PVMS 8th Grade Math Year-at-a-Glance Completed 1-14-14 Quarter 1 Quarter 2 Quarter 3 Quarter 4 8.NS.1 8.NS.2 8.EE.1 8.EE.2 8.EE.3 8.EE.4 8.EE.5 8.EE.6 8.EE.7 8.EE.8 8.F.1 8.F.2 8.F.3 8.F.4 8.F.5 8.SP.1 8.SP.2 8.SP.3 8.SP.4 8.G.1 8.G.2 8.G.3 8.G.4 8.G.5 8.G.6 8.G.7 8.G.8 8.G.9
CCSS Math Pacing Guide Grade 8 Grade Level: 8th Standard with code: 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Domain: The Number System Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers. Quarter 1: Approximate irrational numbers as rational numbers. Approximately locate irrational numbers on a number line. Estimate the value of expressions involving irrational numbers using rational approximations. (For example, by truncating the decimal expansion of√2 , show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.) Quarter 2: 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.
Grade Level: 8th Standard with code: 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Quarter 1: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares. Evaluate cube roots of small perfect cubes. Know that the square root of 2 is irrational. Quarter 2: 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. Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: When presented with an equation of the form x2= p, Translate this to the form x = plus or minus square root p and evaluate the expression when p is a perfect square. When presented an equation Square root Cube root Irrational Perfect squares Perfect cubes Students know: Characteristics of rational and irrational numbers, Strategies for powering, Strategies for finding and Students understand that/are able to: Fluently determine the square roots of small perfect squares and cube roots of small perfect cubes, Translate equations in the form x2 = p to the EE8.EE.1-4. Compose and decompose numbers to three digits. Level IV Students will: EE8.EE.1-4. Use powers of 10 to compose and decompose numbers. Ex. Recognize 3 x 102 = 300 as another way to state 3 x 100 = 300. Ex. 5 x 101 = ___. Level III Students will: EE8.EE.1-4. Compose and decompose numbers to three digits. Ex. 300 + 50 + 7 = _____. Ex. 57 = _____ + _____. Ex. Show that twelve is one 10 and two ones, or 12 ones, or seven ones and five ones, etc.
Grade Level: 8th Standard with code: 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Quarter 1: Express numbers as a single digit times an integer power of 10. Use scientific notation to estimate very large and/or very small quantities. Compare quantities to express how much larger one is compared to the other. Quarter 2: 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. Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Standard with code: 8.EE.7b Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Quarter 1: Quarter 2: Solve linear equations with rational number coefficients. Solve equations whose solutions require expanding expressions using the distributive property and/ or collecting like terms. 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. Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Solve linear equations in Linear equation Students know: The properties of Students understand that/are able to: EE8.EE.7. Solve algebraic expressions using simple addition Level IV Students will: 8.EE.7. Solve algebraic expressions using two-digit addition and subtraction. Ex. Solve 20 + x, when x =25.
one variable including when manipulation of the expressions in the equation becomes necessary to obtain a solution, if one exists, Provide examples of linear equations which have one solution, infinitely many solutions, or no solutions and use these to describe the characteristics of such equations. operations and equality (Tables 3 and 4) and their appropriate application, The meaning of an equation having no solutions or an infinite number of solutions. Accurately perform algebraic manipulation on equations and justify that each manipulation was allowed by the properties of the operations and equality (Tables 3 and 4). Linear relationships are characterized by a constant rate of change, When algebraic manipulations are done on linear equations in one variable, the result may be x = a, a = a, or a = b, and each of these results means something different, The solutions arrived at through algebraic manipulations on an equation, should make the original equation true. and subtraction. Ex. Solve 35 – x, when x = 12. Level III Students will: EE8.EE.7. Solve algebraic expressions using simple addition and subtraction. Ex. Mark had 10 dollars and needs 15. How many more dollars does he need? Ex. Given a set of basketballs, some in a bag and five outside of the bag, solve for find the total number of basketballs in the set when the bag contains two basketballs. Ex. Find the difference when given the total and the solution (e.g., A student has 10 chocolate chips and a bag of chocolate chips. Solve for the amount the bag contains when the total is 25.) Level II Students will: EE8.EE.7. Solve simple addition and subtraction problems. Ex. Playing a game, roll two dice and add up the dots (dice with dots or dice with numerals). Ex. Using a pictorial representation of numbers, solve the addition and subtraction problems (i.e. three balloons minus one balloon). Level I Students will: EE8.EE.7. Distinguish between a letter and a number. Ex. When asked to write their home address, identify between the letters and numbers in the address. Ex. When a book is read to them, identify the page number. Ex. When looking in a telephone book identify the telephone number vs. the name. CCSS Math Pacing Guide Grade 8 Grade Level: 8th
in graphical or algebraic form, Produce the coordinates of the point of intersection of the two lines and explain the relationship of this point to the two equations when taken simultaneously. Given a real world or mathematical situation involving two linear relationships, Model the situation with linear equations, find the intersection point of the two lines, and interpret this point in terms of the original context. The properties of operations and equality (Tables 3 and 4) and their appropriate application, Graphing techniques for linear equations (using points, using slope-intercept form, using technology), Substitution and addition/subtraction techniques for algebraically finding the solution to simultaneous linear equations. Accurately graph linear equations on coordinate axes (using points, form, or technology), Accurately solve systems of two linear equations algebraically for their common point. Any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true, Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions. CCSS Math Pacing Guide Grade 8 Grade Level: 8th Standard with code: 8.EE.8bc Analyze and solve pairs of simultaneous linear equations. intercept
