This unit focuses on developing students’ understanding of rational numbers, including positive and negative values, decimals, fractions, and mixed numbers in 17 lessons. Following the Next Generation Learning Standards for 7th-grade math in New York, students will learn to operate with rational numbers through various contexts, from arithmetic to real-world applications. Emphasizing mastery in comparing, ordering, and performing operations with rational numbers, this unit builds students’ number sense and prepares them for complex problem-solving. Each lesson integrates key mathematical practices, reinforcing procedural fluency, conceptual understanding, and the application of rational numbers in geometry and multi-step problems.

Through their learning in the Number System students: 

• develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers; 
• extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division;
• explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers by applying properties of operations, and view negative numbers in terms of everyday contexts.

Lessons in This Unit Include:

1. Compare and Order Rational Numbers: Students begin by learning to compare and order rational numbers, including positive and negative integers, fractions, and decimals. They develop strategies for visualizing and sequencing values on the number line.
2. Absolute Value and Opposites: This lesson introduces absolute value as a measure of distance from zero and explores the concept of opposites, helping students understand the role of symmetry on the number line.
3. Adding and Subtracting with Negative Numbers: Students learn the rules for adding and subtracting integers, focusing on developing intuition for combining positive and negative values.
4. Subtraction with Negative Integers: Building on previous knowledge, students practice subtraction with negative integers, reinforcing the concepts of additive inverses and the directionality of values on the number line.

This unit on ratio and proportional reasoning provides 7th-grade students with a deep understanding of how to analyze, represent, and solve problems involving proportional relationships in 22 lessons. The lessons in this unit guide students through using ratio tables, calculating rates, interpreting graphs, and applying proportional reasoning to real-world situations. Students will explore scale drawings, percent change, and comparisons, building critical skills to make informed decisions and solve complex, multi-step problems. Each lesson is designed to reinforce students’ analytical abilities and prepare them for algebraic thinking and practical applications.

Lessons in This Unit Include:

1. Use Ratio Tables to Organize Ratio Problems: Students begin by learning to set up and use ratio tables to solve ratio-based problems, recognizing patterns and relationships between quantities.
2. Calculating Rates and Unit Rates: This lesson focuses on understanding rates, including calculating unit rates, which helps students compare quantities in real-world scenarios.
3. Complex Fractions and Rates: Extending their knowledge, students work with complex fractions in rate problems, applying skills in division and understanding fraction relationships.
4. Determine Proportionality on a Graph: Students learn to identify proportional relationships by analyzing linear patterns and direct variation on graphs.

This unit introduces 7th-grade students to foundational algebraic concepts, including simplifying expressions, solving equations, and analyzing inequalities. Aligned with the Next Generation Learning Standards, this unit emphasizes the development of skills in manipulating expressions, solving equations, and applying algebra to real-world scenarios. Through hands-on practice and real-world applications, students build confidence in algebraic reasoning and prepare for more advanced mathematical problem-solving. This unit is designed to help students understand how to represent and solve problems using algebraic language and operations.

Through their learning in the Number System and the Expressions, Equations, and Inequalities domains, students: 

• explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers by applying properties of operations, and view negative numbers in terms of everyday contexts; 
• use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.

Lessons in This Unit Include:

1. Simplifying Expressions Review: Students begin with a review of simplifying expressions, reinforcing prior knowledge and setting the stage for more complex manipulation of expressions.
2. Combine Like Terms, Distributive Property: This lesson focuses on combining like terms and applying the distributive property, helping students simplify and organize expressions.
3. Factor and Expanding Algebraic Expressions: Students learn to factor and expand expressions, gaining a deeper understanding of expression structure and equivalent forms.
4. Identify Equivalent Linear Expressions: This lesson emphasizes recognizing and creating equivalent expressions by applying properties of operations.

This unit introduces 7th-grade students to core concepts in statistics and probability, including calculating probabilities, interpreting data, and analyzing data distributions. Through hands-on exploration, students learn to calculate and interpret both simple and compound probabilities, make predictions, and analyze data sets using measures of central tendency and variation. The unit culminates in the creation and interpretation of box-and-whisker plots and an exploration of mean absolute deviation (MAD) to understand data spread. This unit builds a strong foundation in data analysis and statistical reasoning, helping students interpret and communicate findings from data.

Through their learning in the Statistics and Probability domain, students: 

• build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations; 
• begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences; 
• extend previous understandings of simple probabilities in grade 6 to calculate probabilities of compound events.

Lessons in This Unit Include:

1. Understanding Probability of an Event: Review: Students begin with a review of basic probability concepts, including the likelihood of an event occurring and understanding probabilities as fractions, decimals, and percentages.
2. Probability of Simple Events: This lesson covers calculating the probability of simple events, reinforcing students’ understanding of favorable outcomes versus total outcomes.
3. Making Predictions with Theoretical Probability: Students use theoretical probability to make predictions about real-world situations, exploring how probability models can predict outcomes over many trials.
4. Probability of Compound Events: Part 1: Students learn to calculate the probability of compound events, such as “and” or “or” events, using models like lists, tables, and tree diagrams.

This unit on geometry introduces 7th-grade students to the study of circles, area calculations, surface area, and angle relationships. Aligned with the Next Generation Learning Standards, this unit builds students’ understanding of two- and three-dimensional shapes, applying area and surface area concepts to compound figures and geometric solids. Additionally, students will explore angle relationships within various shapes, using properties of angles and triangles to solve for unknown values. By the end of the unit, students will be able to analyze and solve problems involving circles, polygons, and three-dimensional shapes, laying a strong foundation for more advanced geometry concepts.

Lessons in This Unit Include:

1. Intro to Circles, Parts, and Pi: Students begin by exploring the properties of circles, including radius, diameter, and circumference, and are introduced to the concept of pi.
2. Circumference: This lesson focuses on calculating the circumference of circles, using the formulas C=2πr and C=πd reinforcing students’ understanding of pi.
3. Area of Circles: Students learn to calculate the area of circles, applying the formula A=r2 and practicing with various circle sizes.
4. Area of Semi-Circles and Quarter Circles: Building on their knowledge of circles, students calculate the area of semi-circles and quarter circles, learning to adjust area formulas for portions of a circle.

7th and 8th Grade Geometry (for advanced students taking Algebra I in 8th grade)

This advanced geometry unit is designed for 7th-grade students preparing to take Algebra I in 8th grade. The unit delves deeply into the study of circles, area and volume calculations, three-dimensional solids, transformations, and key geometry theorems. Students will work on advanced applications of geometric concepts, including transformational geometry and the Pythagorean Theorem, applying these skills to complex problem-solving and real-world scenarios. Aligned with the Next Generation Learning Standards, this unit prepares students for higher-level algebra and geometry by building a strong foundation in spatial reasoning, measurement, and analytical skills.

Lessons in This Unit Include:

1. Area of Circles: Students learn to calculate the area of circles, applying the formula A=r2 and practicing with various circle sizes.
2. Area of Semi-Circles and Quarter Circles: Building on their knowledge of circles, students calculate the area of semi-circles and quarter circles, learning to adjust area formulas for portions of a circle.
3. Transformations and Congruence: This lesson introduces basic transformations (translations, reflections, rotations) and explores the concept of congruence.
4. Similar Figures: Students explore the concept of similarity, learning to identify similar figures and apply scale factors to determine proportional dimensions.