Office of Curriculum, Instruction, and Technology. Mathematics. Grade 7 ABSTRACT

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1 Office of Curriculum, Instruction, and Technology Mathematics Grade 7 ABSTRACT Mathematics at the seventh grade level broadens opportunities for students to apply rules, properties, and theorems of mathematics to real-world applications. Applications of negative exponents to represent extreme numbers and their place values are included. Students (a) solve algebraic equalities and inequalities, (b) recognize and develop finite and infinite sequences, (c) compare linear and exponential growth, (d) compare and contrast theoretical and experimental probabilities, (e) analyze involving angle measurement in the plane, and (f) compare and contrast the effect of dilation on perimeter, area, and volume. Adopted by the Somerville Board of Education on April 22, 2008

2 NJCCCS: Note: (8) indicates benchmarks to be achieved by grade 8 Essential Question: Content: Mathematics Grade 7 September October November December January 4.1(8)A1-7, 4.1(8)B1-5, 4.1(8)C1-3, 4.3(8)C2, 4.3(8)D3, 4.5A1-5, 4.5B1-4, 4.5C1-6, 4.5D1-4, 4.5E1-3, 4.5F1-6 How can mathematical properties be applied? Algebraic Expressions Skills and Topics: perform operations involving signed numbers simplify, evaluate, and use graphing techniques on a number line to illustrate absolute value and arithmetic operations apply the properties of solving equations and inequalities (e.g., additive inverse, multiplicative inverse, addition and multiplication properties) evaluate algebraic expressions with negative integers graph expressions involving absolute values 4.1(8)A1, 4.1(8)B5, 4.3(8)A1, 4.3(8)B1, 4.3(8)C1-2, 4.3(8)D1-5, 4.5D1-4, 4.5E1-3, 4.5F1-6 How are algebraic equations and inequalities represented and solved? Graphing and Solving Algebraic Equations define and identify irrational numbers (e.g., pi) and use rational numbers (e.g., terminating and repeating decimals) create an equation from the information given in a word problem translate a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice-versa 4.1(8)A1-2, 4.1(8)B1-3, 4.1(8)C1, 4.3(8)A1, 4.3(8)B1-2, 4.3(8)C2, 4.5D1-4, 4.5E1-3, 4.5F1, How are patterns recognized? Scientific Notation and Patterns represent extreme numbers in scientific notation with positive and negative exponents (e.g., the distance of planets from the sun, the size of a bacterium) recognize, describe, extend, and create patterns recognize and develop finite and infinite sequences, arithmetic sequences, and geometric sequences 4.3(8)B1-2, 4.3(8)C1-2, 4.3(8)D1-4, 4.5A1-5, 4.5B1-4, 4.5C1-6, 4.5D1-4, 4.5E1-3, 4.5F1-6 How are functions represented graphically? Graphing Functions graph and interpret functions involving two variables and determine the rate of change distinguish between linear and exponential growth (e.g., simple and compound interest) using tables, graphs, and equations evaluate data in various representations to derive patterns and trends use relationships and linear functions to model real-world situations 4.1(8)A3, 4.1(8)B4, 4.2(8)D5-6, 4.4(8)A2, 4.4(8)B1-6, 4.4(8)C1, 4.5D1-6, 4.5E1-3, 4.5F1, How can probabilities be expressed? Probability interpret probabilities as ratios, decimals, and percents determine the probabilities of complementary and compound events (e.g., multiplication rule) with and without replacement make predictions based on experimental and theoretical probabilities apply permutations and combinations to real-world problem solving, including factorial notation use proportions to solve involving percentages and similar figures

3 September October November December January Skills and Topics: evaluate and simplify solve simple linear algebraic expressions solve simple inequalities and graph solutions on a number line equations graphically and algebraically, including slopeintercept form Assessments: Resources: Technology: Chapters 3 and 10 Chapters 2 and 3 Chapters 4 and 10 Chapters 2, 3, and 4 Chapter 4 Chapter 2 Chapters 3, 10, and 11 Chapters 1, 3, and 4 Chapter 9 Chapter 11

4 Writing: Careers: September October November December January Applicable career options are discussed as they arise throughout the mathematics program. Career options include, but are not limited to, architects, artists, carpenters, engineers, general contractors, landscapers, and painters.

