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# 8th Grade Math Curriculum Map

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### 8th Grade Math Curriculum Map

1. 1. 8th Grade Math Curriculum Map 8th Grade Math Curriculum IntroductionThis document contains all mandated 2010 Arizona Mathematical Standards for 8th standards have been organized intounits and clusters. The units represent the major domain under which the identifi represents the collection of similarconcepts within the larger domain. Within these units and clusters the np.rfnrIT to represent a logical progressionof the content knowledge. It is expected that all teachers follow the the following document. OrganizaApproximate TimeApproximate times are based on a 60-minute instructional sessio,n for grades 6-8. ,).;-,," clusters must be taught prior to the 2013 AIMSassessment.Essential QuestionsEssential Questions are to be posed to the students at the beginning 0 the cluster. They are designed to facilitateconceptual development of the content and can be used as a tool for order thinking and inquiry. The students should beable to answer these on their own by the end ofBi2 IdeasBig Ideas are the essential understandings These are the enduring understandings we want students to carrywith them from grade level to grade level. indicative of a student mastering the Big Idea, however they are notalways synonymous. Thus, in cases that the does not include all components of the Big Idea, the Big Idea (forteacher use) has been provided in process. Being aware of such misconceptions allows us to plan for them duringThis document has been organized o~~~nt s . d s and mathematical practices. The content standards are those that represent knowledgespecific to the mathematical standard (~,,~~~ffiains). The mathematical practices describe varieties of expertise that mathematics educators at levels should seek to develop in their stfDl These practices rest on important "processes and proficiencies" with longstanding importance inmathematics education. The content standar&r 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, the8/13/2012 Isaac Elementary School District
2. 2. 8 th Grade Math Curriculum Mappairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to a deeperlevel of understanding and/or should be connected to the other standards in the cluster.Common Core/Cross CurricularThe standards in the Common Core/Cross Curricular column represent possible reading, 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 prioritized using a three-pointscale. Essential standards represent those that are heavily weighted on state In icable in multiple contexts.Important standards are those that are applicable in many contexts and less state/national exa:rns. Useful standards are those the least weight on state/national exams and are likely only useful in a c""Pfiti is denoted in the priority column with the codes E(essential), I (important) and U (useful). This label applies to the content "Lan""1 he skill/process standards that are a priority for thisgrade level are highlighted in blue and are expected to be maste~Jlat this grade level.Key VocabularyThe key vocabulary that should be taught for each of the pertormane~~~ vocabulary. These vocabulary words are codedas tier one (1), tier two (2) or tier three (3). Tier one words are those t~:~rp !er.V,:;oofft~:~should not be explicitly taught. Tier two words arehigh utilitv words that can be used across content lf~t;"nt specific words.ResourcesThe two types of resources listed are the W Resources. All are suggestions that teachers may use to supportinstruction. They are aligned to the standards resources are useful Internet links that can be used for the teachersedification prior to instruction or as a tool during are suggested pages from the adopted texts.Unit/Cluster ProjectThe Unit/Cluster Projects to support students in making connections, critical thinking, higher orderthinking, andlor spiral from all clusters within a unit while cluster project support the standards in aparticular cluster. While do a project with every unit or cluster these resources will support project-based instructionand practice should the .".......,,,...,.AssessmentThe assessment section of the map for teachers to plan the dates that they will give a formative assessment for the cluster. It isexpected that each cluster be assessed ""I1""ln formative assessment. 3/2012 2 Isaac Elementary School District
3. 3. 8th Grade Math Curriculum MapOtherStandards may appear more than once. Each time they should be taught within the context of th~~~ter and/or revisited to a deeper level ofknowledge. Underlined segments of a standard indicate an additional piece of the standard that ~~litelY not covered in previous clusters.[Brackets] will occasionally appear though out the document and indicate clarification of the~~)J~rd. Bracketed information is not a part of thestandard itself. Unit: Number Sense Cluster: The Real Number System nate Time: 1week .......... v .. Essential Questions Big Ideas • that are real numbers? i1~~J;s are classified as either rational or irrational • What is a rational number and irra . • Rational numbers include all integers and non-integers (decimal numbers) that either repeat or terminate. • How do we {,{"In"1l>r • Irrational numbers can be estimated to the nearest integer or to a given place value to increase accuracy of the approximation.8113/2012 3 Isaac Elementary School District
4. 4. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *SIC I PO I Compare and order real MC: Lesson 2-2 numbers including very large and small integers and decimals and fractions close to zero. --­ *SICIP04 Model and solve MC: Lesson 1-3 problems involving absolute value. 8.NS.I. Know that numbers that are 8.MP.2 KA: Converting­ not rational are called irrational. 8.MP.6 repeating-decimals-to­ Understand informally that every 8.MP.7 fractions-l number has a decimal expansion; for rational numbers show that the KA: Converting­ decimal expansion repeats repeating-decimals-to­ eventually, and convert a decimal fractions-2 expansion which repeats eventually into a rational number. Scientific notation Square Square root Standard notation 8.NS.2. Use rational approximations .. -~--~~~~--~~-----r- Decimal KA: Estimating Square of irrational numbers to compare the Fraction Roots to the size of irrational numbers, locate Non-Perfect Square Hundredths them approximately on a Percent line diagram, and Perfect Square of expressions Pi example. Repeating Decimal Repetend Terminating Decimal Truncate Unit Project:8/13/2012 4 Isaac Elementary School District
5. 5. 8th Grade Math Curriculum Map Unit: Number Sense Cluster: Numerical Operations Time: 1 week Essential Questions • Describe how multiplying or dividing a number by less • than one affects the number? • solve problems, radical, decimal, fraction, and percents .8/13/2012 5 Isaac Elementary School District
6. 6. 8th Grade Math Curriculum Map Priority Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S I C2PO I Solve problems with factors, multiples, divisibility or remainders, prime numbers and composite numbers. *S IC2P02 Describe the effect of mUltiplying and dividing a rational number by: • A number less than zero • A number between zero and one • One • A number greater than one *S IC2P05 Simplify numerical expressions using the order of operations that include grouping square roots, cube roots, absolute values and positive exponents. expressions Order of operations Radican Simplify root MC: Lesson 1-7 MC: Lesson 8-3 Unit Project: Asses... rn~n,.!8/13/2012 6 Isaac Elementary School District
7. 7. 8th Grade Math Curriculum Map Unit: Expressions & Equations Cluster: Exponents and Radicals roximate Time: 1.5 week Essential Questions Big Ideas • How do I evaluate an expression? on substitute in values for order of operations. • When do we use the laws of exponents? of exponents are utilized to simplify when base numbers or variables are the • What are the laws of exponents? • There are three laws of exponents: product property, the quotient property and the power property. • How do exponents • Exponents and radicals are inverse operations.8/13/2012 7 Isaac Elementary School District
8. 8. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core CurricuJar *S3C3P02 Evaluate an expression MC: Lesson 1-2 containing variables by substituting rational numbers for the variables. 8.EE.1. Know and apply the 8.MP.2 MC: Lesson 2-9 properties of integer exponents to 8.MP.5 generate equivalent numerical 8.MP.6 expressions. For example, 3x3 =3­ 8.MP.7 3=1/3 3 =1/27 :.;." 8.EE.2. Use square root and cube 8.MP.2 MC: Lesson 3-1 root symbols to represent solutions 8.MP.5 to equations of the form x p and x 8.MP.6 MC: Lesson 3-2 = p, where p is a positive rational 8.MP.7 number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that >/2 is irrational. Simpliest form Simplified expression Solution Square root Rational number Unit Project:8113/2012 8 Isaac Elementary School District
9. 9. 8 th Grade Math Curriculum Map Unit: Expression and Equations Cluster: Scientific Notation Time: 1 week Essential Questions • What is scientific notation used for? express the value of very large or • How do we use scientific notation to express equivalent 1O~~;t, standard notation to scientific notation and rational numbers?8/13/2012 9 Isaac Elementary School District
10. 10. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.EE.3. Use numbers expressed in 8.MP.2 Me: Lesson 2-10 the form of a single digit times an 8.MP.5 integer power of 10 to estimate very 8.MP.6 large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population ofthe United States as 3xIa and the population olthe world as 7xJO and determine that the world populations is more than 20 times larger. 8.EEA. Perform operations with 8.MP.2 numbers expressed in scientific 8.MP.5 notation, including problems where 8.MP.6 both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for operations measurements of very large or very Negative Exponent small quantities (e.g., use Positive Exponent millimeters per year for seafloor Power of 10 spreading). Interpret scientific Scientific Notation notation that has been generated Standard Notation Unit Project:8/13/2012 10 Isaac Elementary School District
11. 11. 8th Grade Math Curriculum Map Unit: Expressions & Equations Cluster: Solving Linear Equations and Graphing Inequalities Time: 3 weeks Essential Questions Big Ideas • How can we use equations to represent real life sitautions? inequalities, and graphs are situations. • What are the different ways that linear equations can be .:~~);Oear equations can be expressed as a graph, an or a table of values.8113/2012 11 Isaac Elementary School District
12. 12. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S4C4P02 Solve geometric problems using ratios and proportions. *S3C4P02 Solve problems involving simple interest rates. *SIC2P03 Solve problems involving percent increase, percent decrease and simple interest rates. KA: Solving Percent Problems KA: Finding Unit Price KA: Solving Percent Problems 2 KA: Finding a Percent ofa Number 8.EE.7 Solve linear equations in one Algebraic Expression MC: Lesson 1-9 variable. Balance Coefficient sides. a. Give examples of Combine Like Terms MC: Lesson I-I 0 in one variable with Constant KA: Solving two step infinitely many Distributive property equations solutions. Equation MC: Lesson 8-1: possibilities is Equivalent Simplifying transforming the Inverse operations expressions simpler forms, until Isolate equation of the form x Like Terms a = b results (where a Linear equations MC: Lesson 8-2: different numbers). Multi-Step equation Two Step Non-Linear Equations Solution Term MC: Lesson 8-4: with8113/2012 12 Isaac Elementary School District
13. 13. 8 th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular the distributive property and variables on both collecting like terms. sides *S3C3P05 Graph an inequality on a number line. Unit Project: Asse8113/2012 13 Isaac Elementary School District
14. 14. sth Grade Math Curriculum Map U nit: Geometry Cluster: Pythagorean Theorem Time: 1 week Essential Questions Big Ideas • How do we apply the Pythagorean Theorem to calculate the distance of ""....... can be used to calculate line segment? 1;::~~J~e Pythagorean Theorem can be used to find the U1.011.-", between two points in two-dimensional and three-dimensional objects. • How can the Pythagorean Theorem • The Pythagorean Theorem can be used to find the missing side of a right triangle • What is a • A Pythagorean Triple is set of three positive integers that satisfy the Pythagorean Theorem.S/13/2012 14 Isaac Elementary School District
15. 15. 8 th Grade Math Curriculum Priority I Standard Mathematica I Common Resources Practices Core/Cross Web Resources Core Curricular 8.G.6 Explain a proof of the 8.MP.3 6-8.WHST.2a-f KA: Introduction to Pythagorean Theorem and its 8.MPA ET08-S1C2-01 the Pythagorean converse. 8.MP.6 Theorem 8.MP.7 8.G.7 Apply the Pythagorean KA: Pythagorean MC: Lesson 3-5, Theorem to determine unknown Theorem Example 3-6 side lengths in right triangles in real-world and mathematical KA: More problems in two and three Pythagorean Theorem dimensions. Leg Examples Perfect Square Pythagorean triples Radical Sign Radican Right triangle Square Root Square root Substituation Three-dimension object Two-dimensions Converse KA: Midpoint MC: Lesson 3-7 Coordinate plan Formula Distance Midpoint Origin Pythagorean triples Quadrants Right triangle SI *S4C3 PO I: Make and test a Midpoint about how to find the Coordinate olane8/13/2012 15 Isaac Elementary School District
16. 16. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular midpoint between any two points in the coordinate plane. Unit Project: Assessment:8113/2012 16 Isaac Elementary School District
17. 17. 8th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Graphing linear equations Time: 3 weeks Essential Questions Big Ideas • How do we use linear equations in real life? to represent a situation and h~rp~~pti graphically, as a table • What is slope? is a change in the independent variable. In ily math, it can be recognized as rise/run or ax. • What are the four types of • We recognize the slope by examing the relationship between the independent and dependent variable. • We can use slope to make conjectures about • geometric figures as well as similarity of equations.8113/2012 17 Isaac Elementary School District
18. 18. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.EE.5. Graph proportional 8.MP.l 8.F.2 KA: Plotting Ordered relationships, interpreting the unit 8.MP.2 8.F.3 Pairs rate as the slope of the graph. 8.MP.3 6-8. RST,7 Compare two different proportional 8.MPA 6- 8.WHST,2b relationships represented in different 8.MP.5 SC08-S5C2-01 ways. For example. compare a 8.MP.6 SC08-S5C2-05 distance-time graph to a distance­ 8.MP.7 time equation to determine which of 8.MP.8 two moving objects has greater speed. 8.EE.6. Use similar triangles to plane explain why the slope m is the same Equivalence between any two distinct points on a Orgin non-vertical line in the coordinate Quadrant plane; derive the equation y mx for Rate of change a line through the origin and the Similar triangles equation y = mx + b for a line Slope intercepting the vertical axis at b. Slope-Intercept fonn X-intercept Y-intercept Unit Project: Assessment:8/13/2012 18 Isaac Elementary School District
19. 19. sth Grade Math Curriculum Map Unit: Functions Cluster: Evaluating Functions ate Time: 3 weeks Essential Questions Big Ideas • What is a function? How do you if a graph represents a function? 4o1vu.,..ip bctwcen variables where one Y (output). We can line test. • What are the different ways to represent a function? function can bc represented with a table, a graph, a verbal description, or an equation. • • A function can be utilized to make conjectures about predicted outcomes.Sl13/2012 ]9 Isaac Elementary School District
20. 20. 8th Grade Math Curriculum Priority I Standard Mathematica I Common Resources Practices Core/Cross Web Resources Core Curricular 8.F.l Understand that a function is a rule 8.MP.l SC08-SSC2-0S KA: Testing if a MC: Lesson 9-2: that assigns to each input exactly one 8.MP.2 relationship is a function I Functions output. The graph of a function is the set of 8.MP.6 ordered pairs consisting of an input and the corresponding output (Function notation is MC: Lesson 9-3: not required in Grade 8). Graphing functions 8.F.3 Interpret the equation y mx + b as 8.MP.2 8.EE.S; 8.EE.7a MC: Lesson 10­ defining a linear function, whose graph is a 8.MP.4 6-8.WHST.1 b slope intercept fonn I: Linear & straight line; give examples of functions 8.MP.5 8-S6C1-03 Nonlinear that are not linear. For example. the 8.MP.6 Functions function A s giving the area ofa square 8.MP.7 as a function ofits side length is not linear because its graph contains the points (1, J). (2.4) and (3.9). which are not on a straight line. Intprfpnt fonn 8.F.2 Compare properties of two functions Algebraic expression each represented in a different way Domain (algebraically, graphically, numerically Function tables, or by verbal descriptions). For Function table example. given a linearfimction Linear equation represented by a table ofvalues and a Linear function linear function represente Non-Linear function expression, determine Point-Slope fonn the greater rate Proportional Quadratic function Range Rate of change Slope-Intercept fonn 8.EE.S Standard ~=.~----~------ Function ....... linear relationship between two 8.SP2 Function table Determine the rate of change and 8.SP.3 Initial value value of the function from a ET08-S1C2-01 Intercept relationship or from two (x, y) values, SC08-SSC2-01 Interpret including reading these from a table or SC08-S1C3-02 Linear relationship Ordered811312012 20 Isaac Elementary School District
21. 21. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular and initial value of a linear function in 8.MP.8 terms of the situation it models, and in terms of its graph or a table of values. 8.F.5. Describe qualitatively the functional 8.MP.2 6-8.WHST.2a-f MC: Lesson 9-6: relationship between two quantities by 8.MPJ ET08-S1 C2-01 Graphing in analyzing a graph (e.g., where the function 8.MP.4 SC08-S5C slope-intercept is increasing or decreasing, linear or 8.MP.5 form nonlinear). Sketch a graph that exhibits the 8.MP.6 qualitative features of a function that has 8.MP.7 been described verbally. 8.SP.3. Use the equation of a linear model 8.MP.2 MC: Lesson 9-4: to solve problems in the context of bivariate 8.MP.4 Slope measurement data, interpreting the slope 8.MP.5 and intercept. For example, in a linear 8.MP.6 model for a biology experiment, interpret a 8.MP.7 MC: Extend 9-5 slope of 1.5 cmlhr as meaning that an additional hour ofsunlight each day is associated with an additional 1.5 em in mature Unit Project: As8/13/2012 21 Isaac Elementary School District
22. 22. 8th Grade Math Curriculum Map Unit: Expressions & Equations Cluster: System of Equations roximate Time: 2 weeks Essential Questions Big Ideas • What is a system of equations? is a collection of equations variables-we use systems of equations to find a solution whose answer will each condition. • What are the ways to solve systems of equations? are three methods for solving system of equations: Graphing, Substitution and Elimination.8/13/2012 22 Isaac Elementary School District
23. 23. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.EE.8. Analyze and solve pairs of 8.MP.1 6-S.RST.? KA: Graphing system Me: Lesson 9-7: simultaneous linear equations. 8.MP.2 ETOS-S1C2-01 of equations word Solving by 8.MP.3 ETOS-S1C2-02 problems graphing a. Understand that solutions to a 8.MP.4 system of two linear equations in two 8.MP.5 variables correspond to points of 8.MP.6 intersection of their graphs, because 8.MP.7 points of intersection satisfy both 8.MP.8 equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For = example, 3x + 2y 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and Simultaneous mathematical problems leading to Slope two linear equations in two Slope-Intercept form variables. For example, given Solution coordinates for two pairs of points, Standard form determine whether the line through the Variable first pair of points intersects the line X-intercept through the second pair. Y -intercept Unit Project:8113/2012 23 Isaac Elementary School District
24. 24. 8th Grade Math Curriculum Map Unit: Geometry Cluster: Surface Area & Volume Time: 1.5 weeks Essential Questions Big Ideas • What is volume? of 3 dimensional space inside x height) • What is the difference between volume and surface area? ~;.;Wl.nH" is labeled with units cubed and surface area • Composite shapes can be decomposed into several different figures (such as circles or any polygon).8113/2012 24 Isaac Elementary School District
25. 25. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S4C 1PO 1 Identify the attributes of circles: radius, diameter, chords, tangents, secants, inscribed angles, central angles, intercepted arcs, circumference, and area. *S4C4P03 Calculate the surface MC: Lesson 7-7, area and volume of rectangular 7-8: Surface Area prisms, right triangular prisms and cylinders. Radius Rectangular Prism Right Triangle Surface Area Triangular prism Vertex Volume Area combining, Composite shapes changing Diameter and solids. Pi Plane figures Radius Solids --­ 6-8.RST.3 Base KA: Volume ofa MC: Lesson 7-5: volumes of cones, cylinders, 6-8. RST.7 Combine sphere Volume of spheres and use them to solve ET08-S2C2-01 Cones Cylinder world and mathematical problems. ET08-S1 C4-01 Edge KA: Face Volume ofa cylinder Height MC: Lesson 7-6: Pi Volume of Cone8113/2012 25 Isaac Elementary School District
26. 26. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.MP.8 Unit Project:8/13/2012 26 Isaac Elementary School District
27. 27. 8 th Grade Math Curriculum Map Unit: Geometry Cluster: Congruence, Similarity and Transformations ~~~:-~te Time: 2 weeks Essential Questions Big Ideas • What is the difference between similarity and congruence? the same shape and same When two figures have the same shape, but different dimensions, they • What are the different types of geometric transformations? transiormations will never change a shapes dimensions. There are congruent transformations (reflection, rotations, translations) and similar transformations (dilations).8/13/2012 27 Isaac Elementary School District
28. 28. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.G.2. Understand that a two­ 8.MP.2 6-8.WHST.2b,f KA: Congruent MC: Lesson 6-4 dimensional figure is congruent to 8.MPA ETOS-S6C1-03 Triangles another if the second can be 8.MP.6 obtained from the first by a 8.MP.7 sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.3. Describe the effect of 8.MP.3 MC: Lesson 4-7, dilations, translations, rotations, and 8.MPA 4-8: Similarity reflections on two-dimensional 8.MP.5 figures using coordinates. 8.MP.6 MC: Lesson 6-6: 8.MP.7 Reflections MC: Lesson 6-7: Translations a.G.l. Verify experimentally the Angle properties of rotations, reflections, Line segment and translations: Parallel lines Quadrant a. Lines are taken to Reflection segments to line Rotation same length. Transformations Translation b. Angles are Verify same measure. c. Parallel lines are lines. S.GA. Understand that a two- S.EE.6 Coordinate plane KA: Similar Triangles dimensional figure is similar to 6-S.WHST.2b,f Dilations another if the second can be ET08-S6C1-03 Orgin obtained from the first by a ETOS-S1C 1-01 Quadrants "--_ _ _ _1 sequence of!ota!iQ(1s,reflections, Reflections8113/2012 28 Isaac Elementary School District
29. 29. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. *S4C2P03 IdentifY lines of symmetry in plane figures or classifY types or symmetries of2 dimensional Unit Project: ssessment:8/13/2012 29 Isaac Elementary School District
30. 30. 8th Grade Math Curriculum Unit: Geometry Cluster: Geometric arguments roximate Time: 1.5 weeks Essential Questions Big Ideas • What are the types of angle relationships? are vertical, iSWpn1-o:>"", alternate interior, • How can you use angle relationships to solve real world IJlU"lii.;l·J1~ have one or more pieces of information about an angle relationship, you can deduce an unknown angle measure.811312012 30 Isaac Elementary School District
31. 31. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.G.S. Use informal arguments to 8.MP.3 6-8.WHST.2b,f establish facts about the angle sum 8.MPA 6-8.WHST.1 b and exterior angle of triangles, about 8.MP.S ET08-S6C 1-03 the angles created when parallel 8.MP.6 ET08-S1 C1-01 lines are cut by a transversal, and 8.MP.7 ET08-S1C3-03 the angle-angle criterion for similarity of triangles. For example, arrange three copies ofthe same triangle so that the sum qfthe three angles appears to form a line, and give an argument in terms transversals why this is so. KA:-!.!.I~---"--- Between Transversals and Parallel Lines KA: Angles at the Intersection of Two Lines a Triangle with Exterior Angles KA: Finding Angles in a Triangle Unit Project:8/13/2012 31 Isaac Elementary School District
32. 32. 8th Grade Math Curriculum Map Unit: Statistics & Probability Cluster: Compound Probabilities and Combinations Time: 2 weeks8113/2012 32 Isaac Elementary School District
33. 33. 8 th Grade Math Curriculum Essential Questions Big Ideas • How does understanding probability help us to make informed • trial an experiment conducts the closer the predictions? probability and the theoretical probabily ranges from 0 to 1 or impossible to can be expressed as a decimal, percent, or a fraction. • If the order of an arrangement matters, it is a • What is the difference permutation. If the order of an arraggement does not matter it is a combination. In other words, a permutation is an ordered combination.8113/2012 33 Isaac Elementary School District
34. 34. 8 th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S2C2PO I Determine theoretical and experimental conditional probabilities in compound probabilities in compound probability experiments. *S2C2P02 Interpret probabilities within a given context and compare the outcome of an experiment to the predictions made prior to performing the experiment. *S2C2P03 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 Combinations Factorial noation Fundamental counting principle Perm utati ons *S2C3P02 Solve Combinations problems and represent Factorial notation principles algebraically Permutations factorial notation. Unit Project:8/1312012 34 Isaac Elementary School District
35. 35. 8 th Grade Math Curriculum Map8/13/2012 35 Isaac Elementary School District
36. 36. 8th Grade Math Curriculum Map Unit: Statistics & Probability Cluster: Graphical Displays of Data roximate Time: Two weeks Essential Questions Big Ideas • At what benchmarks do associations become strong and very strong to show the assocations associations? !-,--lU variable and the • How can different data representations be used to manipulate data? llJ-lCHH.Hli:> can be seen in bivariate categorical data displaying frequency in a two-way table. • Directed graphs are created to represent the reletionship between items.8113/2012 36 Isaac Elementary School District
37. 37. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 8.SP.l. Construct and interpret 8.MP.2 6-S.WHST.2b,f MC: Lesson 9-9: scatter plots for bivariate 8.MP.4 ETOS-S 1C3-01 Interpreting scatter measurement data to investigate 8.MP.5 ETOS-S 1C3-02 plots/line of fit patterns of association between two 8.MP.6 ETOS-S6C 1-03 quantities. Describe patterns such as 8.MP.7 SSOS-S4C 1-01 clustering, outliers, positive or SSOS-S4C2-03 negative association, linear SSOS-S4C1-05 association, and nonlinear SCOS-S1 association. SCOS-S1C3-03 8.SP.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear Linear relationship association, informally fit a straight Negative association line, and informally assess the No association model fit by jUdging the closeness Nonlinear of the data points to the line. relationship Positive association Scatter Associations Bivariate categorical data Dependent variable Independent variable Line of best fit Linear . categorical variables col Negative association the same subjects. Use re No association frequencies calculated for rows Nonlinear columns to describe possible relationship association between the two Positive association variables. For example. collect data Scatter plots students in vour class on8/13/2012 37 Isaac Elementary School District
38. 38. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular whether 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? *S2CIPOISolve problems selecting, constructing, interpreting, and calculating with displays of data, including box and whicker plots and scatter plots. extreme *S2C4POI Use directed graphs to Directed graph solve problems. Eulter circuit Eulter path Hamilton circuit Hamilton Unit Project: ASSAccrnA nt·8113/2012 38 Isaac Elementary School District
39. 39. 8th Grade Math Curriculum Map Unit: Statistics & Probability Cluster: Evaluation of Experimental Design Time: 1 week Essential Questions Big Ideas • How can the design of a survey be biased? "f"rirrlf"nt is important to obtain • Why would someone want to design a biased survey? can be biased or unbiased based on their • Data displays can be manipulated to avance an argument or a particular view point.8113/2012 39 Isaac Elementary School District
40. 40. 8th Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S2CIP03 Describe how summary statistics relate to the shape of the distribution. *S2CIP04 Determine whether information is represented . and appropriately given a graph or a set of data by identifYing sources of bias and compare and contrast the effectiveness of different representations of data. *S2C I POS Evaluate the design of an experiment. Unit Project:8/13/2012 40 Isaac Elementary School District