# Warren County Public Schools 6 th Grade Math KCC 4.1 Unit Title Program of Studies Core Content 4.1 I Can Targets Critical Resources Vocabulary

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1 Estimation Algebraic Thinking Problem Solving These skills should be embedded throughout each unit. MA-6-NPO-S-E2 estimate large and small quantities of objects. MA-6-NPO-S-E1 estimate and mentally compute to solve real-world and/or problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results. MA-6-AT-S-PRF1 recognize, create and extend patterns (give an informal description of the continuation of a pattern and/or generalize a pattern through a verbal rule). MA-6-AT-S-PRF2 represent, interpret and describe function relationships through tables, graphs and verbal rules. *MA estimate to solve real-world and problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results. *MA extend, describe rules for patterns and find a missing term in a pattern from real-world and DOK 3 MA create tables for functions and will apply the tables to solve realworld I can estimate whole numbers using addition, subtraction, multiplication and division. I can estimate fractions using addition, subtraction, multiplication and division. I can estimate decimals using addition, subtraction, multiplication and division. I can estimate percents using addition, subtraction, multiplication and division. I can estimate to solve everyday Math problems with whole numbers. I can estimate to solve everyday Math problems with fractions. I can estimate to solve everyday Math problems with decimals. I can estimate to solve everyday Math problems with percents. I can estimate to solve everyday Math problems checking for reasonable / appropriate computational results. I can recognize patterns. I can create patterns. I can continue a pattern. I can describe how a pattern continues. I can explain the rule of a pattern. I can find a missing term in a pattern. Reasonable computational results Appropriate computational results Estim ate Whole Numbers Fractions Decimals Percents Extend and Describe missing terms patterns rules Create and Apply tables functions (eg. input, output) graphs / grids (eg. coordinate pairs, quadrant 1) verbal rules Multiple Choice #6, pg 10 Multiple Choice #34, pg 38 Open Response #4, pg 15 Multiple Choice #35 36, pg Multiple Choice #37, pg 41 Multiple Choice #38, pg 42 1

2 MA-6-AT-S-PRF2 represent, interpret and describe function relationships through tables, graphs and verbal rules. MA-6-AT-S-VEO2 substitute numerical values for variables and evaluate algebraic expressions. MA-6-AT-S-VEO3 describe, define and provide examples of algebraic expressions based on real-world and/or situations. MA-6-AT-S-EI1 use concrete and/or informal methods to solve equations with one variable that model real-world situations. MA-6-AT-S-EI3 model and solve real-world problems with one variable equations and inequalities (e.g., 8x=4, x + 2>5). MA describe, define, provide examples of, and apply to realworld and problems functions using tables, graphs and verbal rules. *MA substitute values for variables (up to two different variables) and evaluate algebraic expressions. *MA model and solve realworld and problems with simple equations and inequalities (e.g., 8x = 4, x+2 > 5). I can create functions to solve everyday problems through tables graphs verbal rules. I can apply functions to solve everyday problems through tables graphs verbal rules. I can organize input-output coordinate pairs into tables. I can plot points in the first quadrant of a coordinate system/grid. I can substitute values for up to 2 different variables. I can evaluate algebraic expressions. I can describe algebraic expressions based on everyday I can define algebraic expressions based on everyday I can provide examples of algebraic expressions based on everyday I can solve problems using simple formulas. I can model everyday problems with simple equations inequalities. I can solve everyday problems with simple equations inequalities. Substitute and Evaluate values variables algebraic expressions Model and Solve simple equations inequalities Multiple Choice #39, pg 43 2

