Content Strand: Real Number System

Grade 9 Algebra 1, Q1

Standard: A1.NRNS.3 Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Related Standards: CCSSM N.RN.3

Vocabulary: rational number, irrational number, sum, product, nonzero, real numbers, whole numbers, integers, natural numbers, pi (not just 3.14), radical, square root, cube root

Example: Explain why the number 2π must be irrational, given that π is irrational. Answer: if 2π were rational, then half of 2π would also be rational, so π would have to be rational as well.

Strategies/Activities: Process Standards http://mathequalslove.blogspot.com 1. Make sense of problems and persevere in solving Venn Diagram of real number system: them. https://app.box.com/s/5e4ca1ed71280f1e3d7 2. Reason both contextually http://cdn.kutasoftware.com/Worksheets/Alg1/Number and abstractly. %20Sets.pdf http://www.doe.virginia.gov/testing/solsearch/sol/math/8/mess_ 3. Use critical thinking skills to 8-2.pdf justify mathematical reasoning and critique the http://www.mathworksheetsland.com/hsnumbersquan/3mul.htm reasoning of others. l 5. Use a variety of Partner work: mathematical tools effectively http://betterlesson.com/lesson/435707/operation-rational- and strategically. irrational-numbers 6. Communicate http://map.mathshell.org/lessons.php? mathematically and approach unit=9110&collection=8&redir=1 mathematical situations with precision. Grade 9 Algebra 1, Q1

Group activity: pull numbers from bag 7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, pg. 431-432

Exemplar Lessons: http://betterlesson.com/lesson/435707/operation-rational-irrational-numbers

Web Sites: https://www.illustrativemathematics.org/content-standards/tasks/690 http://croitz.blogspot.com/search/label/Real%20Number%20System

Videos: USATestPrep: Number System (2:25), Real Numbers and their Subsets (3:3), Subsets of Real Numbers (4:24), The meaning of irrational numbers (3:38)

www.phschool.com, Web Code: ate-0775, Chapter 1, Lesson 3

https://learnzillion.com/lessonsets/647-identify-rules-for-adding-and-multiplying-rational- and-irrational-numbers

Sample Assessment-like Questions:

Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

http://mathbitsnotebook.com/Algebra1/RatIrratNumbers/RATPractice.html

Multiple Choice: ● What is the product of and ? Is the product rational or irrational? A. 34; rational C. ; irrational B. ; irrational D. ; rational

● Which word best describes the sum of and ? A. rational C. natural Grade 9 Algebra 1, Q1

B. imaginary D. irrational

Open-Ended: 1. Let , where p is a rational number. What type of number is q? Explain your reasoning.

2. How can you determine whether the product of and is rational or irrational without multiplying?

Grade 9 Algebra 1, Q1

Content Strand: Quantities

Standard: A1.NQ.1 Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales when constructing graphs and other data displays.

Related Standards: SCCCR A1.ACE.1 SCCCR A1.AREI.3 CCSSM N.Q.1

Vocabulary: dimensional analysis, product, units of measurements (metric and customary), conversion, rate, ratio, proportion, unit rate, scale factor, similar figures

Example: Include word problems where quantities are given in different units, which must be converted to make sense of the problem. For example, a problem might have an object moving 12 feet per second and another at 5 miles per hour. To compare speeds, students convert 12 feet per second to miles per hour:

which is more than 5 miles per hour.

Strategies/Activities: Process Standards SREB Math Ready: Unit 1 Lesson 3 Task #4 and Unit 3 1. Make sense of problems and Measurement and Proportional Reasoning persevere in solving them. http://map.mathshell.org/tasks.php? 2. Reason both contextually and unit=HA24&collection=9&redir=1 abstractly. http://map.mathshell.org/tasks.php? unit=HA19&collection=9&redir=1 3. Use critical thinking skills to http://mathequalslove.blogspot.com/2012/04/sugar- justify mathematical reasoning and packets-and-proportions.html critique the reasoning of others. http://mathequalslove.blogspot.com/2012/07/pre-algebra- road-trip-pr 4. Connect mathematical ideas http://mathequalslove.blogspot.com/2012/10/foldable- and real-world situations through love.html modeling. http://www.sciencewithmrjones.com/handouts.shtml#http 5. Use a variety of mathematical units tools effectively and strategically. Mr. Jones science class, Scroll down to “Units, Grade 9 Algebra 1, Q1

Measurements, and Conversions”, Look at Navigating the Metric (ppt)” through “Challenging Problems - 6. Communicate mathematically Dimensional Analysis” and approach mathematical situations with precision.

