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.
Standards Covered: 6.PS.1
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.
Standards Covered: 6.NS.2, 6.PFA.4
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.
Standards Covered: 6.MG.3, 6.MG.4, 6.NS.2
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.
Standards Covered: 6.CE.2, 6.PFA.3, 6.NS.2
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.
Standards Covered: 6.PS.1, 6.NS.1, 6.CE.1
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
Standards Covered:
Assessment Window: February 10-14, 2025
Unit 6: Proportional Reasoning
Exploring ratios expands the world of rational numbers. Students will work with ratio tables, unit rates, proportional relationships, and the many ways to represent these relationships. As an application of ratios, students also work with circles to define terms, develop an understanding of pi, and solve problems involving the circumference and area.
Standards Covered: 6.NS.3, 6.MG.1, 6.PFA.1, 6.PFA.2, 6.MG.3
Assessment Window: March 10-14, 2025
Unit 7: Exponents and Applications
Students expand their understanding of numbers as they work with exponents, powers of 10, and perfect squares. They will also continue their work with geometric formulas. Students begin by investigating exponents and recognizing the mathematical patterns of powers of 10. They then explore the connection between exponents and perfect squares, followed by a deeper dive into the area and perimeter formulas for triangles and parallelograms. To apply their understanding, students solve contextual situations involving area and perimeter.
Standards Covered: 6.NS.3, 6.MG.2
Quarter 4
Unit 7: Exponents and Applications
Students expand their understanding of numbers as they work with exponents, powers of 10, and perfect squares. They will also continue their work with geometric formulas. Students begin by investigating exponents and recognizing the mathematical patterns of powers of 10. They then explore the connection between exponents and perfect squares, followed by a deeper dive into the area and perimeter formulas for triangles and parallelograms. To apply their understanding, students solve contextual situations involving area and perimeter.
Standards Covered: 6.NS.3, 6.MG.2
Assessment Window: Week of March 31-April 4, 2025
Unit 8: Statistical Understanding and Furthering the Cycle of Data
As the year concludes, students will explore the mean of a data set as a balancing point. They will then consider how the measures of center are impacted by changes to the set of data values and outliers. Students will then return to working with the data cycle, focusing on circle graphs.
Standards Covered: 6.PS.1, 6.PS.2
Assessment Window: Week of April 21-25, 2025
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.
Standards Covered: 6.PS.1
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.
Standards Covered: 6.NS.2, 6.PFA.4
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.
Standards Covered: 6.MG.3, 6.MG.4, 7.MG.3, 6.NS.2
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.
Standards Covered: 7.PFA.3, 6.CE.2, 6.PFA.3, 6.NS.2
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.
Standards Covered: 7.PFA.3, 6.CE.2, 6.PFA.3, 6.NS.2
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.
Standards Covered: 6.PS.1, 6.NS.1, 6.CE.1, 7.NS.2, 7.PFA.3
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
Standards Covered: 6.PS.1, 6.NS.1, 6.CE.1, 7.NS.2, 7.PFA.3
Assessment Window: January 27-31, 2025
Unit 6: Proportional Reasoning
Exploring ratios expands the world of rational numbers. Students will work with ratio tables, unit rates, proportional relationships, and the many ways to represent these relationships. Students will then extend this work to solve problems, including those in context, involving proportional relationships.
Standards Covered: 6.PFA.1, 6.PFA.2, 7.CE.2, 7.PFA.1, 6.MG.3
Assessment Window: February 24-28, 2025
Unit 7: Proportional Reasoning within Geometry
In this unit, students will extend their work from Unit 6 to geometry. As an application of ratios, students work with circles to define terms, develop an understanding of pi, and solve problems involving the circumference and area. They will then explore additional geometric applications of proportional reasoning, including dilations on the coordinate plane, the similarity of quadrilaterals and triangles, and problems involving scale drawings.
Standards Covered: 6.NS.3, 6.MG., 7.MG.2, 7.MG.4
Assessment Window: March 10-14, 2025
Unit 8: Exponents and Applications
Students expand their understanding of numbers as they work with exponents, perfect squares, square roots, powers of 10, and numbers in scientific notation. They will continue their work with geometric formulas. Students begin by investigating exponents and recognizing the mathematical patterns of powers of 10. They then explore the connection between exponents and perfect squares, followed by a deeper dive into the area and perimeter formulas for triangles and parallelograms. To apply their understanding, students solve contextual situations involving area and perimeter.
Standards Covered: 6.NS.3, 6.MG.2, 7.NS.1, 7.NS.3
Quarter 4
Unit 8: Exponents and Applications
Students expand their understanding of numbers as they work with exponents, perfect squares, square roots, powers of 10, and numbers in scientific notation. They will continue their work with geometric formulas. Students begin by investigating exponents and recognizing the mathematical patterns of powers of 10. They then explore the connection between exponents and perfect squares, followed by a deeper dive into the area and perimeter formulas for triangles and parallelograms. To apply their understanding, students solve contextual situations involving area and perimeter.
