#### Transcript K-8 Mathematics Standards - Lee County Public Schools

Teaching the Next Generation SSS (2007) Equations Threading Through Grades 6-12 In today’s inservice training, we will… engage in activities and in depth discussions that promote higher level thinking skills. connect standards in relation to solving equations with examples. analyze items that prior grade levels have learned. NCTM Process Standards Problem Solving – Developing perseverance and critical thinking – Allow students think time to reach a solution Reasoning and Proof – Mathematical conjectures – Examples and counter examples Communication – Read, write, listen, think, and discuss – Increase the use of appropriate math vocabulary NCTM Process Standards Connections – Integers, expressions, and equations – Other content areas, science – Real-world contexts Representation – Useful tools for building understanding – Concrete - Representational - Abstract – Tables, describe in words, draw a picture, write and solve equations What is Rigor? Rigor Rigor is quality instruction that focuses on the depth of the learning not the breadth. It’s not more work; it’s meaningful, respectful work that requires the student to think deeply and critically to accomplish the assigned tasked. Eric Bergholm, Hillsborough County Public Schools, Florida Strategies for Teaching In Depth Collaborate teaching vertical and horizontal Use cooperative learning (Kagan) strategies to introduce or remediate equations Represent equations using models, vocabulary, pictures, and real world situations Comparison of Standards Grade Level Old GLE’s New Benchmarks K 1st 2nd 3rd 4th 5th 6th 7th 8th 67 78 84 88 89 77 78 89 93 11 14 21 17 21 23 19 22 19 Coding Scheme for NGSSS MA. 912. Subject Grade Level A. 3. 1 Body of Big Idea/ Benchmark Knowledge Supporting Idea MA.912.A.3.1 Identify the threading standards for solving equations. The Common Thread Grade Level/Course 4 6 7 Benchmark Describe mathematical relationships using expressions, equations, and visual representations Write, solve and graph one- and two-step linear equations and inequalities. Formulate and use different strategies to solve one- and two-step linear equations including equations with rational coefficients. 8 Solve literal equations for a specific variable. Algebra 1 Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. Geometry Solve real world problems using right triangles. Algebra 2 Solve logarithmic and exponential equations Pre-Calculus Solve trigonometric equations and real-world problems involving applications of trigonometric equations using technology when appropriate. NGSSS: Equations(6th) MA.6.A.3.2 - Write, solve, and graph one and two step linear equations and inequalities Example: The height of a tree was 7 inches in the year 2000. Each year the same tree grew an additional 10 inches. Write an equation to show the height h of the tree in y years. Let y be the number of years after the year 2000. 12 6th grade y = 10x + 7 10 is the slope (amount that the tree grows each year) 7 is the y intercept (the starting year 2000) NGSSS: Equations(7th) MA.7.A.3.3 - Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational expressions. Example: Which steps would solve ⅔x – 4 = 10 A. Add 4 to both sides of the equation, then multiply both sides by 2/3. B. Add 4 to both sides of the equation, then multiply both sides by 3/2. C. Subtract 4 from both sides of the equation, then multiply both sides by 2/3. D. Subtract 4 from both sides of the equation, then multiply both sides by 3/2. 