Curriculum & Grade 7: Pre-Algebra. Martinsville City Public Schools Revised Summer Updated Summer 2012 TJV

Transcription

1 Curriculum & Grade 4: Pacing Mathematics Guide Grade 7: Pre-Algebra Martinsville City Public Schools Revised Summer 2011 Updated Summer 2012 TJV

2 Martinsville City Public Schools Plan of Action The Martinsville City Public Schools Curriculum Guide was developed using the Standards of Learning for Virginia Public Schools and the State Curriculum work. Also, an emphasis was placed on the integration of 21 st Century Skills into all areas of K-12 education. Martinsville City Public Schools believes that to compete in a global community, all children must develop lifelong independent skills that demonstrate initiative, self direction, and the ability to problem-solve, innovate and create, and communicate by writing and speaking effectively. To provide an avenue for students to develop these important qualifications and provide a more rigorous learning environment, Martinsville City Public Schools encourages problem-based learning in all classrooms. The collaboration between students in this type of learning environment develops skills in leadership, accountability, social, and cross-cultural understanding as they communicate and think critically to problem-solve real world applications of the curriculum. Martinsville City Public Schools Core curriculum prepares students to achieve these 21 st Century skills through competent cross- curricular activities that apply knowledge of concepts learned in other areas of study and in the community. Standard benchmark along with project-based and end of year SOL tests are administered to ensure mastery of the concepts. PALS are used to ensure proficiency in Reading for grades Pre-K through Eight. To further ensure that all students learn to the best of their abilities, a Response to Intervention (RtI) system, using and STAR Reading, is in place to guide classroom instruction, screen and progress monitor students so that intervention and enrichment activities are scheduled based on the students individual needs throughout the year. Curriculum Guide OVERVIEW The Martinsville City Public Schools Curriculum Guide is designed to provide a reference document for each subject and grade level that indicates The Curriculum s Big Ideas, Strategies, Model lessons, & Instruments and suggested time frames to be used as a Guide for classroom instruction. In addition, Learning Targets at a Glance contains an overview of the curriculum taught for each grading for each st subject and grade level. 21 Century Internet Safety procedures are listed, and for Grades Three through Twelve, an SOL Testing Blueprint Target is included to give insight to the strands that will receive the most focus on the SOL s. Two symbols will be used to denote the 21st Century Focus: This symbol is used through to denote a 21 This symbol is used throughout to denote a 21 st Century Global Connection. st Century skill.

3 Learning Overview The Seventh Grade student will be provided many opportunities to engage in experiences involving problem solving, data collection and analysis, and algebraic thinking. The Virginia Standards of Learning provide the foundation for seventh grade mathematics. The standards are organized into 6 strands: Number/Number Sense: The focus of instruction allows students to investigate and develop an understanding of number sense by modeling numbers, using different representations. Students should develop strategies for reading, writing, and judging the size of numbers, fractions and decimals by comparing them, using a variety of models and benchmarks as ferments. Computation and Estimation: The focus of instruction allows students to develop fluency in multiplication and division with whole numbers and decimals, using models, explanation, and proficiency with basic facts and algorithms. Measurement: The focus of instruction allows students to be actively involved in measurement activities that focus on measuring objects and estimating measurements while interacting with their environment. Geometry: The focus of instruction allows students to develop and understanding about how geometric figures relate to each other and begin to use mathematical reasoning to analyze and justify properties and relationships among figures. Probability and Statistics: The focus of instructions allows students to deepen their understanding of concepts of probability by offering opportunities to set up models simulating practical events, engage students in activities to enhance understanding fairness, and activities that instill a spirit of investigation and exploration through use of manipulatives. Curriculum Big Ideas The organizing topics, big ideas, or strands under which student learning is organized and the Understandings, Knowledge and Skills students must develop in order to master these concepts (typically from the standards found in the VDOE curriculum framework). Understandings what we want students to understand about this idea, topic, or concept Knowledge What students must know in order to develop this understanding Skills What students must be able to do in order to demonstrate that understanding, strategies, and models for delivery of the curriculum. Includes suggested teaching strategies, links to model lesson plans links to frequently referenced online sites, and suggested teacher resources and where to find them (online and hard copy, such as texts, primary source documents, etc.) Examples of formative and summative for measuring student mastery of the curriculum. Includes essential questions, writing prompts, sample test items, benchmark test links, model performance-based, and other assessment resources. Standards of Learning that meet the criteria for 21 st Century skills will be identified by this symbol Standards of Learning that meet the 21st Century Learning of Global Connections will be designated with this symbol

