
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs. [d, e]
Mastery
6.NS.1 The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.
6.CE.1 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.
Quarter 3
Continue Unit 5: Operations and Applications of Fractions, Decimals, Percents
In Unit 5, student experiences with integers widen to experiences with positive rational numbers. Students use multiple strategies to express equivalence and compare and order fractions, decimals, and percents, justifying their reasoning. The work with rational numbers expands into multiplying and dividing fractions and solving contextual problems that involve all operations with fractions and mixed numbers. The introduction of percents leads back to the data cycle, where students will continue to build on their data cycle knowledge by collecting, organizing, and representing data in circle graphs. They will use their new knowledge of percent to support both the creation and analysis of circle graphs
Exploration
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs. [d, e]
Mastery
6.NS.1 The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.
6.CE.1 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.
Unit 6: Proportional Reasoning
6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.
Mastery
6.MG.1 The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.
6.PFA.1 The student will use ratios to represent relationships between quantities, including those in context.
6.PFA.2 The student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values).
Targeted Review
6.MG.3 The student will describe the characteristics of the coordinate plane and graph ordered pairs. [a, b, c, d]
Begin Unit 7: Exponents and Applications
6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.
6.MG.2 The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms
Quarter 4
Continue Unit 7: Exponents and Applications
Mastery
6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.
6.MG.2 The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.
Unit 8: Statistical Understanding and Furthering the Cycle of Data
Mastery
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs.
6.PS.2 The student will represent the mean as a balance point and determine the effect on statistical measures when a data point is added, removed, or changed.
Math Grade 6 Extended
Math Grade 6 Extended
Pacing and Unit Guides
Students in Math 6 Extended will extend their knowledge of the four operations from elementary school to rational numbers. They will develop an understanding of proportionality through exploring ratios, tables, graphs, equations, and contextual situations. Students will apply the concept of proportionality to geometry as they work with similar figures and dilations. They will learn about algebra through work with formulas, expressions, equations, and inequalities and engage in the data cycle with a focus on circle graphs.
Quarter 1
Unit 1: Let’s Meet Each Other and The Data Cycle
As the year begins, students learn about each other, their teacher, and the mathematics that will occur during the year. This is accomplished through the introduction of the data cycle. Students will practice formulating good statistical questions, consider different ways to gather data, and learn about how to ensure their sample will be representative of the population. Students will return to the data cycle at multiple points in the year to continue to build on this initial work. During this initial experience with the data cycle, students will consider a variety of graphs they learned in elementary school and how different types of questioning and data collection might result in different graphical representations.
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on circle graphs. [a, b, c, f]
Unit 2: Integers and Inequalities
Students learn about integers, representing them in multiple ways, and using the concept of absolute value to further understand their meaning. An exploration of integers naturally leads to comparing and ordering in both abstract and contextual situations. Once students have a firm grasp of both the value of integers and inequality symbols, students will graph linear inequalities using a number line and consider possible solutions.
Mastery
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order integers.
6.PFA.4 The student will represent a contextual situation using a linear inequality in one variable with
symbols and graphs on a number line.
Unit 3: Coordinate Plane and Congruence
A second dimension is added to locating a point as students apply what they have learned by locating integers on a number line to plotting a point on a coordinate plane. Students will identify and label coordinate plane parts, plot and identify points, determine distances and draw polygons on the coordinate plane. This work with polygons allows the coordinate plane to serve as a tool for exploring congruence of line segments and polygons. Students establish how to communicate using precise mathematical language. This learning occurs in the context of exploring the characteristics of quadrilaterals and comparing and contrasting these characteristics. Students will communicate in mathematics through talk and writing, noting similarities and differences between the properties of parallelograms, rectangles, squares, rhombi, and trapezoids in order to compare, contrast, sort, and classify these quadrilaterals. Students will also apply their knowledge of the properties of quadrilaterals to determine missing sides and angles.
Mastery
6.MG.3 The student will describe the characteristics of the coordinate plane and graph ordered pairs.
6.MG.4 The student will determine congruence of segments, angles, and polygons.
7.MG.3 The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals.
Targeted Review
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order integers.
Begin Unit 4: Operations with Integers and One-Step Linear Equations
Unit 4 allows students to work with representing integers in a variety of ways, leading to computation. Students will learn to add, subtract, multiply, and divide integers, including absolute value and contextual problems. This allows for revisiting plotting ordered pairs on a coordinate plane and applying integer computation to find the distance between two points with the same first or second coordinate. Then, students will apply their knowledge of integer operations to equations, starting with algebraic vocabulary and ending with creating and solving one-step linear equations.
Exploration
7.PFA.3 The student will write and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations. [a, b]
Mastery
6.CE.2 The student will estimate, demonstrate, solve, and justify solutions to problems using operations
with integers, including those in context.
6.PFA.3 The student will write and solve one-step linear equations in one variable, including contextual
problems that require the solution of a one-step linear equation in one variable.
