Curriculum & Grade 4: Pacing Mathematics Guide Grade 6: Pre-Algebra Martinsville City Public Schools Revised Summer 2011 Updated Summer 2012 TJV
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.
Learning Overview The Sixth 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 sixth grade mathematics. The standards are organized into 6 strands: Number/Number Sense: The focus of instruction allows students to master rational numbers, develop an understanding of integers and rational numbers, develop an understanding of the properties of operations on real numbers, and use a variety of representations to develop proportional reasoning. Computation and Estimation: The focus of instruction allows students to develop conceptual and algorithmic understanding of operations with integers and rational numbers, develop and refine estimation strategies, learn to make sense of the mathematical tools they use, and reinforce skills with operations through problem solving and application. Measurement: The focus of instruction allows students to develop measurement skills that provide a natural context and connection among mathematics concepts, measure objects physically and develop understanding of the concepts and processes of measurement, and use concrete materials and practical situations to examine perimeter, area and volume. Geometry: The focus of instruction allows students to expand informal elementary geometrical experiences, learn geometric relationships, apply their understanding of perimeter and area to build conceptual understanding, and explore and develop an understanding of the Pythagorean Theorem. Probability and Statistics: The focus of instructions allows students to develop and awareness of the power of data analysis and probability, explore methods of data collection and use of technology, and explore experimental and theoretical probability. Patterns, Functions, and Algebra: The focus of instruction allows students to extend their knowledge of patterns, learn to use algebraic concepts and terms appropriately, learn to solve equations by using concrete materials, and learn to represent relations by using ordered pairs, tables, rules, and graphs. 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
Learning Targets at a Glance 6 th Grade Math First Quarter 8/13-10/15 Second Quarter 10/16-12/21 Third Quarter 1/8-3/13 Fourth Quarter 3/14-5/22 6.1 Ratios 6.2 Rational Numbers 6.3 Integers 6.4 Mult./Divide fractions 6.5 Positive Exponents/perfect square 6.6 Mult./Divide fractions & mixed numbers 6.7 Solve single-step & multi-step problems 6.8 Order of Operations 6.9 Measurement-ballpark comparisons 6.10 Circles/area & perimeter/volume and Surface 6.11 Ordered pairs 6.12 Congruency 6.13 Properties of quadrilaterals 6.14 Circle graphs 6.15 Mean as a balance point 6.16 Dependent & Independent events in Probability 6.17 Sequences 6.18 Linear equations 6.19 Properties of operations 6.20 Inequalities Grade 6 Mathematics Test Blueprint Summary Table 50 question test Number/Number Sense Computation/Estimation Measurement/Geometry Probability, Statistics, Patterns, Functions and Algebra 10 9 12 19
Suggested Allocation for a 60 Minute Math Block 20 Minutes Bellringer 25 Minutes 5 Minutes 10 Minutes Calendar Activity Skill Lesson Practice/Small Group Instruction
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.
