WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Foundations of Algebra

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1 WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Foundations of Algebra FIRST QUARTER Units (s) Integers 7.3 Polynomials Operations A.2 Perfect Squares Square Roots 7.1i 8. A.3 Real Number System 8.2 Properties A.4 Expressions Order of Operations A.1 Comparing Ordering Rational Numbers Scientific Notation 8.1 Equations A.4 Inequalities 8.1 A. Benchmark Textbook Correlation Additional Resources Tiles Measuring Up 4.8 Clothes Line Activity Find supplement Measuring Up Measuring Up Foldables 1.2 Measuring Up Measuring Up , 2.8 Measuring Up 1

2 8 s s 7.3d Solve practical problems involving addition, subtraction, multiplication, and division with integers. A.2b Model sums and differences of polynomials with concrete objects and their related pictorial representations. A.2d Find sums and differences of polynomials. A.2b Model products and quotients of polynomials with concrete objects and their related pictorial representations. Find products of polynomials. The factors will have no more A.2e than five total terms (i.e. (4x+2)(3x+) represents four terms and (x+1)(2x 2 +x+3) represents five terms). A.2f Find the quotient of polynomials, using a monomial divisor, or a completely factored divisor. 8.c Define a perfect square. 8.a Identify the perfect squares from 0 to i Determine the square root of a perfect square less than or equal to 400. Identify the two consecutive whole numbers between which the 8.b square root of a given whole number from 0 to 400 lies (e.g., 7 lies between 7 and 8 since 7 2 = 49 and 8 2 = 64). Find the positive or positive and negative square roots of a given 8.d whole number from 0 to 400. (Use the symbol to ask for the positive root and when asking for the negative root.) A.3a Express square roots of a whole number in simplest form. Describe orally and in writing the relationships among the sets of 8.2a natural or counting numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. Illustrate the relationships among the subsets of the real number 8.2b system by using graphic organizers such as Venn diagrams. Subsets include rational numbers, irrational numbers, integers, whole numbers, and natural or counting numbers. 8.2c Identify the subsets of the real number system to which a given number belongs. 8.2d Determine whether a given number is a member of a particular subset of the real number system, and explain why. 8.2e Describe each subset of the set of real numbers and include examples and nonexamples. 2

3 s s Identify properties of operations used in simplifying expressions. 7.16a (Commutative, Associative, Distributive, Additive and Multiplicative Identities, Additive and Multiplicative Inverse, and Multiplicative Property of Zero) Identify properties of operations used to solve an equation from among: - the commutative properties of addition and multiplication; - the associative properties of addition and multiplication; 8.1d - the distributive property; - the identity properties of addition and multiplication; - the zero property of multiplication; - the additive inverse property; and - the multiplicative inverse property. 7.16b Apply the properties of operations to simplify expressions. A.4b Simplify expressions using the field properties of the real numbers and properties of equality to justify simplification. Substitute numbers for variables in algebraic expressions and 8.4a 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. Simplify numerical expressions containing: 1) exponents (where the 8.1a base is a rational number and the exponent is a positive whole number); 2) fractions, decimals, integers and square roots of perfect squares; and 3) grouping symbols (no more than 2 embedded grouping symbols). Order of operations and properties of operations with real numbers should be used. A.1a Translate verbal quantitative situations into algebraic expressions and vice versa. A.1c Evaluate algebraic expressions for a given replacement set to include rational numbers. A.1d Evaluate expressions that contain absolute value and square roots b Recognize, represent, compare, and order rational numbers expressed in scientific notation, using both positive and negative exponents. 3

4 s s Apply the order of operations to evaluate formulas. Problems will be 8.4b limited to positive exponents. Square roots may be included in the expressions but limited to perfect squares. Solve two- to four-step linear equations in one variable using 8.1a concrete materials, pictorial representations, and paper and pencil illustrating the steps performed. A.4b Solve equations using the field properties of the real numbers and properties of equality to justify simplification and solution. A.4e Solve multistep linear equations in one variable. A.4a Solve a literal equation (formula) for a specified variable. 8.1b Solve two-step inequalities by showing the steps and using algebraic sentences. 7.1b Graph solutions to inequalities on the number line. 7.1c Identify a numerical value that satisfies the inequality. A.a Solve multistep linear inequalities in one variable. Justify steps used in solving inequalities, using axioms of A.b inequality and properties of order that are valid for the set of real numbers. A.c Solve real-world problems involving inequalities. 4

5 WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Foundations of Algebra SECOND QUARTER Units Relations Functions Coordinate Plane 8.14 Slope A.6 Relation Function Domain Range Transformations 8.8 Verbal Expressions Equations 7.13 Benchmark (s) 8.16 Independent A.1 Dependent Variable 8.17 A.6 A.7 Textbook Correlation Additional Resources , ,

6 8 4 s s 8.14a Graph in a coordinate plane ordered pairs that represent a relation. Describe and represent relations and functions, using tables, graphs, 8.14b words, and rules. Given one representation, students will be able to represent the relation in another form. 8.14c Relate and compare different representations for the same relation. 8.16a Construct a table of ordered pairs by substituting values for x in a linear equation to find values for y. 8.16b Plot in the coordinate plane ordered pairs (x, y) from a table. 8.16c Construct a table of ordered pairs by substituting values for x in a linear equation to find values for y. A.6e Find the slope of a line, given the graph of a line. A.6d Find the slope of a line, given the coordinates of two points on the line. A.6c Find the slope of the line, given the equation of a linear function. A.6f Recognize and describe a line with a slope that is positive, negative, zero, or undefined. A.7a Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function. Represent relations and functions using concrete, verbal, numeric, A.7d graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form. 8.17a Apply the following algebraic terms appropriately: domain, range, independent variable, and dependent variable. 8.17b Identify examples of domain, range, independent variable, and dependent variable. 8.17c Determine the domain of a function. 8.17d Determine the range of a function. A.7b Identify the domain and range of a function presented algebraically or graphically. A.7c For each x in the domain of f, find f(x). 8.17e Determine the independent variable of a relationship. 8.17f Determine the dependent variable of a relationship. A.6b Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept. 6