Targeted Review
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order integers.
Quarter 2
Continue Unit 4: Operations with Integers and One-Step Linear Equations
Unit 4 allows students to work with representing integers in a variety of ways, leading to computation. Students will learn to add, subtract, multiply, and divide integers, including absolute value and contextual problems. This allows for revisiting plotting ordered pairs on a coordinate plane and applying integer computation to find the distance between two points with the same first or second coordinate. Then, students will apply their knowledge of integer operations to equations, starting with algebraic vocabulary and ending with creating and solving one-step linear equations.
Exploration
7.PFA.3 The student will write and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations. [a, b]
Mastery
6.CE.2 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context.
6.PFA.3 The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equation in one variable.
Targeted Review
6.NS.2 The student will reason and use multiple strategies to represent, compare, and order integers.
Unit 5: Operations and Applications of Fractions, Decimals, Percents
In Unit 5, student experiences with integers widen to experiences with positive rational numbers. Students use multiple strategies to express equivalence and compare and order fractions, decimals, and percents, justifying their reasoning. The work with rational numbers expands into multiplying and dividing fractions and solving contextual problems that involve all operations with fractions and mixed numbers. The introduction of percents leads back to the data cycle, where students will continue to build on their data cycle knowledge by collecting, organizing, and representing data in circle graphs. They will use their new knowledge of percent to support both the creation and analysis of circle graphs.
Exploration
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs. [d, e]
Mastery
6.NS.1 The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.
6.CE.1 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.
7.NS.2 The student will reason and use multiple strategies to compare and order rational numbers.
7.PFA.3 The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equation in one variable.
Quarter 3
Continue Unit 5: Operations and Applications of Fractions, Decimals, Percents
In Unit 5, student experiences with integers widen to experiences with positive rational numbers. Students use multiple strategies to express equivalence and compare and order fractions, decimals, and percents, justifying their reasoning. The work with rational numbers expands into multiplying and dividing fractions and solving contextual problems that involve all operations with fractions and mixed numbers. The introduction of percents leads back to the data cycle, where students will continue to build on their data cycle knowledge by collecting, organizing, and representing data in circle graphs. They will use their new knowledge of percent to support both the creation and analysis of circle graphs.
Exploration
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs. [d, e]
Mastery
6.NS.1 The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.
6.CE.1 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.
7.NS.2 The student will reason and use multiple strategies to compare and order rational numbers.
7.PFA.3 The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equation in one variable.
Unit 6: Proportional Reasoning
Mastery
6.PFA.1 The student will use ratios to represent relationships between quantities, including those in context.
6.PFA.2 The student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values).
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
7.PFA.1 The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, equations in y = mx form, and graphs, including problems in context.
Targeted Review
6.MG.3 The student will describe the characteristics of the coordinate plane and graph ordered pairs. [a, b, c, d]
Unit 7: Proportional Reasoning within Geometry
Exploration
6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.
Mastery
6.MG.1 The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.
7.MG.2 The student will solve problems and justify relationships of similarity using proportional reasoning.
7.MG.4 The student will apply dilations of polygons in the coordinate plane.
Begin Unit 8: Exponents and Applications
Mastery
6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.
6.MG.2 The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.
7.NS.1 The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers greater than zero written in scientific notation.
7.NS.3 The student will recognize and describe the relationship between square roots and perfect squares.
Quarter 4
Continue Unit 8: Exponents and Applications
Mastery
6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.
6.MG.2 The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.
7.NS.1 The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers greater than zero written in scientific notation.
7.NS.3 The student will recognize and describe the relationship between square roots and perfect squares.
Unit 9: Statistical Understanding and Furthering the Cycle of Data
Mastery
6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs.
6.PS.2 The student will represent the mean as a balance point and determine the effect on statistical measures when a data point is added, removed, or changed.
Math Grade 7
Math Grade 7 Pacing and Unit Guides
Students in Math 7 will deepen their understanding of rational numbers and the concept of proportionality. They will extend their work with rational numbers to negative values. Students will continue to develop proportional reasoning through exploring tables, graphs, equations, and contextual situations. They will apply these big ideas as they engage in the data cycle with a focus on histograms, work with similar figures and dilations, explore probability, and learn more about expressions, equations, and inequalities.
Quarter 1
Unit 1: The Data Cycle
As the year begins, students and teachers learn about each other and the mathematics that will occur during the year. This is accomplished through the introduction of the data cycle. Students formulate questions, determine how to gather the data and learn about how to ensure their sample will be representative of the population. Students will use histograms to represent their data, compare with other types of graphs, and determine how histograms can reveal patterns not easily seen in the data set.
Mastery
7.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms.