Standards Covered: 6.NS.3, 6.MG.2, 7.NS.1, 7.NS.3
Assessment Window: Week of March 31-April 4, 2025
Unit 9: Statistical Understanding and Furthering the Cycle of Data
As the year concludes, students will explore the mean of a data set as a balancing point. They will then consider how the measures of center are impacted by changes to the set of data values and outliers. Students will then return to working with the data cycle, focusing on circle graphs.
Standards Covered: 6.PS.1, 6.PS.2
Assessment Window: Week of April 21-25, 2025
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.
Standards Covered: 7.PS.2
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.
Standards Covered: 7.MG.3
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.
Standards Covered: 7.NS.1, 7.NS.2, 7.NS.3, 7.CE.1, 7.PFA.2, 7.PS.2
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.
Standards Covered: 7.PS.1, 7.NS.2, 7.PS.2
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.
Standards Covered: 7.PS.1, 7.NS.2, 7.PS.2
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.
Standards Covered: 7.CE.2, 7.PS.2
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.
Standards Covered: 7.PFA.2, 7.PFA.1, 7.CE.2
Assessment Window: January 13 to January 17, 2025
Quarter 3
Unit 7: Expressions, Equations, and Inequalities
Students will build on their understanding of rational numbers, expressions, and equations. They will write, generate, and simplify algebraic expressions, solve two-step equations, and create contextual (real-life) problems. They will also learn to solve inequalities. Evaluating expressions with rational numbers will be explored.
Standards Covered: 7.PFA.2, 7.PFA.3, 7.PFA.4, 7.MG.3
Assessment Window: February 24-28, 2025
Unit 8: Connecting Expressions to Surface Area and Volume
In this unit, students will build on their earlier work by evaluating expressions using given replacement values for the variables. They will apply what they know about expressions to create and use formulas. They will explore real-life problems related to surface area and volume, determine when to use each concept, and calculate surface area and volume with given measurements. Additionally, students will review how to simplify numerical expressions, practicing the order of operations without a calculator.
Standards Covered: 7.PFA.2, 7.MG.1
Assessment Window: March 10-14, 2025
Unit 9: Proportional Reasoning within Geometry
In this unit, students will deepen their understanding of geometry by examining how surface area and volume change when one dimension is multiplied by a scale factor and connect this concept to proportional relationships. They will also explore additional geometric applications of proportional reasoning, including dilations on the coordinate plane, the similarity of quadrilaterals and triangles, and problems involving scale drawings.
Standards Covered: 7.MG.1, 7.MG.2, 7.MG.4, 7.CE.2
Quarter 4
Unit 9: Proportional Reasoning within Geometry
In this unit, students will deepen their understanding of geometry by examining how surface area and volume change when one dimension is multiplied by a scale factor and connect this concept to proportional relationships. They will also explore additional geometric applications of proportional reasoning, including dilations on the coordinate plane, the similarity of quadrilaterals and triangles, and problems involving scale drawings.
Standards Covered: 7.MG.1, 7.MG.2, 7.MG.4, 7.CE.2
Assessment Window: Week of April 21-25, 2025
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.
Standards Covered: 8.PS.3, 7.PS.2, 8.PS.2
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.
Standards Covered: 8.MG.2, 7.PFA.2, 8.PFA.1, 8.MG.5, 8.PS.2
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.
Standards Covered: 8.MG.2, 8.MG.1, 7.CE.1, 8.CE.1, 8.MG.1
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.
Standards Covered: 8.MG.4, 8.NS.1, 8.NS.2, 8.PS.2
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.
Standards Covered: 8.PFA.4, 8.MG.4, 7.MG.1, 8.MG.2, 8.MG.1
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.
Standards Covered: 7.PFA.2, 7.PFA.1, 7.CE.2
Quarter 3
Unit 6: Solving Inequalities
In the previous unit, students worked with modeling contextual and mathematical problems with algebraic equations and had ample opportunities to learn the procedures for solving multi-step equations. They will apply these skills to solve mathematical and contextual problems involving inequalities. They will also represent solutions on number lines and make meaning of the inequality’s solution as a continuous set of numbers greater than or less than a boundary value. They will also have to distinguish between situations that require equations versus situations that require inequalities. They will connect their learning of the data cycle, specifically with boxplots, to their understanding of inequalities.