4 Learning Targets at a Glance 7th Grade Pre-Algebra First Quarter 8/13-10/15 Second Quarter 10/16-12/21 Third Quarter 1/8-3/13 Fourth Quarter 3/14-5/ Integers 7.16a,b,d Properties of Operations -Real Numbers 7.1 a-d Rational Numbers 7.12 Tables, Graphs, Rules and words 7.13a Algebraic Expressions 7.2 Variable Expressions 7.13b Algebraic Expressions 7.14 Linear Equations 7.15 Inequalities 7.16 Properties of Operations 7.8 Transformations 7.7 Quadrilaterals 7.5a Volume/Surface Cylinders 7.5b Volume/Surface Rec. Prisms & Cylinders 7.4 Proportional Reasoning 7.6 Plane Figures 7.5c Rectangular Prism-change attributes 7.10 Fundamental Counting Principle 7.9 Probability(experimental/theoretical) 7.11 Histograms Number/Number Sense Computation/Estimation Grade 7 Mathematics Test Blueprint Summary Table 50 question test Measurement/Geometry Probability, Statistics, Patterns, Functions and Algebra

5 Suggested Allocation for a 60 Minute Math Block Bellringer Skill Lesson Practice/Small Group Instruction 20 minutes 10 minutes 30 minutes 0%

6 21 st Century Internet Safety Procedures 1. Teachers should review all internet sites and links prior to using them in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site. Checking for broken links and paying attention to inappropriate pop-ups or solicitations of information. 2. Teachers should circulate throughout the classroom while students are on the internet to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should ically check and update any web addresses that they have on their MCPS webpage. 4. Teachers should assure that the use of these websites correlate with the objectives of the lesson and provide students with the appropriate challenges.

7 1 st SOL 7.3 The student will a.) Model addition, subtraction, multiplication and division of integers b.) Add, subtract, multiply and divide integers. Model addition, subtraction, multiplication and division of integers using pictorial representations of concrete manipulatives. Add, subtract, multiply and divide integers. Simplify numerical expressions involving addition, subtraction, multiplication and division of integers using order of operations. Solve practical problems involving addition, subtraction, multiplication, and division with integers. Integers Numberline Two-color counters Algeblocks Calculators Math school Module 3 Algebra school Module 1.2 NLVM -Rectangle Multiplication of Intergers -Color chips 7.3 -Integers: Multiplication/Division -Integers: Addition/Subtraction 7.3 Integers SOL 7.3

8 1 st SOL 7.16 The student will 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 e.) the multiplicative property of zero Identity properties of operations used in simplifying expressions Apply the properties of operations to simplify expressions Zero Commutative Property Associative Property Multiplicative Identity Properties Multiplicative Inverse Property Property of Zero Distributive Property Math school Module 1.3, 1.4 Algebra school Module Properties 7.16 Order of Operations and Properties SOL 7.16

9 1 st SOL 7.1 The student will a.) Investigate and describe the concept of negative exponents for powers of ten b.) Determine scientific notation for numbers greater than zero c.) Compare and order fractions, decimals, percents and numbers written in scientific notation d.) Determine square roots e.) Identify and describe absolute value for rational numbers mathematical communication, mathematical reasoning, connections, and representation to Recognize powers of 10 with negative exponents by examining patterns Write a power of 10 with a negative exponent in fraction and decimal form Write a number greater than 0 in scientific notation Compare and determine equivalent relationships between numbers larger than 0 written in scientific notation Represent a number in a fraction, decimal, and percent forms. Compare, order, and determine equivalent relationships among fractions, decimals, and percents. Decimals are limited to the thousandths place, and percents are limited to the tenths place. Ordering is limited to no more than 4 numbers. Order no more than 3 numbers greater than 0 written in scientific notation Determine the square root of a perfect square less than or equal to 400. Exponential Notations Base Exponent Power Perfect Square Natural Numbers Fraction Bars Base-10 Blocks Fraction Circles Graph Paper Numberlines Calculators Math school Module 5.6, 3.1 Algebra school Module 1.4, Powers of Ten -Scientific Notation -Ordering Fractions -Square Roots -Absolute Value 7.1c Comparing and Ordering 7.1b Whole Numbers SOL 7.1