Unit 2: Thinking Like a Mathematician
Students establish how to communicate using precise mathematical language. This learning occurs in the context of exploring the characteristics of quadrilaterals and comparing them. Students will communicate in mathematics through talk and writing, noting similarities and differences between the properties of parallelograms, rectangles, squares, rhombi, and trapezoids to compare, contrast, sort, and classify these quadrilaterals. Students will also apply their knowledge of the properties of quadrilaterals to determine missing sides and angles.
Mastery
7.MG.3 The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals.
Assessment Window: September 16 to September 20, 2024
Unit 3: Rational Numbers
Students continue the idea of comparing and sorting as they explore rational numbers. In this unit students will investigate perfect squares, square roots, powers of 10, and numbers in scientific notation. Students will use multiple strategies to compare and order rational numbers and apply that knowledge to ordering and comparing numbers in scientific notation. Throughout this unit students will estimate, solve, and justify solutions for a variety of contextual problems involving rational numbers. The data cycle should be revisited here as analyzing histograms provides context for problem solving with rational numbers.
Mastery
7.NS.1 The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers greater than zero written in scientific notation.
7.NS.2 The student will reason and use multiple strategies to compare and order rational numbers.
7.NS.3 The student will recognize and describe the relationship between square roots and perfect squares.
7.CE.1 The student will estimate, solve, and justify solutions to multistep contextual problems involving operations with rational numbers.
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [a]
TARGETED REVIEW
7.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms.
Assessment Window: October 14 to October 18, 2024
Begin Unit 4: Connecting Rational Numbers and Probability
Students will apply their knowledge of comparing rational numbers in this unit while exploring experimental and theoretical probability. The data cycle should be revisited in this unit using experimental probability to make predictions with data collected and represented.
Mastery
7.PS.1 The student will use statistical investigation to determine the probability of an event and investigate and describe the difference between the experimental and theoretical probability.
Targeted Review
7.NS.2 The student will reason and use multiple strategies to compare and order rational numbers.
7.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms.
Quarter 2
Continue Unit 4: Connecting Rational Numbers and Probability
Students will apply their knowledge of comparing rational numbers in this unit while exploring experimental and theoretical probability. The data cycle should be revisited in this unit using experimental probability to make predictions with data collected and represented.
Mastery
7.PS.1 The student will use statistical investigation to determine the probability of an event and investigate and describe the difference between the experimental and theoretical probability.
Targeted Review
7.NS.2 The student will reason and use multiple strategies to compare and order rational numbers.
7.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms.
Unit 5: Proportional Reasoning
Students will continue using rational numbers and problem-solving to explore practical problems involving proportional relationships. Ratio tables, missing values in proportions, unit conversion, and percentages are all applications of proportional reasoning to be explored in this unit. The data cycle should be revisited in this unit using percentages to analyze a histogram and make predictions.
Mastery
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Targeted Review
7.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms.
Assessment Window: December 2 to December 6, 2024
Unit 6: Applying Proportional Reasoning within Functions
Students will continue to investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, graphs, problems in context, and equations in the form y = mx. As students make connections between equations and other representations, they will evaluate expressions for replacement values and review solving one-step equations from sixth grade.
Exploration
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [d]
Mastery
7.PFA.1 The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, equations in y = mx form, and graphs, including problems in context.
Targeted Review
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Assessment Window: January 13 to January 17, 2025
Quarter 3
Unit 7: Expressions, Equations, and Inequalities
Exploration
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [d]
Mastery
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [b, c]
7.PFA.3 The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equation in one variable.
7.PFA.4 The student will write and solve one- and two-step linear inequalities in one variable, including problems in context, that require the solution of a one- and two-step linear inequality in one variable.
Targeted Review
7.MG.3 The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals. [c, d]
Assessment Window: February 24 to February 28, 2025
Unit 8: Connecting Expressions to Surface Area and Volume
Mastery
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [d]
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. [a, b, c]
Assessment Window: March 10 to March 14, 2025
Unit 9: Proportional Reasoning within Geometry
Mastery
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. [d, e]
7.MG.2 The student will solve problems and justify relationships of similarity using proportional reasoning.
7.MG.4 The student will apply dilations of polygons in the coordinate plane.
Targeted Review
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Quarter 4
Continue Unit 9: Proportional Reasoning within Geometry
Mastery
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. [d, e]
7.MG.2 The student will solve problems and justify relationships of similarity using proportional reasoning.
7.MG.4 The student will apply dilations of polygons in the coordinate plane.
Targeted Review
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Math Grade 7 Extended
Math Grade 7 Extended
Pacing and Unit Guides
Students in Math 7 Extended are building the foundation necessary for success in Algebra I and other high-school mathematics courses. Using the real number system, students dive deeper into complex equations and expressions while making connections with geometry and statistical concepts through the data cycle. Students explore transformations through linear equations and apply this knowledge to contextual situations.
