6th Grade Common Core Curriculum

Transcription

1 Quarter 1 I. Whole Numbers and Decimals E.2 Identify and choose appropriate processes to compute fluently with multi-digit M06.A-N.2 Compute with multidigit numbers and find common factors and multiples. Formative Summative (Benchmark and/or Diagnostic if applicable) Intentionally vague to allow for professional development opportunities for school entities and Intermediate Unit E.3 Develop and/or apply number theory concepts to find common factors and multiples. M06.A-N.2.1 Compute with multidigit numbers using the four arithmetic operations with or without a calculator. M06.A-N.2 Compute with multidigit numbers and find common factors and multiples. M06.A-N.2.2 Apply number theory concepts (specifically, factors and multiples). A. Computation of Whole Numbers B. Computation of Decimals (3) Use concepts to solve non-routine problems using whole number operations (+,,, ). (3) Use concepts to solve non-routine problems using decimal operations (+,,, ). M06.A-N Solve problems The Number involving operations (+,,, ) System 6.NS with whole numbers, decimals (through thousandths), straight computation, or word M06.A-N Solve problems The Number involving operations (+,,, ) System 6.NS with whole numbers, decimals (through thousandths), straight computation, or word Compute fluently with multi-digit numbers and find common factors and multiples. 2. Fluently divide multi-digit numbers using the standard algorithm. Compute fluently 3. Fluently add, subtract, with multi-digit multiply, and divide multi-digit numbers and find decimals using the standard common factors and algorithm for each operation. multiples. (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems (2) completing division of fractions and extending the notion of number to the numbers, which includes negative numbers Difference Product Quotient Sum Dividing withtwo Digit Divisors Multiplying Thousandths by Thousandths Multiplication Charts Decimal Worksheets ( C. Greatest (4) Apply concepts to Common Factor find the GCF and LCM and Least of two given Common Multiple M06.A-N Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. M06.A-N Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express as 4(9 + 2). The Number System 6.NS Compute fluently with multi-digit numbers and find common factors and multiples. 4. Find the greatest common factor of two whole numbers less than or equal to 100 and 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 factor. For example, express as 4 (9 + 2). (3) writing, interpreting, and using expressions and equations (4) developing statistical thinking Greatest Common Factor Least Common Multiple Composite Numbers Prime Numbers Prime Factorization Greatest Common Factor Game Factor Trees, GCF, & LCM ( m) D. Distributive (4) Apply concepts to Property show the connection of Expressing Sums the Distributive Property to a given equation/problem. M06.A-N Apply the The Number distributive property to express a System 6.NS sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express as 4(9 + 2). Compute fluently with multi-digit numbers and find common factors and multiples. 4. (See I.C.) Distributive Property Multiplication Properties II. Fractions E.1 multiplication and division to divide fractions by fractions. M06.A-N.1 multiplication and division to divide fractions by fractions. M06.A-N.1.1 Solve real-world and mathematical problems involving division of fractions.

2 A. Dividing Fractions (3) Draw conclusions to formulate answers for word problems involving division of fractions by fractions. M06.A-N Interpret and The Number compute quotients of fractions System 6.NS (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) (3/4), explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = (a/b) (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board? multiplication and division to divide fractions by fractions. 1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Reciprocal "Of" Multiplying and Dividing Fractions Multiplication Wrap-Ups Multiplication Chart Fraction Bars Quarter 2 III. Integers/ Rational Numbers E.4 M06.A-N.3 M06.A-N.3.1 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and locations on the number line and coordinate plane. M06.A-N.3 Formative Summative (Benchmark and/or Diagnostic if applicable) Intentionally vague to allow for professional development opportunities for school entities and Intermediate Unit A. Representing Positive and Negative Numbers in Real World Contexts (3) Investigate the use of positive and negative numbers throughout daily life. M06.A-N.3.2 Understand ordering and absolute value of rational M06.A-N Represent The Number quantities in real-world contexts System 6.NS using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). 5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Integers Positive Integers Negative Integers Rational Numbers Positive and Negative Integers on a Number Line Thermometer Number Lines B. Number Line (4) Create a coordinate plane and plot integers and rational numbers on the plane. M06.A-N Locate and plot The Number integers and other rational System 6.NS numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane. 6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from grades to represent points on the line and in the plane with negative number coordinates. The Number Line Extended Number Lines C. Opposites (4) Prove that the opposite of an opposite number is the number itself and not its opposite. M06.A-N Determine the The Number opposite of a number and recognize System 6.NS that the opposite of the opposite of a number is the number itself (e.g., ( 3) = 3, and that 0 is its own opposite). 6. (See III.B.) 6.a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite. Opposites Printable Number Lines Number Lines Vertical Thermometer