7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-8 and 1-9

Exemplar Lessons: http://betterlesson.com/lesson/614611/dimensional-analysis https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-18 https://www.engageny.org/resource/algebra-i-module-1-topic-d-lesson-25

Web Sites:

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Ratios and Proportions (0:50), Using Indirect Measurement (1:22 sec), Dimensional Analysis (2:4)

www.phschool.com, Web Code: ate-0775, Chapter 3, Lessons 4, 5

For fun: https://www.youtube.com/watch?v=ZfcHMwh8Ujs

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p. 67-68; 73-74 Grade 9 Algebra 1, Q1 http://mathbitsnotebook.com/Algebra1/Units/UNUnitsPractice.html

Multiple Choice: A pipe is leaking at the rate of 8 fluid ounces per minute. Use dimensional analysis to find out how many gallons the pipe is leaking per hour. A. 3,840 gal/h C. 3.75 gal/h B. 0.02 gal/h D. 17.07 gal/h

Open Ended: Express 75 kilometers per hour in meters per second. Grade 9 Algebra 1, Q1

Content Strand: Quantities

Standard: A1.NQ.3* Choose a level of accuracy appropriate to limitations on measurement when reporting quantities in context.

Related Standards: SCCCR A1.NQ.2 CCSSM N.Q.1

Vocabulary: accuracy, precision, tolerance, units of measurements (metric and customary)

Example: Determining price of gas by estimating to the nearest cent is appropriate because you

will not pay in fractions of a cent but the cost of gas is .

Strategies/Activities: Process Standards http://www.thirteen.org/edonline/ntti/resources/lessons/si 1. Make sense of problems and gnificant/c.html persevere in solving them. http://tinyurl.com/ng42rh5 http://www.mathsisfun.com/accuracy-precision.html 2. Reason both contextually and abstractly.

3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others.

4. Connect mathematical ideas and real-world situations through modeling. 5. Use a variety of mathematical tools effectively and strategically.

6. Communicate mathematically and approach mathematical Grade 9 Algebra 1, Q1

situations with precision.

7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Sections 1-10

Exemplar Lessons: http://betterlesson.com/lesson/627899/precision-vs-accuracy

Web Sites: https://www.illustrativemathematics.org/content-standards/HSN/Q/A/3

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Sets of Numbers and Appropriate Units (2:12)

https://learnzillion.com/lessonsets/399-choose-a-level-of-accuracy-appropriate-to- limitations-on-measurement

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p.81-82 http://mathbitsnotebook.com/Algebra1/Units/UNUnitsPractice.html

Multiple Choice: ● Four students calculated the volume of a 12.8 oz container. Their results are shown in the table. Whose calculation is the most accurate? Student Volume (oz) Wally 12.546 Rex 12.59 Grade 9 Algebra 1, Q1

Amanda 12.69 Joni 12.75

A. Wally’s C. Amanda’s B. Rex’s D. Joni’s

● Which of these measurements is the most precise? A. 4 m C. 1.3 km B. 127 mm D. 5.14 cm

Open Ended: Write the possible range for the measurement 47 cm 2.2%. Round to the nearest hundredth if necessary.

Grade 9 Algebra 1, Q1

Content Strand: Structure and Expressions

Standard: A1.ASE.1* Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear; quadratic; exponential.)

Related Standards: SCCCR A1.NQ.1 CCSSM A.SSE.1

Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression, algebraic expression, verbal expression, evaluate, substitute, sum, difference, product, quotient, squared, square root, cubed, cube root, less than, more than, is (equal), double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of, power, exponent, per, ratio, order of operations

Example: 1. Suppose the cost of cell phone service for a month is represented by the expression 0.40s + 12.95. Students can analyze how the coefficient of 0.40 represents the cost of one minute (40¢), while the constant of 12.95 represents a fixed, monthly fee, and s stands for the number of cell phone minutes used in the month. Similar real-world examples, such as tax rates, can also be used to explore the meaning of expressions.

2. A box of chocolates at Rhebb’s is computed by charging for each kind of chocolate. Caramels cost $0.40 each. Butter Creams cost $0.30 each. Chocolate Covered Cherries cost $0.60 each. For a particular sale this equation describes the cost of purchase. 0.40a + 0.30b + 0.60c = 8.00 A. What does each of the variables in the equation represent? B. What are the coefficients and what do they represent? C. What does the 8.00 represent?