Standards Covered: 7.PFA.4, 8.PFA.5, 8.PS.2
Assessment Window: February 3-7, 2025
Unit 7: The Data Cycle Continues and Scatterplots Take the Lead
The data cycle re-emerges here with an emphasis on scatterplots. It is important to guide students in distinguishing between situations that are best represented by a boxplot versus a scatterplot. Students investigate bivariate data and learn how it can represent a function with a defined domain and range. They then continue through the data cycle by constructing scatterplots, identifying relationships, analyzing, and justifying the data patterns, and drawing a line of best fit.
Standards Covered: 8.PS.3, 8.PFA.2, 8.PS.2
Assessment Window: February 24-28, 2025
Unit 8: Lines and Their Equations from Transformations
The concept of the line of best fit prompts students to think about the actual lines and equations that define functions. They build on their previous knowledge of 𝑦 = 𝑚𝑥 from seventh grade by using translations to see how 𝑦-intercepts affect the graph. Additionally, students look at how reflections can change the slope. They also apply these ideas to polygons and real-life situations. As they create linear equations, it is crucial to keep discussing the data cycle and the ways data might have been gathered to correspond with the line.
Standards Covered: 8.PFA.3, 8.MG.3, 8.PS.3, 8.PFA.2
Assessment Window: March 24-28, 2025
Quarter 4
Unit 9: Independent or Dependent Events
Students delve into probability by exploring experimental and theoretical probability from Grade 7 and independent and dependent events, including the role replacement plays in influencing outcome, from Grade 8. As students calculate probability, they also have the opportunity to review rational numbers. This unit also extends the data cycle, incorporating discussions on how analyzing data and interpreting graphs can provide valuable insights for answering probability-related questions.
Standards Covered: 7.PS.1, 8.PS.1, 8.PS.2, 8.PS.3
Assessment Window: Week of April 21-25, 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.
Standards Covered: 8.PS.3, 8.PS.2
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.
Standards Covered: 8.MG.2, 8.PFA.1, 8.MG.5, 8.PS.2
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.
Standards Covered: 8.MG.2, 8.MG.1, 8.CE.1, 8.MG.1
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.
Standards Covered: 8.MG.4, 8.NS.1, 8.NS.2, 8.PS.2
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.
Standards Covered: 8.PFA.4, 8.MG.4, 8.MG.2, 8.MG.1
Assessment Window: January 13 to January 17, 2025
Quarter 3
Unit 6: Solving Inequalities
In the previous unit, students worked with modeling contextual and mathematical problems with algebraic equations and had ample opportunities to learn the procedures for solving multi-step equations. They will apply these skills to solve mathematical and contextual problems involving inequalities. They will also represent solutions on number lines and make meaning of the inequality’s solution as a continuous set of numbers greater than or less than a boundary value. They will also have to distinguish between situations that require equations versus situations that require inequalities. They will connect their learning of the data cycle, specifically with boxplots, to their understanding of inequalities.
Standards Covered: 8.PFA.5, 8.PS.2
Assessment Window: February 3-7, 2025
Unit 7: The Data Cycle Continues and Scatterplots Take the Lead
The data cycle re-emerges here with an emphasis on scatterplots. It is important to guide students in distinguishing between situations that are best represented by a boxplot versus a scatterplot. Students investigate bivariate data and learn how it can represent a function with a defined domain and range. They then continue through the data cycle by constructing scatterplots, identifying relationships, analyzing, and justifying the data patterns, and drawing a line of best fit.
Standards Covered: 8.PS.3, 8.PFA.2, 8.PS.2
Assessment Window: February 24-28, 2025
Unit 8: Lines and Their Equations from Transformations
The concept of the line of best fit prompts students to think about the actual lines and equations that define functions. They build on their previous knowledge of 𝑦 = 𝑚𝑥 from seventh grade by using translations to see how 𝑦-intercepts affect the graph. Additionally, students look at how reflections can change the slope. They also apply these ideas to polygons and real-life situations. As they create linear equations, it is crucial to keep discussing the data cycle and the ways data might have been gathered to correspond with the line.
Standards Covered: 8.PFA.3, 8.MG.3, 8.PS.3, 8.PFA.2
Assessment Window: March 24-28, 2025
Quarter 4
Unit 9: Independent or Dependent Events
Students delve into probability by examining independent and dependent events, including the role replacement plays in influencing outcomes. This builds directly off of the work students did in 7th grade, examining the fundamental principles of probability and exploring the differences between experimental and theoretical probability. This unit also extends the data cycle, incorporating discussions on how analyzing data and interpreting graphs can provide valuable insights for answering probability-related questions.
Standards Covered: 8.PS.1, 8.PS.2, 8.PS.3
Assessment Window: Week of April 21-25, 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.
Standards Covered: A.EO.1, A.F.2, A.ST.1
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.
Standards Covered: A.EO.1, A.ST.1, A.F.1
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.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A.F.2, A.F.1
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.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A2.EI.1
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.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A2.EI.1
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.
