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1 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 7 (Pre-Algebra) 8 th Grade Mathematics 1 st Quarter Units (s) 7.3a, b, c 8.2 a, b, c, d 7.1i 8.5 a, b, c, d 7.1 a, b, c, d 8.1b 8.1a 8.4 a, b 7.16 a, b 8.15 d 7.14 a, b 7.15 a, b, c 8.15 a, b 1 7, , , 1 3, Textboo k Correlat ion Additional Resources VDOE Lesson Plans Vocabulary Number line Two-color counter Algebra tiles MU 8, 11, 12, 13, 14 MU (older version) 12, 13 Integers: Addition and Subtraction Integers: Mult. and Division MU 9 GS 3 Graphic organizers Venn diagrams Real number sorts Organizing Numbers Real numbers Natural numbers Counting numbers Whole numbers Integers Rational numbers Irrational numbers Subsets Attributes Grid paper Clothes line Activity Number line Perfect Squares and Square Roots Perfect square Square root Scientific notation Comparing Ordering Equivalency 1 MU 2, 3 GS 17 Orders of Operations Evaluating Algebraic Operations Expression Rational numbers Numerical expression Order of operations Power of a number Exponent Algebraic expressions Variable Foldables Flash cards Note cards MU (older version) 4, 5, 6 Basketball point guard Identity; no change Solving Equations Properties of Operations Properties Properties Commutative Associative Identity elements Additive identity Multiplicative identity Distributive Additive inverse Multiplicative inverse Identity Inverse Algebra blocks Graph paper Grid paper MU 43, 44, 45, 46, 47 MU (older version) 37, 38, 39, 40 Equations Inequalities Equation One-step Two-step Multi-step (3 and 4 step) Inequality Numerical value

2 No Calculator Model addition, subtraction, multiplication, and division of integers using pictorial representations of concrete manipulatives. 4 This will be the only skill for Pre-Algebra without a calculator. Review Add integers. Subtract integers. Multiply integers. Divide integers. Solve practical problems involving addition, subtraction, multiplication, and division with integers. 8.2a Describe orally and in writing the relationships among the sets of natural or counting numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. 8.2b Illustrate the relationships among the subsets of the real number system by using graphic organizers such as Venn diagrams. Subsets include rational numbers, irrational numbers, integers, whole numbers, and natural or counting numbers c 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 non-examples. 8.2f Recognize that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. 8.5c Define a perfect square and review exponents. 8.5a Identify the perfect squares from 0 to i Determine the square root of a perfect square less than or equal to 400. Estimate and determine the two consecutive integers between Identify the consecutive whole numbers between which the square root of a 3 which a square root lies (expanded beyond whole numbers). 8.5b given number from 0 to 400 lies (e.g lies between 7 and 8 since 7 = 8.5d 2 49 and 8 = 64). Find the positive or positive and negative square roots of a given whole number from 0 to 400. (Use the symbol when asking for the negative root.) to ask for the positive root and 2

3 Compare and order no more than 5 real numbers expressed as integers, fractions, mixed numbers, decimals, percents, numbers written in scientific notation, radicals (includes positive and negative square roots), and pi. Use rational approximations of irrational numbers to compare and order real numbers. 7.1a Recognize powers of 10 with negative exponents by examining patterns. 7.1b Write a power of 10 with negative exponents in fraction and decimal form. 7.1c Write a number greater than 0 in scientific notation. 7.1d Recognize a number greater than 0 in scientific notation. Compare and determine equivalent relationships between numbers larger 7.1e than 0 written in scientific notation. Recognize, represent, compare, and order rational numbers expressed in 8.1b scientific notation, using both positive and negative exponents. 8.1a Simplify algebraic expressions in one variable; represent algebraic expressions using concrete materials. 8.4a Evaluate algebraic expressions limited to whole number exponents and integer bases; limit number of replacements to 3; represent expressions using concrete/pictorial representations. Emphasis is placed on the application of properties of real numbers and properties of equality/inequality. This is just a review to recall prior knowledge. 8.4b 8.15d Review Simplify numerical expressions containing: 1) exponents (where the base is a rational number and the exponent is a positive whole number; 2) fractions, decimals, integers, and square roots of perfect squares; 3) grouping symbols (no more than 2 embedded grouping symbols). Order of operations and properties of operations with real numbers should be used. Substitute numbers for variables in algebraic expressions and simplify the expressions by using the orders of operations. Exponents are positive and limited to whole numbers less than 4. Square roots are limited to perfect squares. Apply the orders 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. 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; - the distributive property; - the identity properties of addition and multiplication - the zero property of multiplication - the additive inverse property; and - the multiplicative inverse property Like terms: recognize and combine. 3