3 I can explain how the change in one quantity affects change in another table graph input/output table. Place Value & Number Sense Whole Numbers, Decimals, and Fractions Weeks 1-5 MA-6-NPO-S-NS1 continue to develop number sense using fractions, decimals and percents, including percents greater than 100% and improper fractions. MA-6-NPO-S-PNO2 simplify fractions and determine equivalent fractions MA-6-NPO-S-RP1 develop meaning of percent and how to determine a percentage *MA provide examples of and identify fractions, decimals and percents. DOK 1 MA describe and provide examples of representations of numbers (whole numbers, fractions in simplest form, mixed numbers, decimals, percents) and operations in a variety of equivalent forms using models, diagrams, and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences), based on real-world and I can identify the place value of a whole number up to the hundred billions. I can identify the place value of a decimal down to the hundredthousandths. I can identify a number as a fraction not in simplest terms in simplest terms proper improper mixed I can identify a number as a decimal. I can identify a number as a percent. I can give examples of a fraction not in simplest terms in simplest terms proper improper mixed I can give examples of a decimal. I can give examples of a percent. Identify and Provide Examples of: 1. Decimals place value 2. Fractions simplest form mixed numbers equivalent 3. Percents Describe and Provide Examples of: diagrams symbols grids rectangular arrays number sentences Multiple Choice #1, pg 5 skillswise/numbers / g6_31_x1.htm Multiple Choice #2 3, pg / math/index.htm nav/vlibrary.html interactivate/activities/ Multiple Choice #4 5, pg 8 9 3

4 MA-6-NPO-S-NS5 compare, order and convert between whole numbers, fractions, decimals and percents using concrete materials, drawings or pictures and symbols (e.g., <,,>,,=,, order on a number line). MA-6-NPO-S-NS4 explore positive integral exponents (e.g. squares, cubes). MA-6-NPO-S-NS2 extend applications of operations (+,,, ) to include fractions and decimals. *MA convert between any two of the following numbers: fractions, decimals, and percents (less than or equal to 100%); and will compare and order these numbers. *MA add, subtract, multiply, and divide whole numbers, fractions, and decimals to solve real world problems and apply order of operations to simplify numerical expressions. I can convert a fraction into a decimal. I can convert a fraction into a percent. I can convert a decimal into a fraction in simplest form. I can convert an improper fraction to a mixed number. I can convert a mixed number to an improper fraction. I can convert a decimal into a percent. I can convert a percent into a decimal. I can convert a percent into a fraction in simplest form. I can compare fractions, decimals and percents (greater than, less than or equal to). I can order fractions, decimals and percents (number lines, greatest to least, least to greatest). I can add whole numbers to solve everyday I can subtract whole numbers to solve everyday I can multiply whole numbers to solve everyday I can divide whole numbers to solve everyday I can simplify fractions to lowest terms. I can identify equivalent fractions. I can add fractions with like denominators improper fractions with unlike denominators mixed numbers with like denominators mixed numbers with unlike denominators mixed numbers with regrouping I can subtract fractions with like denominators improper fractions with unlike Convert, com pare, and order: fractions decimals percents Identify and Apply: addend, sum difference factor product dividend divisor quotient order of operations Multiple Choice #10, pg 14 s/ fractions/olympic.fraction s.html Multiple Choice #7 9, pg

5 MA-6-NPO-S-NO3 explain and/or demonstrate inversely-related operations (addition and subtraction; multiplication and division). MA explain operations (addition and subtraction; multiplication and division) are inversely related. denominators mixed numbers with like denominators mixed numbers with unlike denominators mixed numbers with regrouping. I can multiply fractions mixed numbers. I can find the reciprocal of a whole number mixed number fraction. I can divide fractions mixed numbers. I can add decimals to solve everyday I can subtract decimals to solve everyday I can multiply decimals to solve everyday I can divide decimals to solve everyday I can find the percentage of a number. I can use order of operations to simplify everyday I can identify positive exponents. Explain: inverse related operations (e.g. +, -, x, / ) Multiple Choice #10, pg 14 5

