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- 1. 7th Grade Math Curriculum Map 7th Grade Math Curriculum Map IntroductionThis document contains all mandated 2010 Arizona Mathematical Standards for 7th 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. 7th 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. 7th Grade Math Curriculum Map Unit: Ratios of Proportional Relationships Cluster: Rate of Change Approximate Time: 3 weeks Essential Questions Big Ideas Why is it important to know proportions? Students will understand that proportional relationships are used to solve real-world situation. How is rate of change and proportions related? 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 an independent constant rate. What is a proportional relationship? Students will understand proportional relationship can be displayed in tables, graphs, and real-life contextual situations9/10/2012 3 Isaac Elementary School District
- 4. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C1PO2. Find or use factors, multiples, Composite number Factor Tree MC: 4-1 or prime factorization within a set of GCF numbers. Exponents Factors LCM Multiples Prime number Prime factorization 7.RP.1. Compute unit rates associated with 7.MP.2. 6-8.RST.7 Complex fractions Proportion MC: 6-1, 6-2 ratios of fractions, including ratios of 7.MP.6. SC07-S1C2-04 Denominator lengths, areas and other quantities ET07-S1C1-01 Equivalent Ratio and Proportion measured in like or different units. For Numerator example, if a person walks ½ mile in each Rate ¼ hour, compute the unit rate as the Ratio complex fraction ½/¼ miles per hour, Reciprocal equivalently 2 miles per hour. 7.RP.2. Recognize and represent 7.MP.1. 6-8.WHST.2c-f Constant Proportions (Rectangle) MC: 6-3 proportional relationships between 7.MP.2. 6-8.WHST.1c Coordinate pair quantities. 7.MP.3. 6-8.RST.7 Coordinate plane Proportions (Cake) 7.MP.4. 6-8.RST.4 Equation a. Decide whether two quantities are in a 7.MP.5. ET07-S6C2-03 Graph Proportions (Whats proportional relationship, e.g., by testing 7.MP.6. ET07-S1C1-01 Origin your rate?) for equivalent ratios in a table or 7.MP.7. SC07-S1C4-01 Proportions graphing on a coordinate plane and 7.MP.8. SC07-S2C2-03 Table Proportions (Walk the observing whether the graph is a straight Unit rate plank) line through the origin. Units b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.9/10/2012 4 Isaac Elementary School District
- 5. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S3C3PO4. Translate between graphs Function MC: 1-10, 3-7 and tables that represent a linear Linear equation. Translate Unit Project: Assessment:9/10/2012 5 Isaac Elementary School District
- 6. 7th Grade Math Curriculum Map Unit: Ratios of Proportional Relationships Cluster: Ratio and Percent Approximate Time: 2 week Essential Questions Big Ideas How is percent and proportions related? Students will understand the relationship between percents and proportions and how every percent is a proportion. What is the difference between percent change and net change? Students 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 proportional reasoning can be used to solve real-world Students will utilize proportions to scale real-world problems. figures. e.g. maps and building blueprints9/10/2012 6 Isaac Elementary School District
- 7. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C3PO4. Estimate the measure of Approximate MC: 6-4 an object in one system of units given Conversion the measure of that object in another Estimate system and the approximate Measure conversion factor. Ratio 7.G.1. Solve problems involving 7.MP.1. 6-8.RST.7 Area Scaling MC: 6-8 scale drawings of geometric figures, 7.MP.2. SC07-S1C2-04 Figures such as computing actual lengths and 7.MP.3. SS07-S4C6-03 Length areas from a scale drawing and 7.MP.4. SS07-S4C1-01 Model reproducing a scale drawing at a 7.MP.5. SS07-S4C1-02 Scale different scale. 7.MP.6. ET07-S1C1-01 7.MP.7. 7.MP.8. 7.RP.3. Use proportional 7.MP.1. 6-8.RST.3 Commisions Percent MC: 6-9, 7-1, 7-2, relationships to solve multistep ratio 7.MP.2. SS07-S5C3-01 Decrease 7-3, 7-4, 7-5, 7-6, and percent problems. Examples: 7.MP.3. SC07-S4C3-04 Error 7-7, 7-8, 7-9 simple interest, tax, markups and 7.MP.4. SC07-S4C3-05 Fees markdowns, gratuities and 7.MP.5. Gratuities commissions, fees, percent increase 7.MP.6. Increase and decrease, percent error. 7.MP.7. Markdowns markups 7.MP.8. Percent Ratio Simple interest Tax Unit Project: Assessment:9/10/2012 7 Isaac Elementary School District