3. A company uses two different-sized trucks to deliver sand. The first truck can transport x cubic yards, and the second x cubic yards. The first truck makes S trips to a job site, while the second makes T trips. What do the following expressions represent? A. S + T B. x + y C. xS + yT Strategies/Activities: http://cdn.kutasoftware.com/Worksheets/PreAlg/Evaluati Process Standards ng%20Variable%20Expressions.pdf Grade 9 Algebra 1, Q1

1. Make sense of problems and http://cdn.kutasoftware.com/Worksheets/Alg1/Variable persevere in solving them. %20and%20Verbal%20Expressions.pdf 2. Reason both contextually and http://cdn.kutasoftware.com/Worksheets/Alg1/Evaluating abstractly. %20Expressions.pdf http://mathequalslove.blogspot.com/2012/08/a-peek-at- 3. Use critical thinking skills to my-algebra-1-interactive.html justify mathematical reasoning and critique the reasoning of others. http://www.math-play.com/Algebraic-Expressions- Millionaire/algebraic-expressions-millionaire.html 4. Connect mathematical ideas and real-world situations through http://teachers.henrico.k12.va.us/math/hcpsalgebra1/mo modeling. dule1-1.html 6. Communicate mathematically http://teachers.henrico.k12.va.us/math/hcpsalgebra1/mo and approach mathematical dule1-2.html situations with precision. http://www.math-drills.com/algebra.shtml#translating 7. Identify and utilize structure and patterns. http://illuminations.nctm.org/Lesson.aspx?id=2583 https://itunes.apple.com/us/app/5-dice-order-operations- game/id572774867?ls=1&mt=8

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-1 SREB Math Ready: Unit 1 Lesson 6 Task 11 and Task 13

Exemplar Lessons: https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.SSE.A.1%20Lesson %20Interpreting%20Expressions.docx http://betterlesson.com/lesson/resource/1988596/do-now-problem-docx http://betterlesson.com/lesson/541540/linear-expressions-and-word-problems https://www.engageny.org/resource/algebra-i-module-1-topic-b-lesson-6 https://www.engageny.org/resource/algebra-i-module-1-topic-b-lesson-7

Web Sites: Interpreting Expressions https://commoncorealgebra1.wikispaces.hcpss.org/Unit+1 Grade 9 Algebra 1, Q1

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508 USATestPrep: Evaluate Algebraic Expressions, Simplifying Expressions www.phschool.com, Web Code: ate-0775, Chapter 1, Lessons 1, 2

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations Holt Algebra 1 Test Prep: p. 10-11 http://mathbitsnotebook.com/Algebra1/AlgebraicExpressions/AEexpressPractice.html

Multiple Choice: ● At the zoo, a child pays c dollars for a ticket and an adult pays g dollars. Explain in words the meaning of . A An adult ticket costs twice as much as a child ticket. . B An adult ticket costs half as much as a child ticket. . C Twice as many child tickets as adult tickets are sold. . D Half as many adults as children go to the zoo. .

● A clothing store is having a sale where all T-shirts are $10. The sales tax is 5%.Dan buys n T-shirts during this sale, the total cost of his purchase will be 10n + 0.05(10n). Interpret the meaning of 0.05(10n) in this context.

A. The expression 0.05(10n) represents the price of each T-shirt. B. The expression 0.05(10n) represents the cost of Dan’s purchase before tax. C. The expression 0.05(10n) represents the total tax on Dan’s purchase. D. The expression 0.05(10n) represents the total cost of Dan’s purchase.

Open Ended: 1. Explain the meaning of the exponent 3 in the algebraic expression .

2. Hana makes beaded bracelets for sale. The materials for each bracelet cost $2.00 and she sells the bracelets for $7.25 each. To find her profits, she writes the equation p =7.25x - 2.00x. Explain what the variable x represents.

