Pacing Guide. Seventh Grade Math. Shelburne Middle School Staunton City Schools Staunton, Virginia June 2010

Transcription

1 Pacing Guide Seventh Grade Math Shelburne Middle School Staunton City Schools Staunton, Virginia June 2010

2 Pacing Overview Dates (2001 SOLs) SOL (2009 SOLs) Topics Aug Aug. 20 Intro/Pretest/Problem Solving Strategies/Centers Problem Solving Strategies Aug. 23 Aug , Polygons and Quadrilaterals 7.10 removed to 4 th grade Aug. 30 Sept , a, b 7.1 ( Identify/Compare/Contrast) Integers to include Number Line, Absolute Value, Additive Inverse Property, Adding, Subtracting, Multiplying, Dividing, Word Problems. Sept. 20 Oct , Exponents, Square Roots, Order of Operations, Properties ( all properties except Distributive) Oct. 12 Oct a-b 7.1 %, decimal, fractions 10/18 to 10/22 Benchmark 1 (?) Oct. 25 Nov a-f 7.1 Scientific Notation to include negative exponents. Compare and order all. Nov. 8 Nov , , 7.6 Ratios, Unit Rate, Proportions, Scale, Similar Figures Nov. 18 Dec Sale Price, Tax, Tip and Simple Interest Dec. 13 Dec Coordinate Plane Jan. 3 Feb a 7.21 Removed by a, 7.15a Feb. 15 March 4 7.8, Moved to 6 th grade Arithmetic and Geometric Sequences, Tree Diagrams, Counting Principle. Functions. Expressions, Equations, Inequalities, Verbal to Algebraic, Distributive Property 1/18 to 1/22 Benchmark 2 (?) Find area, perimeter and area by subdividing irregular polygons Volume and Surface Area (Formulas) How change in the attributes changes the overall volume. March 7 April Review Coordinate Plane, Transformations to include Reflections, Translation, Rotations and Dilation 3/18 to 3/22 Benchmark 3 (?) April 4 April , 7.17, Graphs, Mean, Mode, Median, Range (7.16 moved to 5 th grade) April 25 May , Find missing score, Probability SOL Review May 9 May 20 New Content 7.4 Conversions Metric-Customary SOL Review May 23 June 3 New Content Two Step Equations 2 P a g e

3 Geometry (SMS) Aug. 23 Aug The student will compare and contrast the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid. Deductive reasoning and inference will be used to classify quadrilaterals The student will identify and draw the following polygons: pentagon, hexagon, heptagon, octagon, nonagon, and decagon. Geometry: Basic Ideas 7.9 Geometry: Plane Use variables in formulas 7.9 Geometry: Spatial 7.10 Geometry: Basic Ideas 7.10 A. Identify the classification(s) to which a quadrilateral belongs. B. Compare and contrast attributes of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid. C. Classify quadrilaterals, using deductive reasoning and inference. A. Identify by the number of sides or number of angles the following polygons: pentagon, hexagon, heptagon, octagon, nonagon, and decagon. B. Draw a pentagon, hexagon, heptagon, octagon, nonagon, and decagon, using a variety of tools. contrast compare identify draw determine write express Classify Identify Draw Use Venn Diagrams, charts and other graphic organizers to show how one quadrilateral may appear in several subsets of other quadrilaterals. Mastery*(See Notes) 2009 SOL 7.7 Isosceles trapezoid to be included. 3 P a g e

4 Computation and Estimation Aug. 30 Sept. 17 Integers (SMS) 7.5 The student will formulate rules for and solve practical problems involving basic operations (addition, subtraction, multiplication, and division) with integers. Rational Numbers Operations/ Estimation 7.5 A. Formulate rules for adding integers. B. Formulate rules for subtracting integers. C. Formulate rules for multiplying integers. D. Formulate rules for dividing integers. E. Solve practical problems involving addition, subtraction, multiplication, and division with integers. Formulate Solve Mastery*(See Notes) 2009 SOL To include Absolute Value, Number Line Incorporated into 7.3 and P a g e