Quarter 1
Unit 1: Let’s Meet the Data Cycle, Histograms, and Boxplots
As the year begins, students learn about each other and the teacher and the mathematics that will occur during the year. This is accomplished through introduction of the data cycle. Students formulate questions, determine how to gather data and learn about how to ensure their sample will be representative of the population. Students explore different types of data, understanding the difference in univariate and bivariate data. Students explore components of graphical displays that can be misleading and how statistical bias might affect data collection
Exploration
8.PS.3 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on scatterplots. [a, b]
Mastery
7.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms.
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on boxplots.
Assessment Window: September 2 to September 6, 2024
Unit 2: Equivalent Expressions
Students now explore and examine the relationships among equivalent expressions as they relate to order of operations, area and perimeter of composite figures, surface area and volume of square-based pyramids, and volume of cones and cylinders. Students will represent algebraic expressions, applying the distributive property and combining like terms. Students will use their knowledge of the order of operations to generate equivalent expressions as they relate to find the area and perimeter of composite figures. Students will also explore how to find the surface area of square-based pyramids and the volume of square-based pyramids and cones. Students will understand how equivalent expressions show different aspects of an expression, just like different ways of representing data reveal various connections from the same information.
Exploration
8.MG.2 The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids. [a, b, c]
Mastery
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables.
8.PFA.1 The student will represent, simplify, and generate equivalent algebraic expressions in one
variable.
8.MG.5 The student will solve area and perimeter problems involving composite plane figures, including
those in context.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. [j]
Assessment Window: September 30 to October 4, 2024
Unit 3: New Contexts for Equations We Know How to Solve
Students will transition from expressions to two-step equations, building upon what they learned in Math 7 Standard 7.PFA.3 and applying it to different contexts. Students should have the opportunity to explore vertical, adjacent, supplementary, and complementary angles as this exploration will allow students to solve one- and two- step equations. Contextual problems should include volume, surface area, tax, tip, and
discount, using proportions and equations.
Exploration
8.MG.2 The student will investigate and determine the surface area of square-based pyramids and the
volume of cones and square-based pyramids. [d]
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent
angles, supplementary angles, and complementary angles to determine the measure of unknown
angles. [b]
Mastery
7.CE.1 The student will estimate, solve, and justify solutions to multistep contextual problems involving
operations with rational numbers.
8.CE.1 The student will estimate and apply proportional reasoning and computational procedures to
solve contextual problems.
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent
angles, supplementary angles, and complementary angles to determine the measure of unknown
angles. [a]
Assessment Window: October 28 to November 1, 2024
Quarter 2
Unit 4: Irrational Numbers Enter the Real Number System
Students connect this unit to the prior unit by recognizing the answers were most likely rational numbers. Students then can explore perfect square roots and begin exploring non-perfect square roots on number lines. This will allow students to dig into irrational numbers and explore how they fit in the real number system. Finally, students can explore the Pythagorean Theorem and understand when these equations produce solutions that are rational or irrational.
Exploration
8.MG.4 The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.
Mastery
8.NS.1 The student will compare and order real numbers and determine the relationships between real numbers.
8.NS.2 The student will investigate and describe the relationship between the subsets of the real number system.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. [a, b]
Assessment Window: November 18 to November 22, 2024
Unit 5: New Equations and Contexts in Geometry
Now that students have exposure to the entire real number system, we return to solving multi step equations with context. As surface area and volume formulas are equations and problems in context may have students find a dimension, students should revisit these concepts in this unit. It is important in this unit to discuss the nature of one solution so that a connection can be made in the next unit of inequalities with many solutions.
Mastery
8.PFA.4 The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equation in one variable.
8.MG.4 The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context.
8.MG.2 The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids.
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. [b]
Targeted Review
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. [a]
Assessment Window: January 13 to January 17, 2025
Unit 6: Applying Proportional Reasoning within Functions
Students will continue to investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, graphs, problems in context, and equations in the form y = mx. As students make connections between equations and other representations, they will evaluate expressions for replacement values and review solving one-step equations from sixth grade.
Exploration
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [d]
Mastery
7.PFA.1 The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, equations in y = mx form, and graphs, including problems in context.
Targeted Review
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Quarter 3
Unit 7: Expressions, Equations, and Inequalities
Exploration
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [d]
Mastery
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [b, c]
7.PFA.3 The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equation in one variable.
7.PFA.4 The student will write and solve one- and two-step linear inequalities in one variable, including problems in context, that require the solution of a one- and two-step linear inequality in one variable.
Targeted Review
7.MG.3 The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals. [c, d]
Assessment Window: February 24 to February 28, 2025
Unit 8: Connecting Expressions to Surface Area and Volume
Mastery
7.PFA.2 The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. [d]
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. [a, b, c]
Assessment Window: March 10 to March 14, 2025
Begin Unit 9: Proportional Reasoning within Geometry
Mastery
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. [d, e]
7.MG.2 The student will solve problems and justify relationships of similarity using proportional reasoning.
7.MG.4 The student will apply dilations of polygons in the coordinate plane.