Grade 9 Algebra 1, Q1

Content Strand: Reasoning with Equations and Inequalities

Standard: A1.AREI.3* Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Related Standards: SCCCR A1.AREI.1 SCCCR A1.ASE.1 SCCCR A1.ACE.1 CCSSM A.REI.1

Vocabulary: equation, variable, constant, inverse operation, order of operations, coefficient, solution, properties of equality, no solution, infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms

Example:

● ● ax + 7 = 12

●

Strategies/Activities: Process Standards https://commoncorealgebra1.wikispaces.hcpss.org/file/de tail/A.CED.A.1%20Task%20Setting%20the%20Table.doc 1. Make sense of problems and http://mathequalslove.blogspot.com/2013/11/algebra-1- persevere in solving them. inb-pages-solving-equations.html 2. Reason both contextually and abstractly. http://www.quia.com/mc/540939.html http://www.quia.com/cc/540939.html 3. Use critical thinking skills to http://www.math-play.com/One-Step-Equation- justify mathematical reasoning Game.html and critique the reasoning of http://www.quia.com/cb/77775.html others.

http://cdn.kutasoftware.com/Worksheets/Alg1/One-Step 4. Connect mathematical ideas %20Equations.pdf and real-world situations through http://cdn.kutasoftware.com/Worksheets/Alg1/Two-Step modeling. %20Equations.pdf 5. Use a variety of mathematical Grade 9 Algebra 1, Q1 http://cdn.kutasoftware.com/Worksheets/Alg1/Multi-Step tools effectively and %20Equations.pdf strategically. http://cdn.kutasoftware.com/Worksheets/Alg1/Absolute %20Value%20Equations.pdf 6. Communicate mathematically and approach mathematical situations with precision.

7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-2, 1-3, 1-4, 1-5, 1-7 SREB Math Ready Unit 2 Equations

Exemplar Lessons: https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.CED.A.1%20Lesson %20Solving%20Equations%20with%20Algebra%20Tiles.docx https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-11 https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-12 https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-13 http://betterlesson.com/lesson/537089/two-step-equations http://betterlesson.com/lesson/521026/solving-multi-step-equations-comparing- processes-day-2-of-4

Web Sites: Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Solve 1-variable Equations (2:19), Solve Two-Step Equations (2:00), Solve Multi-step Equations (2:18)

www.phschool.com, Web Code: ate-0775, Chapter 2: Lessons 4, 5; Chapter 3: Lesson 1, 2, 3, 6 http://www.onlinemathlearning.com/solving-two-step-equations-integers.html

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations Grade 9 Algebra 1, Q1

Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60 http://mathbitsnotebook.com/Algebra1/LinearEquations/LEPracEquations.html

Multiple Choice: ● Solve 50q - 43 = 52q - 81. A. q = 38 C. q = -38 B. q = -19 D. q = 19

Open Ended: 1. Solve the equation. 3(x + 4) - 1 = 3x + 2

2. Solve 7b + 3 - 4b = 3 - 3(b + 4). Grade 9 Algebra 1, Q1

Content Strand: Reasoning with Equations and Inequalities

Standard: A1.AREI.1* Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

Related Standards: SCCCR A1.AREI.3 SCCCR A1.ACE.1 CCSSM A.REI.1

Vocabulary: equation, variable, constant, order of operations, inverse operations, multiplicative inverse (reciprocal), equivalent, like terms, properties: commutative, associative, distributive, reflexive, identity, equality, substitution

Example: ● Explain why the equation x/2 + 7/3 = 5 has the same solutions as the equation 3x + 14 = 30. Does this mean that x/2 + 7/3 is equal to 3x + 14? ● Show that x = 2 and x = -3 are solutions to the equation x^2 + x = 6. Write the equation in a form that shows these are the only solutions, explaining each step in your reasoning. ● Transform 2x – 5 = 7 to 2x = 12 and tell what property of equality was used.

Strategies/Activities: http://mathequalslove.blogspot.com/2013/11/algebra-1- Process Standards inb-pages-solving-equations.html 1. Make sense of problems and http://map.mathshell.org/lessons.php? persevere in solving them. unit=8245&collection=8&redir=1 http://schoolhouseteachers.com/wp- 2. Reason both contextually and content/uploads/2013/03/March-Through-Equations.pdf abstractly.

https://tusd.haikulearning.com/abrown/mrs.../cms.../3543 3. Use critical thinking skills to 1149.doc?t… justify mathematical reasoning and critique the reasoning of others. http://www.corwin.com/upm- data/18260_Gregory_ActDiffClssrm_MSMath_Pages_3 4. Connect mathematical ideas and 0_31.pdf real-world situations through modeling. http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A- Grade 9 Algebra 1, Q1

4d- 6. Communicate mathematically 1.html and approach mathematical situations with precision. http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A- 4d-2.html 7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-2, 1-3, 1-4, 1-5, 1-7 SREB Math Ready Unit 2 Equations

Exemplar Lessons: https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.REI.A.1%20Lesson %20Scales%20of%20Equality.doc

http://betterlesson.com/lesson/526370/justifying-the-solutions-to-linear-equations http://betterlesson.com/lesson/517050/solving-equations-by-constructing-arguments- day-1-of-2