3 D. Interpreting Inequalities E. Ordering (3) Compare rational Rational Numbers numbers in real-world in Real World contexts. Contexts The Number System 6.NS M06.A-N Write, interpret, and The Number explain statements of order for System 6.NS rational numbers in real-world contexts. Example: Write 3 C > 7 C to express the fact that 3 C is warmer than 7 C. 7.a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. 7. Understand ordering and absolute value of rational 7.b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 oc > 7 oc to express the fact that 3 oc is warmer than 7 oc. Horizontal Number Line Thermometer F. Absolute Value (2) Relate the distance of a positive number on the number line and that same number as a negative from zero. M06.A-N Interpret the The Number absolute value of a rational number System 6.NS as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a real-world situation. Example: For an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars, and recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. 7. (See III.E.) 7.c.Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. 7.d.Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Absolute Value Concepts of Absolute Value IV. IV. Coordinate Plane b2.3.6.a.2 Graph points in all four quadrants on the M06.A-N.3 coordinate plane to solve real world and M06.A-N.3.1 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and locations on the number line and coordinate plane. M06.A-N.3 M06.A-N.3.2 Understand ordering and absolute value of rational A. Four Quadrants (3) Construct a coordinate plane with all four quadrants and differentiate between the positve and negative integers within the plane. M06.A-N Locate and plot The Number integers and other rational System 6.NS numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane. 6. (See III.B.) 6.b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Quadrant X-axis Y-Axis Coordinate Plane Graph Paper Ruler B. Plotting Points (3) Investigate the location of various points on a coordinate plane. M06.A-N Locate and plot The Number integers and other rational System 6.NS numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane. 6. (See III.B.) 6.c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. X-Coordinate Y-Coordinate Ordered Pair Coordinate Plane Jeopardy Horizontal Number Line Vertical Number Line

4 C. Solving Problems by Plotting Points (3) Explain phenomena in terms of concepts to find distances between points within a coordinate plane. M06.A-N Solve real-world and The Number mathematical problems by System 6.NS plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Coordinate Plane Examples Graph Paper Ruler V. Ratio Concepts D.1 concepts and use solve M06.A-R.1 ratio reasoning to M06.A-R.1.1 Represent and/or solve real world and mathematical problems using rates, ratios, and/or percents. A. Describing Ratio Relationships (2) Relate ratio language and notation between two quantities. M06.A-R Use ratio language Ratios and and notation (such as 3 to 4, Proportional 3:4, 3/4) to describe a ratio Relationships 6.RP relationship between two quantities. Example 1: The ratio of girls to boys in a math class is 2:3, because for every 2 girls there are 3 boys. Example 2: For every five votes candidate A received, candidate B received four votes. 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. Ratio The Golden Ratio B. Unit Rate and Ratios (3) Formulate an answer that involves unit rate and constant speed scenarios for real-world situations. M06.A-R Find the unit rate a/b associated with a ratio a:b (with b 0), and use rate language in the context of a ratio relationship. Example 1: This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. Example 2: We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. Ratios and Proportional Relationships 6.RP 2. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. ^1 Rate Unit Rate What's Your Rate? Unit Price Game M06.A-R Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? C. Making and Comparing Tables (3) Use concepts to solve non-routine problems involving tables to find missing values. M06.A-R Construct tables of Ratios and equivalent ratios relating Proportional quantities with whole-number Relationships 6.RP measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios. 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 3.a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Equivalent Ratios D. Solve Unit Rate Problems (3) Draw conclusions involving unit rate problems involving unit pricing and constant speed. M06.A-R Solve unit rate problems including those involving unit pricing and constant speed. Ratios and Proportional Relationships 6.RP 3.(See IV.C) 3.b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

