Decimals (POD s) Percent 6.2. Single-step & 6.1. Percents MU 1 1. Clothes Line Base 10 blocks Number lines Grid paper IXL

Transcription

1 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 6 Enriched 1 st Quarter Unit Review ( th ) Fraction Decimals Percent Improper Mixed Fractions Decimals (POD s) Fraction Mult. & Division (s) Ratios Fractions Decimals Addition & 6. Single-step & 6.1 Percents Subtraction Multi-step Single-step & Problems Multi-step Problems Textbook Correlation MU MU MU 1 1 Single-step & Multistep Problems MU MU MU Additional Resources VDOE Lesson Plans Field Goals, Balls, and Nets Clothes Line Base 10 blocks Number lines Grid Paper Rational Speed Matching Clothes Line Base 10 blocks Number lines Grid paper Clothes Line Base 10 blocks Number lines Grid paper Fraction Circles Fraction Manipulatives Arrays Paper folding Repeated addition Repeated subt. Fraction strips Area models Modeling Multiplication of Fractions Modeling Division of Fractions Word problem problem-solving strategies Practical Problems involving decimlas Vocabulary Ratio Part-to-whole Part-to-part (same quantity) Whole-towhole Part-to-part (different quantity) Numerator Denominator Equivalent fraction Simplify Ratio Decimal point Place Value Terminating decimals Repeating decimals Ascending Descending Percent Hundredths Ratio Simplest form Inverse operation Sum, Total, In all, Altogether Difference, Left, Less than How much more/farther Divisor Dividend Quotient Factors Product Estimate Approximate 1

2 0 Use in 1 st and 2 nd Week POD s. Review Multiplication and Division facts, Simplifying fractions. 6.1a Describe a relationship within a set by comparing part of the set to the entire set. 6.1b Describe a relationship between two sets by comparing part of one set to a corresponding part of the other set c Describe a relationship between two sets by comparing all of one set to all of the other set. 6.1d Describe a relationship within a set by comparing one part of the set to another part of the same set. Represent the relationship that makes a comparison by using the notations 6.1 e a, a:b, a to b. b 6.1f Create a relationship in words for a given ratio expressed symbolically. 6.2d Represent a fraction by shading a grid. 6.2e Represent in fraction form a given shaded region of a 10-by-10 grid. 6.2b Represent fraction on a number line. 8 Equivalencies, Comparing, and Ordering (Denominators of 12 or less or factors of 100.) 6.2g 3 Compare two fractions with denominators of 12 or less using manipulatives, pictorial representations, number lines, and symbols (,,,, ). Review Finding GCF and LCM. Review Improper fraction to mixed numbers, and vice versa. No more than fractions. Emphasis placed on proper and improper fractions and mixed numbers! 6.2i Order no more than 3 fractions (fractions with denominators of 12 or less), in ascending and descending order. 6.2d Represent a decimal by shading a grid. 6.2e Represent in decimal form a given shaded region of a 10-by-10 grid. 6.2b Represent decimals on a number line. Compare two decimals through thousandths using manipulatives, pictorial 6.2f representations, number lines, and symbols (,,,, ). No more than decimals. Order no more than 3 decimals (decimals through thousandths) in ascending 6.2i and descending order. 6.2d Represent a percent by shading a grid. 6.2e Represent in percent form a given shaded region of a 10-by-10 grid. 6.2b Represent percents on a number line. 6.2h Compare two percents using pictorial representations and symbols (,,,, ). 6.2i Order no more than 3 percents in ascending and descending order. Describe orally and in writing the equivalent relationship among decimals, 6.2c percents, and fractions that have denominators that are factors of

3 Con t 8 9 Equivalencies, Comparing, and Ordering (Denominators of 12 or less or factors of 100.) 6.2a No more than fractions, decimals, and percents. Emphasis placed on proper and improper fractions and mixed numbers! 6.2i Denominators of 12 or less or factors of 100. Proper or improper fractions. 6.6b Proper or improper fractions Proper or improper fractions Proper or improper fractions 6.a 6.b 6.6a 6.6c Divisors are limited to 3-digit numbers with decimal divisors limited to hundredths. 6.7a Identify the decimal and percent equivalents for numbers written in fraction form including repeating decimals. Order no more than 3 fractions, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less), in ascending and descending order. Solve single-step and multi-step practical problems that involve addition and/or subtraction with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less, and express answers in simplest form. Demonstrate multiplication and division of fractions using multiple representations. Model algorithms for multiplying and dividing with fractions using appropriate representations. Multiply and divide with fractions and mixed numbers. Answers are expressed in simplest form. Solve single-step and multi-step practical problems that involve multiplication and/or division with fractions and mixed numbers that include denominators of 12 or less, and express answers in simplest form. Solve single-step and multi-step practical problems involving addition, subtraction, multiplication, and division with decimals expressed to thousandths with no more than two operations. 0 days (Q 1) 3

