Math 7 Units
Gap Work: Integers
(From Unit 6)
Suggested Pacing: 8 days
In this unit, students will develop a deep understanding of how to perform all four operations—addition, subtraction, multiplication, and division—with integers and rational numbers. Through structured lessons and real-world problem-solving, students will explore patterns, properties, and relationships between numbers, laying a strong foundation for algebraic thinking.
Unit 2: Solve Problems Involving Geometry
Suggested Pacing: 22 days
In Unit 2, students will develop their understanding of geometric relationships and measurement. They will learn how to determine actual measurements from scale drawings and explore the specific conditions that result in the formation of a unique triangle. Students will apply their knowledge of angle relationships—such as complementary, supplementary, vertical, and adjacent angles—to find unknown angle measures. The unit also focuses on three-dimensional geometry, where students will calculate the surface area and volume of right prisms and right pyramids. Additionally, students will solve problems involving the circumference and area of circles, deepening their ability to apply formulas in real-world and mathematical contexts.
Unit 3: Proportional Relationships
Suggested Pacing: 16 days
Unit 3 focuses on proportional relationships, teaching students to represent these relationships using tables, graphs, and equations. Students will learn to determine the constant of proportionality and apply proportional reasoning to solve both single-step and multi-step problems. The unit also emphasizes recognizing graphs of proportional relationships and introduces the concept of slope, helping students understand the unit rate informally as a measure of the line's steepness. Additionally, students will develop the critical skill of distinguishing proportional relationships from other types of relationships. This comprehensive approach ensures students gain a thorough understanding of proportional relationships and their applications in various mathematical contexts.
Unit 4: Solve Problems Involving Percentages
Suggested Pacing: 20 days
This unit develops students’ understanding of percents as proportional relationships and equips them with tools to solve a wide range of real-world and mathematical percent problems. Students will explore how the percent equation represents a proportion and use it to find the part, whole, or percent. The unit emphasizes problem-solving strategies and conceptual understanding through applications such as percent increase and decrease, markups and markdowns, interest, tax, tip, commission, discount, and percent error.
Unit 5: Sampling and Statistics
Suggested Pacing: 17 days
Unit 5 focuses on data analysis and statistics, teaching students to represent and interpret data using various measures and visual tools. Students will learn to calculate and apply measures of central tendency (mean, median, and mode) and measures of variability (range, interquartile range, and mean absolute deviation). The unit emphasizes creating and interpreting visual representations of data, including stem-and-leaf plots and histograms. Students will develop the critical skill of choosing appropriate statistical measures and graphical representations for different types of data sets. Additionally, students will learn to analyze data distributions and draw meaningful conclusions from their analyses. This comprehensive approach ensures students gain a thorough understanding of basic statistical concepts and their applications in various real-world contexts.
Unit 6: Solve Problems Involving Operations with Integers and Rational Numbers
Suggested Pacing: 20 days
In this unit, students will deepen their understanding of rational numbers, their decimal representations, and the properties of exponents. They will learn to convert fractions into decimals and determine whether they are terminating or nonterminating, as well as apply the four operations (addition, subtraction, multiplication, and division) to all rational numbers. The unit will then expand into exponential properties including zero and negative exponents, product and quotient of powers, and power of a power rules. Finally, students will apply their knowledge of coordinate geometry to find distances between points, and calculate the perimeter and area of polygons using ordered pairs on the coordinate plane.
Unit 7: Work with Linear Expressions
Suggested Pacing: 13 days
Unit 7 focuses on algebraic expressions, teaching students to simplify, factor, and apply the distributive property to rewrite and solve expressions. Students will learn to factor common terms (using the GCF) and use multiple strategies to break down expressions into products of factors. The unit emphasizes understanding how to manipulate expressions to prepare for solving equations and inequalities in future units. Students will develop the critical skill of recognizing equivalent expressions and applying properties of operations to simplify and factor expressions accurately. This comprehensive approach ensures students gain a thorough understanding of expressions, combining like terms, distributing, and factoring and build a strong foundation for advanced algebraic concepts such as equations and inequalities.
Unit 8: Solve Problems Using Equations and Inequalities
Suggested Pacing: 13 days
In this unit, students will learn how to represent real-world and mathematical situations using algebraic expressions, equations, and inequalities. They will develop strategies to evaluate and simplify expressions and solve multi-step equations and inequalities that include rational numbers. Students will explore how these algebraic tools can help describe patterns, solve problems, and make decisions in everyday life.