5 E. Percent of a Quantity (3) Assess a percent of a quantity as a rate per 100. M06.A-R Find a percent of a Ratios and quantity as a rate per 100 (e.g., Proportional 30% of a quantity means 30/100 Relationships 6.RP times the quantity); solve problems involving finding the whole, given a part and the percent. 3.(See IV.C) 3.c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. F. Ratio Reasoning Ratios and Proportional Relationships 6.RP 3.(See IV.C) 3.d. Use convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Quarter 3 VI. Algebraic B.1 M06.B-E.1 numerical and M06.B-E.1.1 Identify, write, and evaluate numerical and Formative Summative (Benchmark and/or Diagnostic if applicable) Intentionally vague to allow for professional development opportunities for school entities and Intermediate Unit A. Exponents (4) Apply concepts to solve for problems involving exponents. 1. Write and evaluate numerical expressions involving wholenumber exponents. Exponents Base Power B. Numerical C. Writing Verbal (3) Formulate an expression and solve the expression involving whole-number exponents. (4) Analyze verbal descriptions to write M06.B-E Write and evaluate numerical expressions involving whole-number exponents. M06.B-E Write expressions from verbal descriptions. Example: Express the description five less than twice a number as 2y Write and evaluate numerical expressions involving wholenumber exponents. 2. Write, read, and evaluate expressions in which letters stand for 2.a. Write expressions that record operations with numbers and with letters standing for For example, express the calculation Subtract y from 5 as 5 y. Expression Writing Balancing Understanding with Order of Operations ji i D. Parts of an Expression (3) Differentiate parts of a mathematical expression to solve a problem. M06.B-E Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors. 2. (See VI.C.) 2.b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Term Coefficient

6 E. Evaluating (3) Critique expressions to solve for real-world M06.B-E Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world Example: Evaluate the expression b2 5 when b = (See VI.C.) 2.c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/ Variables Order of Operations Constant F. Applying Properties of Operations (4) Apply concepts of the properties of operations to make equivalent M06.B-E Apply the properties of operations to generate equivalent Example 1: Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x. Example 2: Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y). Example 3: Apply properties of operations to y + y + y to produce the equivalent expression 3y. 3. Apply the properties of operations to generate equivalent For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Associative Commutative Distributive Identity Variable Properties of Numbers G. Equivalent (3) Construct an equivalent expression for a given expression. M06.B-E Apply the properties of operations to generate equivalent Example 1: Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x. Example 2: Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y). Example 3: Apply properties of operations to y + y + y to produce the equivalent expression 3y. 4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. VII. Equations B.2 Understand the process of solving M06.B-E.2 Interpret and solve a one-variable equation or one-variable inequality and apply to real-world and B.3 M06.B-E.2.1 Create, solve, and Represent and analyze quantitative interpret one variable relationships between dependent equations or and independent variables. inequalities in real-world and M06.B-E.3 Represent and analyze quantitative relationships between dependent and independent variables. M06.B-E.3.1 Use variables to represent two quantities in a real-world problem that change in relationship to one another. A. Solving Equations by Substituting in Values (3) Assess whether a given number makes an equation or inequality true. M06.B-E Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Algebra Tiles Algebra Planet Blaster Equation Game

7 B. Using (3) Formulate Variables to Write expressions to represent Real World problems in math or Expression real-world situations. M06.B-E Write expressions to represent real-world or 6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Solving One-Step Equations Using Equations C. Write Equations to Solving Real- World Problems (3) Formulate and solve real-world equations using M06.B-E Write expressions to represent real-world or M06.B-E Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all non-negative rational 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational Real World Problems D. Writing Inequalities (3) Construct an inequality to represent constraints in math or real-world problems using a number line. M06.B-E Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines. 8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Inequalities Game E. Analyze Quantitative Relationships (4) Analyze the relationship between the independent and dependent variables. M06.B-E Write an equation to express the relationship between the dependent and independent variables. M06.B-E Analyze the relationship between the dependent and independent variables using graphs and tables, and/or relate these to an equation. 9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Independent Variable Dependent Variable Quarter 4 VIII. Statistics and Probability B.1 Use a set of numerical data to develop an and recognize statistical variability. M06.D-S.1 Demonstrate statistical variability by summarizing and describing distributions B.2 Use numerical data and apply statistical properties to summarize M06.D-S.1.1 Display, analyze, and describe a distribution. and summarize numerical data sets in relation to their context. Formative Summative (Benchmark and/or Diagnostic if applicable) Intentionally vague to allow for professional development opportunities for school entities and Intermediate Unit A. Statistical Questions Statistics and Probability 6.SP Develop statistical variability. 1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages. Statistical Question