14 NGSSS: Equations(8th) MA.8.A.4.1 - Solve literal equations for a specified variable. Example: The following equation tells you how much simple interest you will earn if you invest an amount of money (P) at a specified rate (r), for a given amount of time (t): I = Prt. Solve for P. 15 8th grade I = Prt. Solve for P I = Prt rt rt P = I_ rt NGSSS: Equations - Algebra MA.912.A.3.1 - Solve linear equations with one variable that include simplifying algebraic expressions. A B 3(2x+5) = 10x-3+2x x + 5(x-1) = 7 C D 10x + 12=2(5x + 6) 5(x + 4)= x +2x +6 17 Algebra 1 A. 3(2x + 5) = 10x – 3 + 2x 6x + 15 = 12 x – 3 Distributive & combine like terms -6x -6x 15 = 6x – 3 +3 +3 18 = 6x 6 6 x=3 Algebra 1 B. x + 5(x – 1) = 7 Distributive property x + 5x – 5 = 7 Combine like terms 6x – 5 = 7 +5 +5 6x = 12 6 6 x=2 Algebra 1 C. 10x + 12 = 2(5x + 6) 10x + 12 = 10x + 12 All real numbers or infinite solutions Algebra 1 D. 5(x + 4) = x + 2x + 6 5x + 20 = 3x + 6 Distributive and combine like terms -3x -3x 2x + 20 = 6 -20 -20 2x = - 14 2 2 x = -7 NGSSS: Equations - Geometry MA.912.G.5.4 - Solve real-world problems involving right triangles Example: The distance of the base of a ladder from the wall it leans against should be at least 1/3 of the ladder's total length. Suppose a 12-ft ladder is placed according to these guidelines. Give the minimum distance of the base of the ladder from the wall. How far up the wall will the ladder reach? 22 Geometry One third of the ladder is the base 1/3(ladder) = base 1/3(12) = 4 = base The base is at least 4 feet. NGSSS: Equations – Algebra 2 MA.912.A.6.5 – Solve equations that contain radical expressions. Example: Solve the following equation for x: 24 Algebra 2 Solve +5 +5 3x2 + 10x = 5 square both sides 3x2 + 10x = 25 -25 -25 3x2 + 10x – 25 = 0 Factor (3x – 5)(x +5) = 0 Solve for x. 3x – 5 = 0 x+5=0 x = 5/3 x=-5 NGSSS: Equations – Pre-Calculus MA.912.T.3.4 – Solve trigonometric equations and real-world problem s involving applications of trigonometric equations using technology when appropriate. Example: Solve 2 sin(x) +1=0 on the interval [0, 2p) 26 Pre Calculus 2sin(x) + 1 = 0 -1 -1 2sin(x) = -1 2 2 Sin(x) = -1/2 X = 7π/6, 11π/6 NGSSS: Equations – Calculus MA.912.C.3.8 – Solve optimization problems. Example: You want to enclose a rectangular field with an area of 5,000 m^2. Find the shortest length of fencing you can use. Calculus The minimum perimeter (length of the fencing) would be if the rectangular field is a square. Therefore: If x is the side of the square, then x2 = 5000 (area) x = 5000 m The shortest length of fencing is the perimeter of the square, 4 times x or approximately 282.843 m Textbook Prentice Hall Website www.pearsonsuccessnet.com Access Codes for Florida courses 2011 Algebra 1 PHMADP11FLENA1B Geometry PHMADP11FLENGB Algebra 2 PHMADP11FLENA2B * Then create your own username and password. Holt/Larson Website http://my.hrw.com User Name: JRUTTER26 Password: z7d8w Glencoe Website www.connectED.mcgraw-hill.com Username: florida02 Password: math2011 Graphing Technology Standards (New) MA.912.A.3.12 Graph linear equations/inequalities with and without graphing technology. MA.912.A.4.9 Find approximate solutions for polynomial equations. MA.912.A.7.1 Graph quadratic equations with and without graphing technology. MA.912.A.7.10 Find approximate solutions of quadratic equations MA.912.A.9.2 Graph conic sections with and without using graphing technology. Algebra 1 Pre-AP Activity Holt McDougal Larson Florida textbook Investigating application of equations Through TI-Nspire Accessing the textbook website Select Holt McDougal Florida Larson textbook Select Videos and Activities tab Select TI-Nspire activities Select TI-Nspire Larson Algebra 1 activities Accessing the textbook website Select Holt McDougal Florida edition Algebra 1 (2011) – Scroll down to locate Select All TI products Choose Lesson HM.1.1.4 – Materials correlated