1. REQUIREMENT INFORMATIONASSESSMENT INFORMATION TD3 Textbook Resource Glencoe Math: Course 2 Note: The Standards in each unit are not required to be taught in order. Every attempt should be made to teach material in the quarter to which it has been assigned. NWEA/MAP Assessment AZMerit Assessment AZMerit is a computer-based test which provides engaging questions and measures critical thinking skills for college and career readiness. For schools that are not yet ready, a paper-based version is available. AZMerit is aligned to Arizona’s state learning standards which detail what students should be able to do at each grade level. The test is designed to measure student learning and progress towards readiness for college and career. HOW TO READ THE CURRICULUM MAP Standards are grouped into units in each quarter. Example : Quarter 1: Unit 1 Knowledge for each standard appears directly adjacent to the strand and standard identification. When part of a standard is crossed out, that part of the standard will be addressed in a later unit. “Big Ideas” are what the students will understand by the end of the unit. “Essential Questions” stimulate ongoing thinking of “Big Ideas.” Key terms come from the Standards as well as additional academic words to support instruction. Standards are labeled by grade level (7), domain (EE), cluster (A), and standard (1). Example: 7.EE.A.1. The Big Ideas, Essential Questions, and Key Terms are student friendly language.(They are also highlighted in Blue) 1 7th GRADE - MATH 3/1/2016 Tempe Elementary School District #3 7 th GRADE NWEA/MAP INFORMATION Spring National Norm (2011) 244

2. Overview of Math Domains for 7 th Grade Ratios and Proportional Relationships (RP) Analyze proportional relationships and use them to solve real‐world and mathematical problems. The Number System (NS) Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Expressions and Equations (EE) Use properties of operations to generate equivalent expressions. Solve real‐life and mathematical problems using numerical and algebraic expressions and equations. Geometry (G) Draw, construct and describe geometrical figures and describe the relationships between them. Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume. Statistics and Probability (SP) Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models. 23/1/2016Tempe Elementary School District #3 7th GRADE - MATH

3. Standards for Mathematical Practices (MP) Standards Students are expected to: Explanations and Examples 7.MP.1. Make sense of problems and persevere in solving them. In Grade 7, students solve problems involving ratios and rates and discuss how they solved them. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?” 7.MP.2. Reason abstractly and quantitatively. In Grade 7, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations. 7.MP.3. Construct viable arguments and critique the reasoning of others. In Grade 7, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (e.g., box plots, dot plots, histograms). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?”, and “Does that always work?” They explain their thinking to others and respond to others’ thinking. 7.MP.4. Model with mathematics. In Grade 7, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students explore covariance and represent two quantities simultaneously. They use measures of center and variability and data displays (e.g., box plots and histograms) to draw inferences, make comparisons and formulate predictions. Students use experiments or simulations to generate data sets and create probability models. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context. 3 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

4. Standards for Mathematical Practices (MP), continued Standards Students are expected to: Explanations and Examples 7.MP.5. Use appropriate tools strategically. Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 7 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. Students might use physical objects or applets to generate probability data and use graphing calculators or spreadsheets to manage and represent data in different forms. 7.MP.6. Attend to precision. In Grade 7, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students define variables, specify units of measure, and label axes accurately. Students use appropriate terminology when referring to rates, ratios, probability models, geometric figures, data displays, and components of expressions, equations or inequalities. 7.MP.7. Look for and make use of structure. Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables making connections between the constant of proportionality in a table with the slope of a graph. Students apply properties to generate equivalent expressions (e.g., 6 + 2x = 2 (3 + x ) by distributive property) and solve equations (e.g. 2c + 3 = 15, 2c = 12 by subtraction property of equality; c=6 by division property of equality). Students compose and decompose two‐ and three‐ dimensional figures to solve real world problems involving scale drawings, surface area, and volume. Students examine tree diagrams or systematic lists to determine the sample space for compound events and verify that they have listed all possibilities. 7.MP.8. Look for and express regularity in repeated reasoning. In Grade 7, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d = ad/bc and construct other examples and models that confirm their generalization. They extend their thinking to include complex fractions and rational numbers. Students formally begin to make connections between covariance, rates, and representations showing the relationships between quantities. They create, explain, evaluate, and modify probability models to describe simple and compound events. 7th GRADE - MATH 43/1/2016Tempe Elementary School District #3