Standards Covered: A.EO.1, A.EO.3, A.EO.4, A2.EO.2
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.
Standards Covered: A.F.2, A.ST.1, A.F.2
Quarter 3
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.
Standards Covered: A.F.2, A.ST.1, A.F.2
Assessment Window: February 3-7, 2025
Unit 7: Operations with Polynomials
Students will expand their analytical skills to include polynomial operations such as sums, differences, products, quotients, and factoring. Emphasis will be placed on using concrete objects, along with pictorial and symbolic models, as well as applying the distributive property and area models to visualize the relationship between multiplication and factoring. Students will demonstrate the equality of quadratic expressions in multiple forms.
Standards Covered: A.EO.2, A2.EO.3
Assessment Window: March 10-14, 2025
Unit 8: Quadratic Functions
This unit will build on the procedural fluency developed in Unit 7 by linking factoring to the graphical representation of solutions. Students will then progress to solving quadratic equations that cannot be factored and will explore whether a quadratic function has one, two, or no real solutions. Additionally, students will investigate other key characteristics of quadratic function graphs—such as the vertex, 𝑥-intercepts, 𝑦-intercept, domain, and range—and will practice evaluating these functions. Finally, students will apply their skills to connect quadratic models to contextual situations.
Standards Covered: A.EI.3, A.F.2, A.ST.1
Quarter 4
Unit 8: Quadratic Functions
This unit will build on the procedural fluency developed in Unit 7 by linking factoring to the graphical representation of solutions. Students will then progress to solving quadratic equations that cannot be factored and will explore whether a quadratic function has one, two, or no real solutions. Additionally, students will investigate other key characteristics of quadratic function graphs—such as the vertex, 𝑥-intercepts, 𝑦-intercept, domain, and range—and will practice evaluating these functions. Finally, students will apply their skills to connect quadratic models to contextual situations.
Standards Covered: A.EI.3, A.F.2, A.ST.1
Assessment Window: Week of April 7-11, 2025
Unit 9: Function Synthesis
This final unit solidifies the connections and distinctions between the types of functions studied throughout the course. Students will refine their understanding of transformational graphing for quadratic and exponential functions in the forms 𝑓(𝑥) + 𝑘 and 𝑘𝑓(𝑥). They will now compare and contrast the characteristics of graphs across all three function types: linear, quadratic, and exponential. Additionally, the unit revisits the data patterns introduced in Unit 1, as students analyze data sets and scatterplots to identify whether a linear or quadratic model provides the best fit.
Standards Covered: A.F.2, A.ST.1, A.F.2, A.ST.1
Assessment Window: Week of April 28 – 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.
Standards Covered: G.RLT.1
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.
Standards Covered: G.RLT.2, G.RLT.1
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.
Standards Covered: G.RLT.3, G.RLT.1
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.
Standards Covered: G.TR.1, G.RLT.1
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.
Standards Covered: G.TR.2, G.TR.3, G.RLT.1, G.RLT.2
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.
Standards Covered: G.TR.4, G.TR.2, T.CT.2, G.RLT.1, G.TR.1, G.TR.2, G.TR.3
Quarter 3
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.
Standards Covered: G.TR.4, G.TR.2, T.CT.2, G.RLT.1, G.TR.1, G.TR.2, G.TR.3
Unit 7: Quadrilaterals & Polygons
Exploring the unique characteristics of quadrilaterals and polygons enables us to prove their existence and unlock further insights. Once we establish the fundamental properties, we can confidently apply them to analyze and understand these geometric shapes.
Standards Covered: G.PC.1, G.PC.2, G.RLT.1, G.RLT.2, G.TR.1, G.TR.2
Unit 8: Three-Dimensional Figures
Students begin with nets of solid figures and use these to develop formulas for surface area and lateral area. This thinking allows students to calculate surface area and volume of composite figures. Students further expand on this thinking to determine the effect changing one or more dimensions of a figure has on any derived measures of the new figure. Proportional reasoning comes into play when comparing surface area and volume of similar three-dimensional figures.
Standards Covered: G.DF.1, G.DF.2, G.RLT.1
Unit 9: Circles
Students move their thinking from polygons to circles in the final unit. Students apply coordinate geometry when working with the equation of the circle. Circles are also considered outside of the coordinate plane when looking at the proportional relationships that exist between parts of the circle and the entire circle.
Standards Covered: G.PC.3, G.PC.4, T.CT.1, G.RLT.1
Quarter 4
Unit 9: Circles
Students move their thinking from polygons to circles in the final unit. Students apply coordinate geometry when working with the equation of the circle. Circles are also considered outside of the coordinate plane when looking at the proportional relationships that exist between parts of the circle and the entire circle.
Standards Covered: G.PC.3, G.PC.4, T.CT.1, G.RLT.1