This foundational unit in the 6th-grade curriculum focuses on building strong number sense skills in 26 lessons. By engaging in a variety of activities, students will gain proficiency with decimal and fraction operations, understand factors and multiples, explore integers, and navigate the coordinate plane. These topics are broken down into manageable sections, allowing students to build confidence and mastery in operations, place value, number relationships, and geometric applications. This unit is designed to promote both procedural fluency and conceptual understanding, setting students up for success as they progress through more complex math concepts.  

Through their learning in the Number System domain, students: 

• use the meaning of fractions and relationships between multiplication and division to understand and explain why the procedures for dividing fractions make sense; 
• extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, particularly negative integers; 
• reason about the order and absolute value of rational numbers and about the location of points on a coordinate plane.

Lessons in This Unit Include:

1. Add and Subtract Decimals: Students begin by reviewing place value and practicing addition and subtraction with decimals, focusing on lining up decimal points and rounding for accuracy.
2. Multiply Decimals: This lesson introduces decimal multiplication, emphasizing place value shifts and positioning the decimal in products.
3. Division Algorithm with Whole Numbers: Students revisit division basics with whole numbers, learning efficient division strategies and strengthening their division fluency.
4. Division with Whole Numbers: Focusing on problem-solving, this lesson continues with whole number division, applying the skills to multi-digit numbers.
5. Dividing Whole Numbers to Thousandths: Expanding on division, students learn to divide to a greater precision, practicing with thousandths to build accuracy with small values.

This unit on Ratio and Proportional Reasoning introduces 6th-grade students to the foundational concepts of ratios, rates, and proportional relationships in 20 lessons. Through a mix of visual representations, real-life applications, and problem-solving activities, students develop an understanding of how to compare quantities, analyze relationships, and apply these skills to practical situations. This unit builds critical thinking and reasoning skills, setting the stage for more complex algebraic concepts.

Through their learning in the Ratios and Proportional Relationships domain, students: 

• use reasoning about multiplication and division to solve ratio and rate problems about quantities; 
• connect understanding of multiplication and division with ratios and rates by viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities; 
• expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions.

Lessons in This Unit Include:

1. Understanding Ratios: Students are introduced to the concept of a ratio, learning how to express and interpret comparisons between two quantities. Visual models and real-world examples help solidify this foundational concept.
2. Equivalent Ratios: Building on the understanding of basic ratios, students explore equivalent ratios, using models and tables to see how ratios represent the same relationship even when scaled up or down.
3. Unit Rates: Students learn to determine unit rates by finding the “per one” quantity, a skill that is essential for comparing rates and solving proportional problems.
4. Ratios and Rates in Tables and Graphs: This lesson connects ratios and rates to data representation, teaching students how to organize ratios in tables and plot them on graphs to reveal patterns and relationships.

This unit introduces students to the essential building blocks of algebra, covering expressions, equations, and inequalities in 25 lessons. By mastering these foundational skills, students will learn to evaluate and simplify expressions, solve equations, and analyze inequalities. Through real-world contexts and practical applications, students deepen their understanding of mathematical relationships and problem-solving skills, preparing them for more advanced algebraic concepts in later grades.

Through their learning in the Expressions, Equations, and Inequalities domain, students:

• write expressions and equations that correspond to given situations, using variables to represent an unknown and describe relationships between quantities; 
• understand that expressions in different forms can be equivalent, and use the properties of operations to rewrite and evaluate expressions in equivalent forms; 
• use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations.

Lessons in This Unit Include:

1. Evaluate Exponents: Students begin by exploring exponents, understanding them as repeated multiplication, and practicing how to evaluate expressions with whole number exponents.
2. Evaluate Numerical Expressions: This lesson covers the order of operations (PEMDAS), teaching students to evaluate complex numerical expressions step-by-step.
3. Evaluate Algebraic Expressions: Students learn to substitute values for variables in algebraic expressions and evaluate the results, solidifying their grasp of variable use.
4. Evaluate Expressions with Fractions and Decimals: Extending their evaluation skills, students practice with expressions that include fractions and decimals, reinforcing their accuracy with different number types.

This geometry unit introduces 6th-grade students to foundational geometric concepts, focusing on the properties of shapes, area, surface area, and volume in 15 lessons. Students will engage in hands-on activities, visualizations, and real-world applications to understand the structure of two- and three-dimensional shapes. By exploring these concepts, students will build spatial reasoning skills and become comfortable with geometry’s practical and theoretical aspects, preparing them for more advanced geometry in later grades.

Through their learning in the Geometry domain, students:

• find areas of polygons, and surface areas of prisms, and use area models to understand perfect squares; 
• extend formulas for the volume of a right rectangular prism to fractional side lengths and use volume models to understand perfect cubes.

Lessons in This Unit Include:

1. Introduction to Geometry and Geometric Vocabulary: Students learn essential geometric terms, including points, lines, line segments, rays, angles, and planes. They also discuss how these elements combine to form shapes.
2. Classifying 2D Shapes: This lesson focuses on identifying and classifying polygons based on properties like the number of sides, angles, and symmetry. Students explore triangles, quadrilaterals, and other polygons.
3. Measuring and Classifying Angles: Students learn to measure angles using a protractor and classify them as acute, right, obtuse, or straight. They also practice identifying angles within various shapes.
4. Properties of Triangles: This lesson dives deeper into triangles, discussing types (scalene, isosceles, equilateral) and properties, including angle sums and relationships within each type.

This unit introduces students to fundamental concepts in statistics and probability, focusing on collecting, analyzing, and interpreting data in 17 lessons. Students will explore probability through theoretical and experimental methods, learn to make predictions, and investigate how statistical tools can describe and summarize data. By working with different types of data representations, students will develop skills in creating, reading, and comparing data displays, setting a strong foundation for data literacy and decision-making based on statistical reasoning.

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

• learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected; 
• understand the probability of a chance event and develop probability models for simple events.

Lessons in This Unit Include:

1. Introduction to Probability: Students are introduced to basic probability concepts, including outcomes, events, and likelihood, using familiar real-life examples to build intuition.
2. Theoretical Probability: This lesson covers theoretical probability, where students learn to calculate the probability of an event based on known outcomes and explore probability as a measure between 0 and 1.
3. Making Predictions with Theoretical Probability: Students use theoretical probability to make predictions, learning how probability can help anticipate outcomes over time.
4. Experimental Probability: Moving from theory to practice, students conduct experiments to observe outcomes, calculate experimental probabilities, and compare these to theoretical predictions.