6 Operations Whole Numbers and Decimals Weeks 6-14 MA-6-NPO-S-PNO1 determine prime numbers, composite numbers, prime factorization, factors, multiples, greatest common factor and least common multiple. MA-6-NPO-S-PNO3 use prime numbers, composite numbers, factors, multiples and divisibility to solve MA-6-NPO-S-NS3 develop place value of large and small numbers, including decimals. *MA identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). I can identify a number as prime. I can identify a number as composite. I can use prime factorization to figure out the least common multiple of a set of numbers to solve everyday I can use prime factorization to figure out the greatest common factor of a set of numbers to solve everyday I can use divisibility rules to solve everyday I can use prime factorization to figure out if a number is composite. Identify and Apply: prime numbers composite numbers prime factorization (to find least common multiples and greatest common factors) divisibility rules Multiple Choice #13, pg 17 (1.3.1) MA-6-NPO-S-RP2 develop meaning of ratio (e.g., describe and compare two sets of data using ratios and appropriate notations: 3:5, MA describe and apply ratios to solve realworld I can explain ratios to solve everyday I can apply ratios to solve everyday Describe / Explain and Apply ratios m/maths/ty-numprops.php 6

7 3,3 to 5). 5 MA-6-NPO-S-RP3 define and apply ratios to solve realworld MA-6-NPO-S-PNO4 explore and/or demonstrate how applications of properties (e.g., commutative, associative, inverse and identity for addition and multiplication) show relationships among numbers and operations. MA identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to simplify numerical expressions. DOK 1 I can identify the use of the commutative property of addition. I can identify the use of the commutative property of multiplication. I can identify the use of the associative property of addition. I can identify the use of the associative property of multiplication. I can identify the use of the identity property of addition. I can identify the use of the identity property of multiplication. Identify: the commutative property (addition and multiplication) the associative property (addition and multiplication) the identity property (addition and multiplication) Sim plify: numerical expressions Multiple Choice #14, pg 18 7

9 polygons); apply these properties and figures to solve real-world regular polygons), and will apply these elements and figures to solve real-world and dimensional figures sides vertices angles congruent parts. I can describe two dimensional figures circles triangles quadrilaterals regular polygons. sides edges faces bases vertices congruent parts MA-6-G-S-SR5 describe, provide examples of and identify properties (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms and pyramids). MA-6-G-S-SR6 describe and provide examples of congruent and similar plane figures; apply congruent and similar plane figures to solve real-world MA describe, provide examples of, and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common threedimensional figures (spheres, cones, cylinders, prisms, and pyramids). MA identify and describe congruent figures, and will apply congruent figures to solve real-world and I can identify congruent figures. I can provide examples of congruent figures. I can apply congruent figures to solve everyday Describe and Provide Examples of: threedimensional shapes (spheres, cones, cylinders, pyramids, cubes, triangular and rectangular prisms) nets congruent figures similar figures Multiple Choice #23 24, pg (3.1.4) Multiple Choice #25, pg 29 (3.1.5) MA I can identify similar figures. I can provide examples of similar 9

10 identify similar figures and apply similar figures to solve real-world and figures. I can apply similar figures to solve everyday MA-6-G-S-TS1 determine lines of symmetry for a plane figure, sketch plane figures with multiple lines of symmetry and apply line symmetry to real-world and/or situations. MA-6-G-S-TS2 transform (translate and reflect across a horizontal or vertical line) figures in the first quadrant of the coordinate plane and determine new coordinates of the shape after transformation. MA-6-G-S-TS3 explore the rotation of a figure in a plane in the first quadrant, with and without manipulatives MA describe, provide examples of, and apply line symmetry to real-world and *MA : reflect figures across a horizontal or vertical line in the first quadrant; translate figures in a plane in the first quadrant and determine the coordinates of the image after transformation in the first quadrant. I can reflect figures across a horizontal line in the first quadrant. vertical line in the first quadrant. I can identify the lines of symmetry for a plane figure. I can sketch plane figures with multiple lines of symmetry. I can apply line symmetry to everyday I can translate figures in a plane in the first quadrant. I can determine the coordinates of the image after a transformation in the first quadrant. I can rotate a figure in a plane in the first quadrant. Describe and provide examples of: symmetry line(s) of symmetry Transformations 90º rotations reflections across a vertical line and a horizontal line translations images Open Response #5, pg 17 (3.2.2) 10