5. 7 th Grade Key Terms ALL CAPS Term = second and final year of appearance 5 Absolute value Absolute value symbol (| |) acute triangle addition property of equality addition property of inequality additive identity property additive inverse property adjacent angle algebra tiles algebraic expression associative property average bar notation symbol circumference coefficient commission commutative property complementary angle complex fraction compound event congruent constant constant of proportionality cross section dependent event diameter direct variation discount distribution distributive property division property of equality division property of inequality double box plot double dot plot experimental probability fee gratuity histogram independent event inequality integer interquartile range like terms lower quartile markdown markup mean mean absolute deviation median mode multiplication property of equality multiplication property of inequality multiplicative identity property multiplicative inverse property multiplicative property of zero negative (-) net non-proportional obtuse triangle per percent (%) percent error pi (π) plane positive (+) principal proportional radius random sample range rate rate of change ratio rational number relative frequency repeating decimal right triangle sample space scale scale drawing scale factor scale model similar simple event simple interest simplest form solution set statistics stem-and-leaf plot substitution subtraction property of equality subtraction property of inequality supplementary angle surface area tax term terminating decimal theoretical probability tree diagram uniform probability unit rate upper quartile variability variable vertical angle zero pair 3/1/2016Tempe Elementary School District #3 7th GRADE - MATH

6. Tempe Elementary School District #36 7 The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 4 The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 5 Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. 3/1/2016 7th GRADE - MATH

7. Quarter 1 Unit 1 Suggested Number of Days: 10 Days Big Ideas/Enduring Understandings: Ratios and rates are multiplicative comparisons of two quantities or measurements. Essential Questions: What are ratios and rates? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems. G.A: Draw, construct, and describe geometrical figures and describe the relationships between them. Key Terms AZCCRSKnowledgeSkills ratio rate unit rate per complex fraction constant of proportionality proportional non-proportional scale scale factor 7.RP.A.1 Unit rateC OMPUTE unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Note: For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. 7.RP.A.2 Also in Q1-Unit 2 Proportional relationships Equivalent ratios R ECOGNIZE and REPRESENT proportional relationships between quantities. a.D ECIDE whether two quantities are in a proportional relationship, e.g., by TESTING for equivalent ratios in a table or GRAPHING on a coordinate plane and OBSERVING whether the graph is a straight line through the origin. b.I DENTIFY the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7th GRADE - MATH 73/1/2016 Tempe Elementary School District #3

8. c.R EPRESENT 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.E XPLAIN 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. 7.G.A.1 Also in Q4-Unit 13 Scale drawingsS OLVE problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Resources: http://bit.ly/1Tfnk8f 8 7th GRADE - MATH 3/1/2016 Tempe Elementary School District #3

9. Quarter 1 Unit 2 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: Proportional relationships are recognized or represented through tables, graphs, equations, diagrams and verbal descriptions. Essential Questions: How are proportional relationships recognized or represented? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems. Key Terms AZCCRSKnowledgeSkills direct variation rate of change distributive property 7.RP.A.2 Also in Q1-Unit 1 Proportional relationships Equivalent ratios Coordinate plane Constant of proportionality Equations R ECOGNIZE and REPRESENT proportional relationships between quantities. a.D ECIDE whether two quantities are in a proportional relationship, e.g., by TESTING for equivalent ratios in a table or GRAPHING on a coordinate plane and OBSERVING whether the graph is a straight line through the origin. b. I DENTIFY the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. R EPRESENT 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. 7th GRADE - MATH 93/1/2016Tempe Elementary School District #3

10. d.E XPLAIN 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. 7.EE.B.4 Also in Q2-Unit 6, Q2-Unit 7 Variables Simple equations Word problems Solutions Use variables to REPRESENT quantities in a real-world or mathematical problem, and CONSTRUCT simple equations and inequalities to SOLVE problems by reasoning about the quantities. a.S OLVE word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. S OLVE equations of these forms fluently. C OMPARE an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Note: For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b.S OLVE word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. G RAPH the solution set of the inequality and interpret it in the context of the problem. Note: 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. Note: Focus is limited to one-step proportional equations. Students will solve multi-step equations in Units 6 & 7. Resources: http://bit.ly/1UZF9ul 10 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