Unit 9: Probability
Suggested Pacing: 12 days
Unit 9 begins with dimensional analysis (Unit 8 Lesson 7), teaching students how to perform unit conversions using conversion factors. It then transitions into probability, exploring simple probability for single events, compound probability for multiple events, and the concept of sample space - the set of all possible outcomes in a probability experiment. Students will learn to calculate probabilities, understand probability rules, and apply these concepts to real-world scenarios. The unit aims to develop students' analytical skills through various problem-solving exercises, connecting mathematical theory to practical applications.
Math 7 Accelerated
Unit 2: Proportional Relationships
Suggested Pacing: 10 days
In this unit, students will explore proportional relationships through various representations, including tables, graphs, and equations. They will learn to identify and determine the constant of proportionality, which is crucial for understanding how these quantities relate to each other.
Students will apply proportional reasoning to solve both single- and multi-step problems, enhancing their critical thinking and problem-solving skills. They will also develop the ability to recognize graphs of proportional relationships, gaining insight into how the unit rate serves as a measure of the slope, reflecting the steepness of the line.
Finally, students will distinguish between proportional relationships and other types of relationships, deepening their understanding of mathematical concepts and their applications in real-world scenarios.
Unit 3: Solve Problems Involving Percentages
Suggested Pacing: 14 days
Students will use proportional reasoning to find the percent or part in a percent problem and explain how the percent equation reflects a proportional relationship. They will apply the percent equation to solve various real-world problems, including situations involving tips, taxes, and fees. Additionally, students will tackle percent increase and decrease scenarios, as well as problems involving markups, markdowns, simple interest, loan or savings interest, final savings, payment amounts, and percent error. Throughout, they will use the percent equation to calculate either the percent or the part, reinforcing their understanding of proportional relationships in practical contexts.
Unit 4: Sampling and Statistics
Suggested Pacing: 10 days
Students will identify the most appropriate measure of center to accurately represent a given data set. They will explore and compare different measures of variability, including range, interquartile range (IQR), and mean absolute deviation (MAD), understanding how each reflects data spread in unique ways.
Students will analyze the means of multiple samples to make predictions about the population mean and describe the variability within the distribution of these sample means, building foundational skills in statistical inference. Using interquartile range, students will compare the medians of two populations, while employing mean absolute deviation to compare their means, deepening their understanding of how variability measures inform comparisons between data sets.
This unit emphasizes interpreting data through appropriate statistical measures to make informed conclusions about populations based on sample data.
Unit 5: Solve Problems Involving Operations with Integers and Rational Numbers
Suggested Pacing: 7 days
Students will add rational numbers and analyze additional expressions that result in a sum of zero, while also understanding the conditions that lead to positive or negative sums. They will explore subtraction of rational numbers using number lines, and investigate the rules for multiplying signed numbers. Students will compute and interpret the quotient of two rational numbers in real-world situations, and use the order of operations to solve multi-step problems. They will develop an understanding of additive inverses, recognizing that a number and its inverse have the same absolute value and sum to zero. Throughout, students will apply properties of operations to solve problems involving positive and negative numbers, and use their skills to solve real-world problems involving the addition, multiplication, and division of rational numbers.
Unit 6: Congruence and Similarity
Suggested Pacing: 16 days
Students will determine measures of figures using scale drawings and develop a solid understanding of key geometric transformations: translations, reflections, rotations, and dilations. They will perform these transformations and describe sequences that map one figure (the preimage) onto another (the image).
Students will learn to explain when two figures are congruent by identifying rigid motions that connect them. Additionally, they will determine whether pairs of triangles are similar by applying the Angle-Angle similarity criterion.
This unit emphasizes hands-on practice with transformations and reasoning about congruence and similarity, enabling students to build strong spatial and geometric reasoning skills.
Unit 7: Work with Linear Expressions
Suggested Pacing: 8 day
Students will combine like terms to simplify expressions and use the Distributive Property to expand linear expressions. They will add and subtract linear expressions, then interpret the resulting equivalent expressions. Additionally, students will factor linear expressions and interpret the meaning of a factored expression. Conceptually, they will demonstrate understanding of combining like terms, expanding, adding, subtracting, and factoring linear expressions. Procedurally, they will recognize like terms, simplify expressions, and apply the Distributive Property accurately. They will also factor linear expressions by identifying the greatest common factor (GCF) and rewriting the expression using parentheses.
Unit 8: Solve Problems Using Equations and Inequalities
Suggested Pacing: 12 days
Students will develop proficiency in writing and solving linear equations and inequalities across various forms. They will solve two-step equations in the forms px+q=r and p(x+q)=r, building confidence in manipulating expressions.