- 8. 7th Grade Math Curriculum Map Unit: The Number System Cluster: The Number Line Approximate Time: 3 weeks Essential Questions Big Ideas What is distance? Students will understand that absolute value is the distance between two units. What is a number? Students will understand that all real numbers fit on a number line i.e. rational and irrational How can the four arithematic operations can be representated on a number Students will understand that arithematic operations line? (addition, subtraction, multiplication, and division) can be representated on a number line. How is subtraction and the additive inverse related? Students will understand that subtracting a number is the same as addings its additive inverse. How is division and the multiplicative inverse related? Students will understant that dividing by a number is the same as multiplying by its multiplicative Why can’t you divide by 0? inverse. Students will understand that you cannot divide by 0.9/10/2012 8 Isaac Elementary School District
- 9. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C3PO1. Estimate and apply Benchmark benchmarks for rational numbers and Estimate common irrational numbers. Integers Irrational numbers Rational numbers Terminating decimal Whole number *S1C3PO3. Estimate square roots of Consecutive MC: 1-3, 12-1 numbers less than 1000 by locating them Perfect square between two consecutive whole numbers. Radical Square roots 7.NS.1. Apply and extend previous 7.MP.2. 6-8.WHST.2f Absolute value MC: 2-1, 2-2, 2-4, understandings of addition and subtraction 7.MP.4. 6-8.WHST.2b Addend 2-5 to add and subtract rational numbers; 7.MP.7. 6-8.RST.3 Additive inverse represent addition and subtraction on a 6-8.RST.7 Difference horizontal or vertical number line diagram. ET07-S1C1-01 Equation SS07-S4C5-04 Equivalent expression a. Describe situations in which opposite Horizontal quantities combine to make 0. For example, Inverse properties a hydrogen atom has 0 charge because its Multiplicative inverse two constituents are oppositely charged. Minuend Operations b. Understand p + q as the number located Opposite a distance |q| from p, in the positive or Subrahead negative direction depending on whether q Sum is positive or negative. Show that a number Variable and its opposite have a sum of 0 (are Vertical additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real- world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers.9/10/2012 9 Isaac Elementary School District
- 10. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C1PO3. Compare and order rational Ascending order MC: 4-9 numbers using various models and Descending order representations. Greater than Greatest Least Less than Rational number 7.NS.2. Apply and extend previous 7.MP.2. 6-8.RST.4 Convert MC: 2-6, 2-8 understandings of multiplication and 7.MP.4. 6-8.RST.5 Denominator division and of fractions to multiply and 7.MP.7. SC07-S1C3-01 Dividend divide rational numbers. SS07-S5C3-04 Divisor Factor a. Understand that multiplication is Fractions extended from fractions to rational Numerator numbers by requiring that operations Product continue to satisfy the properties of Properties operations, particularly the distributive -Communative property, leading to products such as (– -Associative 1)(–1) = 1 and the rules for multiplying -Identity signed numbers. Interpret products of -Distributive rational numbers by describing real-world Quotient contexts. Repatend Terminates b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Unit Project: Assessment:9/10/2012 10 Isaac Elementary School District
- 11. 7th Grade Math Curriculum Map Unit: The Number System Cluster: Order of Operation Approximate Time: 1 week Essential Questions Big Ideas What are grouping symbols? Grouping symbols include: Parentheses, absolute value, A base raised to the 0 power is what value? Why? square and cube roots, brackets, and braces Do we apply the rules of multiplication before division whilst using order of Using the order of operations to evaluate expressions operations to evaluate an expression? is essential. Do we apply the rules of addition before subtraction whilst using order of operations to evaluate an expression? When would we express a number in scientific notation? 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.9/10/2012 11 Isaac Elementary School District
