Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given contextual or mathematical situations involving multiplicative comparisons, Use rate language to explain the relationships between ratio of two quantities and the associated unit rate of one of the quantities in terms of the other. Unit rate Ratio Rate language Students know: Characteristics of multiplicative comparison situations, Rate and ratio language, Techniques for determining unit rates. Students understand that/are able to: Explain relationships between ratios and the related unit rates, Represent contextual relationships as ratios. EE6.RP.1-3. Demonstrate a simple ratio relationship. Level IV Students will: EE6.RP.1-3. Use a ratio to describe a relationship using numbers and objects. Ex. Given an even number of red and twice as many green beads, identify the ratio of green beads compared to red beads. Ex. While preparing a recipe, fill in a ratio of flour to sugar (e.g., one cup of sugar to four cups of flour.) Ex. Compare the number of male students to female students. Ex. Given the quantity of materials available and the number of groups who will conduct a science experiment, use a ratio relationship to describe how much each group will receive. Level III Students will: EE6.RP.1-3. Demonstrate a simple ratio relationship. Ex. Give a pen and a pencil to each classmate. Ex. After the teacher explains what materials each group needs, use a C to tell another student to get two cups for one table. Level II Students will: EE6.RP.1-3. Complete a pattern given a simple ratio. Ex. Take two steps on a number line each time the teacher says “step.” Ex. Give a ratio of two-to-one, complete a BBB pattern (e.g., jump, jump, clap; jump, jump, clap). Level I Students will: EE6.RP.1-3. Identify a one-to-one relationship. Ex. Given a stack of napkins, give a napkin to each classmate. Ex. When sorting mail in the main office, place one copy of the school newsletter in each teacher’s mailbox. Ex. Touch each object as teacher counts.
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given any two whole numbers less than or equal to 100, Strategically select and apply strategies for finding the greatest common factor of the two numbers and justify that the strategy used does produce the correct value for the greatest common factor, Use the distributive property to write an equivalent expression for the sum of the two numbers as the product of the greatest common factor of the two numbers, and the sum of two whole numbers with no common factor. [i.e., if the two whole numbers are 36 and 8, 36+8 = 4(9+2)]. Given two whole numbers less than or equal to 12, Strategically select and apply strategies for finding the least common multiple of the two numbers and justify that the strategy used does produce the correct value for the least common multiple. Greatest common factor Least common multiple Distributive property Students know: Strategies for determining the greatest common factor of two numbers, Strategies for determining the least common multiple of two numbers, Distributive Property of Multiplication over addition. Students understand that/are able to: Apply strategies for determining greatest common factors and least common multiples, Use the distributive property to express the sum of two whole numbers 1 to 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. EE6.NS.4. N/A EE6.NS.4. N/A
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.NS.6a Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 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. Domain: The Number System Cluster: Apply and extend previous understandings of numbers to the system of rational numbers. Quarter 1: Quarter 2: Identify a rational number as a point on the number line. Identify the location of zero on a number line in relation to positive and negative numbers Recognize opposite signs of numbers as locations on opposite sides of 0 on the number line Reason that the opposite of the opposite of a number is the number itself. Quarter 3: Quarter 4: Make sense of problems and persevere in solving them Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.NS.6b Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 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. Domain: The Number System Cluster: Apply and extend previous understandings of numbers to the system of rational numbers. Quarter 1: Quarter 2: Recognize the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located Reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y axis, e.g., (x,y) and (-x,y) Recognize that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x axis, e.g., (x,y) and (x,-y) Quarter 3: Quarter 4: Make sense of problems and persevere in solving them Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.NS.7a Understand ordering and absolute value of rational numbers. 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. Domain: The Number System Cluster: Apply and extend previous understandings of numbers to the system of rational numbers. Quarter 1: Quarter 2: Order rational numbers on a number line Interpret statements of inequality as statements about relative position of two numbers on a number line diagram. Quarter 3: Quarter 4: Make sense of problems and persevere in solving them Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.NS.7b Understand ordering and absolute value of rational numbers. 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. Domain: The Number System Cluster: Apply and extend previous understandings of numbers to the system of rational numbers. Quarter 1: Quarter 2: Write, interpret, and explain statements of order for rational numbers in real-world contexts Quarter 3: Quarter 4: Make sense of problems and persevere in solving them Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.EE.2b Write, read, and evaluate expressions in which letters stand for numbers. 