4 10 4 Apply properties of real numbers and properties of equality/inequality. Solve multi-step equations, up to four steps; coefficients and numeric terms will be rational; equations may contain expressions that need expansion using the distributive property or require combining like terms. Solve multi-step linear inequalities in one variable on one or both sides of the inequality symbol, including practical problems, and graph the solution on a number line. Represent and demonstrate steps for solving one- and two-step equations in Review one variable using concrete materials, pictorial representations, and algebraic sentences. 7.14b Solve one- and two-step linear equations in one variable. Solve two- to four-step linear equations in one variable using concrete 8.15a materials, pictorial representations, and paper and pencil illustrating the steps performed. Review 8.15b Represent and demonstrate steps in solving inequalities in one variable using concrete materials, pictorial representations, and algebraic sentences. Solve two-step inequalities by showing the steps and using algebraic sentences. 8.15c Graph solutions to inequalities on the number line. Review Identify a numerical value that satisfies the inequality. Q 1 (41 days) 4

5 Textbook Correlati on Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 7 (Pre-Algebra) 8 th Grade Mathematics 2 nd Quarter Units (s) 7.2 a, b, c, d 7.13 a, b, c, d 8.1b 7.4 b, c, d 8.3 a, b 7.4 e 8.3 c, d, e, f, g, h 8.10 a, b, c, d, e 7.7 a, b , , 5 2, , 5 7 Additional Resources VDOE Lesson Plans Vocabulary MU 9 MU (older version) 34 Items to stack Arithmetic and Geometric Sequences Sequence Numerical pattern Arithmetic sequence Common difference Succeeding number Term Geometric sequence Common ratio Variable expression Consecutive terms Flash cards Foldables Note cards MU (older version) 4, 5, 6 Basketball point guard Idenitiy; no change, Translate and Evaluate MU 4, 5, 6, 7, 8 GS 5 Ordering Numbers Scientific notation Ascending order Descending order 5 4, 5 5, 5 7 Recipes Scale drawings Maps Advertisements Percent MU 12, 15 MU (older version) 9, 14,GS 6, 13, Proportions Do You Like to Spend Money? The Scoop on Ice Cream Proportion Product of means Product of extemes Increase Decrease Rate Ratio Scale drawings Scale factors 5 6 7, 6 8, MU 14, 15, 16 GS 12 Checkbook Check registry Percent of Increase and Decrease Pay check, Discount price, Temperature, Simple interest, Sales tax, Installment buying, Percent, Denominator, Discount, Original price, Principle, Rate, Rate of interest, Loan, Investment, Total value, Total cost, Percent increase, Percent decrease, Percent of change, Rate of growth, Markup, Rate decline, Ratio, Deposit, Debit, Withdrawal MU 37, 38 GS 31 Diagrams Concrete materials Pythagorean Theorem Right triangle Square Hypotenuse Legs Altitude Base Pythagorean Theorem Pythagorean triples Diagonal Chart, Model Graphic organizers Venn diagram MU 23 MU (older version) 19, 20 Matchbox 4 wheeler Quadrilateral Sort Quadrilateral Closed plane Parallelogram Rectangle Square Rhombus Trapezoid Attributes