11 MA-6-G-S-CG1 identify and graph ordered pairs on a positive coordinate system, identifying the origin, axes and ordered pairs. MA-6-G-S-CG2 apply graphing in the positive coordinate system to solve real-world and MA-6-M-S-MPA1 find perimeter of regular and irregular polygons in metric and U.S. customary units. MA-6-M-S-MPA2 read and use measurement tools (e.g., rulers, scales, protractors, *MA identify and graph ordered pairs on a positive coordinate system (Quadrant I), correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve realworld and *MA measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and problems: area and perimeter of triangles; area and perimeter of quadrilaterals I can identify ordered pairs on a positive coordinate system. I can graph ordered pairs on a positive coordinate system. I can identify origin x axis y axis ordered pairs. I can apply graphing in the coordinate system to solve everyday I can measure lengths to the nearest eighth of an inch. I can measure lengths to the nearest centimeter. I can estimate measurements in standard units using fractions decimals. I can estimate to find angle measures segment measures. I can read measurement tools rulers scales protractors angle rulers. I can use measurement tools to find angle measures segment measures. I can explain how measurements and measurement formulas are related different. I can measure lengths to find the area of triangles in metric units in customary units. Identify, Graph, Apply, and Problem Solve with: Coordinate Grid Systems coordinate planes coordinates/ ordered pairs quadrants x axis y axis origin Measure, Determine, and Use: angle measures and segment measures length, width, base, height area Multiple Choice #26, pg 30 (3.3.1) Multiple Choice #15 17, pg (2.1.1) 11

12 angle rulers). MA-6-M-S-MPA3 find area of plane figures composed of triangles, squares and rectangles by subdividing and measuring; use square units appropriately. MA-6-M-S-MPA4 estimate and find angle measures and segment measures. MA-6-M-S-MPA5 estimate measurements in standard units, including fractions and decimals. MA-6-M-S-MPA6 explain how measurements and measurement formulas are related or different (e.g., compare the perimeter with the area of a rectangle). MA-6-M-S-SM1 describe and provide examples of U.S. Customary and metric units of measurement; use these units to solve real-world and/or MA-6-M-S-SM2 estimate, compare and convert (meaning to make ballpark comparisons/not memorize conversion factors between U.S. and metric units of measurement for length, weight/mass and volume/capacity within the (rectangles, squares); (using the Pythagorean theorem will not be required as a strategy) and area and perimeter of compound figures composed of triangles and quadrilaterals. MA estimate measurements in standard units including fractions and decimals. *MA explain how measurements and measurement formulas are related or different (perimeter and area of rectangles). 12 I can measure lengths to find the perimeter of triangles in metric units in customary units. I can measure lengths to find the area of quadrilaterals: Rectangles in metric units in customary units Squares in metric units in customary units. I can measure lengths to find the perimeter of quadrilaterals: Rectangles in metric units in customary units Squares in metric units in customary units. I can identify a compound figure composed of triangles and quadrilaterals. I can find the area of a compound figure composed of triangles and quadrilaterals. I can find the perimeter of a compound figure composed of triangles and quadrilaterals. I can estimate units of measurement for weight/mass volume/capacity I can compare units of measurement for weight/mass volume/capacity I can convert units of measurement for weight/mass volume/capacity perimeter Regular Polygons triangles quadrilaterals Irregular Polygons compound figures Units of Measure customary units metric units square units Measurement Tools protractors angle rulers scales rulers Estimate and Explain: measurements in standard units Measurements including fractions or decimals Formulas for perimeter and area of rectangles (how they are related or different) Convert and use: Customary (U.S.) and Metric units Multiple Choice #19, pg 23 (2.1.2) Multiple Choice #20, pg 24 (2.1.3) Multiple Choice #21 22, pg (2.2.1)

