What is a rational number? When are numbers written in scientific notation? Prerequisite/Extension SOL 5.2a 5.18c 6.2a 6.3a 7.1b 7.3a A.1 AII.1 1 8.4 – Order of Operations The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Essential Question(s) What is the role of the order of operations when evaluating expressions? Prerequisite/Extension SOL 5.7 6.8 7.13a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Substitute numbers for variables in algebraic expressions and simplify the expressions by using the order of operations. Exponents are positive and limited to whole numbers less than 4. Square roots are limited to perfect squares. Apply the order of operations to evaluate formulas. Problems will be limited to positive exponents. Square roots may be included in the expressions but limited to perfect squares. Key Vocabulary PEMDAS DOE Lesson Chapter 1 Lesson 1 Chapter 2 Lesson 7 Resources/Lessons 3 8.15a,c – Equations The student will a) solve multistep linear equations in one variable with the variable on one and two sides of the equation; c) identify properties of operations used to solve an equation. Essential Question(s) How does the solution to an equation differ from the solution to an inequality? The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Solve two- to four-step linear equations in one variable using concrete materials, pictorial representations, and paper and pencil illustrating the steps performed. Identify properties of operations used to solve an equation from among: Key Vocabulary Equation Linear Equation DOE Lesson Plans Chapter 1 Lessons 5 – 7 Chapter 6 Lessons 1 – 4
2 8.16 - Graphing Equations The student will a linear equation in two variables. Essential Question(s) What types of real life situations can be represented with linear equations? Prerequisite/Extension SOL 6.20 7.15a The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Construct a table of ordered pairs by substituting values for x in a linear equation to find values for y. Plot in the coordinate ordered pairs (x, y) from a table. Connect the ordered pairs to form a straight line (a continuous function). Interpret the unit rate of the proportional relationship graphed as the slope of the graph, and compare two different proportional relationships represented in different ways.† Key Vocabulary Linear Equation DOE Lesson Plans Chapter 3 Lessons 4 & 5 Chapter 11 Lesson 5 Resources/Lessons 2 8.3 - Problem Solving The student will solve practical problems involving rational numbers, percents, ratios, and proportions; and determine the percent increase or decrease for a given situation. Essential Questions What is difference between percent increase and percent decrease? What is a percent? Prerequisite/Extension SOL 5.4 5.5b 5.6 6.1 6.2 6.6b 6.7 7.4 7.6 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to a proportion given the relationship of equality between two ratios. Solve practical problems by using computation procedures for whole numbers, integers, fractions, percents, ratios, and proportions. Some problems may require the application of a formula. Maintain a checkbook and check registry for five or fewer transactions. Compute a discount or markup and the resulting sale for one discount or markup. Compute the percent increase or decrease for a one-step equation found in a real life situation. Compute the sales tax or tip and resulting total. Substitute values for variables in given formulas. For example, use the simple interest formula to determine the value of any missing variable when given specific information. Key Vocabulary Percent Discount Simple Interest Percent of Change Percent Increase Percent Decrease DOE Lesson Plans Chapter 2 Lessons 4 & 5 Chapter 4 Lessons 1 – 4, 6 & 7 Chapter 5 Resources/Lessons
Use the relationships among supplementary, complementary, vertical, and adjacent angles to solve practical problems.† 2 8.10 - Pythagorean Theorem The student will a) verify the Pythagorean Theorem; and b) apply the Pythagorean Theorem. Essential Question(s) How can the area of squares generated by the legs and the hypotenuse of a right triangle be used to verify the Pythagorean Theorem? Prerequisite/Extension SOL 5.13a,b 6.12 7.6 G.8 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Identify the parts of a right triangle (the hypotenuse and the legs). Verify a triangle is a right triangle given the measures of its three sides. Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement. Find the measure of a side of a right triangle, given the measures of the other two sides. Solve practical problems involving right triangles by using the Pythagorean Theorem. Key Vocabulary Right Triangle Pythagorean Theorem Hypotenuse Leg DOE Lesson Plans Chapter 3 Lessons 2 & 3 Resources/Lessons 2 8.11 - Composite Plane Figures The student will solve practical area and perimeter problems involving composite plane figures. Essential Question(s) How does knowing the areas of polygons assist in calculating the areas of composite figures? Prerequisite/Extension SOL 5.9 6.10a,b,c,d The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Subdivide a figure into triangles, rectangles, squares, trapezoids and semicircles. Estimate the area of subdivisions and combine to determine the area of the composite figure. Use the attributes of the subdivisions to determine the perimeter and circumference of a figure. Apply perimeter, circumference and area formulas to solve practical problems. Key Vocabulary Polygon Perimeter Area DOE Lesson Plans Chapter 2 Lesson 6 Chapter 7 Lessons 6 & 7 Activity Lab – Chapter 4 Lesson 4b (page 185) Resources/Lessons 2 8.7 – Volume & Surface Area The student will a) investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Key Vocabulary Volume Surface Area Prism Cylinder Cone