2012 8th grade_math_curriculum_guide


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2012 8th grade_math_curriculum_guide

  1. 1. 8th Grade Math Curriculum Map 8th Grade Math Curriculum Map IntroductionThis document contains all mandated 2010 Arizona Mathematical Standards for 8th grade mathematics. The standards have been organized intounits and clusters. The units represent the major domain under which the identified standards fall. The cluster represents the collection of similarconcepts within the larger domain. Within these units and clusters the performance objectives have been sequenced to represent a logical progressionof the content knowledge. It is expected that all teachers follow the sequence of units and clusters as described in the following document. OrganizationApproximate TimeApproximate times are based on a 60-minute instructional session for grades 6-8. All units and clusters must be taught prior to the 2013 AIMSassessment.Essential QuestionsEssential Questions are to be posed to the students at the beginning of the cluster and revisited throughout the cluster. They are designed to facilitateconceptual development of the content and can be used as a tool for making connections, higher order thinking and inquiry. The students should beable to answer these on their own by the end of the cluster.Big IdeasBig Ideas are the essential understandings that are critical for students’ learning. These are the enduring understandings we want students to carrywith them from grade level to grade level. Answering the Essential Questions is indicative of a student mastering the Big Idea, however they are notalways synonymous. Thus, in cases that the answer to the Essential Question does not include all components of the Big Idea, the Big Idea (for teacheruse) has been provided in italics.Common MisconceptionsThese are common misunderstandings students bring to the learning process. Being aware of such misconceptions allows us to plan for them duringinstruction.Content Standards and Mathematical PracticesThis document has been organized by content standards and mathematical practices. The content standards are those that represent knowledgespecific to the mathematical standard (The five domains). The mathematical practices describe varieties of expertise that mathematics educators atall levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance inmathematics education. The content standards and mathematical standards have been paired to represent possible combinations of content standardswith mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, thepairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to adeeper level of understanding and/or should be connected to the other standards in the cluster.9/10/2012 1 Isaac Elementary School District
  2. 2. 8th Grade Math Curriculum MapCommon Core/Cross CurricularThe standards in the Common Core/Cross Curricular column represent possible reading, writing, math and language standards that can be reinforcedor taught through the mathematical content standards with which they are paired.PriorityWith input from grade level teachers, standards have been prioritized in two ways. The content standards have been prioritized using a three-pointscale. Essential standards represent those that are heavily weighted on state/national exams, foundational, and/or applicable in multiple contexts.Important standards are those that are applicable in many contexts and less heavily weighted on state/national exams. Useful standards are thosewith the least weight on state/national exams and are likely only useful in a specific context. This is denoted in the priority column with the codes E(essential), I (important) and U (useful). This label applies to the content standards only. The skill/process standards that are a priority for thisgrade level are highlighted in blue and are expected to be mastered at this grade level.Key VocabularyThe key vocabulary that should be taught for each of the performance objectives is listed under key vocabulary. These vocabulary words are codedas tier one (1), tier two (2) or tier three (3). Tier one words are those that are very common and should not be explicitly taught. Tier two words arehigh utility words that can be used across content areas or contexts. Tier three words are content specific words.ResourcesThe two types of resources listed are the Web Resources resources and the Core Resources. All are suggestions that teachers may use to supportinstruction. They are aligned to the standards listed in the same row. The web resources are useful Internet links that can be used for the teacher’sedification prior to instruction or as a tool during instruction. The core resources are suggested pages from the adopted texts.Unit/Cluster ProjectThe Unit/Cluster Projects are possible projects that teachers can use to support students in making connections, critical thinking, higher order thinking,and/or spiraling curriculum. Unit projects support standards from all clusters within a