13 Number Theory and Fractions Weeks U.S. customary system and within the metric system: length (e.g., parts of an inch, inches, feet, yards, miles, millimeters, centimeters, meters, kilometers); weight/mass (e.g., pounds, tons, grams, kilograms); volume/capacity (e.g., cups, pints, quarts, gallons, milliliters, liters). MA-6-AT-S-PRF2 represent, interpret and describe function relationships through tables, graphs and verbal rules. MA-6-AT-S-PRF3 organize inputoutput coordinate pairs into tables and plot points in the first quadrant of a coordinate (Cartesian) system/grid. MA-6-AT-S-VEO1 explore the use of variables in expressions and equations. MA-6-AT-S-VEO2 substitute *MA convert units within the same measurement system and use these units to solve real-world MA create tables for functions and will apply the tables to solve realworld MA describe, define, provide examples of, and apply to realworld and problems functions 13 I can create functions to solve everyday problems through tables graphs verbal rules. I can apply functions to solve everyday problems through tables graphs verbal rules. I can organize input-output coordinate pairs into tables. I can plot points in the first quadrant of a coordinate system/grid. I can substitute values for up to 2 different variables. I can evaluate algebraic expressions. I can describe algebraic expressions based on everyday I can define algebraic (within and between) Customary and Metric Units for: Weight/mass (pounds, tons, grams, and kilograms) Volume/capacity (cups, pints, quarts, gallons, milliliters and liters) Length and Width (parts of an inch, inches, feet, yards, miles, millimeters, centimeters, meters and kilometers) Create/Interpret Ordered Pairs in: Tables Graphs Functions Plotting points in the first quadrant Apply: Tables Graphs Functions Verbal rules Organize: Input/output Multiple Choice #37, pg 41 (5.1.3) Multiple Choice #38, pg 42 (5.2.1)

14 Data Analysis & Probability Weeks numerical values for variables and evaluate algebraic expressions. MA-6-AT-S-VEO3 describe, define and provide examples of algebraic expressions based on real-world and/or situations. MA-6-AT-S-EI1 use concrete and/or informal methods to solve equations with one variable that model realworld situations. MA-6-AT-S-EI2 solve problems involving simple formulas MA-6-AT-S-EI3 model and solve real-world problems with one variable equations and inequalities (e.g., 8x=4, x + 2>5). MA-6-DAP-S-DR2 collect, organize, construct, analyze and interpret data in a variety of graphical methods, including line plots, line graphs, circle graphs, bar graphs and stem-and-leaf plots. MA-6-DAP-S-ES1 pose questions; collect, organize and display data. MA-6-DAP-S-DR3 compare data from various types of graphs. using tables, graphs and verbal rules. MA substitute values for variables (up to two different variables) and evaluate algebraic expressions. MA model and solve realworld and problems with simple equations and inequalities (e.g., 8x = 4, x+2 > 5). *MA analyze and make inferences from data displays 14 expressions based on everyday I can provide examples of algebraic expressions based on everyday I can solve problems using simple formulas. I can model everyday problems with simple equations inequalities. I can solve everyday problems with simple equations inequalities. I can explain how the change in one quantity affects change in another table graph input/output table. I can collect data organize data construct data displays analyze data. I can analyze graphical methods tables & charts drawings line plots line graph circle graphs bar graphs stem & leaf plots pictographs Venn diagrams. I can make inferences tables & charts drawings line plots line graph circle graphs bar graphs stem & leaf plots pictographs Venn diagrams. I can pose appropriate questions from a set of Substitute: Values for numerical variables (up to two different variables) Define, Evaluate, Describe, and Solve Algebraic Expressions Model and Solve: Real world problems with: (Simple equations with one variable and inequalities) Collect, Organize, Construct, Compare, Analyze, and Infer: data displays drawings tables/charts Multiple Choice #39, pg 43 g.com/ index.html Open Response #3, pg 13 proportions/index.html