- 12. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S1C2PO4. Represent and interpret Exponents MC: 1-2, p. LA2 – numbers using scientific notation Scientific notation LA5 (positive exponents only). Standard form Standard notation 7.NS.3. Solve real-world and 7.MP.1. 6-8.RST.3 Grouping MC: 1-4 mathematical problems involving the 7.MP.2. Order of operations four operations with rational 7.MP.5. PEMDAS/GEMS numbers. (Computations with rational 7.MP.6. Rational numbers numbers extend the rules for 7.MP.7. Complex fractions manipulating fractions to complex 7.MP.8. fractions.) Unit Project: Assessment:9/10/2012 12 Isaac Elementary School District
- 13. 7th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Properties of Evaluating Expressions Approximate Time: 1 week Essential Questions Big Ideas What is a variable? Students will understand that a variable is just a number that is replaced with a letter. What does it mean when one thing is equivalent to another thing? Students will be able to use properties of operations What is a coefficient? to add, subtract, factor, and expand expressions with rational coefficients. Students will look at a given problem and be able to express it in a different context.9/10/2012 13 Isaac Elementary School District
- 14. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 7.EE.1. Apply properties of 7.MP.2. 6-8.RST.5 Coefficients MC: 1-8 operations as strategies to add, 7.MP.6. Combine subtract, factor, and expand linear 7.MP.7. Distributive property expressions with rational coefficients. Expressions Linear expressions Terms 7.EE.2. Understand that rewriting an 7.MP.2. 6-8.WHST.1b-c Convert expression in different forms in a 7.MP.6. 6-8.WHST.2b-c Expression problem context can shed light on 7.MP.7. 6-8.RST.3 the problem and how the quantities 7.MP.8. 6-8.RST.7 in it are related. For example, a + SS07-S5C2-09 0.05a = 1.05a means that “increase SC07-S2C2-03 by 5%” is the same as “multiply by 1.05.” Unit Project: Assessment:9/10/2012 14 Isaac Elementary School District
- 15. 7th Grade Math Curriculum Map Unit: Expressions and Equations Cluster: Solving Equations Approximate Time: 2 weeks Essential Questions Big Ideas How do we translate a written or verbal description into an algebraic Students will be able to create an equation or equation? inequality from a given text or real-world scenario. What is the difference between an expression and an equation? Students will understand the difference between an What is an inequality? expression, equation, and inequality. Students will be able to solve for a missing piece of information from a specific problem or text. Students will be able to check the reasonableness of an answer.9/10/2012 15 Isaac Elementary School District
- 16. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S3C3PO2. Evaluate an expression Evaluate MC: 1-6 containing one or two variables by Substitute substituting numbers for the variables. 7.EE.3. Solve multi-step real-life and 7.MP.1. 6-8.WHST.1b-c Estimate MC: 1-7 mathematical problems posed with 7.MP.2. 6-8.WHST2b Reasonable positive and negative rational 7.MP.3. 6-8.RST.7 Solve numbers in any form (whole numbers, 7.MP.4. ET07-S6C2-03 fractions, and decimals), using tools 7.MP.5. strategically. Apply properties of 7.MP.6. operations to calculate with numbers 7.MP.7. in any form; convert between forms 7.MP.8. 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 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 7.EE.4. Use variables to represent 7.MP.1. 6-8.SRT.3 Equation quantities in a real-world or 7.MP.2. 6-8.RST.4 Inequality mathematical problem, and construct 7.MP.3. Inverse operations simple equations and inequalities to 7.MP.4. solve problems by reasoning about 7.MP.5. the quantities. 7.MP.6. 7.MP.7. a. Solve word problems leading to 7.MP.8. equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its9/10/2012 16 Isaac Elementary School District
- 17. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. Graph the solution set of the 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 of sales you need to make, and describe the solutions. *S5C2PO9. Solve logic problems Conditional statement using multiple variables and multiple Logic conditional statements using words, pictures, and charts. *S5C2PO10. Demonstrate and Deductive reasoning explain that the process of solving equations is a deductive proof. Unit Project: Assessment:9/10/2012 17 Isaac Elementary School District
