Salisbury Township School District Planned Course of Study 6 th Grade Math Salisbury Inspire, Think, Learn, Grow Together!

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1 Topic/Unit: The Number System Big Ideas/Enduring Understandings: Multiplication and division have an inverse relationship that is used in dividing fractions. Previous understanding of numbers can be extended to the system of rational numbers. Integers are plotted on horizontal or vertical number lines. Pairs of integers are graphed in a coordinate plane in one of the four quadrants. Common factors and multiples are used to describe real world problems Distributive property can be applied to identify common factors. Multi-digit numbers can be added, subtracted, multiplied and divided. Essential Questions: How does the understanding of the inverse relationship between multiplication and division help us to solve problems involving fractions and decimals in a real world context? How can you use a number line to represent real life events, values of integers, absolute value and opposites of numbers? How can greatest common factor and least common multiple be used to solve real world problems? How can I find a common factor and use the distributive property to represent a sum of two whole numbers? How does my previous understanding of the four operations transfer to operations with decimals? PA Academic Standards (PA Common Core): CC E.1, CC E.2, CC E.3, CC E.4 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. Tier 3 Vocabulary: quotient, divisor, dividend, reciprocal, inverse, remainder, decimal, sum, difference, factor, product, greatest common factor (GCF), multiple, common multiple, least common multiple (LCM), positive numbers, negative numbers, opposite numbers, coordinate plane, x-axis, y-axis, origin, ordered pair, x-coordinate, y-coordinate, quadrants, integers, rational numbers, inequality, absolute value, Page 1

2 Concepts: Competencies: Instructional Practices: Assessments: The student will know: Division is the opposite of multiplication Whole numbers and decimals can be added, subtracted, multiplied and divided. The terms factors, multiples, greatest common factor and least common multiple. Factors can be used in the distributive property to express a sum of two whole numbers. Quantities can be represented by positive and negative numbers. The meaning of opposites of numbers. Integers and other rational numbers can be represented on a horizontal or vertical number line. Integers can be represented as pairs on a coordinate plane. Comparing rational numbers in real-world contexts. The student will be able to: Multiply fractions and use the inverse to divide fractions Add, subtract, multiply and divide whole numbers and decimals. Identify the factors and multiples of a number. Find the greatest common factor or two whole numbers less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factors. Represent quantities in real world contexts using positive and negative numbers. Determine the opposite of a number. Students use the Big Ideas textbook on-line to view tutorials, utilize interactive learning tools, and access book materials at home for further exploration and Related Textbooks/Workbooks for further explanation and Websites for further practice: Videos for students to learn the topics and/or use for reteaching topics: Notebook presentations Classroom Discussion and questioning Think/Pair Share Quizzes, tests, practice packets, graded assignments Study Island Common Core, The Number System, practice problems Manga High Challenges White board and other hold-ups Chalkboard Splash A-Z Sentence Starters Thumbs up/down Exit cards Unit pricing partner/group project. Page 2

3 Absolute value is a numbers distance from zero. The coordinate plane is divided into 4 quadrants. Locate and plot integers and other rational numbers on horizontal or vertical number line. Locate and plot pairs of integers and other rational numbers on a coordinate plane. Interpret, write and explain statements of inequality as statements about the relative position of two numbers on a number line diagram and in real-world contexts. Interpret absolute value as magnitude for a positive or negative quantity in a real world situation. Graph points in all four quadrants of the coordinate plane. Find distances between points with the same first coordinate or same second coordinate. Rally Coach 4 Corners Dice partner Group collaboration to explore concepts Individual/Partner/Group Projects Page 3

4 Topic/Unit: Ratios and Proportional Relationships Big Ideas/Enduring Understandings: Solving ratio and rate problems. Essential Questions: How can you use ratios, rates, unit rates, and proportions to describe changes in real-life situations and problems? How can equivalent ratios be represented as a table of values and graphed on a coordinate plane? How are percents and ratios related? How can ratios/proportions be used to solve measurement conversion problems? PA Academic Standards (PA Common Core): CC.21.6.D.1 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. Tier 3 Vocabulary: ratio, simplest form, equivalent ratios, rate, unit rate, unit price, cross product, coordinate plane, ordered pair, x- coordinate, y-coordinate, first quadrant, proportion, percent, conversion factor Concepts: Competencies: Instructional Practices: Assessments: The student will know: Ratios are the comparison of two numbers, that can compare a part to a part, a part to a whole, or a whole to a part. The student will be able to: Compare two numbers using a ratio in real-world situations. Represent ratios in three different ways. Students use the Big Ideas textbook on-line to view tutorials, utilize interactive learning tools, and access book materials at home for further exploration and Quizzes, tests, practice packets, graded assignments Study Island Common Core, Ratios and Proportional Relationships, practice problems Manga High Challenges Page 4

