d. Apply properties of operations as strategies to add and subtract rational numbers. 7.EE.1 Use properties of operations to generate equivalent expressions. 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. September – October 8.EE.7.a 8.EE.7.b A-REI.3 Unit Title: Solving One-Step and Two-step and Multi-step Equations and Inequalities 8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. :Solve linear equations in one variable: a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different Review key properties of identify, commutative, associative and distributive Simplify variable expressions Solve one step equations by addition or subtraction Solve one step equations by multiplying or dividing Solve inequalities by adding or subtracting Solve inequalities by multiplying or Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Observation Class discussions Homework Problem of the day Journal entry Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1 5.1.12.D.2 5.2.8.E.1 Technology 8.1.4.A.1 8.1.P.C.1 21st Century Life and Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1
numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. A-REI.3 Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. dividing Solve two and multi step equations and inequalities Language Arts L.8.2.a L.8.2.c SL.8.1.d W.8.1.c W.8.2.d October 8.NS.1 8.NS.2 8.EE.7.a 8.EE.7.b A-REI.3 Unit Title: Using Decimals in Equations 8.NS Know that there are numbers that are not rational, and approximate them by rational numbers. 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal 8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Round and estimate decimals Write formulas using a spreadsheet Solve equations with decimals Recognize that repeating decimals correspond to fractions and determine their fractional equivalents Construct meanings for common irrational numbers, such pi and the square root of 2 Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Observation Class discussions Homework Problem of the day Journal entry Graphing calculator activity – Mean and Median Spreadsheet activity Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1 5.1.12.D.2 Technology 8.1.4.A.1 8.1.8.A.4 8.1.P.C.1 21st Century Life and Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1
Solve linear equations in one variable: a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. A-REI.3 Solve equations and inequalities in one variable 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Language Arts L.8.2.a L.8.2.c SL.8.1.d W.8.1.c W.8.2.d November 8.EE.1 8.EE.3 8.EE.4 8.NS.1 8.NS.2 7.NS.3 Unit Title: Factors, Fractions, and Exponents 8.EE.1 1. Know and apply the properties of integer exponents to generate equivalent numerical Use exponentiation to find whole number powers of numbers. Use and explain procedures for Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Observation Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1 5.1.12.D.2
by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. 8.EE.1 Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 8.EE.7.a a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. terminating and repeating decimals as fractions To add and subtract fractions and mixed numbers To multiply and divide fractions Use dimensional analysis to convert units of measure Solving equations by adding or subtracting fractions Solving equations by multiplying fractions Solve multi-step equations with fractions and decimals To find powers of products To find powers of quotients Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1 Language Arts SL.8.1.d W.8.1.c W.8.2.d January – February 8.EE.5 8.EE.8.a 8.EE.8.b 8.EE.8.c 8.F.1 Unit Title: Linear Functions 8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. To review the coordinate plane To determine whether a relation is a function Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1
8.F.2 8.F.3 8.F.4 8.F.5 8.SP.1 8.SP.2 8.SP.3 8.SP.4 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 8.EE.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. To graph relations and functions To use tables, graphs, or listed numerically to determine the slope of the function. To find solutions of equations with two variables To graph linear equations with two variables To find the slope of a line To use form in graphing a linear equation To write a function rule for a word relationship To write a function rule by analyzing a table or graph To interpret and draw scatter plots To use scatter plots to find trends To solve systems of equations of linear equations by graphing To solve systems of linear equations to solve problems To solve systems of linear Observation Class discussions Homework Problem of the day Journal Graphing calculator activities Rap song 5.1.12.D.2 Technology 8.1.4.A.1 8.1.P.C.1 21st Century Life and Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1 Visual and Performing Arts 1.3.8.B.2 1.3.8.B.4 Language Arts L.8.2.a L.8.2.c SL.8.1.d W.8.1.c W.8.2.d
columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? February – March 8.G.1.a 8.G.1.b 8.G.1.c 8.G.2 8.G.3 8.G.4 8.G.5 Unit Title: Geometry – Spatial thinking 8.G.1 1. Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 8.G.2. Understand that a figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the Identify vertical angles Identify complementary angles Identify supplementary angles Identify corresponding angles Identify missing measures on a plane that had at least two parallel lines and one transversal To identify corresponding parts of congruent triangles To determine whether triangles are congruent To graph translations Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Observation Class discussions Homework Problem of the day Journal Graphing calculator activities “Angle” challenge Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1 5.1.12.D.2 Technology 8.1.4.A.1 8.1.P.C.1 21st Century Life and Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1 Language Arts L.8.2.a L.8.2.c SL.8.1.d W.8.1.c W.8.2.d two-
congruence between them. 8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.4. Understand that a figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. To describe translations To identify a line of symmetry To graph a reflection of a geometric figure To graph rotations To identify rotational symmetry To describe the effect of dilations on figures using coordinates March 8.G.9 7.G.4 7.G.6 Unit Title: Area and Volume 8.G.9 Know the formulas for the volumes of cones, cylinders, and Find the area and perimeter of geometric figures made by combining Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1
8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. MAY - JUNE S-CP.1 S-CP.2 S-CP.3 Unit Title: Probability S-CP Understand independence and conditional probability and use them to interpret data S-CP.1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). S-CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. S-CP.3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. To use a tree diagram and the Counting Principle To find theoretical probability by counting outcomes To calculate probabilities of independent events To calculate probabilities of dependent events To use permutations To use combinations To find experimental probability To use simulations To choose a sample for a survey of population To make estimates about populations Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Observation Class discussions Homework Problem of the day Journal Probability activity Scientific Calculator activity Graphing Calculator activity Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1 5.1.12.D.2 Physical Education 2.5.8.C.1 Technology 8.1.4.A.1 8.1.P.C.1 21st Century Life and Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1 Language Arts L.8.2.a L.8.2.c SL.8.1.d W.8.1.c W.8.2.d
JUNE A-APR.1 Unit Title: Introduction to Polynomials A-APR Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomials 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials Adding and subtracting polynomials Multiplying a polynomial by a polynomial Multiplying binomials Daily Lesson Quizzes Checkpoint quizzes Chapter Test Teacher Observation Class discussions Homework Problem of the day Science 5.1.8.A.2 5.1.8.B.2 5.1.8.C.2 5.1.8.D.1 5.1.12.D.2 Physical Education 2.5.8.C.1 Technology 8.1.4.A.1 8.1.P.C.1 21st Century Life and Career Skills 9.1.8.A.1 9.1.12.A.1 9.1.4.B.1 9.1.8.B.1 Language Arts SL.8.1.d W.8.1.c W.8.2.d