unit while cluster project support the standards in a particularcluster. While it is not required that a teacher do a project with every unit or cluster these resources will support project-based instruction andpractice should the teacher choose to implement them.AssessmentThe assessment section of the map has been left blank for teachers to plan the dates that they will give a formative assessment for the cluster. It isexpected that each cluster be assessed using a common formative assessment.OtherStandards may appear more than once. Each time they should be taught within the context of the cluster and/or revisited to a deeper level ofknowledge. Underlined segments of a standard indicate an additional piece of the standard that was likely not covered in previous clusters.[Brackets] will occasionally appear though out the document and indicate clarification of the Standard. Bracketed information is not a part of thestandard itself.9/10/2012 2 Isaac Elementary School District
  3. 3. 8th Grade Math Curriculum Map Unit: Number Sense Cluster: The Real Number System Approximate Time: 1week Essential Questions Big Ideas  What are real numbers?  Real numbers are classified as either rational or irrational numbers.  What is a rational number and irrational number?  Rational numbers include all integers and non-integers (decimal numbers) that either repeat or terminate.  How do we compare and order real numbers?  Irrational numbers can be estimated to the nearest integer or to a given place value to increase accuracy of the approximation.9/10/2012 3 Isaac Elementary School District
  4. 4. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C1PO1 Compare and order real Ascending order MC: Lesson 2-2 numbers including very large and Descending order small integers and decimals and Counting number fractions close to zero. Integers Natural number Real number Whole number *S1C1PO4 Model and solve Absolute value MC: Lesson 1-3 problems involving absolute value. 8.NS.1. Know that numbers that are 8.MP.2 8.EE.4 Approximate KA: Converting- not rational are called irrational. 8.MP.6 8.EE.7b Estimation repeating-decimals-to- Understand informally that every 8.MP.7 6-8.RST.4 Exponents fractions-1 number has a decimal expansion; for 6-8.RST .7 Irrational numbers rational numbers show that the Iterative KA: Converting- decimal expansion repeats Order repeating-decimals-to- eventually, and convert a decimal Rational numbers fractions-2 expansion which repeats eventually Real numbers into a rational number. Scientific notation Square Square root Standard notation 8.NS.2. Use rational approximations 8.MP.2 8.G.7 Decimal KA: Estimating Square of irrational numbers to compare the 8.MP.4 8.G.8 Fraction Roots to the Hundredths size of irrational numbers, locate 8.MP.7 6-8.RST.5 Non-Perfect Square them approximately on a number 8.MP.8 ET08-S1C2-01 Percent line diagram, and estimate the value Perfect Square of expressions (e.g., π2). For Pi example, by truncating the decimal Repeating Decimal expansion of √2, show that √2 is Repetend between 1and 2, then between 1.4 Terminating Decimal and 1.5, and explain how to continue Truncate on to get better approximations Unit Project: Assessment:9/10/2012 4 Isaac Elementary School District
  5. 5. 8th Grade Math Curriculum Map Unit: Number Sense Cluster: Numerical Operations Approximate Time: 1 week Essential Questions Big Ideas  Describe how multiplying or dividing a number by less than  Estimate, compute, determine reasonable answers. one affects the number?  Choose real numbers to solve problems, radical, decimal, fraction, and percents.9/10/2012 5 Isaac Elementary School District
  6. 6. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C2PO1 Solve problems with Composite number factors, multiples, divisibility or Factor remainders, prime numbers and Multiple composite numbers. Divisible Remainder Prime number *S1C2PO2 Describe the effect of Divide multiplying and dividing a rational Dividend number by: Divisor  A number less than zero Factor  A number between zero and one Multiply  One Product Quotient  A number greater than one Rational number *S1C2PO5 Simplify numerical Absolute value expressions using the order of Cube root operations that include grouping Evaluate symbols, square roots, cube roots, Exponents absolute values and positive Grouping symbols exponents. Numerical expressions Order of operations Radican Simplify Square root *S5C1PO1 Create an algorithm to MC: Lesson 1-7 solve problems involving indirect measurements, using proportional MC: Lesson 8-3 reasoning, dimensional analysis and the concepts of density and rate. Unit Project: Assessment:9/10/2012 6 Isaac Elementary School District