Targeted Review
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Quarter 4
Continue Unit 9: Proportional Reasoning within Geometry
Mastery
7.MG.1 The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. [d, e]
7.MG.2 The student will solve problems and justify relationships of similarity using proportional reasoning.
7.MG.4 The student will apply dilations of polygons in the coordinate plane.
Targeted Review
7.CE.2 The student will solve problems, including those in context, involving proportional relationships.
Assessment Window: April 21 to April 25, 2025
Pre-Algebra
Pre-Algebra
Pacing and Unit Guides
Students in Pre-Algebra are building the foundation necessary for success in high school mathematics. Using the real number system, students dive deeper into complex equations and expressions while making connections with geometry and statistical concepts through the data cycle. Students explore transformations through linear equations and apply this knowledge to contextual situations.
Quarter 1
Unit 1: Let’s Meet the Data Cycle, and Boxplots
As the year begins, students learn about each other and the teacher and the mathematics that will occur during the year. This is accomplished through introduction of the data cycle. Students formulate questions, determine how to gather data and learn about how to ensure their sample will be representative of the population. Students explore different types of data, understanding the difference in univariate and bivariate data. Students explore components of graphical displays that can be misleading and how statistical bias might affect data collection.
Exploration
8.PS.3 The student will apply the data cycle (formulate questions; collect or acquire ;data; organize and represent data; and analyze data and communicate results) with ;a focus on scatterplots. [a, b]
Mastery
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with ;a focus on boxplots.
Assessment Window: September 2 to September 6, 2024
Unit 2: Equivalent Expressions
Students now explore and examine the relationships among equivalent expressions as they relate to order of operations, area and perimeter of composite figures. Students will represent algebraic expressions, applying the distributive property and combining like terms. Students will use their knowledge of the order of operations to generate equivalent expressions as they relate to find the area and perimeter of composite figures. Students will understand how equivalent expressions show different aspects of an expression, just like different ways of representing data reveal various connections from the same information.
Exploration
8.MG.2 The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids. [a, b, c]
Mastery
8.PFA.1 The student will represent, simplify, and generate equivalent algebraic expressions in one variable.
8.MG.5 The student will solve area and perimeter problems involving composite plane figures, including those in context.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. [j]
Assessment Window: September 30 to October 4, 2024
Unit 3: New Contexts for Equations We Know How to Solve
Students will transition from expressions to two-step equations, building upon what they learned in Math 7 Standard 7.PFA.3 and applying it to different contexts. Students should have the opportunity to explore vertical, adjacent, supplementary, and complementary angles as this exploration will allow students to solve one- and two- step equations. Contextual problems should include volume, surface area, tax, tip, and
discount, using proportions and equations.
Exploration
8.MG.2 The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids. [d]
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. [b]
Mastery
8.CE.1 The student will estimate and apply proportional reasoning and computational procedures to solve contextual problems.
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. [a]
Assessment Window: October 28 to November 1, 2024
Quarter 2
Unit 4: Irrational Numbers Enter the Real Number System
Students connect this unit to the prior unit by recognizing the answers were most likely rational numbers. Students then can explore perfect square roots and begin exploring non-perfect square roots on number lines. This will allow students to dig into irrational numbers and explore how they fit in the real number system. Finally, students can explore the Pythagorean Theorem and understand when these equations produce solutions that are rational or irrational.
Exploration
8.MG.4 The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.
Mastery
8.NS.1 The student will compare and order real numbers and determine the relationships between real numbers.
8.NS.2 The student will investigate and describe the relationship between the subsets of the real number system.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. [a, b]
Assessment Window: November 25 to November 29, 2024
Unit 5: New Equations and Contexts in Geometry
Now that students have exposure to the entire real number system, we return to solving multi step equations with context. As surface area and volume formulas are equations and problems in context may have students find a dimension, students should revisit these concepts in this unit. It is important in this unit to discuss the nature of one solution so that a connection can be made in the next unit of inequalities with many solutions.
Mastery
8.PFA.4 The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equation in one variable.
8.MG.4 The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.
8.MG.2 The student will investigate and determine the surface area of squarebased pyramids and the volume of cones and square-based pyramids.
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. [b]
Targeted Review
8.MG.1 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. [a]
Assessment Window: January 13 to January 17, 2025
Quarter 3
Unit 6: Solving Inequalities
Mastery
8.PFA.5 The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear inequality in one variable.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. [g, h]
Assessment Window: February 3 to February 7, 2025
Unit 7: The Data Cycle Continues and Scatterplots Take the Lead
Mastery
8.PS.3 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on scatterplots.
8.PFA.2 The student will determine whether a given relation is a function and determine the domain and range of a function.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. [a, b, c]
Assessment Window: February 24 to February 28, 2025
Unit 8: Lines and Their Equations from Transformations
Mastery
8.PFA.3 The student will represent and solve problems, including those in context, by using linear functions and analyzing their key characteristics (the value of the y-intercept (b) and the coordinates of the ordered pairs in graphs will be limited to integers).
