6 th Grade Math Curriculum Course Information: Course 1 of Prentice Hall Common Core

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1 6 th Grade Math Curriculum Course Information: Course: Length: Description: Course 1 of Prentice Hall Common Core 1 period/day Mathematics at the 6 th grade level will cover a variety of fundamental math skills, along with application of real-life scenarios. Students will fluently add, subtract, multiply, and divide whole numbers, decimals, and fractions. Students will apply their understanding of place value, operations, and inverse operations to explore algebraic number theories. In addition, students will begin to compute/explore the concept of ratios and unit rates. Geometric reasoning will be applied to shapes as students begin to learn formulas. As students begin to work with numbers, they will extend their knowledge to statistical variability and distributions by using plots and graphs. Essential Understanding: The sixth grade curriculum is designed to focus but not be limited to four critical areas using a variety of mathematical practices. 1. Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems. 2. Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers. 3. Writing, interpreting, and using expression and equations. 4. Develop understanding of statistical thinking. Theme Samples: 1. Number Properties and Decimals 2. Expressions and Equations 3. Number Theory 4. Fraction Operations 5. Ratios and Percents 6. Integers and Rational Numbers 7. The Coordinate Plane 8. Geometry and Measurement 9. Data and Graphs

2 Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically. 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Course Objectives and Expectations Students will fluently, add, subtract, multiply, and divide whole numbers and decimals using standard algorithms. Students will extend their understanding of arithmetic to algebraic expressions and equations. Using variables to represent unknown numerical values and to write and solve equations. Students will apply understanding of place value, operations, and inverse operations. Finding and using the greatest common factor and least common multiple of whole numbers. Applying and extending previous understandings of multiplication and division of fractions. Simplifying and computing fractions as the concepts of ratios and rates are explored in realworld and mathematical problems. Using tools strategically to order integers and model to represent addition and subtraction of integers with same or different signs. Ordering pairs by graphing integers on the coordinate plane and represent and analyze quantitative relationships between dependent and independent variables. Reasoning the relationships among shapes as the use of formulas to determine area, surface area, and volume of 2D-3D shapes. Develop understandings of statistical variability and distributions by displaying numerical data in plots and graphs.

3 Student Objectives Students will understand properties, use order of operations to simplify expressions, and being able to read, write and round decimals. Students will be able to add, subtract, multiply and divide decimals. Students will evaluate algebraic expressions and solve them in real-world scenarios while using mental math strategies and to solve equations with inverse operations. Students will be able to use divisibility rules, use exponents to simplify expressions with exponents and to factor numbers to find the prime factorization of numbers. Students will be able to compute the greatest common factor and least common multiple and to use the distributive property and simplifying expressions. Students will solve fractions and mixed numbers with the four operations fluently and to solve equations with fractions. Students will be able to write ratios, unit rate, and unit costs in the standard algorithm and realword scenarios. Students will be able to use equivalent ratios & rates and to solve measurement units and to begin using percents to write equivalent ratios and to find equivalent forms of fractions, decimals and percents. Students will use integers, opposites, and absolute values to represent real world scenarios and to compare and order rational numbers while expressing and identifying solutions of inequalities. Students will be able to name and graph points and polygons on coordinate plane and to create a function table and write an equation and to use the data in a table. Students will be able to solve problems involving areas of parallelograms, triangles, and complex figures, to identify three-dimensional figures and to find the surface area of prisms and pyramids. Students will be able to find the volume of rectangular prisms with fractional edge lengths. Students will be able to find the mean, median, mode, range, IQR, and mean absolute deviation of a set of data and to organize the data on frequency tables, dot plots, histograms and box-andwhisker plots and to understand how the information relates to the shape of data and distribution.

4 Pacing Quarter 1 Number Properties and Decimals; Number Theory Quarter 2 Integers and Rational Numbers, Expressions/Equations and fractions Quarter 3 Fractions, Ratios, Percents Quarter 4 Ratios, percents, coordinate plane, geometry & data/graphs Montana Common Core Standard 6.EE.2; 6.EE.3; 6. EE.6; 6.NS.2; 6.NS.3 6.EE.1; 6. EE.7 6.EE.2; 6.EE.5; 6.EE.6, 6.EE.7; 6.NS.1 6.NS.5; 6.NS.6; 6.NS.7 6.NS.1; 6.EE.5; 6.EE.6; 6.EE.8 6.RP.1; 6.RP.2; 6.RP.3; 6.EE.9; 6.G.1; 6.G.2; 6.G.3; 6.SP.1; 6.SP.2; 6.SP.3; 6.SP.4; 6.SP.5 Timeline 1. Fundamental Skills Review days 2. Number Properties and Decimals days 3. Expressions and Equations days 4. Number Theory days 5. Fraction Operations days 6. Ratios and Percents days 7. Integers and Rational Numbers days 8. The Coordinate Plane days 9. Geometry and Measurement days 10. Data and Graphs days

5 Content Quarter 1 Fundamental Skills A. Place Value for whole number and decimals B. Whole number operations with multi-digits C. Decimal Operations D. Adding & Subtracting Fractions Number Properties and Decimals A. Properties of Operations B. Order of Operations C. Understanding Decimals D. Adding and Subtracting Decimals E. Multiplying Decimals F. Dividing Decimals Number Theory A. Divisibility And Mental Math B. Exponents C. Prime Numbers And Prime Factorization D. Greatest Common Factor E. Least Common Multiple F. Distributive Property Quarter 2 Quarter 3 Integers and Rational Numbers A. Exploring Integers B. Comparing and Ordering Integers C. Rational Numbers D. Comparing and Ordering Rational Numbers E. Inequalities F. Solving One-Step Inequalities Expression and Equations A. Variables And Expressions B. Writing Algebraic Expressions C. Using Number Sense To Solve One-Step Equations D. Solving Addition Equations E. Solving Subtraction Equations F. Solving Multiplication And Division Equations G. Simplifying Algebraic Expressions

6 Number Theory A. Multiplying Fractions And Mixed Numbers B. Modeling Fraction Division C. Dividing Fractions D. Dividing Mixed Numbers E. Equations With Fractions Ratios and Percents A. Ratios B. Unit Rates C. Equivalent Ratios And Rates D. Using Ratios To Convert Measurements Units E. Understanding Percents F. Percents, Fractions, And Decimals G. Finding The Percent Of A Number H. Finding The Whole Quarter 4 Coordinate Plane A. Points In The Coordinate Plane B. Polygons In The Coordinate Plane C. Functions D. Graphing Functions E. Functions in the Real World Geometry and Measurement A. Areas Of Parallelograms and Triangles B. Areas Of Polygons C. Three-Dimensional Figures and Spatial Reasoning D. Surface Area Of Prisms and Pyramids E. Volumes Of Rectangular Prisms Data and Graphs A. Find the mean B. Median and Mode C. Frequency Tables and Dot Plots D. Box and Whisker Plots E. Histograms F. Variability of Data G. Shape of Distributions H. Statistical Questions

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11 Resources Prentice Hall Course 2 Mathematics Common Core 2013 Edition Prentice Hall Course 2 Mathematics Montana Common Core Standards for Mathematical Practice & Content from Office of Public Instruction WEBPAGE; Denise Juneau, State Superintendent Montana Office of Public Instruction

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