11. Quarter 1 Unit 3 Suggested Number of Days: 10 Days Big Ideas/Enduring Understandings: The whole and the proportional relationship are essential for solving a ratio and percent problem. Essential Questions: What are essential components of a ratio and percent problem? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems. EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Key Terms AZCCRSKnowledgeSkills percent (%) simple interest principal tax markup markdown discount gratuity commission fee percent error 7.RP.A.3 Multi step ratio and percent problems U SE proportional relationships to SOLVE multistep ratio and percent problems. Note: Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.EE.B.3 Also in Q1-Unit 4, Q2-Unit 5 Positive and negative rational numbers Properties of operations S OLVE multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), USING tools strategically. A PPLY properties of operations to CALCULATE with numbers in any form; CONVERT between forms as appropriate; and ASSESS the reasonableness of answers using mental computation and estimation strategies. Note: 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, 7th GRADE - MATH 113/1/2016Tempe Elementary School District #3

12. 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. Note: Focus on positive rational numbers. Resources: http://bit.ly/24QHE57 12 7th GRADE - MATH 3/1/2016 Tempe Elementary School District #3

13. Quarter 1 Unit 4 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: The additive inverse property explains how to combine opposite quantities. Essential Questions: What is important for understanding how to add and subtract integers? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Key Terms AZCCRSKnowledgeSkills rational number integer positive (+) negative (-) absolute value absolute value symbol (| |) associative property commutative property additive identity property additive inverse property zero pair 7.NS.A.1 Rational numbers Number line Opposite quantities Distance Additive inverse Absolute value Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a.Describe situations in which opposite quantities combine to make 0. Note: For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. b.Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are 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 7th GRADE - MATH 13 3/1/2016 Tempe Elementary School District #3

14. Properties of operations 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.A PPLY properties of operations as strategies to ADD and SUBTRACT rational numbers. 7.NS.A.3 Also in Q2-Unit 5 Real-world and mathematical problems Rational numbers S OLVE real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Note: Focus on addition and subtraction of positive and negative rational numbers. 7.EE.B.3 Also in Q1-Unit 3, Q2-Unit 5 Positive and negative rational numbers Properties of operations S OLVE multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), USING tools strategically. A PPLY properties of operations to CALCULATE with numbers in any form; CONVERT between forms as appropriate; and ASSESS the reasonableness of answers using mental computation and estimation strategies. Note: 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. Note: Focus on problem situations involving addition and subtraction of rational numbers. Resources: http://bit.ly/1R1nXh9 14 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

15. Quarter 2 Unit 5 Suggested Number of Days: 8 Days Big Ideas/Enduring Understandings: Previous knowledge of multiplication, division, and properties of operations support strategies used in understanding integers. Essential Questions: How can multiplying and dividing integers be understood? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Key Terms AZCCRSKnowledgeSkills multiplicative identity property multiplicative inverse property multiplicative property of zero repeating decimal terminating decimal bar notation symbol 7.NS.A.2 Multiplication and division Rational numbers Products of rational numbers Integers Quotients of rational numbers Properties of operations Apply and extend previous understandings of multiplication and division and of fractions to multiply and 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 signed numbers. Interpret products of rational numbers by describing real-world contexts. 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. 7th GRADE - MATH 153/1/2016Tempe Elementary School District #3

16. Long divisiond.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. 7.NS.A.3 Also in Q1-Unit 4 Real-world and mathematical problems Rational numbers Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Note: Focus on multiplication and division with positive and negative rational numbers. 7.EE.B.3 Also in Q1-Unit 3, Q1-Unit 4 Positive and negative rational numbers Properties of operations Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Note: 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. Note: Focus on problem situations involving multiplication and division with rational numbers. Resources: http://bit.ly/1TT9Fnj 16 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