4 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 6 Enriched 2 nd Quarter Unit (s) Exponents Perfect Squares 6. Natural number exponents Integers 6.3 Integer Operations Orders of Operations 6.8 Including integers Textbook Correlation MU MU Properties 6.19 Including the application of properties and properties of equality Equations 6.18 Include 1-step practical problems and the application of properties 2-step equations (7.1) 2 6, Inequalities 6.20 Include 1-step (add and subtract only), graph and identify values 1-and-2 step inequalities (7.1) Verbal and Algebraic Equations/ Expressions Coordinate Plane 6.11 Additional Resources Square stackems Number line Goldfish project Number line on floor Foldables Property project Foldables Hands on equations Number tiles Number line Coordinate plane (floor, picture) Grid paper VDOE Lesson Plans Vocabulary Perfecting Squares Exponential notation Base, Exponent, Factor Power of a number Perfect square Geometric square Squared, Cubed Ground Zero Integer Negative integer Positive integer Opposite Absolute Value Additive Inverse Property Order Up! Pick and Choose Orders of operations Reciprocal GEMDAS Grouping includes: Parentheses and Absolute Value symbols Identity elements Field properties and properties of equality Equation Vocabulary Balanced Equation One-step equation Mathematical expression Term Variable Coefficient Positive rational Solution Justify the steps Inequalities Solutions Number line Open circles Closed circles Solution set What is the Point? Give or Take a Few Coordinate Coordinate plane Point Ordered pair Quadrant Origin x-axis y-axis x-coordinate y-coordinate

5 Limitations changed to whole number exponents verses natural number exponents (A non-zero base number raised to the zero power) 6.a 6.b 6.c Recognize and describe patterns with exponents that are natural numbers, by using a calculator. Recognize and describe patterns of perfect squares no to exceed using grid paper, square tiles, tables, and calculators. 2 20, by Recognize powers of ten by examining patterns in a place value chart: 10,000, 3 10 = 1,000, 2 10 = 100, 1 10 = 10, 0 10 = 1. Integer operations: including the addition, subtraction, 6.3b Represent an integer on a number line. multiplication, and division of integers. Include the additive inverse property at this point. 6.3a Identify an integer represented by a point on a number line. Practical problems involving integers. 6.3e Identify and describe the absolute value of an integer. 6.3c Compare and order integers, using a number line. 6.3d Compare integers, using mathematical symbols <, >, and =. Orders of operations extended to include integer operations, Simplify expressions by using the orders of operations in a demonstrated stepby-step exponents limited to 1, 2, and 3, and absolute value symbols. 6.8a approach. The expressions should be limited to positive values and not include braces { } or absolute value. Keep integer operations to no more than 3 operations within the expressions. 6.8b Find the value of numerical expressions, using orders of operations, mental mathematics, and appropriate tools. Exponents are limited to positive values. Review Commutative, Associative, and Distributive property. Apply properties of real numbers and properties of Identify a real number equation that represents each property of operations equality/inequality while solving equations. 6.19a with real numbers, when given several real number equations. (identity property for addition and multiplication, multiplicative property of zero, and inverse property for multiplication. Test the validity of properties by using examples of the properties of 6.19b operations on real numbers. Identify the property of operations with real numbers that is illustrated by a 6.19c real number equation. Identify and use the following algebraic terms appropriately: equation, 6.18c variable, expression, term, and coefficient. Apply properties. Coefficients are limited to integers and unit Represent and solve a one-step equation, using a variety of concrete materials fractions. 6.18a such as colored chips, algebra tiles, or weights on a balance scale. Solve one-step equation practical problems. 6.18b Solve a one-step equation by demonstrating the steps algebraically. Represent and demonstrate steps for solving 1-and-2 step equations using Enhanced Apply properties 7.1a concrete materials and pictorial representations and algebraic sentences. Enhanced Apply properties 7.1b Solve 1-and-2 step equations in one variable. Enhanced Apply properties 7.1c Solve practical problems that require the solution of a 1-and-2 step linear equation. 10 =

6 6 2 3 Solve 1-step inequalities involving addition and subtraction and graph solutions on a number line. 6.20a Identify a value or values that is a solution to an inequality. 6.20b Given a simple inequality with integers graph the relationship on a number line. Given the graph of a simple inequality with integers represent the inequality two different ways using symbols (<, >,, Enhanced Apply properties 7.1 Solve 1-and-2 step linear inequalities in one variable, including practical problems, involving addition, subtraction, multiplication, and division, and graph the solution on a number line. Write verbal expressions and sentences as algebraic New expressions and equations; and vice versa a Identify and label the axes of a coordinate plane. 6.11b Identify and label the quadrants of a coordinate plane. Coordinate values are limited to integers. Identity the quadrant or the axis on which a point is positioned by examining the 6.11c coordinates (ordered pair) of the point. 6.11d Graph ordered pairs 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 6.11e axes of the coordinate plane. ). 2 days (Q 2) 6

