Course: Algebra 1 1st Nine Weeks Unit 1: Variables and Algebraic Expressions CLE: Instructional Guide Estimated Time: 3 Weeks; August 16-Sept 3 CLE 3102.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition. CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations. CLE 3102.2.2 Understand properties of and relationships between subsets and elements of the real number system CLE 3102.3.2 Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials. Essential Question: What is the unknown? Unit Vocabulary: Expressions, Integers, Irrational Numbers, Rational Numbers, Real Number System, Subsets, Evaluate, commutative, Associative, Distributive, Inverse, Identity Element, Closure, Reflexive, Symmetric, Transitive, Operation Properties of Equality, Like Terms Prerequisite Skills: compute with integers, fractions, and decimals; understand basic exponents; order of operations, variables Checks for State Performance Understanding Indicators Assessments Instructional Resources CLE3102.1.3 3102.1.9 Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality). 3102.1.10 Use algebraic properties to develop a valid mathematical argument SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems. Order of Operations - Section 1.3 – Order of Operations - Check calculator exercise (order of operations), Example 4, P18. - Order of Operations Bingo Game: http://illuminations.nctm.org/LessonDetail.aspx?id=L 730 - Webquest: http://imet.csus.edu/imet10/portfolio/esquivel_w/284/ WebQuest.html#task - Video: http://www.teachertube.com/viewVideo.php?video_id =10544&title=Who_s_Aunt_Sally____Order_of_Ope rations - Properties Games: http://www.quia.com/mc/151692.html - Order of Operations Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1 Connections ACT Connections - Substitute whole numbers for unknown quantities to evaluate expressions. - Write expressions, equations, or inequalities with a single variable for common pre-algebra settings. - Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers. Worksheets/Order%20of%20Operations.pdf - Properties Matching Worksheet: http://jcschools.net/dynamic/math/worksheets/propertieswks htalg1.pdf - Bike Racer Game: http://www.classzone.com/books/algebra_1/game/ch 02.htm - Order of Operations game: http://www.quia.com/cm/61109.html CLE3102.2.1 3102.2.1 Recognize and use like terms to simplify expressions. 3102.2.2 Apply the order of operations to simplify and evaluate algebraic expressions. 3102.2.4 Operate efficiently with both rational and irrational numbers Like Terms/Simplify/Evaluate Expressions - Review 1.1 – Variables in Algebra, P3, Section 1.1 - Introduce Like Terms and Simplify by Combination, P100, Section 2.6 o PowerPoint: www.tcc.edu/vml/Math04/Simplifying%20Expre ssions.ppt o Simplifying Expressions with video http://www.schooltube.com/video/33c83aa3300c4 1fa8e43/Simplifying-Algebraic-Expressions - Simplifying Expressions Online Lesson: http://www.montereyinstitute.org/courses/Algebra%2 0IA/course%20files/multimedia/lesson02/lessonp.ht ml - Evaluate Expressions PowerPoint: http://www.google.com/search?hl=en&safe=active&q =evaluate+expressions+powerpoint&aq=f&aqi=g1&a ql=&oq=&gs_rfai= - Evaluating Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1 Worksheets/Evaluating%20Expressions.pdf ACT Connection - Combine like terms. CLE3102.2.2 3102.2.7 Identify the subsets in the real number system and understand their relationships. 3102.2.8 Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line. SPI 3102.2.3 Describe and/or order a given set of real numbers including both rational and irrational numbers. - Number Sets Online Lesson: http://www.glencoe.com/sites/texas/student/mathem atics/assets/animation/algebra1/ALG1CIM1-8.swf - Number Sets Online Lesson: http://www.montereyinstitute.org/courses/Algebra%2 0IA/course%20files/multimedia/lesson01/lessonp.ht ml - Algebra 1 Springboard Lesson: “Sorting It All Out” - “Where Do I Live?” Activity: http://www.algebralab.org/activities/activity.aspx?file =Science_WhereDoILive.xml - Number Sets Worksheet: Evaluating Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg1 Worksheets/Evaluating%20Expressions.pdf CLE3102.3.2 3102.3.3 Justify correct results of algebraic procedures using extension