5 NJCCCS: Note: (8) indicates benchmarks to be achieved by grade 8 Essential Question: Content: Mathematics Grade 7 February March April May June 4.2(8)A1-5, 4.2(8)B1, 4.4(8)C2, 4.4(8)D1, 4.5A1-5, 4.5B1-4, 4.5C1-6, 4.5D1-6, 4.5E1-3, 4.5F1, What is the relationship among points, lines, and planes? Tools of Geometry Skills and Topics: apply concepts involving lines, angles, and planes (e.g., parallel and perpendicular lines, intersecting planes) identify, locate, and determine the value of complementary, supplementary, vertical, interior, and exterior angles, and those resulting from angle bisectors and perpendicular bisectors apply concepts involving the sum of the measures of the interior and exterior angles of a polygon 4.1(8)B3, 4.1(8)C1-2, 4.2(8)A1-5, 4.2(8)C1-2, 4.2(8)D1-5, 4.2(8)E1-4, 4.5D1-6, 4.5E1-3, 4.5F1, How can geometric formulas and properties be used to solve real-world? Geometric Properties and Formulas evaluate numeric and algebraic expressions involving square roots (e.g., using the Pythagorean theorem) apply the Pythagorean theorem to real-world situations use dimensional analysis to solve involving different units of measurement within the same system solve involving compound measurement units (e.g., miles per hour, pounds per square inch, persons per square mile) 4.2(8)A1, 4.2(8)A3-5, 4.2(8)B1-2, 4.2(8)E1-4, 4.5D1-6, 4.5E1-3, 4.5F1, What is the impact of dilation on the volume and surface area of a figure? Volume and Surface Area of Three-Dimensional Figures use formulas to find the surface area and volume of cones, cylinders, prisms, pyramids, and spheres describe the impact of a dilation on the perimeter and area of a plane figure describe the impact of a dilation on the surface area and volume of a three-dimensional figure apply the concept of similarity on scale drawings, similar figures, and threedimensional models 4.3(8)B1-2, 4.4(8)A1-4, 4.5D1-4, 4.5E1-3, 4.5F1-6 How can sets of data be used to predict trends? Central Tendencies apply concepts of central tendency (e.g., mean, median, mode) and display the data numerically and graphically (e.g., boxand-whisker plot, scatter plot) develop and present arguments based on measures of central tendency analyze the effect of additional data on measures of central tendency estimate the lines of best fit within a range of data 4.4C1-3, 4.4D1, 4.5A1-5, 4.5B1-4, 4.5C1-6, 4.5D1-4, 4.5E1-3, 4.5F1-6, 5.1(8)A2-3 How can discrete mathematics concepts be used to analyze trends in natural phenomena and societal issues? Discrete Mathematics use vertex-edge graphs to represent and find solutions to practical use iterative procedures to generate geometric patterns (e.g., fractals) use Venn diagrams to solve real-world with three attributes apply Euler circuits to problem-solving situations

6 February March April May June Skills and Topics: use formulas to find the perimeter and area of irregular figures perform all transformations (e.g., reflections, rotations, translations, dilations) of an image in the coordinate plane Assessments: Resources: Technology: Chapters 7 and 8 Chapters 8 and 9 Chapters 7 and 8 Chapters 8 and 9 Chapter 8 Chapter 9 Chapter 1 Chapters 2 and 8 Chapter 2 Chapter 10

7 Technology: Writing: Careers: February March April May June Applicable career options are discussed as they arise throughout the mathematics program. Career options include, but are not limited to, architects, artists, carpenters, engineers, general contractors, landscapers, and painters.