- 18. 7th Grade Math Curriculum Map Unit: Geometry Cluster: Angles Approximate Time: 1 week Essential Questions Big Ideas What is the difference between equal, approximate, and congruent? Students will understand the difference between equal, approximate, and congruent. Which angle relationships are congruent? Which are not? Students will utilize the properties of angles to solve for the measure of an unknown angle. Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S4C1PO5. Identify corresponding Congruent parts of congruent figures. Corresponding Figures 7.G.5. Use facts about 7.MP.3. ET07-S1C4-01 Adjacent supplementary, complementary, 7.MP.4. Angles vertical, and adjacent angles in a 7.MP.5. Complemenatry multi-step problem to write and 7.MP.6. Exterior solve simple equations for an 7.MP.7. Interior unknown angle in a figure. Same-Side Straight Supplementary Transversal Vertical angles Unit Project: Assessment:9/10/2012 18 Isaac Elementary School District
- 19. 7th Grade Math Curriculum Map Unit: Geometry Cluster: Geometric Properties Approximate Time: 1 week Essential Questions Big Ideas What is a cross section? Students will be able to determine what type of 2-D What is a 3D shape? figure is yeilded from a cross section of a 3-D figure. What is a 2D shape? Students will understand that the number of sides a polygon directly translates to the sum of its interior angles, regardless of shape. Students will know what the parts of a triangle are and how they are related to each other.9/10/2012 19 Isaac Elementary School District
- 20. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S4C1PO4. Describe the Interior angles relationship between the number of Polygon sides in a regular polygon and the Product sum of its interior angles. Sides Sum 7.G.2. Draw (freehand, with ruler 7.MP.4. 6-8.RST.4 Line segments and protractor, and with technology) 7.MP.5. 6-8.RST.7 Parallelism geometric shapes with given 7.MP.6. 6-8.WHST.2b-2f SC07- Perpendicularity conditions. Focus on constructing 7.MP.7. S1C2-04 Points triangles from three measures of 7.MP.8. ET07-S1C2-01 Protractor angles or sides, noticing when the ET07-S6C1-03 Quadrilateral conditions determine a unique Straight edge triangle, more than one triangle, or Triangle no triangle. Vertex 7.G.3. Describe the two-dimensional 7.MP.2. 6-8.WHST.1b 2-D figures that result from slicing three- 7.MP.4. 6-8.WHST.2b 3-D dimensional figures, as in plane 7.MP.5. Base sections of right rectangular prisms 7.MP.7. Cross section and right rectangular pyramids. Cube Cylinder Face Right prism Right pyramid Vertex Unit Project: Assessment:9/10/2012 20 Isaac Elementary School District
- 21. 7th Grade Math Curriculum Map Unit: Geometry Cluster: Circumference and Area Approximate Time: 2 weeks Essential Questions Big Ideas What is the difference between perimeter, area, surface area and Students will be able to determine the parts of a volume? circle. I.e. circumference, area, arc, chord, diameter, radius, and center point. Why is volume units cubed and surface area units squared? Students will understand that perimeter is the measurement of length, having neither width nor height. 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.9/10/2012 21 Isaac Elementary School District
- 22. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 7.G.4. Know the formulas for the 7.MP.1. 6-8.WHST.1d Area area and circumference of a circle 7.MP.2. SC07-S2C2-03 Circumference and solve problems; give an 7.MP.3. ET07-S6C2-03 Diameter informal derivation of the 7.MP.4. ET07-S1C4-01 Pi relationship between the 7.MP.5. Radius circumference and area of a circle. 7.MP.6. 7.MP.7. 7.MP.8. *S4C1PO1. Recognize the Arc relationship between central angles Central angle and intercepted arcs; identify arcs Chord and chords of a circle. *S4C4PO2. Identify polygons Perimeter having the same perimeter or area. Polygons *S5C1PO1. Create an algorithm to Algorithm determine the area of a given Composite figure composite figure. 7.G.6. Solve real-world and 7.MP.1. 6-8.WHST.2a Faces mathematical problems involving 7.MP.2. ET07-S1C4-01 Net area, volume and surface area of 7.MP.3. Surface area two- and three-dimensional objects 7.MP.4. Volume composed of triangles, 7.MP.5. quadrilaterals, polygons, cubes, and 7.MP.6. right prisms. 7.MP.7. 7.MP.8. Unit Project: Assessment:9/10/2012 22 Isaac Elementary School District
- 23. 7th Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Stats and Data Approximate Time: 2 weeks Essential Questions Big Ideas What is a random sample and why are they used to colelct data? Students will understand that a random sample is valid to making inferences and generalization about How can we design a random sample from a population? a population if there is an even representation. Students will understand that there is a margin of error in making inferences with a random sample.9/10/2012 23 Isaac Elementary School District