7 8 s s Demonstrate 90, 180, 270, and 360 clockwise and counterclockwise 8.8b rotations of a figure on a coordinate grid. The center of rotation will be limited to the origin. 8.8a Demonstrate the reflection of a polygon over the vertical or horizontal axis on a coordinate grid. 8.8c Demonstrate the translation of a polygon on a coordinate grid. 8.8d Demonstrate the dilation of a polygon from a fixed point on a coordinate grid. 8.8e Identify practical applications of transformations including, but not limited to, tiling, fabric, and wallpaper designs, art and scale drawings. 8.8f Identify the type of transformation in a given example. 8.3a Write a proportion given the relationship of equality between two ratios. Solve practical problems by using computation procedures for whole 8.3b numbers, integers, fractions, percents, ratios, and proportions. Some problems may require the application of a formula. 7.4b Solve a proportion to find a missing term. Apply proportions to convert units of measurement between the U.S. 7.4c Customary System and the metric system. Calculators may be used. Apply proportions to solve practical problems, including scale drawings. 7.4d Scale factors shall have denominators no greater than 12 and decimals no less than tenths. Calculators may be used. 7

8 WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Foundations of Algebra THIRD QUARTER Unit Consumer Perimeter Surface Area Pythagorean Angles Benchmark (s) 7.4 Circumference Volume Theorem Area D models Textbook Correlation Additional Resources

9 s s 7.4e Using % as a benchmark, mentally compute %, %, 1%, or 20% in a practical situation such as tips, tax and discounts. 8.3c Maintain a checkbook and check registry for five or fewer transactions. 8.3d Compute a discount or markup and the resulting sale price for one discount or markup. 8.3f Compute the sales tax or tip and resulting total. 8.3g 8.3h 8.3e Substitute values for variables in given formulas. For example, use the simple interest formula I = prt to determine the value of any missing variable when given specific information. Compute the simple interest and new balance earned in an investment or on a loan for a given number of years. Compute the percent increase or decrease for a one-step equation found in a real life situation. 8.11a 8.11b 8.11c 8.7e 8.7d 8.7c 8.7b 8.7f 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. Investigate and compute the surface area of a rectangular prism using concrete objects, nets, diagrams and formulas. Investigate and compute the surface area of a right cylinder using concrete objects, nets, diagrams and formulas. Investigate and compute the surface area of a cone by calculating the sum of the areas of the side and the base, using concrete objects, nets, diagrams and formulas. Investigate and compute the surface area of a square or triangular pyramid by finding the sum of the areas of the triangular faces and the base using concrete objects, nets, diagrams and formulas. Investigate and compute the volume of prisms using concrete objects, nets, diagrams, and formulas. 9

10 (con t) s s 8.7f Investigate and compute the volume of cylinders using concrete objects, nets, diagrams, and formulas. 8.7f Investigate and compute the volume of cones using concrete objects, nets, diagrams, and formulas. 8.7f Investigate and compute the volume of pyramids using concrete objects, nets, diagrams, and formulas. 8.7a Distinguish between situations that are applications of surface area and those that are applications of volume. 8.7g Solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids. 8.a Identify the parts of a right triangle (the hypotenuse and the legs). 8.b Verify a triangle is a right triangle given the measures of its three sides. 8.c Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement. 8.d Find the measure of a side of a right triangle, given the measures of the other two sides. 8.e Solve practical problems involving right triangles by using the Pythagorean Theorem. 8.6a Measure angles of less than 360 to the nearest degree, using appropriate tools. 8.6b Identify and describe the relationships between angles formed by two intersecting lines. 8.6c Identify and describe the relationship between pairs of angles that are vertical. 8.6d Identify and describe the relationship between pairs of angles that are supplementary. 8.6e Identify and describe the relationship between pairs of angles that are complementary. 8.6f Identify and describe the relationship between pairs of angles that are adjacent. 8.9a Construct three-dimensional models, given the top or bottom, side, and front views. 8.9b Identify three-dimensional models given a two-dimensional perspective.

11 WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Foundations of Algebra FOURTH QUARTER Unit Probability Scatterplots Benchmark Review for Concepts (s) Box-and-Whisker 8.12 A. Textbook Correlation Additional Resources 6.9. Days s s 7.9a Determine the theoretical probability of an event. 7.9b Determine the experimental probability of an event. 7.9c Describe changes in the experimental probability as the number of trials increases. Investigate and describe the difference between the probability of an 7.9d event found through experiment or simulation versus the theoretical probability of that same event. 7.b Determine the probability of a compound event containing no more than 2 events. 8.12a Determine the probability of no more than three independent events. 8.12b Determine the probability of no more than two dependent events without replacement. 8.12c Compare the outcomes of events with and without replacement. Collect, organize, and interpret a data set of no more than 20 items 8.13a using scatterplots. Predict from the trend an estimate of the line of best fit with a drawing. 8.13b Interpret a set of data points in a scatterplot as having a positive relationship, a negative relationship, or no relationship. A.a Compare, contrast, and analyze data, including data from real-world situations displayed in box-and-whisker plots. 11

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Virginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning

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