17. Quarter 2 Unit 6 Suggested Number of Days: 14 Days Big Ideas/Enduring Understandings: Properties of operations support strategies used in evaluating expressions and solving equations. Real-world situations can be solved by creating, interpreting, and evaluating expressions and equations. Essential Questions: Why are properties of operations important? How can real-world situations be solved? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster EE.A: Use properties of operations to generate equivalent expressions. EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Key Terms AZCCRSKnowledgeSkills substitution variable algebraic expression algebra tiles coefficient term like terms constant simplest form addition property of equality subtraction property of equality multiplication property of equality division property of equality 7.EE.A.1 Linear expressionsA PPLY properties of operations as strategies to ADD, SUBTRACT, FACTOR, and EXPAND linear expressions with rational coefficients. 7.EE.A.2 ExpressionsU NDERSTAND that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Note: For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” 7.EE.B.4 Also in Q1-Unit 2, Q2-Unit 7 Variables Simple equations Word problems Solutions U SE variables to REPRESENT quantities in a real-world or mathematical problem, and CONSTRUCT simple equations and inequalities to SOLVE problems by REASONING about the quantities. a.S OLVE word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational 7th GRADE - MATH 173/1/2016Tempe Elementary School District #3

18. Long divisionnumbers. S OLVE equations of these forms fluently. C OMPARE an algebraic solution to an arithmetic solution, IDENTIFYING the sequence of the operations used in each approach. Note: For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b.S OLVE word problems leading to inequalities of the form px+q>r or px+q < r, where p, q, and r are specific rational numbers. G RAPH the solution set of the inequality and INTERPRET it in the context of the problem. Note: 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. Note: Focus is on expressions and equations. Resources: http://bit.ly/1Op060j 18 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

19. Quarter 2 Unit 7 Suggested Number of Days: 8 Days Big Ideas/Enduring Understandings: An inequality is graphed to show all possible solutions. Inequalities can be used to show disproportionate values in real-life situations. Essential Questions: Why are inequalities graphed? What situations can be shown using inequalities? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Key Terms AZCCRSKnowledgeSkills inequality solution set addition property of inequality subtraction property of inequality multiplication property of inequality division property of inequality 7.EE.B.4 Also in Q1-Unit 2, Q2-Unit 6 Variables Simple equations Inequalities Word problems Solutions Word problems Solution set Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a.Solve word problems leading to 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. Note: For example, the perimeter of a rectangle is 54 cm. Its 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. 7th GRADE - MATH 19 3/1/2016Tempe Elementary School District #3

20. Note: 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. Resources: http://bit.ly/1Op1U9G 20 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

21. Quarter 2 Unit 8 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: Probability is the likelihood of an event occurring. Data can be collected to create an experimental probability to predict future events. Essential Questions: What is probability? How can the outcome of future events be predicted? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster SP:C: Investigate chance processes and develop, use, and evaluate probability models. Key Terms AZCCRSKnowledgeSkills experimental probability theoretical probability uniform probability relative frequency sample space simple event tree diagram 7.SP.C.5 Probability Likelihood Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.C.6 Probability Data Frequency Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Note: 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. 7th GRADE - MATH 213/1/2016Tempe Elementary School District #3

22. 7.SP.C.7 Probability model Uniform probability Frequencies D EVELOP a probability model and USE it to FIND probabilities of events. C OMPARE probabilities from a model to observed frequencies; if the agreement is not good, EXPLAIN possible sources of the discrepancy. a.D EVELOP a uniform probability model by ASSIGNING equal probability to all outcomes, and USE the model to determine probabilities of events. Note: For example, if a 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.D EVELOP a probability model (which may not be uniform) by OBSERVING frequencies in data generated from a chance process. Note: 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? Resources: http://bit.ly/1OsmuRa 22 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

23. Quarter 3 Unit 9 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: Representations show the sample space and probability of the events. Essential Questions: What do representations of compound events show? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster SP:C: Investigate chance processes and develop, use, and evaluate probability models. Key Terms AZCCRSKnowledgeSkills compound event dependent event independent event 7.SP.C.8 Compound events Probability Sample space Simulation Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a.Understand that, just as with simple events, the probability of a compound 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 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 which compose the event. c.Design and use a simulation to generate frequencies for compound events. 7th GRADE - MATH 23 3/1/2016 Tempe Elementary School District #3