of properties of real numbers to algebraic expressions. ACT Connection: - Locate points on the number line and in the first quadrant. - Order fractions. Course: Algebra 1 1st Nine Weeks Unit 2: Solving Equations CLE: Instructional Guide Estimated Time: 3 Weeks; Sept 7-Sept 27 CLE 3102.1.3 Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition. CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations. CLE 3102.3.4 Solve problems involving linear equations and linear inequalities CLE 3102.3.5 Manipulate formulas and solve literal equations. CLE 3102.4.1 Use algebraic reasoning in applications involving geometric formulas and contextual problems. CLE 3102.4.2 Apply appropriate units of measure and convert measures in problem solving situations. Essential Question: What strategies can be used to solve for unknowns in algebraic equations? Unit Vocabulary: Absolute Value, Coefficient, Constant, Equation, Property of Equality, Proportion, Ratio, Rational Numbers, Real Number Properties (Commutative, Associative, Distributive, Inverse, Identity, Symmetric, Transitive, Equality), Variable Prerequisite Skills: solve one and two-step equations and inequalities; find absolute value of a given number; use formulas such as area, perimeter, familiar with metric and customary measures; write and solve ratios and proportions, like terms, opposite, reciprocal Checks for Understanding State Performance Indicators CLE3102.1.2 3102.1.5 Use formulas, equations, and inequalities to solve realworld problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems. CLE 3102.1.3 3102.1.9 Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality). SPI 3102.1.2 Write an equation symbolically to express a contextual problem. Assessments Instructional Resources - Deep Sea Diver Game: http://www.classzone.com/books/algebra_1/game/c h01.htm - Algebraic Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/ Alg1Worksheets/Variable%20and%20Verbal% 20Expressions.pd SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems. - Evaluating Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/Alg 1Worksheets/Evaluating%20Expressions.pdf Connections ACT Connections: - Write expressions, equations, or inequalities with a single variable for common pre-algebra settings. - Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent. CLE3102.2.1 3102.2.1 Recognize and use like terms to simplify expressions. 3102.2.4 Operate efficiently with both rational and irrational numbers. CLE3102.3.4 3102.3.11 Solve multistep linear equations with one variable. 3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions. 3102.3.14 Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line. SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. - - CLE31024.1 3102.4.1 Using algebraic expressions solve for measures in geometric figures as well as for perimeter, area, and volume. CLE3102.4.2 3102.4.5 Use dimensional analysis to convert rates and measurements both Mummy Chase Review Game: http://www.classzone.com/books/algebra_1/game/ch 4/ch04.htm Solving Equations Game: http://www.studystack.com/matching-1857 Bike Racer Review Game: http://www.classzone.com/books/algebra_1/game/ch 06.htm Battleship – Solving Equations Game: http://www.quia.com/ba/36544.html Rags to Riches Equations Game: http://www.quia.com/ba/36544.html Jeopardy – Solving Equations: http://www.quia.com/cb/77775.html Brain Pop – Solving Equations: http://www.glencoe.com/sec/math/brainpops/000631 01/00063101.swf Brain Pop – Two-Step Equations: http://www.glencoe.com/sec/math/brainpops/000631 04/00063104.html Video Lesson: http://www.montereyinstitute.org/courses/Algebra%2 0IA/course%20files/multimedia/lesson03/lessonp.htm l Algebra 1 Springboard Lesson: “What’s the Error?” SPI 3102.4.1 Develop and apply strategies to estimate the area of any shape on a plane grid. Area Estimation Video Lesson: http://www.glencoe.com/sites/common_assets/mathe matics/geom_2010/math_in_motion/animations/MIM _geo_11-4extend.swf - Area Estimation Teacher Lesson: http://www.lessonopoly.org/svef/?q=node/6138# SPI 3102.4.4 Convert rates and measurements - Unit Conversion Examples: http://www.alysion.org/dimensional/fun.htm - Unit Conversion Lesson 1: http://www.glencoe.com/sites/common_assets/ mathematics/geom_2010/pt/GM_0-2-1.swf ACT Connections - Solve some routine two-step arithmetic problems. - Solve one-step equations having integer or decimal answers. - Solve real-world problems using first-degree equations. - Write equations and inequalities that require planning, manipulating, and/or solving. - ACT Connection - Solve multi-step arithmetic problems that involve planning or converting units of measure. within a system and between systems and check the appropriateness of the solution. - Unit Conversion Lesson 2: http://www.glencoe.com/sites/common_assets/ mathematics/geom_2010/pt/GM_0-2-2.swf - Unit Conversion Lesson 3: http://www.glencoe.com/sites/common_assets/ mathematics/geom_2010/pt/GM_0-2-3.swf - Unit Conversion Lesson 4: http://www.glencoe.com/sites/common_assets/ mathematics/geom_2010/pt/GM_0-2-5.swf “Paying For Your Wheels” NCTM Lesson: http://illuminations.nctm.org/LessonD etail.aspx?id=L708 Earthshine, Chapter 1, Theresa Nelson A small bottle of Dragon Blood can be purchased for $50. Bring in bottles of various sizes with the price labeled on each bottle. Have students to make standard measurement conversions for bottles of various products to find the price per gallon for each item. Have students explain at least one of their conversions. Course: Algebra 1 1st Nine Weeks Unit 3: Solving Inequalities CLE: Instructional Guide Estimated Time: 2 Weeks; Sept 28 - Oct 7 CLE 3102.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution. CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations. CLE 3102.3.4 Solve problems involving linear equations and linear inequalities Essential Question: How does the solution of the equation x – 5 = 12 differ from the solution of the inequality x – 5 < 12? When do you use an open circle for graphing inequalities? When do you use a closed circle for graphing inequalities? Unit Vocabulary: Inequality, Irrational Numbers, Number Line, Rational Numbers, Real Numbers, Real Number Properties (Commutative, Associative, Distributive, Inverse, Identity, Symmetric, Transitive, Equality), Variable, Compound Inequalities Prerequisite Skills: Checks for Understanding CLE 3102.1.2 3102.1.5 Use formulas, equations, and inequalities to solve realworld problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems. 3102.1.9 Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality). CLE3102.2.1 3102.2.1 Recognize and use like terms to simplify expressions. 3102.2.4 Operate evaluate expressions given values, inequality symbols, solution, number line, absolute value, algebraic properties, like terms State Performance Indicators SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems. Assessments Instructional Resources Connections - Evaluating Expressions Worksheet: http://www.kutasoftware.com/FreeWorksheets/ Alg1Worksheets/Evaluating%20Expressions.p df ACT Connections: - Write expressions, equations, or inequalities with a single variable for common pre-algebra settings. - Write equations and inequalities that require planning, manipulating, and/or solving. efficiently with both rational and irrational numbers CLE3102.3.4 3102.3.13 Solve multistep linear inequalities with one variable and graph the solution on a number line. 3102.3.14 Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line. SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. - - Solving Inequalities Tutorial: http://www.montereyinstitute.org/courses/Algebra% 20IA/course%20files/multimedia/lesson06/lessonp. html Absolute-Value Equations Tutorial: http://www.montereyinstitute.org/courses/Algebra% 20IA/course%20files/multimedia/lesson08/lessonp. html ACT Connections - Solve first-degree inequalities that do not require reversing the inequality sign. - Write equations and inequalities that require planning, manipulating, and/or solving. - Identify the graph of a linear inequality on the number line. - Solve simple absolute value inequalities. “Fireworks, Safety, and Mathematics”: http://www.glencoe.com/sites/texas/st udent/mathematics/assets/interactive _lab/algebra1/A1_07/A1_07_dev_100 .html Texas Instruments Calculator Activity: http://education.ti.com/educationporta l/activityexchange/activity_detail.do?ci d=us&activityid=4421