5 Number and Number Sense Aug. 30 Sept. 17 Patterns, Fractions & Percents (SMS) 7.3 The student will identify and apply the following properties of operations with real numbers: a) the commutative and associative properties for addition and multiplication; b) the distributive property; c) the additive and multiplicative identity properties; d) the additive and multiplicative inverse properties; and e) the multiplicative property of zero. Number Sense/Number Theory 7.3 Algebra Representation & Relationship 7.3 Include Whole Numbers, Fractions, and Decimals. A. Identify the real number equation that represents each property of operations with real numbers, when given several real number equations. B. Explore the properties of real numbers, using diagrams and manipulatives. C. Test the validity of properties by using examples of the properties of operations on real numbers. D. Identify the property of operations with real numbers that is illustrated by a real number equation. (identify ) apply (Identify ) Explore Test A. Design a flip book that describes the properties with a picture and an example. Organize a skit Groups will be assigned a property. They will have about minutes to brainstorm and then will present their skit to the class Take Non-Linguistic Notes D. Play the Properties Jeopardy game using properties. The student will identify the property on a given card and be given a certain amount of points. Mastery*(See Notes) Rubric 2009 SOL Additive Inverse Property done with Integers 5 P a g e

6 Number and Number Sense Sept. 20 Oct. 8 Decimal Concepts (SMS) 7.2 The student will simplify expressions that contain rational numbers (whole numbers, fractions, and decimals) and positive exponents, using order of operations, mental mathematics, and appropriate tools. 7.2 Number and Number Sense Students should be able to: A. Simplify expressions by using the order of operations in a demonstrated step-by-step approach. B. Find the value of numerical expressions, using order of operations, mental mathematics, and appropriate tools. Exponents are limited to positive values. Fractions are limited to having denominators of 12 or less. Decimals are limited to the thousandth place. Simplify A. Imitate hand motions to remember the correct order of operations. Create an order of operations pyramid from a pyramid template. Demonstrate their knowledge of PEMDAS by designing a poster. Exponents and Square Roots Mastery*(See Notes) Students recall the hand motions when needed. Pyramid contains the order of operations in the correct order along with a student generated example SOL Exponents and Square Roots 6 P a g e

7 Number and Number Sense Sept. 20 Oct. 8 Patterns, Fractions & Percents (SMS) 7.3 The student will identify and apply the following properties of operations with real numbers: a) the commutative and associative properties for addition and multiplication; b) ***the distributive property; done with Equations and Inequalities*** c) the additive and multiplicative identity properties; d) the additive and multiplicative inverse properties; and e) the multiplicative property of zero. Number Sense/Number Theory 7.3 Algebra Representation & Relationship 7.3 Include Whole Numbers, Fractions, and Decimals. A. Identify the real number equation that represents each property of operations with real numbers, when given several real number equations. B. Explore the properties of real numbers, using diagrams and manipulatives. C. Test the validity of properties by using examples of the properties of operations on real numbers. D. Identify the property of operations with real numbers that is illustrated by a real number equation. (identify ) apply (Identify ) Explore Test B. Design a flip book that describes the properties with a picture and an example. Organize a skit Groups will be assigned a property. They will have about minutes to brainstorm and then will present their skit to the class Take Non-Linguistic Notes D. Play the Properties Jeopardy game using properties. The student will identify the property on a given card and be given a certain amount of points. Mastery*(See Notes) Rubric 2009 SOL Include all properties except Distributive Property. To be added in later in the year. 7.3 SOL also removed identify and added apply 7 P a g e

8 Problem Solving (SMS) Oct. 12 Oct The student will compare, order, and determine equivalent relationships between fractions, decimals, and percents, including use of scientific notation for numbers greater than 10. Rational Numbers: Relationshi ps 7.1 Number Sense/Num ber Theory 7.1 A. Represent a number in fraction, decimal, and percent forms. Fractions will have denominators of 12 or less. B. Compare, order, and determine equivalent relationships among fractions, decimals, and percents. Decimals are limited to the thousandth place, and percents are limited to the tenth place. C. Write a number greater than 10 in scientific notation. D. Compare, order, and determine equivalent relationships between numbers larger than 10 written in scientific notation. E. Compare very large numbers, using scientific notation. F. Order no more than five numbers written as fractions, decimals, percents, and numbers larger than 10 written in scientific notation in ascending (least to greatest) or descending (greatest to least) order. Represent Compare Order Determine Write A. Create a Wanted Poster of a fraction and represent other forms (percents and decimals) as other identities the fraction can have. B. Graph a Human Number Line students will be fractions, decimals, or percents. They will have to place themselves in order on the number line. C, D, E. ( Third Rock from the Sun ) Compare the distances in miles of the planets from the sun. Students compare, order, and write in scientific notation the distances of each of the planets. F. (Flash Cards) Divide the class into groups of four. Give the students flash cards of fractions, decimals, percents, and scientific notation. Have the students analyze the numbers and put the cards in order. (It might be best to have a set of flash cards for each of the levels fractions, decimals, percents, scientific notation.) Mastery* (See Notes) Correct percent and decimal represented for each fraction on the wanted poster. Final product, discussions and communication with other students. Completed activity sheet that contains the correct scientific notation and order for each of the planets distances SOL a and b only 8 P a g e