24. Note: 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? Resources: http://bit.ly/225JWvp 7th GRADE - MATH 24 3/1/2016 Tempe Elementary School District #3

25. Quarter 3 Unit 10 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: Random sampling increases the validity of the results and eliminates biases which allow inferences to be made about the population. Data distribution, variability, and the difference between centers give information about the populations that lead to the inferences. Essential Questions: What benefit does random sampling provide when collecting data for a survey? What information from data can be used to make inferences? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster SP:A: Use random sampling to draw inferences about a population. SP.B: Draw informal comparative inferences about two populations. Key Terms AZCCRSKnowledgeSkills statistics random sample distribution variability mean absolute deviation double box plot double dot plot histogram stem-and-leaf plot interquartile range lower quartile upper quartile mean average median mode range 7.SP.A.1 StatisticsUnderstand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.A.2 Random sampleUse data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Note: For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 7th GRADE - MATH 253/1/2016Tempe Elementary School District #3

26. 7.SP.B.3 Data distributionInformally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Note: For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 7.SP.B.4 Measures of center Measures of variability Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Note: For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Resources: http://bit.ly/1Osoxop 26 7th GRADE - MATH 3/1/2016Tempe Elementary School District #3

27. Quarter 3 Unit 11 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: There is a direct correlation between the circumference and the diameter that maintains the constant ratio of pi. The area of a circle is half the circumference multiplied by the radius. Essential Questions: What happens to the circumference of a circle when the diameter changes? What is the relationship between the area and circumference of a circle? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Key Terms AZCCRSKnowledgeSkills radius diameter pi (π) circumference 7.G.B.4 Area and circumference of a circle Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Resources: http://bit.ly/1Ww11yt 7th GRADE - MATH 273/1/2016Tempe Elementary School District #3

28. Quarter 4 Unit 12 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: A two-dimensional figure is visualized when slicing through a three- dimensional figure. Surface area is the sum of the areas of the two-dimensional surfaces that make up the three-dimensional figure. Essential Questions: What is visualized when a three-dimensional figure is sliced? What is the relationship between area and surface area? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster G.A: Draw, construct, and describe geometrical figures and describe the relationships between them. G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Key Terms AZCCRSKnowledgeSkills plane cross section net surface area 7.G.A.3 Cross sectionD ESCRIBE the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 7.G.B.6 Area Volume Surface area S OLVE real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Resources: http://bit.ly/1TbKQAJ 7th GRADE - MATH 283/1/2016Tempe Elementary School District #3

29. Quarter 4 Unit 13 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: Scale drawings are proportional to the actual object, and the ratio can be used to find the actual measurements. Essential Questions: How can a scale drawing determine the actual measurements of an object? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster G.A: Draw, construct, and describe geometrical figures and describe the relationships between them. Key Terms AZCCRSKnowledgeSkills scale drawing scale model similar 7.G.A.1 Also in Q1-Unit 1 Scale drawingsS OLVE problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Resources: http://bit.ly/1TTaGfb 7th GRADE - MATH 293/1/2016Tempe Elementary School District #3

30. Quarter 4 Unit 14 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: The measurement of angles and length of sides determine the shape of a geometric figure. Special angle relationships determine how to write and solve equations for angle measurements. Essential Questions: How is the shape of a geometric figure determined? What determines how to write and solve equations for angle measurements? Standards for Mathematical Practice: 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Cluster G.A: Draw, construct, and describe geometrical figures and describe the relationships between them. G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Key Terms AZCCRSKnowledgeSkills congruent acute triangle obtuse triangle right triangle supplementary angle complementary angle vertical angle adjacent angle 7.G.A.2 Geometric shapesD RAW (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Note: Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.B.5 Supplementary angles Complementary angles Vertical angles Adjacent angles U SE facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to WRITE and SOLVE simple equations for an unknown angle in a figure. Resources: http://bit.ly/1Ww1gK1 7th GRADE - MATH 303/1/2016Tempe Elementary School District #3