5 Ratios can be written in three different forms. Simplest form is when the ratio terms have no common factors other than 1. Rates are ratios that compare two different kinds of quantities. Unit rates can be found by simplifying the terms to find a new denominator of 1. Rates/prices can be easily compared by finding the unit rate/price. Constant speed can be found using unit rates. Cross-products can be used to compare and find equivalent ratios. Equivalent ratios represented in a table can be written as ordered pairs and graphed on a coordinate plane. Simplify ratios using division. Identify equivalent ratios by simplifying each one separately. Express the difference between a ratio and a rate. Identify and find unit rates in real world situations. Compare relationships between rates/prices using unit rates/prices. Identify equivalent ratios using cross-products. Make a table of equivalent ratios. Determine missing values in a table of equivalent ratios. Graph an ordered pair from a table of values on a coordinate plane. Write proportions based on real-world situations using rates and unit rates. Related Textbooks/Workbooks for further explanation and Websites for further practice: Videos for students to learn the topics and/or use for reteaching topics: Notebook presentations Classroom Discussion and questioning Think/Pair Share Rally Coach 4 Corners Dice partner Group collaboration to explore concepts White board and other hold-ups Chalkboard Splash A-Z Sentence Starters Thumbs up/down Exit cards Page 5

6 Proportions show two equal ratios and can be solved using cross products. Percents are ratios that compare a number to 100 (which will be the denominator). Conversion factors are ratios comparing two measurements and can be used to convert between measurements. Solve proportions using cross products. Write a percent as a rate per 100. Choose and use the appropriate conversion factor for converting measurement units. Individual/Partner/Group Projects Falcon Apps Debate (better buy) Page 6

7 Topic/Unit: Expressions and Equations Big Ideas/Enduring Understandings: Algebraic expressions can be understood using previous knowledge of arithmetic. Equations and Inequalities have applications in the real world. The relationship between two quantities in a real world problem change in relation to one another. Essential Questions: How can algebraic expressions be written and evaluated? How can one-variable equations and inequalities be created, solved and interpreted in real-world and mathematical problems? How can 2 variables change in relation to one another? PA Academic Standards (PA Common Core): CC B.1, CC B.2, CC B.3 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. Tier 3 Vocabulary: numerical expression, exponent, base, variable, algebraic expression, verbal expression, operation, expression, term, constant, variable term, coefficient, evaluate, equivalent expressions, Distributive property, like terms, equivalent, equation, inequality, substitution, independent variable, dependent variable, Concepts: Competencies: Instructional Practices: Assessments: The student will know: A numerical expression is written using numbers, symbols and/or letters to represent a quantity. The student will be able to: Identify the base and exponent in an expression. Write, simplify, and solve expressions using exponents. Students use the Big Ideas textbook on-line to view tutorials, utilize interactive learning tools, and access book materials at home for further exploration and Quizzes, tests, practice packets, graded assignments Study Island Common Core, Expressions and Equations, practice problems Manga High Challenges Page 7

8 An exponent tells how many times the base appears as a factor. Verbal expressions can be translated into algebraic expressions using operations and sometimes variables. An expression may have several parts including terms, constants, variables and coefficients. Expressions are evaluated by finding the value of the expression, often using substitution. Evaluating expressions is used in real-world problems, including formulas. Expressions can be written in various ways, but remain equivalent. The distributive property can be used to identify equivalent expressions. Translate a verbal phrase into an algebraic expression. Identify variables, terms, variable terms, constants, and coefficients in expressions. Substitute a numerical value for a variable to evaluate an expression. Use formulas to solve various real-world problems. Write expressions using variables, given real-world word problems. Find equivalent expressions using the distributive property. Simplify expressions using the distributive property and combining like terms. Substitute values in an equation/inequality to determine which values make the equation/inequality true. Related Textbooks/Workbooks for further explanation and Websites for further practice: Videos for students to learn the topics and/or use for reteaching topics: Notebook presentations Classroom Discussion and questioning Think/Pair Share Rally Coach 4 Corners Dice partner Group collaboration to explore concepts White board and other hold-ups Chalkboard Splash A-Z Sentence Starters Thumbs up/down Exit cards Page 8