8.MG.3 The student will apply translations and reflections to polygons in the coordinate plane.
Targeted Review
8.PS.3 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on scatterplots.
8.PFA.2 The student will determine whether a given relation is a function and determine the domain and range of a function.
Assessment Window: March 24 to March 28, 2025
Quarter 4
Unit 9: Independent or Dependent Events
Mastery
8.PS.1 The student will use statistical investigation to determine the probability of ;independent and dependent events, including those in context.
Targeted Review
8.PS.2 The student will apply the data cycle (formulate questions; collect or acquire ;data; organize and represent data; and analyze data and communicate results) with ;a focus on boxplots.
8.PS.3 The student will apply the data cycle (formulate questions; collect or acquire ;data; organize and represent data; and analyze data and communicate results) with ;a focus on scatterplots.
Assessment Window: April 21 to April 25, 2025
Advanced Algebra
Advanced Algebra
Pacing and Unit Guides
How can Algebra help us beyond school? As we explore situations, what do we notice? Are there patterns of interest? If there are, how can we describe these patterns and how can they help us make predictions and decisions? What language and mathematical ideas do we use to increase our precision? As new topics
are introduced, students will work with informal descriptions of contextual data and generalize what they see. It is important to allow the students time to describe the patterns without the burden of using formal symbols or vocabulary. The formalization of these ideas is developed as students generalize concepts through the exploration of specific functions. This generalization leads towards proficiency with abstract symbolic manipulation. Students will complete the course with the conceptual understanding and procedural skills for success in continued study of advanced mathematics.
Quarter 1
Unit 1: Using the Data Cycle with Bivariate Data
While exploring patterns, students will use the data cycle to structure their process. Relationships in bivariate data will be the basis of formulating investigative questions and collecting or acquiring data. Tables and scatterplots will provide representations of the data for students to begin making observations and communicating inferences about the patterns and relationships.
Exploration
A.EO.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. [a]
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [a, f]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate
data in scatterplots and determining the curve of best fit using linear and quadratic functions. [a, b, c,
h, i]
Unit 2: Linear Functions in Context
The focus of Unit 2 will be on generalized linear relationships; recognizing there is a constant rate of change (slope) and a starting point (y-intercept). Students will also recognize limitations (domain and range) of the model in the context of real-world data sets and make predictions using the model (finding values of a function). This unit serves a conceptual transition from the open-ended exploration of bivariate data in Unit 1 and a more formal, rigorous approach to linear equations and inequalities in Unit 3.
Exploration
A.EO.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. [a]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate data in
scatterplots and determining the curve of best fit using linear and quadratic functions. [d, e, f, g, h, i] linear
models.
Mastery
A.F.1 The student will investigate, analyze, and compare linear functions algebraically and graphically, and
model linear relationships. [a, b, f, h]
Assessment Window: September 9 to September 13, 2024
Unit 3: Linear Functions
Students will build upon contextual and generalized concepts as they represent linear equations and inequalities algebraically. This will include comparison of various forms of linear functions (slope-intercept, standard, point-slope) to explore the benefits of each approach. Students will formalize their understanding of linear functions by interpreting various forms of a linear model with and without context.
Exploration
A.EO.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. [a]
A.EI.1 The student will represent, solve, explain, and interpret the solution to multistep linear equations and inequalities in one variable and literal equations for a specified variable. [d]
A.EI.2 The student will represent, solve, explain, and interpret the solution to a system of two linear
equations, a linear inequality in two variables, or a system of two linear inequalities in two variables.
[d, e]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate
data in scatterplots and determining the curve of best fit using linear and quadratic functions. [f]
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [a]
Mastery
A.F.1 The student will investigate, analyze, and compare linear functions algebraically and graphically, and
model linear relationships. linear only
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate
data in scatterplots and determining the curve of best fit using linear and quadratic functions. [d, e]
Targeted Review
A.F.1 The student will investigate, analyze, and compare linear functions algebraically and graphically, and
model linear relationships. [b]
Assessment Window: October 14 to October 18, 2024
Unit 4: Solving Linear Equations, Inequalities, and Systems
The abstraction of algebra continues in this unit as students expand their ability to algebraically and graphically represent, solve, explain, and interpret solutions to linear equations and inequalities (including systems). Students refine understanding of equality within algebraic situations, and the preservation of the relationship between expressions when operating on equations and inequalities.
Exploration
A.EO.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. [a]
Mastery
A.EI.1 The student will represent, solve, explain, and interpret the solution to multistep linear equations and inequalities in one variable and literal equations for a specified variable.
A.EI.2 The student will represent, solve, explain, and interpret the solution to a system of two linear
equations, a linear inequality in two variables, or a system of two linear inequalities in two variables.