7 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 6 Enriched 3 rd Quarter Unit (s) Proportional Relationships (6.12 New) Unit Rates Ratio Tables Estimates 6.9 Customary and Metric Similar Figures (7.6) Circle Graphs 6.1 Histogram (7.11) Polygons Quadrilaterals 6.13 Congruency 6.12 Regular Polygons and Lines of Symmetry Circles, Triangles & Rect. (6.10) Circumference, Peri./Area Rectangular Prism Surface Area, Volume Mean 6.1 Textbook Correlation Additional Resources Measuring Mania May I have VDO E Less on Plan Vocabulary Proportional Relationships (7.) Supplement Additive relationship Multiplicative relationship Ratio table Unit rate Proportional and Non- Proportional Relationships 7, 8, 9 1, 9 2 MU 3 20 to 3 22 MU 3 2 to 3 27 Weight & Measuring book Liter measurement set Gallon measurement set Mass Weight U.S. Customary System Metric system MU MU -2 - Graph project Fries with That? Data Survey Scale, key, title Bar Graphs Line graphs Circle graphs Supplement 8 7 MU 37 Polygon Power point Quad Power point Quad sort Tearing angles Chart, graphic organizer Venn diagram Exploring Quadrilaterals Quad,Parallelogra m, Rectangle, Square,Rhombus, Trapezoid, Kite, Bisect, Parallel sides, Adjacent sides, Bases, Legs, Diagonal,Congrue nt Attributes, Sum of interior angles 7 Construction of congruent segments, angles, and polygons Side to Side Congruent figures Non-congruent figures Corresponding angles Hatch marks 9 3 to 9 9 MU 3 28 to Sir Cumference & the Dragon of Pi = Pi Sir Cumference & the Isle of Immeter, Area & Circumfere. 3-D shapes, Formula sheet,tiles, one-inch cubes, adding machine tape, graph paper, geoboards, tracing paper Going the Distance Out of the Box Area, Perimeter, Circumference Radius, Diameter Pi Rectangular prism Volume Area of base Surface area 7 1 MU 6 Balance point project ( question, color coded post-its) Balancing Act Measures of center Mean Median Mode Balance point Numerical average Data set

8 2 6 Make a table of equivalent ratios to represent a proportional (New) relationship between two quantities; when given a ratio. 6.12a Make a table of equivalent ratios to represent a proportional (New) relationship between two quantities; when given a practical 6.12b situation. Identify the unit rate of a proportional relationship (New) represented by a table of values or a verbal description, 6.12c including those represented in a practical situation. Unit rates are limited to positive values. Determine a missing value in a ratio table that represents a (New) prop. relationship between two quantities using a unit rate. 6.12d Determine whether a proportional relationship exists between (New) two quantities, when given a table of values or a verbal 6.12e description, including those represented in a practical situation Determine whether a proportional relationship exists between (New) two quantities given a graph of ordered pairs. 6.12f Make connections between and among multiple (New) representations of the same proportional relationship using 6.12g verbal descriptions, ratio tables, and graphs. Enhanced 7.a Write proportions that represent equivalent relationships between two sets. Enhanced 7.b Solve a proportion to find a missing term. Enhanced Apply proportions to solve practical problems including scale drawings. Scale 7.c factors shall have denominators no greater than 12 and decimals no less than tenths. Enhanced 7.6 Write proportions to express the relationships between the lengths of corresponding sides of similar figures. Enhanced 7.6 Use proportions to determine the missing measures of similar figures. Estimate the conversion of units of length between the U.S. Customary 6.9a system and the metric system by using ballpark comparisons. Ex: 1 L 1 qt. Ex: L qts. Estimate measurements by comparing the object to be measured against a 6.9b benchmark. Estimate the conversion of units of weight/mass between the U.S. 6.9a Customary system and the metric system by using ballpark comparisons. Ex: 1 L 1 qt. Ex: L qts. Estimate measurements by comparing the object to be measured against a 6.9b benchmark. 8