9 Like terms have the same variable(s) raised to the same power and can be combined. Equations, which show two equivalent expressions, are different from inequalities, which show a relationship between two expressions (,,, ). Substitution is used to determine if a specific number in a set makes an equation or inequality true. Real world problems can be represented using algebraic expressions. Key words can give clues as to which operation should be used to solve an equation. The goal to solving an equation is to isolate the variable. Identify key words that mean addition, subtraction, multiplication, and division. Solve equations by using opposite operations to isolate the variable. Graph solutions to inequalities using a number line. Identify independent and dependent variables in a word problem and equation. Find the function rule that represents a relationship between an independent and dependent relationship. Create a table of ordered pairs, and graph them on a coordinate plane. Individual/Partner/Group Projects Page 9

10 The rule for solving equations is: Whatever is done to one side of an equation must be done to the other in order to maintain its equality. Opposite operations are used to keep the two sides of an equation equal. Real world situations can be translated into expressions using inequalities. Inequalities can be represented on a number line. The value of a dependent variable depends on the value of an independent variable. The relationship can be represented by an equation or function rule, which can then be graphed on a coordinate plane. Page 10

11 Topic/Unit: Geometry Big Ideas/Enduring Understandings: Solve problems (real world and mathematical) involving area, surface area, and volume. Essential Questions: What is the meaning of area, volume and surface area of figures? How can the area, volume, and surface area be determined using formulas? How can nets represent three-dimensional objects and be used to find surface area? How can vertices of a polygon be graphed on a coordinate plane? PA Academic Standards (PA Common Core): CC A.1 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. Tier 3 Vocabulary: area, formula, polygon, rectangular prism, rectangular solid, vertex, volume, coordinate plane, coordinate grid, axis, axes, ordered pair, three-dimensional figure, faces, prism, base, net, triangular prism, hexagonal prism, pyramid, surface area, Concepts: Competencies: Instructional Practices: Assessments: The student will know: The area of a figure is the number of square units needed to exactly cover a figure. The formula for the area of a rectangle and a triangle. The student will be able to: Describe the meaning of the area of a figure. Determine the area of a square, rectangle and triangle by substituting known values into the appropriate formula. Students use the Big Ideas textbook on-line to view tutorials, utilize interactive learning tools, and access book materials at home for further exploration and Quizzes, tests, practice packets, graded assignments Study Island Common Core, Geometry, practice problems Manga High Challenges White board and other hold-ups Page 11

12 Formulas can be used to find the area of special quadrilaterals (parallelogram, rhombus, trapezoid), but formulas will be provided. Area can be found by substituting the known values into the formula and solving the equation. A polygon is a closed shape whose sides are line segments. Area of a irregular or compound polygon can be found by composing or decomposing separate shapes within or around the polygon A rectangular prism (solid) is a solid figure in which all six faces are rectangles. The volume of a rectangular prism is the amount of space a prism takes up. The formula for the volume of a rectangular prism. Determine the area of special quadrilaterals (parallelogram, rhombus, trapezoid) using a given formula. Determine the area of irregular and compound polygons by composing and decomposing shapes within or around the polygon. Identify a rectangular prism by its shape and description. Describe the meaning of the volume of a figure. Determine the volume of a rectangular prism by substituting known values into a formula, which will be provided. Plot points on a coordinate plane using ordered pairs with positive and negative numbers. Use coordinates to locate the vertices of a polygon on a coordinate plane. Related Textbooks/Workbooks for further explanation and Websites for further practice: Videos for students to learn the topics and/or use for reteaching topics: Notebook presentations Classroom Discussion and questioning Think/Pair Share Rally Coach 4 Corners Dice partner Group collaboration to explore concepts Chalkboard Splash A-Z Sentence Starters Thumbs up/down Exit cards Geometry Survival Guide (student created booklet with drawings and labels for shapes and definitions) Page 12

13 The number lines on a coordinate plane (grid) are called axes (singular is axis). Each point on a coordinate plane is named by an ordered pair written in the form (x,y), where x represents the horizontal distance from zero and y represent the vertical distance from zero on the number line. Positive numbers are to the right of zero on the x-axis and above zero on the y-axis. Negative numbers are to the left of zero on the x-axis and below the zero on the y-axis. Given the coordinates of the vertices of a polygon, side lengths and area of the polygon can be determined. A three-dimensional figure is a solid figure that may have flat or curved faces (bases). A prism has two parallel faces with rectangular sides. Find side lengths and area of a polygon in a coordinate plane. Identify prisms and pyramids by shape and description. Represent three-dimensional figures using nets made of rectangles and triangles. Describe the meaning of the surface area of a figure. Determine the surface area of prisms by finding the separate areas of the shapes and adding them together (sometimes by drawing a net to show the shapes). Use formulas to determine the surface area of triangular and rectangular prisms. Individual/Partner/Group Projects Geometry Survival Guide (student created booklet with drawings and labels for shapes and definitions) Page 13