9 Problem Solving (SMS) Oct. 25 Nov The student will compare, order, and determine equivalent relationships between fractions, decimals, and percents, including use of scientific notation for numbers greater than 10. Rational Numbers: Relationshi ps 7.1 Number Sense/Num ber Theory 7.1 A. Represent a number in fraction, decimal, and percent forms. Fractions will have denominators of 12 or less. B. Compare, order, and determine equivalent relationships among fractions, decimals, and percents. Decimals are limited to the thousandth place, and percents are limited to the tenth place. C. Write a number greater than 10 in scientific notation. D. Compare, order, and determine equivalent relationships between numbers larger than 10 written in scientific notation. E. Compare very large numbers, using scientific notation. F. Order no more than five numbers written as fractions, decimals, percents, and numbers larger than 10 written in scientific notation in ascending (least to greatest) or descending (greatest to least) order. Represent Compare Order Determine Write Compare Order C. Create a Wanted Poster of a fraction and represent other forms (percents and decimals) as other identities the fraction can have. D. Graph a Human Number Line students will be fractions, decimals, or percents. They will have to place themselves in order on the number line. C, D, E. ( Third Rock from the Sun ) Compare the distances in miles of the planets from the sun. Students compare, order, and write in scientific notation the distances of each of the planets. F. (Flash Cards) Divide the class into groups of four. Give the students flash cards of fractions, decimals, percents, and scientific notation. Have the students analyze the numbers and put the cards in order. (It might be best to have a set of flash cards for each of the levels fractions, decimals, percents, scientific notation.) Mastery* (See Notes) Correct percent and decimal represented for each fraction on the wanted poster. Final product, discussions and communication with other students. Completed activity sheet that contains the correct scientific notation and order for each of the planets distances SOL To include scientific notation with negative exponents. 9 P a g e

10 Computation and Estimation Nov. 8 Nov. 17 Proportions, Rates (SMS) 7.6 The student will use proportions to solve practical problems, which may include scale drawings, that contain rational numbers (whole numbers, fractions, and decimals) and percents. Proportional Reasoning 7.6 A. Write proportions that represent equivalent relationships between two sets. B. Solve a proportion to find a missing term. C. Apply proportions to solve problems that involve percents. D. Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and/or decimals no less than tenths. use Write Solve Apply Mastery*(See Notes) 7.11 The student will determine if geometric figures quadrilaterals and triangles are similar and write proportions to express the relationships between corresponding parts of similar figures. Proportion A. Identify corresponding sides and Identify al corresponding angles of similar figures. Write Reasoning Examine 7.11 B. Write proportions to express the express relationships between the lengths of corresponding sides of similar figures. C. Examine congruence of corresponding angles and proportionality of corresponding sides to determine if quadrilaterals or triangles are similar. 10 P a g e

11 Problem Solving (SMS) Nov. 18 Dec The student will a) solve practical problems using rational numbers (whole numbers, fractions, decimals) and percents; and b) solve consumer-application problems involving tips, discounts, sales tax, and simple interest. Rational Numbers: Operations/ Estimation 7.4 Students should be able to: A. Determine solutions to everyday problems involving whole numbers, decimals, fractions, and percents. Fractions are limited to having denominators no greater than 12. B. Compute the tip and total bill for a meal. C. Compute a discount and the resulting (sale) price for one discount. D. Compute the sales tax for purchased items. E. Compute the simple interest earned on an investment or a loan for a specified number of years and/or months. Determine Solve Compute Real life applications A. Create Recipe/Money problems in the form of a word problem. B. ( Go Out to Eat ) Be given menus from local restaurants and be asked to role play ordering meals, compute the cost of the meals, including tip and tax. C. Use sale papers to compute the amount of discounts and sale price of items listed. Students can also shop for the best price of an item from various stores. D. Have students calculate sales tax on exercise C. E. Research car magazines/real estate magazines to calculate total cost of a vehicle or house for a specified number of years. Mastery*(See Notes) Student Work Correct calculations for each bill Students will defend their choices 2009 SOL To include using 10% as a benchmark to calculate discounts without a calculator. 11 P a g e