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate
data in scatterplots and determining the curve of best fit using linear and quadratic functions. [f, g]
EXTENSION
A2.EI.1 The student will represent, solve, and interpret the solution to absolute value equations and
inequalities in one variable. [b, d]*
*Additional Advanced Content: See Unit Guide
Quarter 2
Continue Unit 4: Solving Linear Equations, Inequalities, and Systems
The abstraction of algebra continues in this unit as students expand their ability to algebraically and graphically represent, solve, explain, and interpret solutions to linear equations and inequalities (including systems). Students refine understanding of equality within algebraic situations, and the preservation of the relationship between expressions when operating on equations and inequalities.
Exploration
A.EO.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. [a]
Mastery
A.EI.1 The student will represent, solve, explain, and interpret the solution to multistep linear equations
and inequalities in one variable and literal equations for a specified variable.
A.EI.2 The student will represent, solve, explain, and interpret the solution to a system of two linear
equations, a linear inequality in two variables, or a system of two linear inequalities in two variables.
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate data
in scatterplots and determining the curve of best fit using linear and quadratic functions. [f, g]
EXTENSION
A2.EI.1 The student will represent, solve, and interpret the solution to absolute value equations and
inequalities in one variable. [b, d]*
*Additional Advanced Content: See Unit Guide
Assessment Window: November 25 to November 29, 2024
Unit 5: Non-Linear Expressions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Mastery
A.EO.1 The student will represent verbal quantitative situations algebraically and evaluate these
expressions for given replacement values of the variables.
A.EO.3 The student will derive and apply the laws of exponents.
A.EO.4 The student will simplify and determine equivalent radical expressions involving square roots
of whole numbers and cube roots of integers.
EXTENSION
A2.EO.2 The student will perform operations on and simplify radical expressions. [b]
Assessment Window: January 6 to January 10, 2025
Unit 6: Exponential Functions
Students will move from contextualized situations in units 2-4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Exploration
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including
quadratic, and exponential functions, and model quadratic and exponential relationships. [a]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and
represent data; and analyze data and communicate results) with a focus on representing bivariate data
in scatterplots and determining the curve of best fit using linear and quadratic functions. [a, b, h]
Mastery
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including
quadratic, and exponential functions, and model quadratic and exponential relationships. [e, f, g, h]
exponential functions.
Quarter 3
Continue Unit 6: Exponential Functions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Exploration
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [a]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions. [a, b, h]
Mastery
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [e, f, g, h] exponential functions.
Unit 7: Operations with Polynomials
MASTERY
A.EO.2 The student will perform operations on and factor polynomial expressions in one variable.
EXTENSION
A2.EO.3 The student will perform operations on polynomial expressions and factor polynomial expressions in one and two variables. [b, c]
Assessment Window: March 10 to March 14, 2025
Unit 8: Quadratic Functions
Mastery
A.EI.3 The student will represent, solve, and interpret the solution to a quadratic equation in one variable.
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [a, b, c, d, g, h] quadratic functions
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions. [e, h, i]
Quarter 4
Continue Unit 8: Quadratic Functions
Mastery
A.EI.3 The student will represent, solve, and interpret the solution to a quadratic equation in one variable.
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [a, b, c, d, g, h] quadratic functions
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions. [e, h, i]
Assessment Window: April 7 to April 11, 2025
Unit 9: Function Synthesis
Mastery
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [h]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions. [a, b, c, d]
Targeted Review
A.F.2 The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. [a, b, c, f]
A.ST.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions. [e]
Assessment Window: April 28 to May 2, 2025
Advanced Geometry
Advanced Geometry
Pacing and Unit Guides
Geometry allows us to understand and make connections to the physical world around us. In this course, students will analyze physical relationships through the development of conjecture and proof using transformational, coordinate, algebraic methods, and logical means. Students will develop efficient strategies for the proof and classification of two- and three-dimensional objects and the use of properties to solve problems.
Quarter 1
Unit 1: Venn Diagrams and Introduction to Logic
Venn diagrams and logic provide vehicles through which we can understand and model relationships and categorizations, including geometric relationships. These key components to geometrical thinking are revisited throughout the year when working with theorems, postulates, definitions, and examples.
Mastery
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams. *See Unit Guide for Additional Advanced Content (Truth Tables and Two Column Proofs)
Unit 2: Parallel Lines
The angle relationships formed when parallel lines are cut by a transversal are foundational to the study of geometry. In this unit, students will explore, analyze, and use those relationships to prove conjectures, solve problems, and apply to contextual situations.
Mastery
G.RLT.2 The student will analyze, prove, and justify the relationships of parallel lines cut by a transversal. *See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.
Unit 3: Symmetry and Transformations
Students have been working with symmetry and transformations since elementary school in both geometric and algebraic contexts. This unit provides an opportunity to formalize these ideas and use this knowledge to justify similarity and congruence in geometric figures.
Mastery
G.RLT.3 The student will solve problems, including contextual problems, involving symmetry and transformation.