  7. 7. 8th Grade Math Curriculum Map Unit: Expressions & Equations Cluster: Exponents and Radicals Approximate Time: 1.5 week Essential Questions Big Ideas  How do I evaluate an expression?  To evaluate an expression substitute in values for given variables and follow order of operations.  When do we use the laws of exponents?  Laws of exponents are utilized to simplify expressions when base numbers or variables are the same.  What are the laws of exponents?  There are three laws of exponents: product property, the quotient property and the power property.  How do exponents and radicals relate to one another?  Exponents and radicals are inverse operations.9/10/2012 7 Isaac Elementary School District
  8. 8. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S3C3PO2 Evaluate an expression Expression MC: Lesson 1-2 containing variables by substituting Rational number rational numbers for the variables. Substitute Variable 8.EE.1. Know and apply the 8.MP.2 Equivalent KA: Exponent Rules Power MC: Lesson 2-9 properties of integer exponents to 8.MP.5 Evaluate to a Power generate equivalent numerical 8.MP.6 Exponents expressions. For example, 3 ×3 =3– 2 –5 8.MP.7 Integers KA: Exponent Rules 2 3 = 1/33 = 1/27 Numerical expression Rational numbers 8.EE.2. Use square root and cube 8.MP.2 8.G.7 Coefficient MC: Lesson 3-1 root symbols to represent solutions to 8.MP.5 8.G.8 Constant 2 equations of the form x = p and x = 3 8.MP.6 6-8.RST.4 Cube root MC: Lesson 3-2 p, where p is a positive rational 8.MP.7 Equation number. Evaluate square roots of Evaluate small perfect squares and cube roots Irrational number of small perfect cubes. Know that √2 Perfect cube is irrational. Perfect square Simpliest form Simplified expression Solution Square root Rational number Unit Project: Assessment:9/10/2012 8 Isaac Elementary School District
  9. 9. 8th Grade Math Curriculum Map Unit: Expression and Equations Cluster: Scientific Notation Approximate Time: 1 week Essential Questions Big Ideas  What is scientific notation used for?  Scientific notation is how we express the value of very large or very small numbers.  How do we use scientific notation to express equivalent forms of  We can convert standard notation to scientific notation and visa rational numbers? versa.9/10/2012 9 Isaac Elementary School District
  10. 10. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.EE.3. Use numbers expressed in the 8.MP.2 Base MC: Lesson 2-10 form of a single digit times an 8.MP.5 Coefficient integer power of 10 to estimate 8.MP.6 Convert very large or very small quantities, Estimate and to express how many times as Mathematical much one is than the other. For operations example, estimate the population of Negative Exponent 8 the United States as 3×10 and the Positive Exponent population of the world as 7×10 and Power of 10 determine that the world populations Scientific Notation is more than 20 times larger. Standard Notation 8.EE.4. Perform operations with 8.MP.2 8.NS.1 Base numbers expressed in scientific 8.MP.5 8.EE.1 Coefficient notation, including problems where 8.MP.6 ET08-S6C1-03 Convert both decimal and scientific notation Estimate are used. Use scientific notation and Mathematical choose units of appropriate size for operations measurements of very large or very Negative Exponent small quantities (e.g., use millimeters Positive Exponent per year for seafloor spreading). Power of 10 Interpret scientific notation that has Scientific Notation been generated by technology. Standard Notation Unit Project: Assessment:9/10/2012 10 Isaac Elementary School District
  11. 11. 8th Grade Math Curriculum Map Unit: Expressions & Equations Cluster: Solving Linear Equations and Graphing Inequalities Approximate Time: 3 weeks Essential Questions Big Ideas  How can we use equations to represent real life sitautions?  Algebraic equations, inequalities, and graphs are representative of real life situations.  What are the different ways that linear equations can be expressed?  Linear equations can be expressed as a graph, an equation, or a table of values.9/10/2012 11 Isaac Elementary School District
  12. 12. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S4C4PO2 Solve geometric Cross Multiply problems using ratios and Equivalence proportions. Equations Ratio Proportions *S3C4PO2 Solve problems involving Equation simple interest rates. Principal Rate Simple interest *S1C2PO3 Solve problems involving Interest rate KA: Finding Unit Rates percent increase, percent decrease Mark down and simple interest rates. Mark up KA: Solving Percent Percent change Problems Profit Simple interest KA: Finding Unit Price Tax Tip KA: Solving Percent Problems 2 KA: Finding a Percent of a Number 8.EE.7 Solve linear equations in one 8.MP.2 8.F.3 Algebraic Expression KA: Solving equations MC: Lesson 1-9 variable. 8.MP.5 8.NS.1 Balance with variables on both 8.MP.6 6-8.RST Coefficient sides. a. Give examples of linear 8.MP.7 ET08-S1C3-01 Combine Like Terms MC: Lesson1-10 equations in one variable with one Constant KA: Solving two step solution, infinitely many solutions, or Distributive property equations no solutions. Show which of these Equation MC: Lesson 8-1: possibilities is the case successively Equivalent Simplifying transforming the given equation into Inverse operations expressions simpler forms, until an equivalent Isolate equation of the form x = a, a = a, Like Terms or a = b results (where a and b are Linear equations MC: Lesson 8-2: different numbers). Multi-Step equation Two Step Equations Non-Linear b. Solve linear equations with Solution rational number coefficients, Term MC: Lesson 8-4: including equations whose solutions Equations with require expanding expressions using variables on both the distributive property and sides collecting like terms.9/10/2012 12 Isaac Elementary School District
  13. 13. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S3C3PO5 Graph an inequality on Coefficient KA: Graphing a number line. Greater than (>) inequalities number line Greater than or equal (>) Inequality Isolate Less than (<) Less than or equal (<) Number line Variable Unit Project: Assessment:9/10/2012 13 Isaac Elementary School District
  14. 14. 8th Grade Math Curriculum Map Unit: Geometry Cluster: Pythagorean Theorem Approximate Time: 1 week Essential Questions Big Ideas  How do we apply the Pythagorean Theorem to calculate the distance of a  The Pythagorean Theorem can be used to calculate line segment? the distance between two points.  The Pythagorean Theorem can be used to find the distance between two points in two-dimensional figures and three-dimensional objects.  How can the Pythagorean Theorem be applied to triangles?  The Pythagorean Theorem can be used to find the missing side of a right triangle  What is a Pythagorean Triple?  A Pythagorean Triple is set of three positive integers that satisfy the Pythagorean Theorem.9/10/2012 14 Isaac Elementary School District
  15. 15. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.G.6 Explain a proof of the 8.MP.3 6-8.WHST.2a-f Approximation KA: Introduction to the Pythagorean Theorem and its 8.MP.4 ET08-S1C2-01 Base Pythagorean Theorem converse. 8.MP.6 Converse 8.MP.7 Equaation Exponents Hypotenuse Irrational number Isolate Leg Pythagorean triples Right triangle Square root Substituation 8.G.7 Apply the Pythagorean 8.MP.1 8.NS.2 Coordinate Plane KA: Pythagorean MC: Lesson 3-5, 3- Theorem to determine unknown side 8.MP.2 ET08-S2C2-01 Equation Theorem Example 6 lengths in right triangles in real- 8.MP.4 Hypotenuse world and mathematical problems in 8.MP.5 Inverse Operations KA: More two and three dimensions. 8.MP.6 Isolate Pythagorean Theorem 8.MP.7 Leg Examples Perfect Square Pythagorean triples Radical Sign Radican Right triangle Square Root Square root Substituation Three-dimension object Two-dimensions object 8.G.8 Apply the Pythagorean 8.MP.1 8.NS.2 Converse KA: Midpoint Formula MC: Lesson 3-7 Theorem to find the distance 8.MP.2 ET08-S6C1-03 Coordinate plan between two points in a coordinate 8.MP.4 Distance system. 8.MP.5 Midpoint 8.MP.6 Origin 8.MP.7 Pythagorean triples Quadrants Right triangle Slope *S4C3P01: Make and test a Midpoint conjecture about how to find the Coordinate plane midpoint between any two points in Origin the coordinate plane. Quadrants Conjecture9/10/2012 15 Isaac Elementary School District
  16. 16. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core Unit Project: Assessment:9/10/2012 16 Isaac Elementary School District
  17. 17. 8th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Graphing linear equations Approximate Time: 3 weeks Essential Questions Big Ideas  How do we use linear equations in real life?  We use linear equations to represent a situation and the situation can be expressed graphically, as a table of values, or as an equation.  What is slope?  Slope (m) is a change in the independent variable. In math, it can be recognized as rise/run or .  What are the four types of slope?  We recognize the slope by examing the relationship between the independent and dependent variable.  How do we use slope to make arguments?  We can use slope to make conjectures about geometric figures as well as similarity of equations.9/10/2012 17 Isaac Elementary School District
  18. 18. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.EE.5. Graph proportional 8.MP.1 8.F.2 Negative slope KA: Plotting Ordered relationships, interpreting the unit 8.MP.2 8.F.3 Non-Linear Pairs rate as the slope of the graph. 8.MP.3 6-8.RST.7 Origin Compare two different proportional 8.MP.4 6- 8.WHST.2b Positive slope relationships represented in different 8.MP.5 SC08-S5C2-01 Proportion ways. For example, compare a 8.MP.6 SC08-S5C2-05 Proportional distance-time graph to a distance-time 8.MP.7 relationships equation to determine which of two 8.MP.8 Quadrants moving objects has greater speed. Rate of change Simpliest form Slope-Intercept form Solution Term Undefined slope X-Intercept Y-intercept Zero Slope 8.EE.6. Use similar triangles to 8.MP.2 8.F.3; 8.G.4 Coordinate plane explain why the slope m is the same 8.MP.3 6-8.RST.3 Equivalence between any two distinct points on a 8.MP.4 6-8.WHST.1b Orgin non-vertical line in the coordinate 8.MP.5 ET08-S1C2-01 Quadrant plane; derive the equation y = mx 8.MP.7 ET08-S6C1-03 Rate of change for a line through the origin and the 8.MP.8 Similar triangles equation y = mx + b for a line Slope intercepting the vertical axis at b. Slope-Intercept form X-intercept Y-intercept Unit Project: Assessment:9/10/2012 18 Isaac Elementary School District
  19. 19. 8th Grade Math Curriculum Map Unit: Functions Cluster: Evaluating Functions Approximate Time: 3 weeks Essential Questions Big Ideas  What is a function? How do you tell if a graph represents a function?  A function is a relationship between variables where each X (input) has exactly one Y (output). We can determine whether a graph is a function by using the vertical line test.  What are the different ways to represent a function?  A function can be represented with a table, a graph, a verbal description, or an equation.  How can functions be used to serve real world problems?  A function can be utilized to make conjectures about predicted outcomes.9/10/2012 19 Isaac Elementary School District
  20. 20. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.F.1 Understand that a function is a rule 8.MP.1 SC08-S5C2-05 Function KA: Testing if a MC: Lesson 9-2: that assigns to each input exactly one 8.MP.2 Function table relationship is a function Functions output. The graph of a function is the set of 8.MP.6 Input ordered pairs consisting of an input and the Ordered pair KA: Graphical Relations corresponding output (Function notation is Origin and Functions MC: Lesson 9-3: not required in Grade 8). Output Graphing Slope PM: Determining if a functions X-Intercept relationship is a function Y-Intercept 8.F.3 Interpret the equation y = mx + b as 8.MP.2 8.EE.5; 8.EE.7a Function KA: Graphing a line in MC: Lesson 10-1: defining a linear function, whose graph is a 8.MP.4 6-8.WHST.1b Interpret slope intercept form Linear & straight line; give examples of functions that 8.MP.5 ET08-S6C1-03 Linear functions Nonlinear are not linear. For example, the function A = 8.MP.6 Non-linear functions Functions 2 s giving the area of a square as a function of 8.MP.7 Ordered pair its side length is not linear because its graph Origin contains the points (1,1), (2,4) and (3,9), Quadrant which are not on a straight line. Rate of change Slope Slope-Intercept form 8.F.2 Compare properties of two functions 8.MP.1 8.EE.5; 8.F.2 Algebraic expression each represented in a different way 8.MP.2 6-8.RST.7 Domain (algebraically, graphically, numerically in 8.MP.3 6-8.WHST.1b Function tables, or by verbal descriptions). For 8.MP.4 ET08-S1C3-01 Function table example, given a linear function represented 8.MP.5 Linear equation by a table of values and a linear function 8.MP.6 Linear function represented by an algebraic expression, 8.MP.7 Non-Linear function determine which function has the greater rate 8.MP.8 Point-Slope form of change. Proportional Quadratic function Range Rate of change Slope-Intercept form Standard form 8.F.4. Construct a function to model a linear 8.MP.1 8.EE.5 Function relationship between two quantities. 8.MP.2 8.SP2 Function table Determine the rate of change and initial 8.MP.3 8.SP.3 Initial value value of the function from a description of a 8.MP.4 ET08-S1C2-01 Intercept relationship or from two (x, y) values, 8.MP.5 SC08-S5C2-01 Interpret including reading these from a table or 8.MP.6 SC08-S1C3-02 Linear relationship from a graph. Interpret the rate of change 8.MP.7 Ordered pair and initial value of a linear function in terms 8.MP.8 Origin of the situation it models, and in terms of its Quadrant graph or a table of values. Rate of change Slope9/10/2012 20 Isaac Elementary School District
  21. 21. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.F.5. Describe qualitatively the functional 8.MP.2 6-8.WHST.2a-f Analyzing MC: Lesson 9-6: relationship between two quantities by 8.MP.3 ET08-S1C2-01 Decreasing Graphing in analyzing a graph (e.g., where the function 8.MP.4 SC08-S5C2-05 Function slope-intercept is increasing or decreasing, linear or 8.MP.5 Increasing form nonlinear). Sketch a graph that exhibits the 8.MP.6 Linear relationship qualitative features of a function that has 8.MP.7 Nonlinear been described verbally. relationship Qualitative 8.SP.3. Use the equation of a linear model 8.MP.2 8.EE.5 Bivariate MC: Lesson 9-4: to solve problems in the context of bivariate 8.MP.4 8.F.3 measurement Slope measurement data, interpreting the slope 8.MP.5 8.F.4 Equation and intercept. For example, in a linear model 8.MP.6 ET08-S1C3-03 Interpreting for a biology experiment, interpret a slope of 8.MP.7 ET08-S2C2-01 Linear nmodel MC: Extend 9-5 1.5 cm/hr as meaning that an additional hour Slope of sunlight each day is associated with an Y-Intercept additional 1.5 cm in mature plant height. Unit Project: Assessment:9/10/2012 21 Isaac Elementary School District
  22. 22. 8th Grade Math Curriculum Map Unit: Expressions & Equations Cluster: System of Equations Approximate Time: 2 weeks Essential Questions Big Ideas  What is a system of equations?  A system of equations is a collection of equations who are utilizing the same variables—we use systems of equations to find a solution whose answer will satisfy each condition.  What are the ways to solve systems of equations?  There are three methods for solving system of equations: Graphing, Substitution and Elimination.9/10/2012 22 Isaac Elementary School District
  23. 23. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.EE.8. Analyze and solve pairs of 8.MP.1 6-8.RST.7 Coefficient KA: Graphing system of MC: Lesson 9-7: simultaneous linear equations. 8.MP.2 ET08-S1C2-01 Consistent equations word Solving by 8.MP.3 ET08-S1C2-02 Dependent problems graphing a. Understand that solutions to a 8.MP.4 Elimination system of two linear equations in two 8.MP.5 Substitution KA: variables correspond to points of 8.MP.6 Graphing Systems of equations: intersection of their graphs, because 8.MP.7 Equations determining number of points of intersection satisfy both 8.MP.8 Function Table solutions equations simultaneously. Graph Inconsistent b. Solve systems of two linear Independent equations in two variables Infinite solutions algebraically, and estimate solutions Intersect by graphing the equations. Solve Linear equation simple cases by inspection. For Linear function example, 3x + 2y = 5 and 3x + 2y No solution = 6 have no solution because 3x + Ordered pair 2y cannot simultaneously be 5 and 6. Proportional Simultaneous c. Solve real-world and Slope mathematical problems leading to Slope-Intercept form two linear equations in two Solution variables. For example, given Standard form coordinates for two pairs of points, Variable determine whether the line through the X-intercept first pair of points intersects the line Y-intercept through the second pair. Unit Project: Assessment:9/10/2012 23 Isaac Elementary School District
  24. 24. 8th Grade Math Curriculum Map Unit: Geometry Cluster: Surface Area & Volume Approximate Time: 1.5 weeks Essential Questions Big Ideas  What is volume?  Volume is the amount of 3 dimensional space inside an object (length x width x height)  What is the difference between volume and surface area?  Volume is labeled with units cubed and surface area is labeled in units squared.  Composite shapes can be decomposed into several different figures (such as circles or any polygon).9/10/2012 24 Isaac Elementary School District
  25. 25. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S4C1PO1 Identify the attributes of Central Angle circles: radius, diameter, chords, Chord tangents, secants, inscribed angles, Circumference central angles, intercepted arcs, Diameter circumference, and area. Inscribed Angle Intercepted Arc Major Arc Minor Arc Pi Radius Secant Tangent *S4C4PO3 Calculate the surface Cylinder MC: Lesson 7-7, 7- area and volume of rectangular Diameter 8: Surface Area prisms, right triangular prisms and Edge cylinders. Face Lateral Surface Area Net Pi Radius Rectangular Prism Right Triangle Surface Area Triangular prism Vertex Volume *S4C4PO2 Predict results of Area combining, subdividing, and Composite shapes changing shapes of plane figures Diameter and solids. Pi Plane figures Radius Solids 8.G.9. Know the formulas for the 8.MP.1 6-8.RST.3 Base KA: Volume of a sphere MC: Lesson 7-5: volumes of cones, cylinders, and 8.MP.2 6-8.RST.7 Combine Volume of Cylinder spheres and use them to solve real- 8.MP.3 ET08-S2C2-01 Cones KA: world and mathematical problems. 8.MP.4 ET08-S1C4-01 Edge Volume of a cylinder 8.MP.5 Face MC: Lesson 7-6: 8.MP.6 Height Volume of Cone 8.MP.7 Pi 8.MP.8 Radius Sphere Volume Vertex9/10/2012 25 Isaac Elementary School District
  26. 26. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core Unit Project: Assessment:9/10/2012 26 Isaac Elementary School District
  27. 27. 8th Grade Math Curriculum Map Unit: Geometry Cluster: Congruence, Similarity and Transformations Approximate Time: 2 weeks Essential Questions Big Ideas  What is the difference between similarity and congruence?  When two figures have the same shape and same dimensions, they are congruent. When two figures have the same shape, but different dimensions, they are similar.  What are the different types of geometric transformations?  Congruent transformations will never change a shape’s dimensions. There are congruent transformations (reflection, rotations, translations) and similar transformations (dilations).9/10/2012 27 Isaac Elementary School District
  28. 28. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.G.2. Understand that a two- 8.MP.2 6-8.WHST.2b,f Congruency KA: Congruent Triangles MC: Lesson 6-4 dimensional figure is congruent to 8.MP.4 ET08-S6C1-03 Congurent figures another if the second can be 8.MP.6 Coordinate Plane obtained from the first by a 8.MP.7 Ordered pairs sequence of rotations, reflections, Origin and translations; given two Quadrants congruent figures, describe a Reflections sequence that exhibits the Rotations congruence between them. Sequence Translations Two-dimensional figure 8.G.3. Describe the effect of 8.MP.3 6-8.WHST.2b,f Coordinate Plane MC: Lesson 4-7, 4- dilations, translations, rotations, and 8.MP.4 ET08-S6C1-03 Dilations 8: Similarity reflections on two-dimensional 8.MP.5 Ordered pairs figures using coordinates. 8.MP.6 Origin MC: Lesson 6-6: 8.MP.7 Quadrants Reflections Reflections Rotations Translations MC: Lesson 6-7: Two-dimensional Translations figure 8.G.1. Verify experimentally the 8.MP.4 Angle properties of rotations, reflections, 8.MP.5 Line segment and translations: 8.MP.6 Parallel lines 8.MP.7 Quadrant a. Lines are taken to lines, and line 8.MP.8 Reflection segments to line segments of the Rotation same length. Transformations Translation b. Angles are taken to angles of the Verify same measure. c. Parallel lines are taken to parallel lines. 8.G.4. Understand that a two- 8.MP.2 8.EE.6 Coordinate plane KA: Similar Triangles dimensional figure is similar to 8.MP.4 6-8.WHST.2b,f Dilations another if the second can be 8.MP.5 ET08-S6C1-03 Orgin obtained from the first by a 8.MP.6 ET08-S1C1-01 Quadrants sequence of rotations, reflections, 8.MP.7 Reflections translations, and dilations; given two Rotaitons similar two-dimensional figures, Sequence describe a sequence that exhibits the Similar figures similarity between them. Transformation9/10/2012 28 Isaac Elementary School District
  29. 29. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core Translations Two-dimensional *S4C2PO3 Identify lines of Lines of symmetry symmetry in plane figures or classify Reflective symmetry types or symmetries of 2 dimensional Rotational symmetry figures. Line of feflection Unit Project: Assessment:9/10/2012 29 Isaac Elementary School District
  30. 30. 8th Grade Math Curriculum Map Unit: Geometry Cluster: Geometric arguments Approximate Time: 1.5 weeks Essential Questions Big Ideas  What are the types of angle relationships?  The types of angle relationships are vertical, complementary, supplementary, alternate interior, alternate exterior, corresponding.  How can you use angle relationships to solve real world problems?  Once you have one or more pieces of information about an angle relationship, you can deduce an unknown angle measure.9/10/2012 30 Isaac Elementary School District
  31. 31. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.G.5. Use informal arguments to 8.MP.3 6-8.WHST.2b,f Alternate exterior KA: Finding Missing establish facts about the angle sum 8.MP.4 6-8.WHST.1b Alternate interior Angles and exterior angle of triangles, 8.MP.5 ET08-S6C1-03 Angle about the angles created when 8.MP.6 ET08-S1C1-01 Complementary KA: Angles of Parallel parallel lines are cut by a 8.MP.7 ET08-S1C3-03 Congruent Lines transversal, and the angle-angle Corresponding angle criterion for similarity of triangles. Equation KA: Angles Formed For example, arrange three copies of Exterior When a Transversal the same triangle so that the sum of Interior Intersects a Parallel Line the three angles appears to form a Parallel lines line, and give an argument in terms of Similar triangles KA: Angles Formed transversals why this is so. Supplementary Between Transversals Transversal and Parallel Lines Triangle Vertical angles KA: Angles at the Intersection of Two Lines KA: Finding Angles in a Triangle with Exterior Angles KA: Finding Angles in a Triangle Unit Project: Assessment:9/10/2012 31 Isaac Elementary School District
  32. 32. 8th Grade Math Curriculum Map Unit: Statistics & Probability Cluster: Compound Probabilities and Combinations Approximate Time: 2 weeks Essential Questions Big Ideas  How does understanding probability help us to make informed predictions?  The more trial an experiment conducts the closer the experimental probability and the theoretical probabily become.  Probability ranges from 0 to 1 or impossible to certain.  Probability can be expressed as a decimal, percent, or a fraction.  What is the difference between a permutation and a combinations?  If the order of an arrangement matters, it is a permutation. If the order of an arraggement does not matter it is a combination. In other words, a permutation is an ordered combination.9/10/2012 32 Isaac Elementary School District
  33. 33. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S2C2PO1 Determine theoretical Compound events and experimental conditional Conditional probabilities in compound prodbability probabilities in compound Dependent events probability experiments. Experimental probability Favorable outcome Independent events Mutually exclusive Possible outcome Sample space Theoretical probability *S2C2PO2 Interpret probabilities Experimental within a given context and compare probability the outcome of an experiment to the Outcome predictions made prior to Prediction performing the experiment. Theoretical probabilithy *S2C2PO3 Use all possible Dependent events outcomes (sample space) to Independent events determine the probability of Possible outcomes dependent and independent events. Probability Sample Space Tree diagram *S2C3PO1 Represent, analyze and Combinations solve counting problems with or Factorial noation without ordering and repetitions. Fundamental counting principle Permutations *S2C3PO2 Solve counting problems Combinations and represent counting principles Factorial notation algebraically including factorial Permutations notation. Unit Project: Assessment:9/10/2012 33 Isaac Elementary School District
  34. 34. 8th Grade Math Curriculum Map Unit: Statistics & Probability Cluster: Graphical Displays of Data Approximate Time: Two weeks Essential Questions Big Ideas  At what benchmarks do associations become strong and very strong  Scatter plots are used to show the assocations associations? between two variables (independent variable and the  How can different data representations be used to manipulate data? dependent variable).  Associations can be seen in bivariate categorical data by displaying frequency in a two-way table.  Directed graphs are created to represent the reletionship between items.9/10/2012 34 Isaac Elementary School District
  35. 35. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 8.SP.1. Construct and interpret 8.MP.2 6-8.WHST.2b,f Bivariate MC: Lesson 9-9: scatter plots for bivariate 8.MP.4 ET08-S1C3-01 measurement data Interpreting scatter measurement data to investigate 8.MP.5 ET08-S1C3-02 Clusters plots/line of fit patterns of association between two 8.MP.6 ET08-S6C1-03 Correlation quantities. Describe patterns such as 8.MP.7 SS08-S4C1-01 Frequency clustering, outliers, positive or SS08-S4C2-03 Intervals negative association, linear SS08-S4C1-05 Line of best fit association, and nonlinear SC08-S1C3-02 Linear association association. SC08-S1C3-03 Mesaures of central tendency Negative assocation No association Nonlinear assocation Outliers Positive association Scatter plot 8.SP.2. Know that straight lines are 8.MP.2 8.EE.5 Dependent variable widely used to model relationships 8.MP.4 8.F.3 Independent variable between two quantitative variables. 8.MP.5 ET08-S1C3-01 Line of best fit For scatter plots that suggest a 8.MP.6 ET08-S6C1-03 Linear relationship linear association, informally fit a 8.MP.7 SS08-S4C1-05 Negative association straight line, and informally assess No association the model fit by judging the Nonlinear relationship closeness of the data points to the Positive association line. Scatter plots 8.SP.4. Understand that patterns of 8.MP.2 6-8.WHST.2b,f Associations association can also be seen in 8.MP.3 ET08-S1C1-01 Bivariate categorical bivariate categorical data by 8.MP.4 ET08-S1C3-02 data displaying frequencies and relative 8.MP.5 ET08-S1C3-03 Dependent variable frequencies in a two-way table. 8.MP.6 SS08-S4C2-03 Independent variable Construct and interpret a two-way 8.MP.7 SS08-S4C1-05 Line of best fit table summarizing data on two SC08-S1C3-02 Linear relationship categorical variables collected from Negative association the same subjects. Use relative No association frequencies calculated for rows or Nonlinear relationship columns to describe possible Positive association association between the two Scatter plots variables. For example, collect data Summaring from students in your class on whether Variables or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?9/10/2012 35 Isaac Elementary School District
  36. 36. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S2C1PO1Solve problems by Box and whisker plot selecting, constructing, interpreting, Dependent variable and calculating with displays of First quartile data, including box and whicker Independent variable plots and scatter plots. Inter-quartile range Lower extreme Median Outliners Quartiles Range Scatter plots Stem and leaf plot Third quartile Upper extreme *S2C4PO1 Use directed graphs to Directed graph solve problems. Eulter circuit Eulter path Hamilton circuit Hamilton path Unit Project: Assessment:9/10/2012 36 Isaac Elementary School District
  37. 37. 8th Grade Math Curriculum Map Unit: Statistics & Probability Cluster: Evaluation of Experimental Design Approximate Time: 1 week Essential Questions Big Ideas  How can the design of a survey be biased?  The design of an experiment is important to obtain accurate, reliable, and valid data.  Why would someone want to design a biased survey?  Surveys can be biased or unbiased based on their design.  Data displays can be manipulated to avance an argument or a particular view point.9/10/2012 37 Isaac Elementary School District
  38. 38. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S2C1PO3 Describe how summary Extreme values statistics relate to the shape of the Interquartile range distribution. Mean Median Mode Outliers Quartiles Range *S2C1PO4 Determine whether Bar graphs information is represented Box and whisker plot effectively and appropriately given Circle graph a graph or a set of data by Frequency identifying sources of bias and Histrogram compare and contrast the Line graph effectiveness of different Multi-bar graphs representations of data. Multi-line graphs Pictographs Scatter plot Stem and leaf plot Tally charts *S2C1PO5 Evaluate the design of Biased an experiment. Experimental design Random sampling Sample Surveys Unbiased Unit Project: Assessment:9/10/2012 38 Isaac Elementary School District