Math 7 Accelerated Year-At-A-Glance
Unit 2: Proportional Relationships
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
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
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
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
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
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
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
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
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
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
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
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
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.
Please reach out if you would like specific information regarding a lesson or unit.
My email is: tepps@greenville.k12.sc.us