- 24. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 7.SP.1. Understand that statistics can 7.MP.3. SS07-S4C4-04 Generalizaitons be used to gain information about a 7.MP.6. SS07-S4C4-05 Inferences population by examining a sample SC07-S3C1-02 Population of the population; generalizations SC07-S4C3-04 Random sample about a population from a sample ET07-S4C2-01 Representative are valid only if the sample is ET07-S4C2-02 Valid representative of that population. ET07-S6C2-03 Understand that random sampling tends to produce representative samples and support valid inferences. *S2C1PO1. Solve problems by Data selecting, constructing, and Dependent variable interpreting displays of data Independent variable including multi-line graphs and Multi-line graph scatterplots. Scatterplot *S2C1PO2. Interpret trends in a Data Set data set, estimate values for missing Estimated value data, and predict values for points Prediction beyond the range of the data set. Range Trends 7.SP.2. Use data from a random 7.MP.1. 6-8.WHST.1b Simulated sample to draw inferences about a 7.MP.2. SC07-S1C3-04 population with an unknown 7.MP.3. SC07-S1C3-05 characteristic of interest. Generate 7.MP.5. SC07-S1C3-06 multiple samples (or simulated 7.MP.6. SC07-S1C4-05 samples) of the same size to gauge 7.MP.7. SC07-S2C2-03 the variation in estimates or ET07-S1C3-01 predictions. For example, estimate the ET07-S1C3-02 mean word length in a book by ET07-S4C2-02 randomly sampling words from the ET07-S6C2-03 book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Unit Project: Assessment:9/10/2012 24 Isaac Elementary School District
- 25. 7th Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Data Graph and Analysis Approximate Time: 2 weeks Essential Questions Big Ideas Why is the average not a good measure of center to use when reporting Students will understand that measures of center is a data? good way to summarize a set of data, except if there are outliers that skew the data. How do outliers affect a data set? Students will use measure of center to express a set of data and correctly decide which measure of center best fits a given set of data.9/10/2012 25 Isaac Elementary School District
- 26. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 7.SP.4. Use measures of center and 7.MP.1. 6-8.WHST.1b Absolute deviation measures of variability for numerical 7.MP.2. ET07-S1C3-01 Comparative - data from random samples to draw 7.MP.3. ET07-S1C3-02 Inference informal comparative inferences 7.MP.4. ET07-S4C2-01 Interquartile range about two populations. For example, 7.MP.5. ET07-S4C2-02 Measure of center decide whether the words in a chapter 7.MP.6. ET07-S6C2-03 - Mean of a seventh-grade science book are 7.MP.7. SC07-S1C3-01 - Median generally longer than the words in a SC07-S1C3-05 - Mode chapter of a fourth-grade science SC07-S1C4-03 - Range book. SC07-S2C2-03 Population SC07-S4C3-04 SS07-S4C2-01 SS07-S4C4-06 SS07-S4C4-09 *S2C1PO3. Identify outliers and Mean determine their effect on mean, Median median, mode, and range. Mode Range Outlier 7.SP.3. Informally assess the degree 7.MP.1. 6-8.WHST.1b Data distribution of visual overlap of two numerical 7.MP.2. SC07-S1C4-01 Measure of – data distributions with similar 7.MP.3. SC07-S1C4-02 Variability variabilities, measuring the 7.MP.4. SC07-S1C4-03 difference between the centers by 7.MP.5. SS07-S4C1-01 expressing it as a multiple of a 7.MP.6. SS07-S4C1-02 measure of variability. For example, 7.MP.7. SS07-S4C1-05 the mean height of players on the SS07-S4C4-06 basketball team is 10 cm greater than SS07-S4C6-03 the mean height of players on the ET07-S1C3-01 soccer team, about twice the ET07-S1C3-02 variability (mean absolute deviation) ET07-S4C2-01 on either team; on a dot plot, the ET07-S4C2-02 separation between the two ET07-S6C2-03 distributions of heights is noticeable. Unit Project: Assessment:9/10/2012 26 Isaac Elementary School District
- 27. 7th Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Simple and Compound Events Approximate Time: 1 week Essential Questions Big Ideas How can probabilty be used to make informed predictions? Students will understand that the probability of a certain outcome is between 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? Students 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.9/10/2012 27 Isaac Elementary School District