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. Domain: Expressions and Equations Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions. Quarter 1: Quarter 2: Quarter 3: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) Identify parts of an expression as a single entity, even if not a monomial. Quarter 4: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.EE.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. Domain: Expressions and Equations Cluster: Reason about and solve one-variable equations and inequalities. Quarter 1: Quarter 2: Quarter 3: Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Relate variables to a context. Write expressions when solving a or mathematical problem Quarter 4: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.EE.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 numbers. Domain: Expressions and Equations Cluster: Reason about and solve one-variable equations and inequalities. Quarter 1: Quarter 2:* Quarter 3: Define inverse operation. Know how inverse operations can be used in solving one-variable equations. Apply rules of the form x + p = q and px = for cases in which p, q and x are all nonnegative rational numbers, to solve real world and mathematical problems.(There is only one unknown quantity.) Develop a rule for solving one- step equations using inverse operations with nonnegative rational coefficients. Solve and write equations for real-world mathematical problems containing one unknown. Quarter 4: Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
CCSS Math Pacing Guide Grade 6 Grade Level: 6th Standard with code: 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world 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. Domain: Expressions and Equations Cluster: Reason about and solve one-variable equations and inequalities. Quarter 1: Quarter 2: Quarter 3: Identify the constraint or condition in a real-world or mathematical problem in order to set up an inequality. Recognize that inequalities of the form x > c or x < c have infinitely many solutions Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Represent solutions to inequalities or the form x > c or x < c, with infinitely many solutions, on number line diagrams Quarter 4: Make sense of problems and persevere in solving them Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given a real world problem involving two quantities that change in relationship to one another, Represent the context using graphs, tables, and equations, Explain the connections among the representations using mathematical vocabulary including dependent and independent variables. Dependent variables Independent variables Students know: Roles of dependent and independent variables, Correct translation between verbally stated situations and mathematical symbols and notation. Students understand that/are able to: Represent real world problems involving two quantities that change in relationship to one another using equations, graphs, and tables, Use mathematical vocabulary to explain connections among representations of function contexts, Analyze and interpret the relationship between the independent and the dependent variable in a given situation. EE6.EE.9. N/A EE6.EE.9. N/A
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given real world and mathematical problems involving surface area, Use models of the relating net of the 3-D figure to explain and justify solutions and solution paths. Nets Surface area Students know: Measureable attributes of objects, specifically area and surface area, Strategies for representing the surface area of a 3-D shape as a 2-D net. Students understand that/are able to: Communicate the relationships between rectangular models of area and multiplication problems, Model the surface area of 3-D shapes using 2-D nets, Accurately measure and compute area of triangles and rectangles, Strategically and fluently choose and apply strategies for finding surface areas of 3-D figures. EE6.G.4. Identify common shapes. Level IV Students will: EE6.G.4. Relate real-world items as three-dimensional shapes to their representations. Ex. Match the picture of the soda can to the picture of the cylinder, etc. Ex. Identify in the environment items that are three-dimensional when presented with in the two-dimensional format. Level III Students will: EE6.G.4. Identify common three-dimensional shapes. Ex. When presented with a sphere and a cube, name the three-dimensional shape. Ex. Identify spheres and cubes in the classroom. Level II Students will: EE6.G.4. Sort three-dimensional shapes and two-dimensional shapes. Ex. When given a bag of three-dimensional shapes and their two-dimensional pictures, sort into the appropriate three-dimensional or two-dimensional shape. Ex. Label objects as three-dimensional and two-dimensional shapes in the classroom. Level I Students will: EE6.G.4. Match shapes. Ex. When given a picture of a shape, find like shapes in the classroom. Ex. Shape BINGO.
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given a set of numerical data, Determine and interpret measures of center (mean and median) and variability (interquartile range and mean absolute deviation). Measures of center Measures of variation Students know: Measures of center (mean and median) and how they are affected by the data distribution, Measures of variability (interquartile range and mean absolute deviation) and how they are affected by data distribution. Students understand that/are able to: Determine measures of center and variability for a set of numerical data, Interpret measures of center and variability for a set of numerical data. EE6.SP.3. N/A EE6.SP.3. N/A
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given a set of numerical data, Organize and display the data using plots on a number line, including dot plots, histograms, and box plots. Dot plot Histograms Box plots Students know: Techniques for constructing dot plots, histograms, and box plots. Students understand that/are able to: Organize and display data using dot plots, histograms, and box plots. EE6.SP.4. N/A (See EE6.SP.1-2) EE6.SP.4. N/A (See EE6.SP.1-2)