SOL 6.1 The student will describe and compare data, using rations, and will use appropriate notations such as a/b, a to b, and a:b Ratio Corresponding 6.1 Field Goals, Balls, and Nets ARDT (target date Jan. 1 st mathematical communication, mathematical reasoning, connections, and representation to Describe a relationship within a set by comparing part of the set to the entire set Describe a relationship between two sets by comparing part of one set to a corresponding part of the other set Describe a relationship between two sets by comparing all of the one set to all of the other set. Describe a relationship within a set by comparing one part of the set to another part of the same set. Represent a relationship in words that makes a comparison by using the notations a/b, a:b, and a to b. Create a relationship in words for a given ratio expressed symbolically. Notations ESS Graphic Organizer M&M Candies Or Skittles AA.1 AA.9 Chapter 10-1 6.1 Ratio/Proportions SOL 6.1
Content: Mathematics Grade 6 1 st SOL 6.2 The student will a) Investigate and describe fractions, decimals and percents as ratios b) Identify a given fraction, decimal, or percent from a representation c) Demonstrate equivalent relationships among fractions, decimals, and percents d) Compare and order fractions, decimals, and percents mathematical communication, mathematical reasoning, connections, and representation to Identify the decimal and percent equivalents for numbers written in fraction form including repeating decimals Represent fractions, decimals, and percents on a number line Describe orally and in writing the equivalent relationships among decimals, percents, and fractions that have denominations that are factors of 100. Represent, by shading a grid, a fraction, decimal, and percent Represent in fraction, decimal, and percent form a given shaded region of a grid Compare two decimals through thousandths using manipulatives, pictorial representations, number lines and symbols(see framework for symbols) Compare two fractions with denominations of 12 or less using manipulatives, pictorial representations, numberlines, and symbols (see framework for symbols) Compare two percents using pictorial representations and symbols Fractions Decimals Percents Equivalent Rational Number Cards Large Numberline r Converting Rational Numbers Chart Representing Rational Numbers Cards Compass Learning AA.11 AA.13 6.2 Rational Speed Matching Chapter 5-6, 5-7, 10-4, 10-6 6.2 Comparing and Ordering 6.2 Percents 6.2 Ratio/Proportion Buckle Down ARDT (target date Jan. SOL 6.2
1 st SOL 6.3 The student will a.) Identify and represent integers b.) Order and compare integers c.) Identify and describe absolute value of integers Identify an integer represented by a point on a number line Represent integers on a number line Order and compare integers using a number line Compare integers, using mathematical symbols (<,=,>). Identify and describe the absolute value of an integer. Integers Positive Integers Negative Integers Absolute Value Rational Number Real Number Whole Number Numberline Index cards or Cardstock Scissors Rational Number Flow Chart Number line clearly denoting zero Whiteboards C.1 C.4 6.3 Ground Zero Course 1 Chapter 8-1 Course 2 Chapter 3-1 6.3 Integers SOL 6.3 Natural Number Markers Erasers Counting Number
1 st SOL 6.4 The student will demonstrate multiple representations of multiplication and division of fractions Demonstrate multiplication and division of fractions using multiple representations Model algorithms for multiplying and dividing with fractions using appropriate representations Fractions Divisior Dividend Algorithms Arrays Numberline V.1 V.13 6.4 Modeling Division of Fractions 6.4 Modeling Multiplication of Fractions 6.4 Fractions SOL 6.4
1 st SOL 6.5 The student will investigate and describe concepts of positive exponents and perfect squares Recognize and describe patterns with exponents that are natural numbers, by using a calculator Recognize and describe patterns of perfect squares not to exceed 20( to the power of 2), by using grid paper, square tiles, tables, and calculators Recognize powers of ten by examining patterns in a place value chart: (see framework for examples) Exponential Notations Base Exponent Power Perfect Square Natural Numbers Perfect Square Charts Perfect Square Grids Multiplication Tables Square Tiles Calculators E.1 E.3 E.9 E.10 6.5 Perfecting Squares Course 2 Chapter 11-1 N/A SOL 6.5 Cubes Grid Paper