- 28. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 7.SP.5. Understand that the probability 7.MP.4. 6-8.WHST.1b Certain of a chance event is a number between 7.MP.5. SS07-S5C1-04 Equally likely 0 and 1 that expresses the likelihood 7.MP.6. ET07-S1C3-01 Favorable outcome of the event occurring. Larger numbers 7.MP.7. ET07-S1C3-02 Impossible indicate greater likelihood. A Likely probability near 0 indicates an unlikely Possible outcome event, a probability around ½ Probability indicates an event that is neither Simple event unlikely nor likely, and a probability Unlikely near 1 indicates a likely event. 7.SP.8. Find probabilities of compound 7.MP.1. 6-8.WHST.2d Compound event events using organized lists, tables, 7.MP.2. ET07-S1C2-01 Sample space tree diagrams, and simulation. 7.MP.4. ET07-S1C2-02 Simulation 7.MP.5. ET07-S1C2-03 Tree diagram a. Understand that, just as with simple 7.MP.7. SC07-S1C4-03 events, the probability of a compound 7.MP.8. SC07-S1C4-05 event is the fraction of outcomes in the SC07-S1C2-02 sample space for which the compound SC07-S1C2-03 event occurs. b. Represent sample spaces for compound events using methods such as 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 compose the event. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Unit Project: Assessment:9/10/2012 28 Isaac Elementary School District
- 29. 7th Grade Math Curriculum Map Unit: Statistics and Probability Cluster: Theoretical and Experimental Probabilities Approximate Time: 2 weeks Essential Questions Big Ideas What are the similarities and differences between experimental and Students will understand that probability is a theory theoritical probability? and is the likelyhood that an event will happen, and not concrete. 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.9/10/2012 29 Isaac Elementary School District
- 30. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core 7.SP.6. Approximate the probability of a 6-8.WHST.1a Conjecture chance event by collecting data on the ET07-S1C2-01 Experimental chance process that produces it and Frequency observing its long-run relative frequency, ET07-S1C2-02 Predict and predict the approximate relative ET07-S1C2-03 Relative frequency given the probability. For ET07-S1C3-01 Theoretical example, when rolling a number cube 600 ET07-S1C3-02 times, predict that a 3 or 6 would be rolled ET07-S4C2-01 roughly 200 times, but probably not exactly ET07-S6C1-03 200 times. ET07-S6C2-03 SC07-S1C2-03 SC07-S1C2-05 SC07-S1C3-05 SC07-S1C4-03 SC07-S1C4-05 SC07-S2C2-03 7.SP.7. Develop a probability model and 6-8.WHST.2d Discrepancy use it to find probabilities of events. SC07-S1C2-02 Frequencies Compare probabilities from a model to ET07-S1C2-01 observed frequencies; if the agreement is ET07-S1C2-02 not good, explain possible sources of the ET07-S1C2-03 discrepancy. ET07-S1C3-01 ET07-S1C3-02 a. Develop a uniform probability model by ET07-S4C2-01 assigning equal probability to all outcomes, ET07-S4C2-02 and use the model to determine ET07-S6C1-03 probabilities of events. For example, if a ET07-S6C2-03 student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?9/10/2012 30 Isaac Elementary School District
- 31. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core Unit Project: Assessment:9/10/2012 31 Isaac Elementary School District
- 32. 7th Grade Math Curriculum Map Unit: Displaying Data Cluster: Data displays Approximate Time: 1 week Essential Questions Big Ideas What is a vertex-edge graph? Students will be able to read a vertex-edge How are vertex-edge graphs used in real life? diagram. What is the difference between a congurent transformation and a similar transformation? Students will be able to use a Venn Diagram to represent algebraic problems. Students will be able to translate, rotate, and reflect geometric figures in a coordinate plane.9/10/2012 32 Isaac Elementary School District
- 33. 7th Grade Math Curriculum Map Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources Practices Curricular Web Resources Core *S2C3PO2. Solve counting Venn diagram problems using Venn diagrams and represent the answer algebraically. *S2C4PO1. Use vertex-edge Circuits graphs and algorithmic thinking to Euler/Hamilton represent and find solutions to Paths practical problems related to Vertex-Edge graphs Euler/Hamilton paths and circuits. *S4C2PO1. Model the result of a Coordinate plane double transformation (translations Origin or reflections) of a 2-dimensional Reflection figure on a coordinate plane using Rotation all four quadrants. Tranformation Translation X-Axis Y-Axis Unit Project: Assessment:9/10/2012 33 Isaac Elementary School District

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