Web Sites:

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Solve 1-variable Equations (2:19), Solve Two-Step Equations (2:00), Solve Multi-step Equations (2:18)

www.phschool.com, Web Code: ate-0775, Chapter 2: Lessons 4, 5; Chapter 3: Lesson 1, 2, 3, 6

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60

http://mathbitsnotebook.com/Algebra1/LinearEquations/LEJustifyPractice.html Grade 9 Algebra 1, Q1

Multiple Choice: Solve the equation 4x - 6 = 34. Write a justification for each step. 4x - 6 = 34 Given equation +6 +6 [1] 4x = 40 Simplify. = [2] x = 10 Simplify.

A. [1] Substitution Property of C. [1] Division Property of Equality; Equality; [2] Subtraction Property of Equality [2] Division Property of Equality B. [1] Addition Property of Equality; D. [1] Addition Property of Equality; [2] Division Property of Equality [2] Reflexive Property of Equality

Open Ended: Solve 3(a + 3) – 6 = 21. Write a reason for each step.

Grade 9 Algebra 1, Q1

Content Strand: Creating Equations

Standard: A1.ACE.1* Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. (Limit to linear; quadratic; exponential with integer exponents.)

Related Standards: SCCCR A1.AREI.1 SCCCR A1.ARE.3 CCSSM A.CED.1

Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression, algebraic expression, verbal expression, equation, evaluate, substitute, sum, difference, product, quotient, squared, square root, cubed, cube root, less than, more than, is (equal), double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of, power, exponent, per, ratio, absolute value, order of operations, constant, inverse operation, solution, properties of equality, no solution, infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms, reasonable, interpret

Example: ● Lava coming from the eruption of a volcano follows a parabolic path. The height h in feet of a piece of lava t seconds after it is ejected from the volcano is given by . After how many seconds does the lava reach its maximum height of 1000 feet?

● Given that the following trapezoid has area 54 cm2, set up an equation to find the length of the base, and solve the equation.

Strategies/Activities: http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A- Process Standards 4d-1.html Grade 9 Algebra 1, Q1

1. Make sense of problems and http://mathequalslove.blogspot.com/2013/11/algebra-1- persevere in solving them. inb-pages-solving-equations.html 2. Reason both contextually and http://mathequalslove.blogspot.com/2012/09/algebra-1- abstractly. inb-pages-over-multi-step.html 3. Use critical thinking skills to http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A- justify mathematical reasoning 4d-2.html and critique the reasoning of http://www.superteachertools.us/jeopardyx/jeopardy- others. review-game.php?gamefile=61123#.VYMOgVVViko 4. Connect mathematical ideas http://map.mathshell.org/lessons.php? and real-world situations through unit=8245&collection=8&redir=1 modeling. 5. Use a variety of mathematical https://www.nsa.gov/academia/_files/collected_learning/ tools effectively and strategically. middle_school/algebra/deciphering_world_problems.pdf 6. Communicate mathematically http://cdn.kutasoftware.com/Worksheets/PreAlg/One- and approach mathematical Step%20Word%20Problems.pdf situations with precision. http://cdn.kutasoftware.com/Worksheets/PreAlg/Two- 7. Identify and utilize structure Step%20Word%20Problems.pdf and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-2, 1-3, 1-4, 1-5, 1-7 SREB Math Ready Unit 2 Equations

Exemplar Lessons: http://betterlesson.com/lesson/443652/more-solving-problems-with-equations http://betterlesson.com/lesson/528877/creating-linear-equations-in-one-variable

Web Sites: Relationships in One Variable https://commoncorealgebra1.wikispaces.hcpss.org/Unit+1 http://calculator.tutorvista.com/solving-equations-with-variables-on-both-sides- calculator.html Grade 9 Algebra 1, Q1

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508 https://learnzillion.com/lessons/1249-writing-algebraic-equations-addition-subtraction

USATestPrep: Solve 1-variable Equations (2:19), Solve Two-Step Equations (2:00), Solve Multi-step Equations (2:18), Word Problems into Equations (2:11) www.phschool.com, Web Code: ate-0775, Chapter 2: Lessons 4, 5; Chapter 3: Lesson 1, 2, 3, 6, 9; Chapter 4: Lesson 6

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60 http://mathbitsnotebook.com/Algebra1/LinearEquations/LEAPPS.html

Multiple Choice:

Paolo can mow the lawn at his family’s home in 2 hours. His younger sister Roberta needs 3 hours to mow the lawn. Paolo and Roberta would like to have 2 lawnmowers so they both can mow at the same time. The siblings need to know how much time working together would save to help convince their parents to get another lawnmower. What equation can the siblings use to determine the time t, in hours, needed to mow the lawn when they work together?