example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Domain: Functions Cluster: Define, evaluate, and compare functions. Quarter 1: Quarter 2: Quarter 3: Identify functions algebraically including slope and y intercept. Identify functions using graphs. Identify functions using tables. Identify functions using verbal Descriptions Compare and Contrast 2 functions with different representations. Draw conclusions based on different representations of functions. 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given two functions in a contextual situation that are Function Students know: Relationships Students understand that/are able to: EE8.F.1-3. Given a function table, identify the missing number. Level IV Students will: EE8.F.1-3. Given a function table, identify the rule and express the rule for the missing variable (e.g., n times 2).
represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions), Use logical reasoning and mathematical vocabulary to interpret the context and compare and contrast the properties of the functions, (e.g., rate of change or slope). between graphs, tables and equations, The role of unit rate in functional representations. Convert among a contextual situation involving a functional relationship, the graph of that relationship, and the equation for that relationship. Functions are relationships between two variables that have a unique characteristic, that being, for each input there exists exactly one output, Functions can be represented in a variety of ways (graphs, tables and equations), each of which provides unique perspectives of the relationship between the variables. Ex. Given a function table, identify the rule to find the missing number.* Ex. Given a function table, identify the rule to find the missing number.* Level III Students will: EE8.F.1-3. Given a function table, identify the missing number. Ex.* Level II Students will: EE8.F.1-3. Identify the relationship between two numbers. Ex. Given choices, tell the relationship between two numbers (e.g., How much more is five than three? Five is two more than three.). Ex. Identify the relationship between two given numbers (e.g., If you double four, you have eight). Level I Students will: EE8.F.1-3. Given a sequence, match the element of a sequence. Ex. Given the sequence 1, 2, 1, 2 and a 1, match to number 1. Ex. Given a sequence of triangle, circle, triangle, circle and a circle, match the circle. *Refer to the Common Core Essential Elements document for diagram. CCSS Math Pacing Guide Grade 8 Grade Level: 8th
Standard with code: 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Domain: Functions Cluster: Use functions to model relationships between quantities. Quarter 1: Quarter 2: Quarter 3: Analyze a graph and describe the functional relationship between two quantities using the qualities of the graph. Sketch a graph given a verbal description of its qualitative features. Interpret the relationship between x and y values by analyzing a graph. 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given graphical Functional Students know: Students understand that/are able to: EE8.F.5. Describe how a graph Level IV Students will: EE8.F.5. Describe how a graph represents a relationship between two quantities and use the
Domain: Geometry Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software. Quarter 1: Quarter 2: Quarter 3: Quarter 4: Define similar triangles Define and identify transversals Identify angles created when parallel line is cut by transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.) Justify that the sum of interior angles equals 180. (For example, arrange three copies of the same triangle so that the three angles appear to form a line.) Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles. Use Angle-Angle Criterion to prove similarity among triangles. (Give an argument in terms of transversals why this is so.) 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Use knowledge of straight angles and mathematical reasoning to, Create informal arguments concerning: facts about the Informal arguments Angle sum Students know: Straight angles = 180 degrees, Definitions for supplementary angles Students understand that/are able to: Use prior knowledge of angles, angle measurement, and mathematical EE8.G.5. Compare measures of angles to a right angle (greater than, less than, or equal to). Level IV Students will: EE8.G.5. Compare measures of angles formed by intersecting lines. Ex. Given intersecting lines, identify linear pair angles. Ex. Given a pair of parallel lines intersected by a third line, identify angles that are the same measure. Level III Students will:
Define key vocabulary: square root, Pythagorean Theorem, right triangle, legs a & b, hypotenuse, sides, right angle, converse, base, height, proof. Be able to identify the legs and hypotenuse of a right triangle. Explain a proof of the Pythagorean Theorem. Explain a proof of the converse of the Pythagorean Theorem. 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given a proof of the Pythagorean Theorem, Use mathematical reasoning and vocabulary to verbally explain the theorem and its Pythagorean Theorem Converse Students know: Pythagorean Theorem Students understand that/are able to: Use mathematical reasoning and vocabulary to verbally explain a EE8.G.6-8. N/A EE8.G.6-8. N/A
solutions and solution paths for finding side lengths in right triangles within the problem contexts. hypotenuse). Represent real-world and mathematical contexts involving right triangles in a variety of formats (e.g., drawings, equations), Justify solutions and solution paths using conceptual understandings and vocabulary related to the Pythagorean Theorem (e.g., right angle, hypotenuse). The properties of right triangles can be used to solve problems. CCSS Math Pacing Guide Grade 8 Grade Level: 8th Standard with code: 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Domain: Geometry Cluster: Understand and apply the Pythagorean Theorem.