Students will also write and solve one-step inequalities involving addition, subtraction, multiplication, and division, reasoning about their solutions within real-world contexts. They will extend their skills to two-step inequalities and model solutions on number lines for clear visual understanding.
Further, students will solve linear equations with variables on both sides and determine the number of solutions such equations possess, reinforcing their conceptual grasp of equation behavior.
This unit emphasizes reasoning, procedural skills, and real-world application, preparing students to solve a variety of linear problems with confidence.
Unit 9: Linear Relationships
Suggested Pacing: 8 days
In this unit, students focus on simplifying linear expressions by combining like terms to build fluency with equivalent expressions and operations. They develop conceptual understanding and procedural skills by recognizing like terms and using properties of operations effectively. Students also engage in language objectives, practicing superlative adjectives and collaborative discussion strategies to strengthen mathematical communication. Building on previous work with equivalent expressions and operations, students will progress to writing and solving equations and applying integer exponents. Additionally, students explore proportional relationships by graphing lines, interpreting slopes as constants of proportionality, comparing different proportional relationships, and deriving linear equations of the form y = kx and y = mx + b. Throughout, students cultivate teamwork and reasoning skills essential for mathematical thinking.
Unit 10: Probability
Suggested Pacing: 9 days
Students will develop a strong foundation in probability by expressing the likelihood of events as numbers between 0 and 1 and classifying events based on their chance of occurring. They will predict relative frequencies and estimate probabilities through hands-on experiments, connecting theoretical concepts to real-world data.
Students will learn to calculate and compare theoretical probabilities with experimental results to deepen their understanding of probability models. They will explore compound events by finding exact probabilities and approximating probabilities through simulations, fostering skills in both calculation and estimation.
This unit emphasizes practical investigation and reasoning about chance, preparing students to analyze and interpret probabilities in a variety of contexts confidently.
Unit 11: Angles
Suggested Pacing:10 days
Students will explore the conditions that determine when a set of side lengths forms a unique triangle, deepening their understanding of triangle construction. They will contrast this with quadrilaterals, investigating why four given side lengths can produce infinitely many different quadrilaterals.
Students will use angle relationships within polygons to find unknown angle measures, focusing on the connections between interior and exterior angles of triangles. They will also explore the angle relationships formed when two parallel lines are intersected by a transversal, including corresponding, alternate interior, and same-side interior angles.
Teachers should encourage students to reason through these relationships visually and analytically, fostering strong geometric intuition and problem-solving skills. This unit builds foundational knowledge of polygon properties and angle reasoning essential for advanced geometry concepts.
Unit 12: Area, Surface Area, and Volume
Suggested Pacing: 10 days
Students will explore key geometric concepts and measurement skills. They will investigate cross sections of three-dimensional figures to deepen spatial reasoning. Teachers will support students in calculating and estimating square and cube roots, strengthening their understanding of roots and their applications.
Students will find surface areas and volumes of composite figures, applying formulas accurately in varied contexts. They will solve problems involving the circumference and area of circles, building fluency with circle measurements. Additionally, students will use volume formulas to calculate volumes of cylinders, cones, and spheres, connecting geometric formulas to real-world shapes.
This unit emphasizes spatial visualization, precise calculation, and problem solving, equipping students with essential skills in geometry and measurement.
Unit 13: Irrational Numbers, Exponents, and Scientific Notation
Suggested Pacing: 19 days
In this unit, students will deepen their understanding of rational and irrational numbers by exploring how to convert rational numbers into repeating decimals. They will use number lines to accurately locate, compare, and order both rational and irrational numbers, building strong number sense.
Students will generate equivalent expressions using zero and negative exponents, applying the properties of powers to rewrite numbers as products of a number between 1 and 10 and a power of 10. This foundation leads to fluency in performing operations—addition, subtraction, multiplication, and division—on numbers expressed in scientific notation.
Teachers should emphasize connections between number representations and operations, guiding students to apply exponent rules consistently.
This unit strengthens students’ skills in working across different number forms and prepares them for more advanced math concepts involving exponents and real-world applications.
Unit 14: Understand and Analyze Functions
Suggested Pacing: 12 days
Students will develop a foundational understanding of functions and their characteristics. They will identify and use qualitative features of relationships, determining whether a relation is a function through tables and mapping diagrams. Students will represent functions in multiple forms (tables, graphs, equations, and verbal situations) and distinguish between linear and nonlinear functions.
Students will analyze functions to interpret key attributes like rate of change and initial value, strengthening their ability to understand how functions model real-world situations. They will also compare functions presented in different representations to deepen their comprehension of functional relationships.
This unit builds critical skills in recognizing, representing, and analyzing functions, preparing students for advanced mathematical reasoning and application.