A. C. B. D.

Open Ended: Jeremy receives a base salary of $25,000 plus 5% commission on his sales. Jeremy received a total salary of $45,000 last year. How much were his total sales? Grade 9 Algebra 1, Q1

Content Strand: Creating Equations

Standard: A1.AREI.11* Solve an equation from f(x) = g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of 𝑦 = �( 𝑥 ) and 𝑦 = g( 𝑥 ). (Limit to linear; quadratic; exponential.)

Related Standards: SCCCR A1.ACE.1 SCCCR A1.ACE.2 SCCCR A1.AREI.3 CCSSM A.REI.11

Example: Strategies/Activities: SREB Math Ready Unit 2 Equations, Lesson 2 Process Standards

1. Make sense of problems and persevere in solving them.

2. Reason both contextually and abstractly.

3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others.

4. Connect mathematical ideas and real-world situations through modeling.

5. Use a variety of mathematical tools effectively and strategically.

6. Communicate mathematically and approach mathematical Grade 9 Algebra 1, Q1

situations with precision.

7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-5 Technology Lab

Exemplar Lessons: http://mathbits.com/MathBits/TISection/Algebra1/SolveEquations.htm

Web Sites: Relationships in One Variable https://commoncorealgebra1.wikispaces.hcpss.org/Unit+1

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p. 21-22, 29, 37-38, 44-45, 58-60 http://mathbitsnotebook.com/Algebra1/LinearEquations/LEPracEquations.html

Multiple Choice: Lila graphed two linear functions, y = f(x) and y = g(x). Use a graphing utility to graph f(x)= 0.9x - 2.1 and g(x) = -1.8x + 1.5. Then use the graph to find the approximate solution to the equation f(x) = g(x).

A. 2.2 C. 0.8 B. 1.3 D. -0.9

Open Ended: Find the x-coordinates of the points of intersection, if any, of the graphs of the following functions. f(x) = -3x + 12 Grade 9 Algebra 1, Q1 g(x) = 2x - 3

Grade 9 Algebra 1, Q1

Content Strand: Creating Equations

Standard: A1.ACE.4* Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

Related Standards: SCCCR A1.AREI.3 SCCCR A1.NQ.1 CCSSM A.CED.4

Vocabulary: variable, inverse operations, literal, formula, coefficient, factors, terms, expressions, numerical expression, algebraic expression, verbal expression, equation, evaluate, substitute, sum, difference, product, quotient, squared, square root, cubed, cube root, less than, more than, is (equal), double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of, power, exponent, per, ratio, order of operations, constant, inverse operation, solution, properties of equality, no solution, infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms, reasonable, interpret

Example: ● The Pythagorean Theorem expresses the relation between the legs a and b of a right triangle and its hypotenuse c with the equation a2 + b2 = c2. ○ Why might the theorem need to be solved for c? ○ Solve the equation for c and write a problem situation where this form of the equation might be useful.

○ Solve for radius r.

● Motion can be described by the formula below, where t = time elapsed, u=initial velocity, a = acceleration, and s = distance traveled s = ut+½at2 ● Why might the equation need to be rewritten in terms of a? ● Rewrite the equation in terms of a.

Strategies/Activities: http://mathequalslove.blogspot.com/2013/06/literal- Process Standards equations-scavenger-hunt.html Grade 9 Algebra 1, Q1

1. Make sense of problems and https://www.mangahigh.com/en- persevere in solving them. us/math_games/algebra/rearranging_forumulas_/literal_e quations 2. Reason both contextually and abstractly. http://www.regentsprep.org/Regents/math/ALGEBRA/AE4 /indexAE4.htm 3. Use critical thinking skills to justify mathematical reasoning http://handsonmathinhighschool.blogspot.com/2012/07/m and critique the reasoning of ade4math-3-literal-equations.html others. http://teachers.henrico.k12.va.us/math/hcpsalgebra1/mod 4. Connect mathematical ideas ule3-5.html and real-world situations through http://teachers.henrico.k12.va.us/math/HCPSalgebra1/A- modeling. 4a.html 5. Use a variety of mathematical tools effectively and strategically.