1 st SOL 6.6 The student will a.) Multiply and divide fractions and mixed numbers b.) Estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division Multiply and divide with fractions and mixed numbers. Answers are expressed in simplest form. Solve single-step and multistep practical problems that involve addition and subtraction with fractions and mixed numbers, with and without regrouping that include like and unlike denominators of 12 or less. Answers are expressed in simplest form. Solve single-step and multistep practical problems that involve multiplication and division with fractions and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form. Simplify Simplest Form Inverse Operations Plain paper for foldable-see foldables Colored pencils Calculators v.1 v.12 6.6 Modeling multiplication of Fractions 6.6 Modeling division of fractions Course 1 Chapter 6-3 thru 6-6 7-2 thru 7-5 4-4 6.6 Fractions SOL 6.6
1 st SOL 6.7 The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals, Solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with decimals expressed to thousandths with no more than two operations. Estimation Calculators Newspapers and/or ads from magazines Shopping List Chart Paper Markers M.1 M.5 6.7 Practical problems involving Decimals Course 1 Chapter 3-4, 6-2, 7-1 N/A SOL 6.7 Practical problems involving decimals (handout)
1 st SOL 6.8 The student will evaluate whole number numerical expressions, using the order of operations. Simplify expressions by using the order of operations in a demonstrated stepby-step approach. The expressions should be limited to positive values and not include braces {} or absolute value Order of Operations Evaluate Exponential Expressions Parentheses Brackets Braces Number Cubes Order of Operations Recording Sheet N/A 6.8 Order Up Course 1 Chapter 1-5 Course 2 Chapter 1-3 6.8 Order of Operations and Properties SOL 6.8
2 nd SOL 6.9 The student will make ballpark comparisons between measurements in the U.S. Customary Systems of measurement and measurements in the metric system. Estimate the conversion of units of length, weight/mass, volume, and temperature between the U.S. Customary system and the metric system by using ballpark comparisons. Estimate measurements by comparing the object to measured against Measure Conversions Length Weight Mass Volume Temperature Thermometer Ruler Scale Measuring devices N/A 6.9 Measuring Mania Chapters 1.8 thru 1.9 2.1 thru 2.7 9.1 thru 9.7 N/A SOL 6.9 U.S. Customary Metric
2 nd SOL 6.10 The student will a.) Define pi ( )as the ratio of the circumference of a circle to its diameter b.) Solve practical problems involving circumference and area of a circle, given the diameter or radius c.) Solve practical problems involving area and perimeter d.) Describe and determine the volume and surface area of a rectangular prism mathematical communication, mathematical reasoning, connections, and representation to Derive an approximation for pi (3.14 or 22/7) by gathering data and comparing the circumference to the diameter of various circles, using concrete materials or computer models. Find the circumference of a circle by substituting a value for the diameter or the radius into the formula C = d or C=2 r. Find the area of a circle by using the formula A= r² Apply formulas to solve practical problems involving area and perimeter of triangles and rectangles. Create and solve problems that involve finding the circumference and area of a circle when given the diameter or radius. Solve problems that require finding the surface area of a rectangular prism, given a diagram of the prism. Solve problems that require finding the volume of a rectangular prism given a diagram of the prism. Area Perimeter Circumference Volume Pi Diameter Radius Rectangular Prism Z.12 Z.22 Z.23 Z.27 Z.33 6.10 Going the Distance 6.10 Out of the Box Chpt. 4-3, 4-5, 4-6 14-3, 14-5 6.10 a, b Circles 6.10 d 3-D Geometry SOL 6.10
2 nd SOL 6.11 The student will a.) Identify the coordinates of a point in a coordinate plan b.) Graph ordered pairs in a coordinate plane mathematical communication, mathematical reasoning, connections, and representation to Identify and label the axes of a coordinate plane Identify and label the quadrants of a coordinate plane Identify the quadrant or the axis on which a point is positioned by examining the coordinates (ordered pairs) of the point Graph the ordered pairs represented by points in the four quadrants and on the axes of a coordinate plane. Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Relate the coordinate of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Coordinate Plane Point Ordered pairs Axes y-axis x-axis quadrants Q.1 Q.3 6.11 What s the point? Chpt. 8-6 6.11a Patterns,Functions, Algebra SOL 6.11
2 nd SOL 6.12 The student will determine congruence of segments, angles, and polygons. Characterize polygons as congruent and noncongruent according to the measures of their sides and angles. Determine the congruence of segments, angles, and polygons given their attributes Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving practical and mathematical problems. Coordinate Segments Angles Polygons Congruent Noncongruent Z.14 Z.15 6.12 Side to Side Course 1 Chpt. 13-6 13-6b 6.12 Polygons SOL 6.12