to this standard Select Applications of equations Print teacher and student worksheets – Either pdf or doc Math Objectives Solving an equation with a real-world application Creating an equation to represent a real-world problem Recognize values of the variable that would not make sense for a real-world problem Vocabulary Equation Variable Download TI-Nspire files Need TI-Nspire Teacher Edition installed on your computer – See your tech specialist Applications_of_equations.tns Student worksheet and Teacher notes Introduce student worksheet Introduce parallel teacher notes Work through student worksheet using TI-Nspire Algebra 2 Activity Pearson Prentice Hall Florida textbook Investigating application of equations Activity/game Accessing the textbook website Mathematics FL Algebra 2 Select Teacher resources Select Chapter 1 Select Activities, games, and puzzles Select Lesson 1-4 activities, games, and puzzles Math Objectives To identify properties of equality To solve single- and multi-step equations To identify sometimes, always, or never statements To solve literal equations Vocabulary Identity Solution of an equation Inverse operations Equation Literal equation Websites Next Generation Sunshine State Standards www.floridastandards.org Academic Plan http://acadplan.leeschools.net/forms/index.htm Webb’s Depth of Knowledge http://deannasheets.com/questioning/Blooms_DOK.p df Websites Continued www.FloridaStandards.org Select Basic and Adult Education, Secondary Grades 9 -12, Mathematics, select your general subject, select your specific class. Algebra 1 Academic Plan Quarter 1 Chapter 1 Sec. 1-1 to 1-7 Chapter 2 Sec. 2-1 to 2-8 Chapter 3 Sec. 3-1 to 3-8 Quarter 1 District Common Exam Algebra 1 Academic Plan Quarter 2 Chapter 4 Sec. 4-1 to 4-7 Chapter 5 Sec. 5-1 to 5-7 Skip 5-2 Chapter 6 Sec. 6-1 to 6-6 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Algebra 1 Academic Plan Quarter 3 Chapter 7 Sec. 7-1 to 7-5 Chapter 8 Sec. 8-1 to 8-8 Quarter 3 District Common Exam From Q1 to Q3 but the emphasis is on Q3. Algebra 1 Academic Plan Quarter 4 Chapter 9 Sec. 9-1 to 9-6 Skip 9-5 Chapter 10 Sec. 10-1 to 10-3 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Algebra 1H Academic Plan Quarter 1 Chapter 1 Sec. 1-1 to 1-6 Skip 1-5 Chapter 2 Sec. 2-1 to 2-7 Chapter 3 Sec. 3-1 to 3-8 Chapter 4 Sec. 4-1 to 4-5 Quarter 1 District Common Exam Algebra 1H Academic Plan Quarter 2 Chapter 4 Sec. 4-1 to 4-7 Chapter 5 Sec. 5-1 to 5-7 Chapter 6 Sec. 6-1 to 6-7 Skip 6-5 to 6-6 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Algebra 1H Academic Plan Quarter 3 Chapter 7 Sec. 7-1 to 7-6 Chapter 8 Sec. 8-1 to 8-4 Chapter 9 Sec. 9-1 to 9-8 Chapter 10 Sec. 10-1 to 10-8 Skip 10-5 Quarter 3 District Common Exam From Q1 to Q3 but the emphasis is on Q3. Algebra 1H Academic Plan Quarter 4 Chapter 11 Sec. 11-1 to 11-2 Chapter 12 Sec. 12-1 to 12-4 Chapter 6 Sec. 6-5 to 6-6 Chapter 8 Sec. 8-5 to 8-6 Chapter 11 Sec. 11-3 to 11-5 Chapter 12 Sec. 12-5 to 12-7 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Geometry Academic Plan Quarter 1 Chapter 1 Sec. 1-1 to 1-8 Skip 1-6 Chapter 2 Sec. 2-1 to 2-6 Skip 2-4 Chapter 3 Sec. 3-1 to 3-8 Skip 3-6 Quarter 1 District Common Exam Geometry Academic Plan Quarter 2 Chapter 4 Sec. 4-1 to 4-7 Chapter 5 Sec. 5-1 to 5-7 Chapter 6 Sec. 6-1 to 6-7 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Geometry Academic Plan Quarter 3 Chapter 7 Sec. 7-1 to 7-5 Chapter 8 Sec. 8-1 to 8-4 Chapter 10 Sec. 10-1 to 10-8 Skip 10-5 Chapter 12 Sec. 12-3 Chapter 11 Sec. 11-1 to 11-3 Quarter 3 District Common Exam From Q1 to Q3 but the emphasis is on Q3. Geometry Academic Plan Quarter 4 Chapter 11 Sec. 11-4 to 11-7 Chapter 12 Sec. 12-1 to 12-5 Chapter 9 Sec. 9-1 to 9-7 Skip 9-4 