6. Communicate mathematically and approach mathematical situations with precision.

7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, Section 1-6 SREB Math Ready Unit 2 Lesson 4 Task 11 and 12

Exemplar Lessons: https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.CED.A.4%20Lesson %20Homecoming.doc

http://betterlesson.com/lesson/443648/solving-literal-equations

Web Sites: https://www.engageny.org/resource/algebra-i-module-1-topic-c-lesson-19

http://betterlesson.com/lesson/443648/solving-literal-equations

Grade 9 Algebra 1, Q1

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Solving Formulas for Specified Variables (2:59)

https://learnzillion.com/lessons/3321-solve-literal-equations

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p. 52-53

http://mathbitsnotebook.com/Algebra1/LinearEquations/LELiteralEquationPractice.html

Multiple Choice: Solve for b. A. C. B. D.

Open Ended:

1. Solve P = 2(l + w) for l.

2. Use the distance formula to find the unknown value. d = 171 mi, r = 19 mi/min, t = ?

Grade 9 Algebra 1, Q1

Content Strand: Real Number System

Standard: A1.AREI.3* Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Related Standards: SCCCR A1.ACE.1 SCCCR A1.AREI.1 CCSSM A.REI.3

Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression, algebraic expression, verbal expression, inequality, evaluate, substitute, sum, difference, product, quotient, less than, more than, double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of, power, exponent, per, ratio, order of operations, constant, inverse operation, solution, properties of equality, no solution, infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms, greater than, greater than or equal to, less than, less than or equal to, is more than, is less than, no more than, no less than, at most, at least, maximum, minimum, compound, and, or, open/closed circle, inclusive, not inclusive, intersection, union, reasonable, interpret

Example: ● 3x > 9 ● Solve for x: 2/3x + 9 < 18

Strategies/Activities: http://misscalculate.blogspot.com/search/label/Algebra Process Standards %20I%20Lessons http://teachers.henrico.k12.va.us/math/hcpsalgebra1/A- 1. Make sense of problems and 5a.html persevere in solving them. http://mathequalslove.blogspot.com/2013/11/one- variable-inequalities-inb-pages.html 2. Reason both contextually and abstractly. http://mathequalslove.blogspot.com/2012/09/algebra-1- inb-pages-over-multi-step.html 3. Use critical thinking skills to justify mathematical reasoning and http://tinyurl.com/nuualln critique the reasoning of others.

http://www.quia.com/rr/521133.html? 4. Connect mathematical ideas and AP_rand=528408548 real-world situations through https://www.mangahigh.com/en- modeling. Grade 9 Algebra 1, Q1 us/math_games/algebra/inequalities/inequalities 5. Use a variety of mathematical tools effectively and strategically. https://www.mangahigh.com/en- us/math_games/algebra/inequalities/two_inequality_sign 6. Communicate mathematically s and approach mathematical situations with precision. https://campus.mangahigh.com/en-us/px/213/0/0 7. Identify and utilize structure and http://www.regentsprep.org/Regents/math/algebra/AE8/p patterns. artnerResource.htm http://cdn.kutasoftware.com/Worksheets/Alg1/Graphing %20Inequalities.pdf http://cdn.kutasoftware.com/Worksheets/Alg1/One-Step %20Inequalities.pdf http://cdn.kutasoftware.com/Worksheets/Alg1/Two-Step %20Inequalities.pdf http://cdn.kutasoftware.com/Worksheets/Alg1/Multi-Step %20Inequalities.pdf http://cdn.kutasoftware.com/Worksheets/Alg1/Compound %20Inequalities.pdf http://cdn.kutasoftware.com/Worksheets/Alg1/Absolute %20Value%20Inequalities.pdf

Resources: Text: Holt McDougal Algebra I Common Core Edition, section 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7

Exemplar Lessons: http://betterlesson.com/lesson/573860/solving-linear-inequalities

https://commoncorealgebra1.wikispaces.hcpss.org/file/detail/A.REI.B.3%20Lesson %20Solving%20Inequalities.docx Grade 9 Algebra 1, Q1

Web Sites: Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Graphing Solutions to Inequalities (2:49), Interpret Solutions: Inequalities (1:18), Solve 1-Variable Inequalities I (1:24), Solve 1-Variable Inequalities II (1:53), Solve Multistep Inequalities (2:18), Solving Linear Inequalities (2:43), Word Problems: Linear Inequalities (2:58) www.phschool.com, Web Code: ate-0775, Chapter 4: Lessons 1, 2, 3, 4, 5