12 Geometry (SMS) Dec. 13 Dec The student will identify and graph ordered pairs in the four quadrants of a coordinate plane. Geometry: Spatial Relations 7.12 A. Identify and label the axes of a coordinate plane. B. Identify and label the quadrants of a coordinate plane. C. Identify the quadrant in which an ordered pair is positioned by examining the ordered pair. D. Graph ordered pairs in the four quadrants of a coordinate plane. E. Identify ordered pairs represented by points in the four quadrants of the coordinate plane. Identify Graph Label Examine Mastery*(See Notes) 12 P a g e

13 Patterns, Functions, and Algebra Jan. 3 Feb The student will identify and describe the number of possible arrangements of several objects, using a tree diagram or the Fundamental (Basic) Counting Principle A. Describe the number of possible arrangements of no more than three types of objects, using a tree diagram. B. Compute the number of possible arrangements of no more than three types of objects by using the Fundamental (Basic) Counting Principle. Describe Compute Mastery*(See Notes) Solving Equations (SMS) 7.19 The student will represent, analyze, and generalize a variety of patterns, including arithmetic sequences and geometric sequences, with tables, graphs, rules, and words in order to investigate and describe functional relationships The student will write verbal expressions as algebraic expressions and sentences as equations The student will use the following algebraic terms appropriately: equation, inequality, and expression The student will a) solve one-step linear equations and inequalities in one variable with strategies involving inverse operations and integers, using concrete materials, pictorial representations, and paper and pencil; and b) solve practical problems requiring the solution of a one-step linear equation. 13 P a g e

14 Jan. 3 Feb. 11 Patterns and Functions Representatio n & Relationship 7.19 Students should be able to: A. Analyze situations to discover a variety of patterns. B. Analyze numeric and geometric sequences to discover a variety of patterns. C. Represent a variety of patterns, using tables, graphs, rules, and words, in order to investigate and describe functional relationships. D. Generalize a variety of patterns. represent analyze generalize solve Analyze Investigate describe Mastery*(See Notes) Algebra Representatio n & Relationship Include Whole Numbers, Fractions, and Decimals A. Write verbal sentences as algebraic expressions. Write verbal sentences as algebraic equations. Write 14 P a g e

15 Jan. 3 Feb. 11 Algebra Representatio n & Relationship Include Whole Numbers, Fractions, and Decimals Algebra Representatio n & Relationship Include Whole Numbers, Fractions, and Decimals A. Apply the following algebraic terms appropriately: equation, inequality, and expression. B. Identify examples of equations, inequalities, and expressions. A. Represent and demonstrate steps in solving equations in one variable, using concrete materials, pictorial representation, and algebraic sentences. B. Represent and demonstrate steps in solving inequalities in one variable, using concrete materials, pictorial representation, and algebraic sentences. C. Translate one-step word problems and practical problems into algebraic equations and solve them. Write Identify Represent demonstrate Translate 2009 SOL To include 2 step equations ( completed later in the year for the school year) ***Include Distributive Property from 7.3*** 15 P a g e

16 Volume, Surface (SMS) Feb. 15 Mar The student, given appropriate dimensions, will a) estimate and find the area of polygons by subdividing them into rectangles and right triangles; and b) apply perimeter and area formulas in practical situations. Measurement Actual/Estimat e 7.7 Geometry: Plane Use variables in formulas 7.7 A. Subdivide a polygon into rectangles and right triangles, estimate the area of the rectangles and/or right triangles to estimate the area of the polygon, and find the area of the rectangles and/or right triangles to determine the area of the polygon. B. Apply perimeter formulas to solve real-life problems. C. Apply area formulas to solve reallife problems. estimate find apply investiga te solve Subdivid e Apply Mastery*(See Notes) 16 P a g e