10 1st SOL 7.12 The student will represent relationships with tables, graphs, rules, and words Describe and represent relations and functions, using tables, graphs, rules, and words, Given on representation, students will be able to represent the relation in another form. Table Graph Rule 7.12 Relationships Round Table N/A 7.12 Patterns, Functions, Algebra SOL 7.12

11 2 nd SOL 7.13 The student will a.) Write verbal expressions as algebraic expressions and sentences as equations and vice versa b.) Evaluate algebraic expressions for given replacement values of the variables Write verbal expressions as algebraic expressions. Expressions will be limited to no more than 2 operations Write verbal sentences as algebraic equations. Equations will contain no more than 1 variable term. Translate algebraic expressions and equations to verbal expressions and sentences. Expressions will be limited to no more than 2 operations. Identify examples of expressions and equations. Apply the order of operations to evaluate expressions for given replacement values of the variables. Limit the number of replacements to no more than 3 per expression. Verbal Expression Algebraic Expression 7.13 Translate and Evaluate N/A 7.13 Patterns, Function, Algebra SOL 7.13

12 2 nd SOL 7.2 The student will describe and represent arithmetic and geometric sequences using variable expressions Analyze arithmetic and geometric sequences to discover a variety of patterns Identify the common differences in a n arithmetic sequence Identify the common ration in a geometric sequence Given an arithmetic or geometric sequence, write a variable expression to describe the relationship between two consecutive terms in the sequence Common ration Common differences Sequences Numeric patterns Geometric sequences 7.2 Arithmetic and Geometric Sequences 7.2 Pattern, Functions, Algebra SOL 7.2

13 2nd SOL 7.13 The student will a.) Write verbal expressions as algebraic expressions and sentences as equations and vice versa b.) Evaluate algebraic expressions for given replacement values of the variables Write verbal expressions as algebraic expressions. Expressions will be limited to no more than 2 operations Write verbal sentences as algebraic equations. Equations will contain no more than 1 variable term. Translate algebraic expressions and equations to verbal expressions and sentences. Expressions will be limited to no more than 2 operations. Identify examples of expressions and equations. Apply the order of operations to evaluate expressions for given replacement values of the variables. Limit the number of replacements to no more than 3 per expression. Verbal Expression Algebraic Expression 7.13 Translate and Evaluate N/A 7.13 Patterns, Function, Algebra SOL 7.13

14 2 nd SOL 7.16 The student will 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 e.) the multiplicative property of zero Identity properties of operations used in simplifying expressions Apply the properties of operations to simplify expressions Zero Commutative Property Associative Property Multiplicative Identity Properties Multiplicative Inverse Property Property of Zero Distributive Property 7.16 Properties 7.16 Order of Operations and Properties SOL 7.16

15 SOL 7.14 The student will a.) Solve one-and two-step linear equations in one variable b.) Solve practical problems requiring the solution of one-and two-step linear equations Linear Equation 7.14 Equations N/A 7.14 Patterns, Function, Algebra SOL nd Represent and demonstrate steps for solving one-and two-step equations in one variable using concrete materials, pictorial representations and algebraic sentences Solve one-and two-step linear equations in one variable Solve practical problems that require the solution of a one- or two-step linear equation

16 2 nd SOL 7.15 The student will a.) Solve one-step inequalities in one variable b.) Graph solutions to inequalities on the numberline c.) Represent and demonstrate steps in solving inequlaities in one variable using concrete materials, pictorial representations and algebraic sentences Graph solutions to inequalities on the number line. Identify a numerical value that satisfies the inequality Inequalities 7.15 Inequalities N/A 7.15 SOL 7.15

17 2 nd SOL 7.16 The student will 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 e.) the multiplicative property of zero Identity properties of operations used in simplifying expressions Apply the properties of operations to simplify expressions Zero Commutative Property Associative Property Multiplicative Identity Properties Multiplicative Inverse Property Property of Zero Distributive Property 7.16 Properties 7.16 Order of Operations and Properties SOL 7.16

18 SOL 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflection, dilations, rotations. And translations) by graphing in the coordinate plane. Transformations Reflections Dilations Rotations Translations Right triangle 7.8 -Rotation -Dilation -Translation and Reflection 3 rd Identify the coordinates of the image of a right triangle or rectangle that has been translated either vertically, horizontally, or a combination of a vertical and horizontal translation Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90º or 180º about the origin Identify the coordinates of the image of a right triangle or rectangle that has been reflected over the x- or y- axis Sketch the image of a right triangle or rectangle translated vertically or horizontally Sketch the image of a right triangle or rectangle that has been rotated 90º or 180º about the origin Sketch the image of a right triangle or rectangle that has been reflected over the x- or y-axis Sketch the image of a dilation of a right triangle or rectangle limited to a scale factor of ¼,½, 2,3,or 4 Rectangle 7.8 Polygons SOL 7.8