14 A triangular prism is a prism with a triangle as each face. A hexagonal prism is a prism with a hexagon as each face. Nets are flat drawings that show all the faces of a threedimensional figure and can be used to determine what a 3-D figure will look like unfolded. A pyramid is a 3-D figure that has only one base, and the faces are triangles that meet at a single point. A pyramid is named by the shape of its base. The surface area of a 3-D figure is the total area of all the faces of the figure. The surface area is determined by adding the area of each part of the figure (sometimes drawing the net for the figure is helpful in finding each area). Formulas, which will be Page 14

15 provided, can be used for finding surface area of a triangular and rectangular prism. Area and volume can be applied to real-world situations and problems. Page 15

16 Topic/Unit: Statistics and Probability Big Ideas/Enduring Understandings: Statistical data is displayed in a variety of ways. Statistical data can be organized, analyzed and summarized to better understand a set of data. Essential Questions: What are the various ways statistical data can be displayed? How can information from statistical displays be used and summarized? How can statistical displays be created? PA Academic Standards (PA Common Core): CC B.1 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. Tier 3 Vocabulary: statistical question, surveys, data, population, sample, distribution, central tendency, mean, median, mode, range, variation, skewed, dot plot, outlier, raw data, bar graph, histogram, frequency table, box-and-whisker plot, upper extreme, lower extreme, quartile, upper quartile, lower quartile, interquartile range, observation, categorical data, numerical data, variability, Concepts: Competencies: Instructional Practices: Assessments: The student will know: A statistical question is one in which you expect the answer to vary. The student will be able to: Identify a statistical question based on population and data taken in a survey. Students use the Big Ideas textbook on-line to view tutorials, utilize interactive learning tools, and access book materials at home for further exploration and Quizzes, tests, practice packets, graded assignments Study Island Common Core, Statistics and Probability, practice problems Manga High Challenges Page 16

17 Statistical questions are asked through surveys, where data is collected from a population or sample. The distribution of a data set is an arrangement of its values showing how often the values occurred. Measures of central tendency are the center of the distribution. Definition of mean, median, mode, range, outlier, interquartile range. Variation is a measure of how spread out the data is. Data has a variety of shapes and can be skewed. Raw data can be organized in a variety of ways to help analyze and summarize the information. Determine measures of central tendency (mean, median, and mode) from a set of data. Determine range from a set of data. Identify how a set of data is skewed. Determine which measure of central tendency or variation would be most useful in a real-world problem. Create and analyze a dot plot from a set of data. Identify and explain the meaning of outliers in a set of data. Create and analyze bar graphs, histograms, and frequency tables from a set of raw data. Related Textbooks/Workbooks for further explanation and Websites for further practice: Videos for students to learn the topics and/or use for reteaching topics: Notebook presentations Classroom Discussion and questioning Think/Pair Share Rally Coach 4 Corners Dice partner White board and other hold-ups Chalkboard Splash A-Z Sentence Starters Thumbs up/down Exit cards Survey project Group collaboration to explore concepts Page 17

18 Dot Plots, Line Graphs, Circle Graphs, Bar Graphs, Histograms and Box-and- Whisker Plots are used to display and help analyze data in different ways. The information in a histogram can also be represented in a frequency table. A box plot consists of a box to represent the middle 50 percent of data and whiskers, or lines, to represent the other 50 percent of the data. Box plots display five important values of a data set: median, upper extreme, lower extreme, upper quartile, and lower quartile. Data can be classified as either numerical or categorical. Identify the 5 important values needed to create a boxand-whisker plot from a set of data: median, upper extreme, lower extreme, upper quartile, lower quartile. Create and analyze a boxand-whisker plot using the 5 important values needed. Determine the interquartile range from the box-andwhisker plot. Determine the difference between categorical and numerical data. Determine which type of statistical display would be most effective in a situation. Describe overall patterns and deviations from the pattern of data. Individual/Partner/Group Projects Survey project- Falcon Appsforms Page 18

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