6 Write verbal expressions and sentences as algebraic expressions and equations; write algebraic expressions and equations as verbal expressions and sentences. Limit computing simple interest given the principal, interest rate, and time (years). 8.3g 7.2a Analyze arithmetic sequences to discover a variety of patterns. 7.2b Identify the common difference in an arithmetic sequence. 7.2a Analyze geometric sequences to discover a variety of patterns. 7.2c Identify the common ratio in a geometric sequence. Given an arithmetic or geometric sequence, write a variable expression to 7.2d describe the relationship between two consecutive terms in the sequence. Write verbal expressions as algebraic expressions. Expressions will be limited 7.13a to no more than 2 operations. Write verbal sentences as algebraic equations. Equations will contain no 7.13b more than 1 variable term. Translate algebraic expression and equations to verbal expressions and 7.13c sentences. Expressions will be limited to no more than 2 operations. 7.13d Identify examples of expressions and equations. Review Solve a proportion to find a missing term. 8.3a Write a proportion given the relationship of equality between two ratios. Solve practical problems by using computational procedures for whole 8.3b numbers, integers, fractions, percents, ratios, and proportions. Some problems may require the application of a formula. Apply proportions to convert units of measurement between the U.S. 7.4c Customary System and the metric system. Calculators may be used. Determine if quadrilaterals or triangles are similar: by examining congruence 7.6c of corresponding angles and proportionality of corresponding sides. Given two similar figures, write similarity statements using symbols such as 7.6d ABC DEF, A corresponds to D, and AB corresponds to DE. Apply proportions to solve practical problems, including scale drawings. Scale 7.4d factors shall have denominators no greater than 12 and decimals no less than tenths. Calculators may be used. Review Percent to decimal, decimal to percent Using 10% as a benchmark, mentally compute 5%, 10%, 15%, or 20% in a 7.4e practical situation such as tips, tax, and discounts. 8.3c Maintain a checkbook and check registry for five or fewer transactions. Compute a discount or markup and the resulting sale price for one discount 8.3d or markup. 8.3f Compute the sales tax or tip and resulting total. Substitute values for variables in given formulas. For example, using the simple interest formula I = pr to determine the value of any missing variable when given specific information. 6

7 10 (con t) 4 Use the relationship between pairs of angles that are vertical, adjacent, supplementary, and complementary to determine the measure of an unknown angle. 8.3h 8.3e 8.6a 8.6b 8.6c 8.6d 8.6e 8.6f 8.6g Compute the simple interest and new balance earned in an investment or 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. Measure angles of less than 360 to the nearest degree, using appropriate tools. Identify and describe the relationships between angles formed by two intersecting lines. Identify and describe the relationship between pairs of angles that are vertical. Identify and describe the relationship between pairs of angles that are supplementary. Identify and describe the relationship between pairs of angles that are complementary. Identify and describe the relationship between pairs of angles that are adjacent. Use the relationships among supplementary, complementary, vertical, and adjacent angles to solve practical problems. Review Parts of triangle 8.10a Identify the parts of a right triangle (the hypotenuse and the legs). 8.10b Verify a triangle is a right triangle given the measures of its three sides c Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement. 8.10d Find the measure of a side of a right triangle, given the measures of the other two sides. 8.10e Solve practical problems involving right triangles by using the Pythagorean Theorem a Compare and contrast attributes of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid. 7.7b Identify the classification(s) to which a quadrilateral belongs, using deductive reasoning and inference. Q 2 (42 days) 7