Chapter 1 Sec. 1-6 If you have the time Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Geometry H Academic Plan Quarter 1 Chapter 1 Sec. 1-1 to 1-7 Chapter 2 Sec. 2-1 to 2-7 Chapter 3 Sec. 3-1 to 3-6 Quarter 1 District Common Exam Geometry H Academic Plan Quarter 2 Chapter 4 Sec. 4-1 to 4-8 Chapter 5 Sec. 5-1 to 5-6 Chapter 6 Sec. 6-1 to 6-7 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Geometry H Academic Plan Quarter 3 Chapter 7 Sec. 7-1 to 7-7 Chapter 8 Sec. 8-1 to 8-7 Chapter 9 Sec. 9-1 Chapter 11 Sec. 11-1 to 11-6 Quarter 3 District Common Exam From Q1 to Q3 but the emphasis is on Q3. Geometry H Academic Plan Quarter 4 Chapter 10 Sec. 10-1 to 10-7 Chapter 12 Sec. 12-1 to 12-7 Chapter 9 Sec. 9-2 to 9-7 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Liberal Arts Academic Plan Quarter 1 PH Algebra 1 Skill Handbook Line Plot Chapter 2 Sec. 2-7 Chapter 1 Sec. 1-2 to 1-8 Chapter 8 Sec. 8-2 to 8-5 Chapter 5 Sec. 5-2 Chapter 2 Sec. 2-1 to 2-5 Chapter 3 Sec. 3-4 to 3-6 Chapter 6 Sec. 6-1 to 6-5 Quarter 1 District Common Exam Liberal Arts Academic Plan Quarter 2 PH Geometry Chapter 1 Sec. 1-6 Chapter 3 Sec. 3-1 Chapter 5 Sec. 5-2 to 5-3 Chapter 4 Sec. 4-1 to 4-3 Chapter 8 Sec. 8-3 to 8-4 Chapter 7 Sec. 7-2 to 7-3 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Liberal Arts Academic Plan Quarter 3 PH Geometry Chapter 3 Sec. 3-4 Chapter 6 Sec. 6-1 to 6-5 Chapter 7 Sec. 7-1, 7-4, and 7-5 Chapter 4 Sec. 4-1 Chapter 8 Sec. 8-1 and 8-2 Chapter 10 Sec. 10-3 to 10-8 Quarter 3 District Common Exam From Q1 to Q3 but the emphasis is on Q3. Liberal Arts Academic Plan Quarter 4 PH Geometry Chapter 7 Sec. 7-6 and 7-7 Chapter 11 Sec. 11-2 PH Algebra 1 Chapter 10 Sec. 10-5 to 10-7 Chapter 7 Sec. 7-1, 7-5, and 7-6 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Algebra 2 Academic Plan Quarter 1 Chapter 1 Sec. 1-1 to 1-6 Chapter 2 Sec. 2-1 to 2-8 Chapter 3 Sec. 3-1 Quarter 1 District Common Exam Algebra 2 Academic Plan Quarter 2 Chapter 3 Sec. 3-2, 3-3 and 3-6 Chapter 4 Sec. 4-1 to 4-5 (part 1) Chapter 4 Sec. 4-6 to 4-8 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Algebra 2 Academic Plan Quarter 3 Chapter 5 Sec. 5-1 to 5-9 Chapter 6 Sec. 6-1 to 6-8 Quarter 3 District Common Exam From Q1 to Q3 but the emphasis is on Q3. Algebra 2 Academic Plan Quarter 4 Chapter 7 Sec. 7-1 to 7-5 Chapter 8 Sec. 8-1 to 8-6 Chapter 9 Sec. 9-1 to 9-5 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Algebra 2H Academic Plan Quarter 1 Chapter 1 Sec. 1-2 Chapter 2 Sec. 2-1, 2-3, 2-5 and 2-7 to 2-9 Chapter 3 Sec. 3-1 to 3-5 Chapter 4 Sec. 4-1 to 4-10 Skip 4-5 Quarter 1 District Common Exam Algebra 2H Academic Plan Quarter 2 Chapter 5 Sec. 5-1 to 5-9 Chapter 6 Sec. 6-1 to 6-6 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Algebra 2H Academic Plan Quarter 3 Chapter 7 Sec. 7-1 to 7-7 Chapter 8 Sec. 8-1 to 8-3 Quarter 3 District Common Exam Algebra 2H Academic Plan Quarter 4 Chapter 9 Sec. 9-2 to 9-7 Chapter 12 Sec. 10-1 to 10-6 Skip 10-5 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4. Pre-Calculus Academic Plan Quarter 1 Chapter 0 Formal Rules of Algebra Chapter 1 Sec. 1-1 to 1-7 Chapter 2 Sec. 2-3 to 2-6 Chapter 4 Sec. 4-1 to 4-5 Quarter 1 District Common Exam Pre-Calculus Academic Plan Quarter 2 Chapter 4 Sec. 4-6 to 4-7 Chapter 5 Sec. 5-1 to 5-5 Chapter 7 Sec. 7-1 to 7-5 Skip 7-4 2nd Semester District Common Exam From Q1 to Q2 but the emphasis is on Q2. Pre-Calculus Academic Plan Quarter 3 Chapter 8 Sec. 8-1 to 8-5 Chapter 9 Sec. 9-1 to 9-5 Skip 9-4 Chapter 10 Sec. 10-1 to 10-5 Quarter 3 District Common Exam Pre-Calculus Academic Plan Quarter 4 Chapter 12 Sec. 12-1 to 12-6 Chapter 3 Sec. 3-1 to 3-4 Final Exam District Common Exam From Q1 to Q4 but the emphasis is on Q4.