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations Holt Algebra 1 Test Prep: p. 104-105, 110-111, 116-118, 124-125, 130-131, 139-140, 146-148 http://mathbitsnotebook.com/Algebra1/Inequalities/IQinequalityPractice.html http://mathbitsnotebook.com/Algebra1/Inequalities/IQCompoundPractice.html http://mathbitsnotebook.com/Algebra1/Inequalities/IQAppliedPractice.html

Multiple Choice: Solve -5h + 3 < -7. A. h > 2 C. h < 2 B. h > -2 D. h < -2

Open Ended: Solve 2x + 7 > x + x + 1. Grade 9 Algebra 1, Q1

Grade 9 Algebra 1, Q1

Content Strand: Real Number System

Related Standards: SCCCR A1.AREI.1 SCCCR A1.AREI.3 CCSSM A.CED.1

Vocabulary: coefficient, factors, variable, terms, expressions, numerical expression, algebraic expression, verbal expression, inequality, evaluate, substitute, sum, difference, product, quotient, squared, square root, cubed, cube root, less than, more than, double, triple, half, third, reduced by, increased by, decreased by, twice, in groups of, power, exponent, per, ratio, absolute value, order of operations, constant, inverse operation, solution, properties of equality, no solution, infinitely many solutions, identity, multiplicative inverse (reciprocal), like terms, greater than, greater than or equal to, less than, less than or equal to, is more than, is less than, no more than, no less than, at most, at least, maximum, minimum, compound, and, or, open/closed circle, inclusive, not inclusive, intersection, union, reasonable, interpret

Example: A total of 66 people attended a field trip to a chocolate factory for a tour. A maximum of 15 people are allowed to tour at one time. Create an inequality to describe how many tour groups to organize? (Let g = the number of groups.)

Strategies/Activities: Process Standards https://www.khanacademy.org/math/pre- algebra/applying-math-reasoning-topic/greater-than-less- 1. Make sense of problems and than/e/inequalities-in-one-variable-1 persevere in solving them. http://teachers.henrico.k12.va.us/math/hcpsalgebra1/A- 2. Reason both contextually and 5a.html abstractly. http://www.algebra-class.com/solving-word-problems-in- algebra-practice.html 3. Use critical thinking skills to justify mathematical reasoning and http://www.doe.state.la.us/lde/uploads/5629.pdf critique the reasoning of others. Grade 9 Algebra 1, Q1

4. Connect mathematical ideas and real-world situations through modeling.

5. Use a variety of mathematical tools effectively and strategically.

6. Communicate mathematically and approach mathematical situations with precision.

7. Identify and utilize structure and patterns.

Resources: Text: Holt McDougal Algebra I Common Core Edition, sections 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7

Exemplar Lessons: http://betterlesson.com/lesson/443651/creating-inequalities-to-solve-problems

Web Sites: http://www.shmoop.com/common-core-standards/ccss-hs-a-ced-1.html

Videos: http://my.hrw.com/tabnav/controller.jsp?isbn=9780547708508

USATestPrep: Graphing Solutions to Inequalities (2:49), Interpret Solutions: Inequalities (1:18), Solve 1-Variable Inequalities I (1:24), Solve 1-Variable Inequalities II (1:53), Solve Multi-step Inequalities (2:18), Solving Linear Inequalities (2:43), Word Problems: Linear Inequalities (2:58) www.phschool.com, Web Code: ate-0775, Chapter 4: Lessons 1, 2, 3, 4, 5, 6

Sample Assessment-like Questions: Assessments: Textbook assignments, Worksheet assignments, Quizzes, Tests, Oral responses, Observations

Holt Algebra 1 Test Prep: p. 104-105, 110-111, 116-118, 124-125, 130-131, 139-140, 146-148 Grade 9 Algebra 1, Q1

http://mathbitsnotebook.com/Algebra1/Inequalities/IQAppliedPractice.html

Multiple Choice:

Mrs. Nelson is buying folding chairs that are on sale for $10. She has $50. Which inequality can be solved to show the number of chairs c Mrs. Nelson can buy? A. 10c < 50 B. 10c > 50

Open Ended 1. A store manager is accepting applications for part-time workers. He can hire no more than 14 people. So far, he has hired 9 people. Write and solve an inequality to determine how many more people the manager can hire.

2. An essay must be at least 500 words long to be accepted. Define a variable and write an inequality for the acceptable number of words in an essay. Graph the solutions.