8 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 7 (Pre-Algebra) 8 th Grade Mathematics 3 rd Quarter Units (s) 8.9 a, b 8.11 a, b, c 8.7 a, b, c, d, e, f, g 8.6 a, b, c, d, e, f 8.14 a, b, c 8.16 a, b, c 8.17 a, b, c, d, e, f 8.8 a, b, c, d, e, f Supplement 9 3 to , , 12 3, 12 4, Supplement Supplement 3 1, 3 2, 3 4 Textboo k Correlat ion Additional Resources VDOE Lesson Plans MU 39 Concrete objects Nets, Diagrams Formula sheet Area and Perimeter 3-D Figures MU GS Concrete objects Nets, Diagrams Formula sheet Volume and Surface Area MU GS Volume and Surface Area MU 46, 50 GS 18, 19, 21 Real-life situations Tables, Graphs, Physical models Coordinate plane Words, Rules Matching Representations Graphing Linear Equations MU 51 GS 18 Sort identifying dependent and independent variables Independent and Dependent Variables MU 32, 33, 34, 35 GS 29, 30 Clocks Coordinate grid Tiling, Fabric, Wallpaper Art, Scale drawings Transformations Vocabulary Polygon, Plane figure Line segments Perimeter, Distance, Area, Length, Composite figure Composite parts Triangles, Rectangles Adjacent sides Base, Height Parallelogram, Trapezoid, Average Circle, Pi, Radius, Circumference Estimate, Subdividing Semicircles Prism Solid figure Congruent Parallel bases Parallel faces Parallelograms Surface area Attribute, Volume Area of base, Height Nets, Polyhedron Pyramid Total surface area Triangular faces Circular cone Right circular cone Prism Solid figure Congruent Parallel bases Parallel faces Parallelograms Surface area Attribute, Volume Area of base, Height Nets, Polyhedron Pyramid Total surface area Triangular faces Circular cone Right circular cone Linear equation Continuous function Constant rate Ordered pairs, Variable Plotting, Coordinate plane Straight line Axes Relations, Function Graph Vertical line Discrete Distinct points Domain Input values Independent variable Range Output values Dependent variable Rotation, Reflection Translation, Dilation Geometric figure Clockwise Counter-clockwise Fixed point Center of rotation Axis, Distance Corresponding point Original figure Scale factor Similar figure Image of polygon Pre-image Horizontal, Vertical 8

9 3 8 8 Review Area and perimeter of polygons. Construct three-dimensional models, given the top or bottom, side, and front 8.9a views. 8.9b Identify three-dimensional models given a two-dimensional perspective. Subdivide a figure into triangles, rectangles, squares, trapezoids, and 8.11a semi-circles. Estimate the area of subdivisions and combine to determine the area of the composite figures. Use the attributes of the subdivisions to determine the perimeter and 8.11b circumference of a figure. Apply perimeter, circumference, and area formulas to solve practical 8.11c problems. Investigate and compute the surface area of a rectangular prism using 8.7e concrete objects, nets, diagrams, and formulas. Investigate and compute the surface area of a right cylinder using concrete 8.7d objects, nets, diagrams, and formulas. Investigate and compute the surface area of a cone by calculating the sum 8.7c 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 8.7b 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, 8.7f diagrams, and formulas. Investigate and compute the volume of cylinders using concrete objects, 8.7f nets, diagrams, and formulas. Investigate and compute the volume of cones using concrete objects, nets, 8.7f diagrams, and formulas. Investigate and compute the volume of pyramids using concrete objects, 8.7f nets, diagrams, and formulas. Distinguish between situations that are applications of surface area and 8.7a those that are applications of volume. Solve practical problems involving volume and surface area of prisms, 8.7g cylinders, cones, and pyramids. 9

10 8 (con t) Describe volume of a rectangular prism when one attribute Compare and contrast the volume and surface area of a prism with a given is multiplied by a factor of ¼, 1/3, ½, 2, 3, or 4; 8.7h set of attributes with a volume of a prism where one of the attributes has been increased by a factor of 2, 3, 5, and 10. describe its surface area when one attribute is multiplied by Describe the two-dimensional figures that result from slicing threedimensional factor of ½ or i figures parallel to the base (e.g. as in plane sections of right rectangular prisms and right rectangular pyramids). 8.14a Graph in a coordinate plane ordered pairs that represent a relation. Determine whether a given relation is a function using Describe and represent relations and functions using tables, graphs, words, discrete points (ordered pairs, tables, and graphs); sets of 8.14b and rules. Given one representation, students will be able to represent the data are limited to no more than 10 ordered pairs. relation in another form. 8.14c Relate and compare different representations for the same relation. Construct a table of ordered pairs by substituting values for x in a linear 8.16a equation to find values for y. 8.16b Plot in the coordinate plane ordered pairs (x,y) from a table. 8.16c Connect the ordered pairs to form a straight line (a continuous function). Slope of a line (positive/negative/zero); identify slope and y- intercept of a linear function; graph a linear function, make connections between representations. 8.16d 8.17a 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. Apply the following algebraic terms appropriately: domain, range, independent variable, and dependent variable. Identify examples of domain, range, independent variable, and dependent variable. 8.17b Incorporate the algebraic vocabulary into the function unit! 8.17c Determine the domain of a function. 8.17d Determine the range of the function. 8.17e Determine the independent variable of a relationship. 8.17f Determine the dependent variable of a relationship. Both translate and then reflect a polygon over the x-or-y axis or reflect a polygon over the x-or-y axis and then translate; Translate a polygon both horizontally and vertically. Restrict dilations to right triangles or rectangles to a scale factor of ¼, ½, 2, 3, or 4 using the origin as center of dilation. Demonstrate 90, 180, 270, and 360 clockwise and counter-clockwise 8.8b rotations of a figure on a coordinate grid. The center of rotation will be limited to the origin. Demonstrate the reflection of a polygon over the vertical or horizontal axis 8.8a on a coordinate grid. 8.8c Demonstrate the translation of a polygon on a coordinate grid. Demonstrate the dilation of a polygon from a fixed point on a coordinate 8.8d grid. Identify practical applications of transformations including, but not limited to, 8.8e tiling, fabric, and wallpaper designs, art and scale drawings. 8.8f Identify the type of transformation in a given example. 10 Q 3 (41 days)

11 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 7 (Pre-Algebra) 8 th Grade Mathematics 4 th Quarter Units (s) 7.9 a, b, c, d 7.10 b 8.12 a, b, c 7.11 a, b, c, d 8.13 a, b Boxplots (New) Textbook Correlation Benchmark Review Review Algebra 1 Concepts Additional Resources VDOE Lesson Plans MU 42 GS 41 Probability kit Number cubes Playing cards MU 29, 30, 31, 32 MU (older version) 24, 25, 26 Colored items Probability What are the Chances? MU 43, 44 GS 40 Graph Line plot Circle graph Stem-and-leaf plot MU 33, 34 MU (older version) 27, 28, 29, 30, 31 Data collection Graphs Scatterplots Numbers in a Name Vocabulary Probability Dependent events Independent events Event Theoretical probability Experimental probability Outcomes Trials Experiments Law of large numbers Comparison Prediction Inference Trends Scatterplot Attributes Line of best fit Horizontal Vertical line 11

12 a Determine the theoretical probability of an event. 7.9b Determine the experimental probability of an event. Describe changes in the experimental probability as the number of trials 7.9c increases. Investigate and describe the difference between the probability of an event 7.9d found through experimental or simulation verses the theoretical probability of that same event. Determine the probability of a compound event containing no more than b events. 8.12a Determine the probability of no more than three independent events. Compare and contrast probability of two Determine the probability of no more than two dependent events without independent/dependent events. 8.12b replacement. 8.12c Compare the outcomes of events with and without replacement. Collect, analyze, display, and interpret a data set using histograms. For collection and display of raw data, limit the data to 20 items Determine patterns and relationships within data sets (e. g. trends). Make inferences, conjectures, and predictions based on analysis of a set of data. Make observations about data displayed limited to Compare and contrast histograms with line plots, circle graphs, and stemand-leaf scatterplots only. plots presenting information from the same data set. Represent data in boxplots, make inferences and compare Collect, organize, and interpret a data set of no more than 20 items using data. 8.13a scatterplots. Predict from the trend an estimate of the line of best fit with a drawing. Interpret a set of data points in a scatterplot as having a positive 8.13b relationship, a negative relationship, or no relationship. 1 Benchmark review. Review 20 Review with Student Portfolio 4 After Rest Algebra 1 concepts: after s and retakes. Q 4 (43 days) 12

Kate Collins Middle School Pre-Algebra Grade 6

Kate Collins Middle School Pre-Algebra Grade 6 1 1 - Real Number System How are the real numbers related? *some numbers can appear in more than one subset *the attributes of one subset can be contained