17 Volume, Surface (SMS) Feb. 15 Mar The student will investigate and solve problems involving the volume and surface area of rectangular prisms and cylinders, using concrete materials and practical situations to develop formulas. Measurement Actual/Estimate Include Whole Numbers, Fractions, and Decimals. 7.8 Geometry: Solid Use variables in formulas 7.8 A. Develop a procedure and formula for finding the surface area of a rectangular prism. B. Solve practical problems that require finding the surface area of a rectangular prism. C. Develop a procedure and formula for finding the surface area of a cylinder. D. Solve practical problems that require finding the surface area of a cylinder E. Develop a procedure and formula for finding the volume of a rectangular prism. F. Solve practical problems that require finding the volume of a rectangular prism. G. Develop a procedure and formula for finding the volume of a cylinder. H. Solve practical problems that require finding the volume of a cylinder Apply Develop Solve Investigate Describe Apply to Real life problems Mastery*(See Notes) 2009 SOL To include investigation into volume, describing volume, and the changes to volume as one measured attribute is changed. 17 P a g e

18 Measurement March 7 April The student, given a polygon in the coordinate plane, will represent transformations rotation and translation by graphing the coordinates of the vertices of the transformed polygon and sketching the resulting figure. Geometry: Spatial Relations SOL A. Identify the coordinates of the image of a polygon that has been translated either vertically or horizontally. B. Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90 or 180 about the origin. C. Sketch the image of a polygon translated vertically or horizontally. D. Sketch the image of a right triangle or rectangle that has been rotated 90 or 180 about the origin. To include all Transformations Reflection over x and y axis Translations including combination ( right, up) etc. Also include horizontally, vertically All Rotations Dilations Identify Sketch Represent Graph Mastery*(See Notes) 18 P a g e

19 Statistics (SMS) April 4 April The student will create and solve problems involving the measures of central tendency (mean, median, mode) and the range of a set of data The student, given a problem situation, will collect, analyze, display, and interpret data, using a variety of graphical methods, including a) frequency distributions; b) line plots; c) histograms; d) stem-and-leaf plots; e) box-and-whisker plots; and f) scattergrams The student will make inferences, conjectures, and predictions based on analysis of a set of data. Data Analysis Representation & Relationships Include Whole Numbers, Fractions, and Decimals A. Examine the range to understand spread or dispersion of the data. B. Describe the three measures of central tendency (mean, median, or mode) and situations in which each would best represent the data for data sets with no more than 20 data points. C. Solve problems by finding the mean of a set of no more than 20 numbers. D. Solve problems by finding the median of a set of data of no more than 20 numbers when the numbers are arranged from least to greatest, including data sets that have one middle number and data sets that have two middle numbers. E. Solve problems by finding the mode of a set of data of no more than 20 numbers. Examine Describe Solve Identify The learner will. Mastery* (See Notes) 19 P a g e

20 F. Identify the mode in a set of data, given that there may be one, more than one, or no mode. G. Solve problems by finding the range of a set of data of no more than 20 numbers. H. Solve problems with multiple identical data points for which the mode is the best descriptor. Two modes are sufficient for data sets with no more than 20 data points I. Solve problems in which some data points are outliers and thus, for which the median is the best descriptor. The data sets will contain no more than 20 data points. J. Solve problems in which the data points are similar and thus, for which the mean is the best descriptor. The data sets will contain no more than 20 data points SOL Some of 7.17 is being moved to other grade levels. Primary focus will be on Histograms and Frequency Distribution Tables 20 P a g e

21 Statistics (SMS) April 25 May The student will investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event The student will create and solve problems involving the measures of central tendency (mean, median, mode) and the range of a set of data. **** Find the missing Score**** Rational Numbers: Relationships 7.14 Probability 7.14 A. Determine the theoretical probability of an event. B. Describe changes in the experimental probability as the number of trials increases. C. Investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event. identify describe create solve collect analyze display interpret Determine Investigate Strategies to Engage the Learner Mastery*(See Notes) 21 P a g e

22 New Content May 9 May 20 Conversions Metric to Customary See New Standards 7.4 New Content May 23 June 3 Solving two step equations See New Standards P a g e