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements,
and use and interpret Venn diagrams.
Unit 4: Triangle Properties
Students use spatial reasoning to form conjectures about whether three given lengths can form a triangle. Exploration is used to determine the relationship between the sides and angles of a triangle. Contextual situations allow for students to see the relevance of these concepts.
Mastery
G.TR.1 The student will determine the relationships between the measures of angles and lengths of sides in triangles, including problems in context. *See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements,
and use and interpret Venn diagrams.
Quarter 2
Unit 5: Similarity and Congruence
Students have been working with similar and congruent figures in various contexts since elementary school. This course provides for a formalized definition of congruent and similar figures. Through exploration, students discover some postulates about congruent and similar figures that allow for some shortcuts to prove whether two figures are congruent or similar. These concepts are used to solve abstract and contextual problems.
Mastery
G.TR.2 The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles. [a, b, c, d exclude HL)
G.TR.3 The student will, given information in the form of a figure or statement, prove and justify two triangles are similar using direct and indirect proofs, and solve problems, including those in context, involving measured attributes of similar triangles. *See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use
and interpret Venn diagrams.
G.RLT.2 The student will analyze, prove, and justify the relationships of parallel lines cut by
a transversal. [a]
Unit 6: Similarity and Right Triangle Ratios
Having worked with similar triangles, students narrow their focus to similar right triangles. Beginning with special right triangles, students apply geometric concepts to determine relationships between the legs and hypotenuse. Expanding to all right triangles allows for the introduction of trigonometric functions. These ratios are used to solve problems.
Mastery
G.TR.4 The student will model and solve problems, including those in context, involving trigonometry
in right triangles and applications of the Pythagorean Theorem.
G.TR.2 The student will, given information in the form of a figure or statement, prove and justify two
triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles. [a, d, HL]
T.CT.2 The student will develop and apply the properties of the unit circle in degrees and radians.
*See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and
interpret Venn diagrams.
G.TR.1 The student will determine the relationships between the measures of angles and lengths of
sides in triangles, including problems in context.
G.TR.2 The student will, given information in the form of a figure or statement, prove and justify two
triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.
G.TR.3 The student will, given information in the form of a figure or statement, prove and justify two
triangles are similar using direct and indirect proofs, and solve problems, including those in context, involving measured attributes of similar triangles.
Quarter 3
Complete Unit 6: Similarity and Right Triangle Ratios
Having worked with similar triangles, students narrow their focus to similar right triangles. Beginning with special right triangles, students apply geometric concepts to determine relationships between the legs and hypotenuse. Expanding to all right triangles allows for the introduction of trigonometric functions. These ratios are used to solve problems.
Mastery
G.TR.4 The student will model and solve problems, including those in context, involving trigonometry in right triangles and applications of the Pythagorean Theorem.
G.TR.2 The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles. [a, d, HL]
T.CT.2 The student will develop and apply the properties of the unit circle in degrees and radians.
T.TT.2 The student will find the area of any triangle and solve for the lengths of the sides and measures of the angles in a non-right triangle using the Law of Sines and the Law of Cosines.
*See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.
G.TR.1 The student will determine the relationships between the measures of angles and lengths of sides in triangles, including problems in context.
G.TR.2 The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.
G.TR.3 The student will, given information in the form of a figure or statement, prove and justify two triangles are similar using direct and indirect proofs, and solve problems, including those in context, involving measured attributes of similar triangles.
Unit 7: Quadrilaterals and Polygons
Mastery
G.PC.1 The student will prove and justify theorems and properties of quadrilaterals and verify and use properties of quadrilaterals to solve problems, including the relationships between the sides, angles, and diagonals.
G.PC.2 The student will verify relationships and solve problems involving the number of sides and measures of angles of convex polygons. *See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.
G.RLT.2 The student will analyze, prove, and justify the relationships of parallel lines cut by a transversal. [a]
G.TR.1 The student will determine the relationships between the measures of angles and lengths of sides in triangles, including problems in context. [e]
G.TR.2 The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles. [b, c]
Unit 8: Three-Dimensional Figures
Mastery
G.DF.1 The student will create models and solve problems, including those in context, involving surface area and volume of rectangular and triangular prisms, cylinders, cones, pyramids, and spheres.
G.DF.2 The student will determine the effect of changing one or more dimensions of a three-dimensional geometric figure and describe the relationship between the original and changed figure.
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.
Begin MASTERY
G.PC.3 The student will solve problems, including those in context, by applying properties of circles.
G.PC.4 The student will solve problems in the coordinate plane involving equations of circles.
*See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.
Quarter 4
Continue Unit 9: Circles
Mastery
G.PC.3 The student will solve problems, including those in context, by applying properties of circles.
G.PC.4 The student will solve problems in the coordinate plane involving equations of circles. *See Unit Guide for Additional Advanced Content
Targeted Review
G.RLT.1 The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams.