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- 1. i h Grade Math Curriculum Map 7th Grade Math Curriculum IntroductionThis document contains all mandated 2010 Arizona Mathematical Standards for ih standards have been organized intounits and clusters. The units represent the major domain under which the identified represents the collection of similarconcepts within the larger domain. Within these units and clusters the _6.+~~ 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 session for grades 6-8. Ii">.. clusters must be taught prior to the 2013 AIMSassessment.Essential QuestionsEssential Questions are to be posed to the students at the beginning 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 ofBig 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 (torteacher use) has been provided in . process. Being aware of such misconceptions allows us to plan for them duringThis document has been organized b ds and mathematical practices. The content standards are those that represent knowledgespecific to the mathematical standard ( ains). The mathematical practices describe varieties of expertise that mathematics educators atall levels should seek to develop in their s . These practices rest on important "processes and proficiencies" with longstanding importance inmathematics education. The content standar 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, the8/1312012 Isaac Elementary School District
- 2. t h 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 icable in multiple contexts.Important standards are those that are applicable in many contexts and less state/national exaffls. Useful standards are thosewith the least weight on state/national exams and are likely only useful in a SjJt::,;lU; is denoted in the priority column with the codes E(essential), I (important) and U (useful). This label applies to the content standar The skill/process standards that are a priority for thisgrade level are highlighted in blue and are expected to be maste~"at this grade level.Key VocabularyThe key vocabulary that should be taught for each ofthe vocabulary. These vocabulary words are codedas tier one (1), tier two (2) or tier three (3). Tier one words are those should not be explicitly taught. Tier two words arehigh utility words that can be used across content n~~n~ ~~ n~~b~+~ 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 standard 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, and/or spiraling 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 tea.-w;;]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 eommon formative assessment.8/1312012 2 Isaac Elementary School District
- 3. t h Grade Math Curriculum MapOtherStandards may appear more than once. Each time they should be taught within the context of andlor revisited to a deeper level ofknowledge. Underlined segments of a standard indicate an additional piece of the standard that not covered in previous clusters.[Bracketsl will occasionally appear though out the document and indicate clarification of the Bracketed information is not a part of thestandard itself. Unit: Ratios of Proportional Relationships Cluster: Rate of Change Time: 3 weeks Essential Questions • Why is it important to know proportions? dents will understand that proportional are used to solve real-world situation. • How is rate of change and proportions • Students will understand that if two quantities are proportional that one varies directly with another. As the rate of one quantity changes, the other quantity changes at on independent constant rate. • What is a nronort • Students will understand proportional relationship can be displayed in tables, graphs, and real-life contextual situations8/13/2012 3 Isaac Elementary School District
- 4. hi Grade Math Curriculum Priority I Standard Mathematica I Common Resources Practices Core/Cross Web Resources Core Curricular *S IC I P02. Find or use factors, MC:4-1 multiples, or prime factorization within a set of numbers. 7.RP.1. Compute unit rates associated 7.MP.2. MC: 6-1,6-2 with ratios of fractions, including ratios of 7.MP.6. lengths, areas and other quantities Ratio and Proportion measured in like or different units. For example, if a person walks !0 mile in each ~ hour, compute the unit rate as the complex fraction !0/~ miles per hour, t>rwi"nltmtlll 2 miles Der hour. 7.RP.2. Recognize and represent Proportions MC: 6-3 proportional relationships between inate pair (Rectangle) quantities. Coordinate plane Equation Proportions (Cake) a. Decide whether two quantities are in a Graph proportional relationship, e.g., by t~~inn ..:1 Origin Proportions (Whats for equivalent ratios in a table or Proportions your rate?) graphing on a coordinate plane and Table observing whether the graph is a straight Unit rate Proportions (Walk the line through the origin. Units plank) b. Identify the constant (unit rate) in tables, diagrams, and proportional c. Represent proportion equations. For example, proportional to the number n purchased at a constant price p, relationship between the total cost number of items can be expressed as d. Explain what a point (x, y) on the graph of a proportional relaticlIls!Jipmellrls_in_--->8/13/2012 4 Isaac Elementary School District
- 5. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular terms of the situation, with special attention to the points (0, 0) and (I, r) where r is the unit rate . .~~..~------~--~------------~~------------------~~~~--~~ *S3C3P04. Translate hplllIP,>n MC: 1-10,3-7 and tables that represent a linear equation. Unit Project: sment:8/13/2012 5 Isaac Elementary School District
- 6. 7h Grade Math Curriculum Map Unit: Ratios of Proportional Relationships Cluster: Ratio and Percent Approximate Time: 2 week Essential Questions • How is percent and proportions related? the relationship between • What is the difference between percent change and net :::~~~tuaems will understand that percents are used to solve real-world problems that include: simple interest, tax, percent change, percent error, fees and commissions. • Describe how • Students will proportions to scale real-world problems. figures. e.g. maps and building blueprints8/1312012 6 Isaac Elementary School District
- 7. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S I C3 P04. Estimate the measure MC: 6-4 of an object in one system of units given the measure of that object in another system and the approximate1------11 conversion factor. .... n n n m _ 7.G.1. Solve problems involving 7.MP.l. 6-8.RST.7 MC: 6-8 scale drawings of geometric figures, 7.MP.2. SC07-S I C2-04 such as computing actual 7.MP.3. SS07 -S4C6-03 and areas from a scale tiro>wino 7.MP.4. SS07 -S4C 1-0 I reproducing a scale 7.MP.5. SS07 -S4C 1-02 different scale. 7.MP.6. ET07-SICI-OI 7.MP.7. 7.MP.8. 7.RP.3. Use proportional MC: 6-9, 7-1, 7-2, relationships to solve multistep ratio 7-3, 7-4, 7-5, 7-6, and percent problems. Examples: 7-7, 7-8, 7-9 simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase Increase and decrease, percent error. Markdowns markups Percent Ratio Simple interest Tax Unit Project:8113/2012 7 Isaac Elementary School District
- 8. 7th Grade Math Curriculum Map Unit: The Number System Cluster: The Number Line Time: 3 weeks8113/2012 8 Isaac Elementary School District
- 9. 7th Grade Math Curriculum Essential Questions Big Ideas • What is distance? • will understand that absolute value is the • What is a number? that all real numbers fit on t.."4RLlVllCU and irrational • How can the four arithematic operations can be representated on a line? operations (addition, subtraction, multiplication, division) can be representated on a number • How is subtraction and the additive inverse related? • Students will understand that subtracting a number • How is division and the multipli"(.ul~ is the same as addings its additive inverse. • Students will understant that dividing by a number • Whv ClInt von CllVHle hVA4:r~"3R:~~:SS81>"""~, is the same as multiplying by its multiplicative Inverse. • Students understand that you cannot divide by o.8113/2012 9 Isaac Elementary School District
- 10. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *SIC3POI. Estimate and apply benchmarks for rational numbers and common irrational numbers. *S IC3 P03. Estimate square roots of MC: 1-3, 12-1 numbers less than 1000 by locating them between two consecutive whole numbers. 7.NS.l. Apply and extend previous 7.MP.2. MC: 2-1, 2-2, 2-4, understandings of addition and subtraction 7.MPA. 2-5 to add and subtract rational numbers; 7.MP.7. represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make O. For example, a hydrogen afom has 0 charge because its Inverse properties two consfifuenfs are oppositely charged. Multiplicative b. Understand p + q as the number inverse a distance I q I from p, in the positive or Minuend negative direction depending on whether q Operations is positive or negative. Show that a number Opposite and its opposite have a sum Subrahead additive inverses). Sum rational numbers b Variable contexts. Vertical c. Understand numbers as adding - q p + (-q). Show between two rational number line is the absolute difference, and apply this world contexts. d. Apply properties of operations as to add and subtract rational 8/13/2012 10 Isaac Elementary School District
- 11. t h Grade Math Curriculum numbers. Priority Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *SIC I P03. Compare and order rational MC: 4-9 numbers using various models and representations. 7.NS.2. Apply and extend previous 7.MP.2. MC: 2-6,2-8 understandings of multiplication and 7.MPA. division and of fractions to multiply and 7.MP.7. divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)(-1) = 1 and the rules for multiplying -Associative signed numbers. Interpret products of -Identity rational numbers by describing rea -Distributive contexts. Quotient Repatend b. Understand that integers can be Terminates divided, provided that the zero, and every quotient non-zero divisor) is a and q are intege p/(-q). Interpret numbers by d c. Apply properties of 0 strategies to multiply and numbers. d. Convert a rational number to a using long division; know that the form of a rational number terminates in Us or8/13/2012 11 Isaac Elementary School District
- 12. t h Grade Math Curriculum Unit Proiect: Unit: The Number System Cluster: Order of Operation ...........vjmate Time: 1 week8/13/2012 12 Isaac Elementary School District
- 13. hi Grade Math Curriculum Essential Questions Big Ideas • What are grouping symbols? • symbols include: Parentheses, absolute • A base raised to the 0 power is what value? Why? and cube roots, brackets, and braces • Do we apply the rules of multiplication before division whilst using ~lClllUll" to evaluate expressions of operations to evaluate an expression? • Do we apply the rules of addition before subtraction operations to evaluate an expression? • When would we express a number in S~!~~~JDt!or • Scientific notation is used to express very large quantities and very small quantities. • Multiplying a number by an exponent with base 10 moves the decimal to the left or right.8/1312012 13 Isaac Elementary School District
- 14. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular "S IC2P04. Represent and interpret MC: 1-2, p. LA2 numbers using scientific notation LA5 (positive exponents 7.NS.3. Solve real-world and 7.MP.l. 6-8.RST.3 MC: 1-4 mathematical problems 7.MP.2. the four operations with rational 7.MP.5. numbers. (Computations with 7.MP.6. rational numbers extend the rules 7.MP.7. for manipulating fractions to 7.MP.8. ~~~~lov fractions. Unit Project: Assessment:811312012 14 Isaac Elementary School District
- 15. i h Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Properties of Evaluating Expressions Time: 1 week Essential Questions Big Ideas • What is a variable? that a variable is a • What does it mean when one thing is equivalent to *uu,",m" will be able to use properties of operations • What is a coefficient? , subtract, factor, and expand expressions with • Students will look at a given problem and be able to express it in a different context.8/13/2012 15 Isaac Elementary School District
- 16. hi Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7 .EE.1. Apply properties of 7.MP.2. 6-8.RST.5 MC: 1-8 operations as strategies to 7.MP.6. and expand linear 7.MP.7. expressions with rational coefficients. 7.EE.2. Understand that rewriting an 7.MP.2. 6-8.WH5T.l b-c expression in different fonns in a 7.MP.6. 6-8.WH5T.2b-c problem context can shed light on 7.MP.7. 6-8.R5T.3 the problem and how the quantities 7.MP.8. 6-8.R5T.7 in it are related. For example, a + 5507-55(2-09 0.05a 1.05a means that "increase SC07-S2C2-03 . 5%" is the same as 1.05. " Unit Project: Assess8/1312012 16 Isaac Elementary School District
- 17. i h Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Solving Equations te Time: 2 weeks Essential Questions Big Ideas • How do we translate a written or verbal description to create an equation or equation? text or real-world scenario. • What is the difference between an expression and an will understand the difference between an • What is an inequality? equation, and inequality. • Students will be able to solve for a missing piece of information from a specific problem or text. • Students be able to check the reasonableness of an answer.8/13/2012 17 Isaac Elementary School District
- 18. Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S3C3P02. Evaluate an expression MC: 1-6 containing one or two variables by substituting numbers for the variables. 7.EE.3. Solve multi-step real-life 7.MP.1. 6-8.WHST.l b-c MC: 1-7 and mathematical problems posed 7.MP.2. 6-8.WHST2b with positive and negative rational 7.MP.3. 6-S.RST.7 numbers in any form (whole 7.MP.4. ET07-S6C2-03 numbers, fractions, and decimals), 7.MP.5. using tools strategically. Apply 7.MP.6. properties of operations to calculate 7.MP.7. with numbers in any form; convert 7.MP.S. between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1110 ofher salary an hour, or $2.50, for a new salary of $27.50. Ifyou want to place a towel bar 9 314 inches long in the center ofa door that is 27 112 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a the exact compufntinJ 7.EE.4. Use va Inverse operations simple equations solve problems by the quantities. a. Solve word problems equations of the form px+q=r p(x+q)=r, where p, q, and rare specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution. identifyina the8/13/2012 18 Isaac Elementary School District
- 19. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular sequence of the operations used in each approach. For example, fhe perimefer of a recfang/e is 54 em. Ifs lengfh is 6 em. Whaf is ifs widfh? b. Solve word problems leading to inequalities ofthe form px+ q>r or px+q < r, where p, q, and rare specific rational numbers. Graph the solution set ofthe inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number ofsales you need to make, and describe the solutions. *SSC2P09. Solve logic problems using mUltiple variables and statement multiple conditional statements Logic words. oictures. and charts. *SSC2POlO. Demonstrate and Deductive reasoning explain that the process of solving . is a deductive Unit Project:8/13/2012 19 Isaac Elementary School District
- 20. ht Grade Math Curriculum Map Unit: Geometry Cluster: Angles Time: 1 week Essential Questions Big Ideas • What is the difference between equal, approximate, and congruent? the difference between congruent. • Which angle relationships are congruent? Which are not? will utilize the properties of angles to solve measure of an unknown angle.8/13/2012 20 Isaac Elementary School District
- 21. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S4CIP05. Identify corresponding parts of congruent figures. 7.G.5. Use facts about 7.MP.3. ET07-S I C4-0 I supplementary, complementary, 7.MP.4. vertical, and adjacent angles in a 7.MP.5. multi-step problem to write and 7.MP.6. solve simple equations for an 7.MP.7. unknown angle in a figure. Unit Project: Unit: Geometry Cluster: Geometric Properties8/13/2012 21 Isaac Elementary School District
- 22. i h Grade Math Curriculum Essential Questions Big Ideas • What is a cross section? • will be able to determine what type of 2-D • What is a 3D shape? from a cross section of a 3-D figure. • What is a 2D shape? that the number of sides a directly translates to the sum of its interior will know what the parts of a triangle are and how they are related to each other.8113/2012 22 Isaac Elementary School District
- 23. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S4C I P04. Describe the relationship between the number of sides in a regular polygon and the sum of its interior angles. 7.G.2. Draw (freehand, with ruler 7.MP.4. 6-8.R5T.4 and protractor, and with technology) 7.MP.5. 6-8.R5T.7 geometric shapes with given 7.MP.6. 6-8.WH5T.2b-2f conditions. Focus on constructing 7.MP.7. 51 C2-04 triangles from three measures of 7.MP.8. ET07-SIC2-01 angles or sides, noticing when the ET07-S6C 1-03 conditions detennine a unique triangle, more than one triangle, or no triangle. 7.G.3. Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Cylinder Face Right prism Right pyramid Vertex Unit Proiect:8/13/2012 23 Isaac Elementary School District
- 24. 7th Grade Math Curriculum Map U nit: Geometry Cluster: Circumference and Area te Time: 2 weeks Essential Questions Big Ideas • What is the difference between perimeter, area, surface area and determine the parts of a . I.e. circumference, area, are, chord, diameter, • Why is volume units cubed and surface area units understand that perimeter is the of length, having neither width nor • Students will understand that area is the measurement of a surface space in a 2-D region, and that the measuring tool used are squares that have a length and width of one unit measure. • Students will understand that volume is the measurement of space that a 3-D object can occupy, and that the measuring tool used are cubes that have a length, width, and height of one unit measure.8/1312012 24 Isaac Elementary School District
- 25. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.GA. Know the fonnulas for the 7.MP.1. 6-S.WHST.ld area and circumference of a circle 7.MP.2. SC07-S2C2-03 and solve problems; give an 7.MP.3. ET07-S6C2-03 infonnal derivation of the 7.MP.4. ET07-S I C4-0 I relationship between the 7.MP.5. circumference and area of a circle. 7.MP.6. 7.MP.7. ,7.MP.S. _ _ _-I-_ _ _ _ _-- relationship between central angles and intercepted arcs; identify arcs and chords of a circle. *S4C4P02. Identify polygons having the same perimeter or area. *S5C I PO I. Create an algorithm to detennine the area of a given 7.G.6. Solve real-world and Faces mathematical problems involving Net area, volume and surface area of Surface area two- and three-dimensional objects Volume composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Unit Project:8/1312012 25 Isaac Elementary School District
- 26. i h Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Stats and Data Time: 2 weeks Essential Questions Big Ideas • What is a random sample and why are they used to colelct data? that a random sample is U1.l~~ll,,;l;:> and generalization about a • How can we design a random sample from a population? population if there is an even representation. will understand that there is a margin of error in making inferences with a random sample.8113/2012 26 Isaac Elementary School District
- 27. hi Grade Math Curriculum Priority I Standard Mathematica I Common Resources Practices Core/Cross Web Resources Core Curricular 7.SP.1. Understand that 17.MP.3. 5507-54(4-04 statistics can be used to gain 7.MP.6. 5507-54(4-05 information about a population 5(07-53( 1-02 by examining a sample of the 5(07-54(3-04 population; generalizations about ET07-54(2-01 a population from a sample are ET07-54(2-02 valid only if the sample is ET07 -S6C2-03 representative of that population. Understand that random sampling tends to produce representative samples and sunnnrt v,;:alirl inf... r... n,......c "S2C1P01. Solve problems by selecting, constructing, and interpreting displays of data including mUlti-line graphs and *S2CIP02. Interpret trends in a data set, estimate values for missing data, and predict values Prediction for points beyond the range of Range the data set. Trends 7.SP.2. Use data from a random Simulated sample to draw inferences about a population with an unknown characteristic of i Generate multiple simulated size to gauge 1(3-01 -51 (3-02 estimates or ET07-54C2-02 example, ET07-56(2-03 word length in randomly sampling the book; predict the school election based on randomly sampled survey Gauge how far off the estimate or Drediction miaht be.8/13/2012 27 Isaac Elementary School District
- 28. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular Unit Project: Assessment:8113/2012 28 Isaac Elementary School District
- 29. Grade Math Curriculum MapUnit: Statistics and ProbabilityCluster: Data Graph and Analysis roximate Time: 2 weeks Essential Questions Big Ideas • Why is the average not a good measure of center to use when reporting that measures of center is a data? a set of data, except if there • How do outliers affect a data set? will use measure of center to express a set of and correctly decide which measure of center best fits a given set of data.8/13/2012 29 Isaac Elementary School District
- 30. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.SP.4. Use measures of center 7.MP.1. 6-8.WHST.l b and measures of variability for 7.MP.2. ET07-S 1C3-01 numerical data from random 7.MP.3. ET07-S 1C3-02 samples to draw informal 7.MP.4. ET07-S4C2-0 1 comparative inferences about 7.MP.S. ET07-S4C2-02 two populations. For example, 7.MP.6. ET07-S6C2-03 decide whether the words in a 7.MP.7. SC07-S 1C3-0 1 chapter of a seventh-grade SC07-S 1C3-0S SC07-S 1C4-03 science book are generally SC07-S2C2-03 longer than the words in a SC07-S4C3-04 chapter of a fourth-grade science SS07-S4C2-0 1 book. *S2C1 P03. Identify outliers and determine their effect on mean, median, mode, and range. 7.SP.3. Informally assess the degree of visual overlap of two Measure of numerical data distributions with Variability similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For mean height of 1C3-01 basketball 1C3-02 than the -S4C2-01 on the soccer ET07-S4C2-02 the variability ET07-S6C2-03 deviation) on dot plot, the the two distributions of noticeable. Unit Proiect:8/1312012 30 Isaac Elementary School District
- 31. t h Grade Math Curriculum Map8/1312012 31 Isaac Elementary School District
- 32. hi Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Simple and Compound Events ate Time: 1 week Essential Questions Big Ideas • How can probabilty be used to make informed predictions? that the probability of a 0, which is impossible to • How does increasing the total number of possible outcomes affect the happen, and 1, which is certain to happen. probability of a given situation? Lqu;;lll~ will understand that the probability that an even will occur is equal to the number of favorable outcome divided by the total number of outcomes. • Students will understand that a sample space is a diagram of all possible outcomes for a given situation.8/13/2012 32 Isaac Elementary School District
- 33. t h Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.5P.5. Understand that the probability 7.MP.4. 6-8.WH5T.1 b of a chance event is a number between 7.MP.5. 5507-55C1-04 o and 1 that expresses the likelihood 7.MP.6. ET07-51 C3-01 of the event occurring. Larger numbers 7.MP.7. ET07-51 C3-02 indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around Y2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.5P.8. Find probabilities of compound 7.MP.1. events using organized lists, tables, 7.MP.2. tree diagrams, and simulation. 7.MP.4. 7.MP.5. a. Understand that, just as with simple 7.MP.7. events, the probability of a compound 7.MP.8. event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space that event. answer to the question: donors have type A probability that it will take donors to find one with Unit Project:8113/2012 33 Isaac Elementary School District
- 34. hi Grade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular Unit: Statistics and Probability Cluster: Theoretical and Experimental Probabilities Time: 2 weeks Essential Questions • What are the similarities and differences between experimental and Students will understand that probability is a theory theoritical probability? is the likelyhood that an event will happen, and • Students will understand that the more trials used in an experimental probability, the closer the probability of an event occuring gets closer to its theoretical probability.8113/2012 34 Isaac Elementary School District
- 35. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular 7.SP.6. Approximate the probability of a 6-S.WHST.l a chance event by collecting data on the ET07-S1C2-01 chance process that produces it and ET07-S 10-02 observing its long-run relative ET07-S 1C2-03 frequency, and predict the approximate relative frequency given the probability. ET07-S 1C3-0 1 For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7.SP.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to dete probabilities of events. student is selected at find the probabilit and the probability b. Develop a may not be uniform) frequencies in data gen chance process. For approximate probability that a penny will land heads up or that tossed paper cup will land ODen-en down.8113/2012 35 Isaac Elementary School District
- 36. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular Do the outcomes for the spinning penny appear to be equally likely based on the observed freauencies? Unit Project:8/1312012 36 Isaac Elementary School District
- 37. 7th Grade Math Curriculum Map Unit: Displaying Data Cluster: Data displays roximate Time: 1 week Essential Questions Big Ideas • What is a vertex-edge graph? to read a vertex-edge diagram. • How are vertex-edge graphs used in real life? • What is the diflerence between a congurent transformation and a similar Students will be able to use a Venn Diagram to transformation? J.Jl;;;:);;1U algebraic problems. Students will be able to translate, rotate, and reflect geometric figures in a coordinate plane.8/13/2012 37 Isaac Elementary School District
- 38. 7thGrade Math Curriculum Priority I Standard Mathematical Common Resources Practices Core/Cross Web Resources Core Curricular *S2C3P02. Solve counting problems using Venn diagrams and represent the answer *S2C4P01. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems related to Euler/Hamilton paths and circuits. *S4C2P01. Model the result of a double transformation (translations or reflections) of a 2-dimensional figure on a coordinate plane using all four quadrants. Unit Project:8/13/2012 38 Isaac Elementary School District

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