19 3 rd SOL 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid Compare and contrast attributes of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid Identify the classification(s) to which a quadrilateral belongs, using deductive reasoning and inferences. Quadrilaterals Parallelograms Rectangles Trapezoids Rhombi Squares 7.7 Quadrilateral Sort 7.7 Polygons SOL 7.7

20 3 rd SOL 7.5 The student will a.) Describe volume and surface area of cylinders b.) Solve practical problems involving the volume and surface area of rectangular prisms and cylinders c.) Describe how changing one measured attribute of a rectangle prism affects its volume and surface area mathematical communication, mathematical reasoning, connections, and representation to Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area Find the surface area of a rectangular prism Solve practical problems that require finding the surface area of a rectangular prism. Find the surface area of a cylinder Solve practical problems that require finding the surface area of a cylinder Find the volume of a rectangular prism Solve practical problems that require finding the volume of a rectangular prism Find the volume of a cylinder Solve practical problems that require finding the volume of a cylinder Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scald factor. Problems will be limited to changing attributes by scale factors only Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to changing attributes by scale factors only. Surface Area Volume Rectangular Prism 7.5 -Surface Area and Volume of a Cylinder -Volume of a Rectangular Prism -Surface Area of a Rectangular Prism -Attributes of a Rectangular Prism D Geometry SOL 7.5

21 SOL 7.4 The student will solve single-step and multistep practical problems, using proportional reasoning. Proportions Equality 7.4 -Sales Tax and Tip -Proportions ARDT (target date Jan. 3 rd mathematical communication, mathematical reasoning, connections, and representation to Write proportions that represent equivalent relationships between two sets. Solve a proportion to find a missing term. Apply proportions to convert units of measurement between the U.S. Customary System and the metric system. Calculators may be used. Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no less than tenths. Calculators may be used. Using 10% as a benchmark, mentally compute 5%, 10%, 15%, or 20% in a practical situation such as tips, tax, and discounts. Solve problems involving tips, tax, and discounts. Limit problems to only one percent computation per problem. ratios Tips Tax Discounts 7.4 Percents SOL 7.4

22 3 rd SOL 7.6 The student will determine whether plane figures-quadrilaterals and triangles- are similar and write proportions to express the relationships between corresponding sides of similar figures mathematical communication, mathematical reasoning, connections, and representation to Identify corresponding sides and corresponding and congruent angles of similar figures using the traditional notation of curved lines for the angles. Write proportions to express the relationships between the lengths of corresponding sides of similar figures. Determine if quadrilaterals or triangles are similar by examining congruence of corresponding angles and proportionality of corresponding sides. Given two similar figures, write similarity statements using symbols such as ΔABC~ΔDEF, A corresponding to D, and AB corresponds to DE Quadrilaterals Triangles Proportions Corresponding Congruent Curved lines 7.6 Similar Figures 7.6 Ratio/Proportions ARDT (target date Jan. SOL 7.6

23 4 th SOL 7.10 The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle Compute the number of possible outcomes by using the Fundamental (Basic) Counting Principle Determine the probability of a compound event containing no more than 2 events Fundamental Counting Principle 7.10 The Real Meal Deal 7.10 Probability SOL 7.10

24 4 th SOL 7.9 The student will investigate and describe the difference between the experimental probability and theoretical probability of an event. Determine the theoretical probability of an event Determine the experimental probability of an event Describe changes in the experimental probability as the number of trials increases Investigate and describe the differences between the probability of an event found through experiment or simulation versus the theoretical probability of that same event Experimental Probability Theoretical Probability 7.9 What are the Chances? 7.9 Probability SOL 7.9

25 4 th SOL 7.11 The student given data in a practical situation, will a.) Construct and analyze histograms b.) Compare and contrast histograms with other types of graphs presenting information from the same data 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 Compare and contrast histograms with line plots, circle graphs, stem-and-leaf plots presenting information from the same data set Circle graph 7.11 Numbers in a Name N/A 7.11 Statistics SOL 7.11