8 B. Measures of (4) Apply concepts of Central Tendency central tendancy to solve a problem. M06.D-S Determine quantitative measures of center (e.g., median, mean, and/or mode) and variability (e.g., range, interquartile range, and/or mean absolute deviation). Statistics and Probability 6.SP Develop statistical variability. 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 5.c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Mean Median Mode Variability Range Interquartile Range Mean Absolute Deviation (MAD) Investigating Mean and Median C. Displaying and Summarizing Data (3) Construct graphs and cite evidence using numerical data collected. M06.D-S Display numerical Statistics and data in plots on a number line, Probability 6.SP including dot plots, histograms, and box-and whisker plots. Summarize and describe distributions. 4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 5. Summarize numerical data in plots on a number line, including dot plots, histograms, and box plots. Dot Plots Histograms Box Plots Tools for Displaying Data Worksheets and Resources on Displaying Data D. Distribution of Data (3) Critique patterns shown throughout the distribution of data. M06.D-S Describe any overall Statistics and pattern and any deviations Probability 6.SP from the overall pattern with reference to the context in which the data were gathered. Develop statistical variability. 2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Statistics Questions, Activities, & Lessons E. Relating to Data Distribution (4) Analyze data distribution for a relationship between measures of center and variability. M06.D-S Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Statistics and Probability 6.SP Summarize and describe distributions. 5.d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. F. Reporting Observations and Describing Attributes Statistics and Probability 6.SP Summarize and describe distributions. 5.a. Reporting the number of observations. 5.b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement IX. Geometry A.1 Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume A.2 M06.C-G.1 Solve real-world and mathematical problems involving area, surface area, and volume. M06.C-G.1.1 Find area, surface area, and volume by applying formulas and using various strategies. A. Area (3) Use concepts to solve non-routine problems involving area of triangles, special quadrilaterals, and irregular or compound polygons. M06.C-G Determine the area Geometry 6.G of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided. M06.C-G Determine the area of irregular or compound polygons. Example: Find the area of a room in the shape of an irregular polygon by composing and/or decomposing. Solve real-world and mathematical problems involving area, surface area, and volume. 1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and 2c. (See VI.D.) Area Scalene Equilateral Isosceles Right Acute Obtuse Hypotenuse Leg Heptagon Nonagon Similar Area of Irregular Figures Triangle Examples Quadrilateral Examples Polygon Examples

9 B. Volume (3) Assess volumes of right rectangular prisms with fractional edge lengths given a formula. M06.C-G Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided. Geometry 6.G Solve real-world and mathematical problems involving area, surface area, and volume. 2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and Volume Surface Area Pitfalls of Packaging 3-D Figures Unit Cubes 2c.(See VI.D.) C. Use (3) Assess area and Coordinate Plane side lengths of a polygon to Find Side using given coordinates. Lengths M06.C-G Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided. Geometry 6.G Solve real-world and mathematical problems involving area, surface area, and volume. 3. 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 of the same second coordinate. Apply these techniques in the context of solving real-world and Quadrant X-Axis Y-Axis Using Coordinates to Draw Polygons Creating Pictures Using Coordinate Plane Worksheet D. 3-D Figures (3) Formulate nets to represent 3-D figures of rectangles and triangles. (3) Assess the surface area of triangular and rectangular prisms using the given formula. M06.C-G Represent threedimensional figures using nets made up of rectangles and triangles. M06.C-G Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided. Geometry 6.G Solve Real-World and Mathematical Problems Involving Area, Surface Area, and Volume. 4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and Cube Rectangular Prism Triangular Prism Cylinder Pyramid Isometric Drawing Tool Finding Surface Area Using Interactive 3D Shapes * Additional websites for practice and review: m n.com