2 nd SOL 6.13 The student will describe and identify properties of quadrilaterals. Sort and classify polygons as quadrilaterals, parallelograms, rectangles, trapezoids, kites, rhombi, and squares based on their properties. Properties include number of parallel sides, angle measures and number of congruent sides. Identify the sum of the measures of the angles of a quadrilateral as 360º Quadrilaterals Parallelograms Rectangles Trapezoids Kites Rhombi Squares Congruent Bases Legs Protractor Z.2, Z.9 Z.11 6.13 Exploring Quadrilaterals Course 1 Chpt. 13-6 6.12 Polygons SOL 6.13
3 rd SOL 6.14 The student given a problem situation, will a.) Construct circle graphs b.) Draw conclusions and make predictions, using circle graphs c.) Compare and contrast graphs that present information from the same data set. Collect, organize, and display data in circle graphs by depicting information as fractional Draw conclusions and make predictions about the data presented in a circle graph Compare and contrast data presented in a circle graph with the same data represented in other graphical forms. Circle graph Z.14 Z.15 R.12, R.18 6.14 May I have fries with that? N/A 6.14 a,b Statistics Lessons 25-27 SOL 6.14
3 rd SOL 6.15 The student will a.) Describe the mean as balance point b.) Decide which measure of center is appropriate for a given purpose Find the mean for a set of data Describe the three measures of center and a situation in which each would best represent a set of data Identify and draw a number line that demonstrates the concept of mean as balance point for a set of data. Mean Balance Point S.1 S.3 6.15 Balancing Act Chpt. 2-6 N/A Lesson 28 SOL 6.15
3 rd SOL 6.16 The student will a.) Compare and contrast dependent and independent events b.) Determine probabilities for dependent and independent events Determine whether two events are dependent or independent Compare and contrast dependent and independent events Determine the probability of two dependent events Determine the probability of two independent events. Dependent event Independent event Outcome Probability S.1 S.3 6.16 It Could Happen Chpt. C.1 C.2 6.16 a, b Probability SOL 6.16
3 rd SOL 6.17 The student will identify and extend geometric and arithmetic sequences. Investigate and apply strategies to recognize and describe the change between terms in arithmetic patterns Investigate and apply strategies t recognize and describe geometric patterns Describe verbally and in writing the relationships between consecutive terms in an arithmetic or geometric sequence Extend and apply arithmetic and geometric sequences to similar situations. Extend arithmetic and geometric sequences in a table by using a given rule or mathematical relationship. Compare and contrast arithmetic and geometric sequences. Identify the common difference for a given arithmetic sequence Identify the common ratio for a given geometric sequence. Pattern T.1 T.5 6.17 Growing patterns and sequences Course 1 Chpt. 7-6 6.17 Patterns, Function and Algebra Lesson 30 SOL 6.17
4 th SOL 6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive solutions. Represent and solve one-step equation, using a variety of concrete materials such as colored chips, algebra tiles, or weights on a balance scale. Solve a one-step equation by demonstrating the steps algebraically. Identify and use the following algebraic terms appropriately: equations, variable, expression, term, and coefficient. Equations Variable Expression Term Coefficient Colored chips Algeblocks Balance scale P.5 6.18 Equations 6.18 Balanced Course 1 Chpt. 1-6 thru 1-7 9-2 thru 9-5 6.18 Patterns, Funtion, Algebra SOL 6.18
4 th SOL 6.19 The student will investigate and recognize a.) The identity properties for addition and multiplication b.) The multiplicative property of zero c.) The inverse property for multiplication Identify a real number equation that represents each property of operations with real numbers, when given several real number equations Test the validity of properties by using examples of the properties of operations on real numbers Identify the property of operations with real numbers that is illustrated by real number equations Commutative Property Distributive Property Associative Property Property of zero Colored chips Algeblocks Balance scale I.3 K.9 6.19 Pick and Choose Course 1 Chpt. 9-1 6.19 a,b,c Patterns, Function, Algebra Lesson 32 SOL 6.19
4 th SOL 6.20 The student will graph inequalities on a numberline. Given a simple inequality with integers, graph the relationship on a numberline Given the graph of a simple inequality with integers, represent the inequality two different ways using symbols (,, >, <) Inequalities Variable Colored chips Algeblocks Balance scale A.8 (4 th grade) 6.20 Give or Take a Few Course 2 N/A ARI Companion N/A Lesson 32 SOL 6.20