15 (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-andleaf plots). DOK 3 data. pictographs bar graphs circle graphs line plots, Venn Diagrams line graphs stem-and-leaf plots MA-6-DAP-S-DR4 relate different representations of data (e.g., tables, graphs, diagrams, plots). Multiple Choice #31, pg 35 MA-6-DAP-S-DR1 select an appropriate graph to represent given data and justify the selection. MA explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related. Make predictions, draw conclusions and verify results of : statistical data probability data Multiple Choice #27, pg 31 *MA determine and construct appropriate data displays (bar graphs, line plots, Determine: diagrams, plots 15

16 MA-6-DAP-S-CD2 determine and apply measures of distribution (mean, median, mode, range). MA-6-DAP-S-ES2 explore how sample size affects the reliability of the outcome. MA-6-DAP-S-P1 describe or determine (e.g., tables, tree diagrams) the sample space of an event. MA-6-DAP-S-P2 investigate solutions to probability problems using counting techniques, tree diagrams, charts and tables. MA-6-DAP-S-CD1 make predictions, draw conclusions and verify results from statistical data Venn diagrams, tables, line graphs), and will explain why the type of display is appropriate for the data. *MA determine and apply the mean, median, mode and range of a set of data. *MA describe or determine (e.g., tables, tree diagrams) the sample space of an event for a realworld or 16 o I can o Collect data o Organize data o Construct data displays o Analyze data o I can analyze graphical methods o Tables and charts o Drawings o Line plots o Line graphs o Circle graphs o Bar graphs o Stem and leaf plots o Pictographs o Venn diagrams I can construct appropriate data display o Tables and charts o Drawings o Line plots o Line graphs o Circle graphs o Bar graphs o Stem and leaf plots o Pictographs o Venn diagrams I can explain why a specific data display is appropriate o Tables and charts o Drawings o Line plots o Line graphs o Circle graphs Determine and Apply: mean median mode range Describe and Determine: tree diagrams sample space tables Investigate: counting techniques charts tree diagrams tables Multiple Choice #'s 28 30, pg 32 34

17 and probability experiments. MA-6-DAP-S-P3 make predictions, draw conclusions and verify results from statistical data and probability experiments. MA-6-DAP-S-P4 determine simple probabilities based on the results of an experiment and make inferences based on the data. MA-6-DAP-S-P5 explore the role of probability in decision making. situation. *MA determine single event probabilities based on the results of an experiment and will make inferences based on the data. DOK 3 o Bar graphs o Stem and leaf plots o Pictographs o Venn diagrams I can determine a set of data's: o o o o Mean Median Mode Range I can apply a set of data's: o o o o Mean Median Mode Range Draw Conclusions/Make Inferences and Verify Results: single event probability statistical data probability experiments Single event probability, results, inferences 17

18 I can compare data from various types of graphs tables & charts drawings line plots line graph circle graphs bar graphs stem & leaf plots pictographs Venn diagrams. I can make predictions from statistical data probability data. I can draw conclusions from statistical data probability data. I can verify results from statistical data probability data. I can determine appropriate data displays tables & charts drawings line plots line graph circle graphs bar graphs stem & leaf plots pictographs Venn diagrams. I can construct appropriate data displays tables & charts drawings line plots line graph circle graphs bar graphs stem & leaf plots pictographs Venn diagrams. I can explain why a specific data display is appropriate tables & charts drawings line plots line graph circle graphs bar graphs stem & leaf plots pictographs Venn diagrams. 18

19 I can determine a set of data s mean median mode range. I can apply a set of data s mean median mode range. I can investigate how sample size affects the reliability of the outcome. I can describe an event s sample space through tables tree diagrams. I can determine an event s sample space through tables tree diagrams. I can investigate solutions to probability problems using counting techniques charts tree diagrams tables. I can determine single event probabilities based on the results of an experiment. I can make predictions from statistical data probability experiments I can make inferences based on the results of an experiment. I can make decisions based on probability. I can investigate the theoretical probability of simple events. 19

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