9 6 Con t 6 Number of data values represented in a circle graph limited in order to make comparisons that have denominators of 12 or less or those that are factors of 100. Compare circle graphs with other graphs now specified as bar graphs, pictographs, and line plots. 6.9a 6.9b 6.9a 6.9b 6.1a Estimate the conversion of units of volume between the U.S. Customary system and the metric system by using ballpark comparisons. Ex: 1 L 1 qt. Ex: L qts. Estimate measurements by comparing the object to be measured against a benchmark. Estimate the conversion of units of temperature between the U.S. Customary system and the metric system by using ballpark comparisons. Ex: 1 L 1 qt. Ex: L qts. Estimate measurements by comparing the object to be measured against a benchmark. Collect, organize, and display data in circle graphs by depicting information as fractional. 6.1b Draw conclusions and make predictions about data presented in a circle graph. Compare and contrast data presented in a circle graph with the same data 6.1c represented in other graphical forms (bar graph and line graph) Enhanced 7.11a Collect, analyze, display and interpret a data set using histograms. Enhanced Make inferences, conjectures, and predictions based on analysis of a set of 7.11b data. Enhanced Compare and contrast histograms with line plots, circle graphs, and stemand-leaf 7.11c plots with the same data set. Sort and classify polygons as quadrilaterals, parallelograms, rectangles, 6.13a trapezoids, kites, rhombi, and squares based on their properties. Properties include number of parallel sides, angle measures, and number of congruent sides. 6.13b Identify the sum of the measures of the angles of a quadrilateral as a 6.12b Identify regular polygons; draw lines of symmetry for regular polygons. 6.12c Characterize polygons as congruent and non-congruent according to the measures of their sides and angles. Determine the congruence of segments, angles, and polygons by direct comparison, 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. 9

10 8 Enhanced Enhanced Determine the effect on measures of center when a value is added, removed, or changed. 6.1c Represent mean as a balance point graphically on a line plot. Derive an approximation for pi (3.1 or 22 ) by gathering data and a 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 6.10b the radius into the formula C = d or C = 2 r. Apply formulas to solve practical problems involving perimeter of triangles 6.10d and rectangles. 6.10c Find the area of a circle by using the formula A= r 2. Apply formulas to solve practical problems involving area of triangles and 6.10d rectangles. Create and solve problems that involve finding the circumference and/or 6.10e area of a circle when given the diameter or radius. Solve problems that require finding the surface area of a rectangular prism, 6.10f given a diagram of the prism with the necessary dimensions labeled. Solve problems that require finding the volume of a rectangular prism, given 6.10g a diagram of the prism with the necessary dimensions labeled. Solve problems that require finding the surface area of a cylinder, given a 7.a diagram of the cylinder with the necessary dimensions labeled. Solve problems that require finding the volume of a cylinder, given a 7.b diagram of the cylinder with the necessary dimensions labeled. 6.1a Find the mean for a set of data. Identify and draw a number line that demonstrates the concept of mean as balance point for a set of data. Describe the three measures of center (mean, median, mode) and a 6.1b situation in which each would best represent a set of data. 3 days (Q 3) 10

11 Westmoreland County Public Schools Integrated Instructional Pacing Guide and Checklist Grade 6 Enriched th Quarter Unit Probability Sequences (s) Review Benchmark Test Review Review Testing Math 7 Proportional Reasoning Textbook Correlation 11 1, 11 2, 11, 11-7 MU 7 to MU 6 9 MU 2009 Correlation Additional Resources VDOE Lesson Plans Probability supplies: dice coins marbles cards colored chips It Could Happen Math 6 Portfolio Binder Growing Patterns and Sequences Math 6 Portfolio Binder Vocabulary Probability Outcomes Dependent event Independent event Simple event Compound event Numerical patterns Linear growth Exponential growth Triangular numbers Polygonal numbers Fibonacci numbers Common difference Common ratio Consecutive term Common factor 11

12 6.16a Determine whether two events are dependent or independent. 6.16b Compare and contrast dependent or independent events. 6.16c Determine the probability of two dependent events. 6.16d Determine the probability of two independent events. Investigate and apply strategies to recognize and describe the change between 6.17a terms in arithmetic patterns. 6.17g Identify the common difference for a given arithmetic sequence. Describe verbally and in writing the relationships between consecutive terms in 6.17c an arithmetic sequence. 6.17d Extend and apply arithmetic sequences to similar situations. Extend arithmetic sequences in a table by using a given rule or mathematical 6.17e relationship. Investigate and apply strategies to recognize and describe geometric patterns. 6.17b 6.17h Identify the common ratio for a given geometric sequence. Describe verbally and in writing the relationships between consecutive terms in a 6.17c geometric sequence. 6.17d Extend and apply geometric sequences to similar situations. Extend geometric sequences in a table by using a given rule or mathematical 6.17e relationship. 6.17f Compare and contrast arithmetic and geometric sequences. 20 ALL Review Portfolio After s and Retakes Proportional Reasoning 12