Quarter 1: Quarter 2: Quarter 3: Quarter 4: Recall the Pythagorean Theorem and its converse. Determine how to create a right triangle from two points on a coordinate graph. Use the Pythagorean Theorem to solve for the distance between the two points. 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given real-world and mathematical problems that can be represented on a coordinate plane, Apply the Pythagorean Pythagorean Theorem Students know: Pythagorean Theorem, Operations and labeling within a Students understand that/are able to: Solve equations involving one variable and square EE8.G.6-8. N/A EE8.G.6-8. N/A
Domain: Geometry Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Quarter 1: Quarter 2: Quarter 3: Quarter 4: Identify and define vocabulary: cone, cylinder, sphere, radius, diameter, circumference, area, volume, pi, base, height Know formulas for volume of cones, cylinders, and spheres Compare the volume of cones, cylinders, and spheres. Determine and apply appropriate volume formulas in order to solve mathematical and real-world problems for the given shape. Given the volume of a cone, cylinder, or sphere, find the radii, height, or approximate for π 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given real-world and mathematical problems involving volumes of cones, cylinders, and Cone Cylinder Sphere Students know: Measurable attributes of objects, specifically Students understand that/are able to: Communicate the relationships between models of volume and EE8.G.9. Identify volume of common measures (cups, pints, quarts, Level IV Students will: EE8.G.9. Apply knowledge of volume. Ex. Use simple units to fill a container with accurate counting. Ex. Uses cubes to fill a small container and estimate the number of cubes it took by mathematical reasoning (addition or multiplication of row/column).
Domain: Statistics and Probability Cluster: Investigate patterns of association in bivariate data. Quarter 1: Quarter 2: Quarter 3: Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association Construct scatter plots for bivariate measurement data Interpret scatter plots for bivariate (two different variables such as distance and time) measurement data to investigate patterns of association between two quantities 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given sets of bivariate measurement data or contextual situations in which bivariate measurement data must be Scatter plots Bivariate measurement Students know: Representations for bivariate data and techniques for Students understand that/are able to: Construct a scatter plot to represent a set of EE8.SP.1-3. N/A EE8.SP.1-3. N/A
collected, Construct and interpret scatter plots, Describe visual patterns observed, (e.g., clustering, outliers, positive or negative association, linear, and association). data Clustering Outliers Positive and negative association Linear and non-linear association constructing each (e.g., tables, scatter plots). bivariate data, Use mathematical vocabulary to describe and interpret patterns in bivariate data. Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated, Negative association in bivariate data can be a very strong association but is an inverse relationship. CCSS Math Pacing Guide Grade 8 Grade Level: 8th Standard with code: 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
Domain: Statistics and Probability Cluster: Investigate patterns of association in bivariate data. Quarter 1: Quarter 2: Quarter 3: Know straight lines are used to model relationships between two quantitative variables Informally assess the model fit by judging the closeness of the data points to the line. Fit a straight line within the plotted data 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 Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors Students: Given a variety of scatterplots representing bivariate data, Determine if the plots which Scatter plot Linear association Students know: Patterns found on scatterplots of bivariate data, (e.g., Students understand that/are able to: Construct a scatter plot to represent a EE8.SP.1-3. N/A EE8.SP.1-3. N/A
suggest a linear relationship, and informally fit a straight line to the data, assess the model fit by judging the closeness of the data points to the line. Quantitative variable linear/non-linear, positive/negative), Strategies for informally fitting straight lines to bivariate data with a linear relationship, Methods for finding the distance between two points on a coordinate plane and between a point and a line. set of bivariate data, Use mathematical vocabulary to describe and interpret patterns in bivariate data, Use logical reasoning and appropriate strategies to draw a straight line to fit data that suggest a linear association, Use mathematical vocabulary, logical reasoning, and closeness of data points to a line to judge the fit of the line to the data. Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated, When visual examination of a scatter plot suggests a linear association in the data, fitting a straight line to the