MATRIX _

Austin Independent School District Austin ISD Instructional Planning Guide – Mathematics Six Weeks IPG- October 5th – November 6th, 24 days; (2 days for 6 weeks review/test) 8th Grade Major Concept #1: Proportional Reasoning Overarching Idea Teacher Guiding Questions Matrix # Matrix Strand Recognizing, understanding, and applying proportional reasoning to ratios, rates, and percents.   11 DAYS How can using ratio tables help students understand relationships between proportional quantities? How are applications involving percents connected to proportional reasoning? How can using ratio tables help students understand percents? Student Expectation Focus TEKS Student Expectations The student is expected to select and use appropriate forms of rational numbers to solve real-life problems involving proportional relationships. (8.1B) The student is expected to select appropriate operations to solve problems involving rational numbers and justify the selections. (8.2A) The student uses appropriate operations to solve problems involving rational numbers in problem situations. (8.2B) The student is expected to use multiplication by a constant factor (unit rate) to represent proportional relationships. (8.2D) Supporting TEKS Student Expectations The student is expected to compare and contrast proportional and nonproportional linear relationships (8.3A) (8.15A and 8.16B) TEKS Knowledge & Skill TAKS OBJ Resource Foundation Activity: Holt: Alternate Opener Lessons 5-1 to 5-4 Core Lesson(s): APIE 8th Sense: Lesson 8.2A (Pages 93-101) Lesson 8.2B (Pages 103-109) Holt: 5-1 Holt: Lab Manual p. L18 – L19 Classroom Practice: 8th Sense Student pages: 97-101 Student pages: 107-109 Time/ Pace Teacher Tools Vocabulary: ratio and equivalent ratio, non-proportional, proportional TAKS Information: The students will be expected to compare and contrast proportional and non-proportional linear relationships and estimate and found solutions to application problems involving percents and other proportional relationships such as similarity and rates. Teacher Notes:  Use 8th Sense Lesson 8.3A to review proportional and non-proportional relationships.  Have students relate to unit rates to real-life situations – i.e. grocery shopping – all price labels give unit rates. Discuss with students why  Have students solve problems on a poster and show solutions using two different strategies. Allow students to present their work to the class. Discuss different strategies with the class.  If time allows, complete 8th Sense Lesson 8.2C. This lesson has the students evaluating problems for reasonable answers.  Have students identify key words in problems that led them to pick the operation. Differentiation Strategies Holt: Reading Strategies 5-1 Comparing Information Re-teach 5-1 Ratios and Proportions Extension Notes: Dimensional Analysis will be taught in the fourth six weeks IPG – These measurement conversions from sheets from Holt were included as an extension to provide practice problems for students to practice using ratio tables. Students must be skilled in finding relationships using ratio tables BEFORE they are shown how to cross-multiply as an algorithm for unfriendly numbers. Ratio tables are based on strong numerical reasoning. Cross products are used only when this reasoning is evident in students’ mastery work with tables. Supporting TEKS Numbers and Operations and Algebraic Thinking Underlying Processes and Tools The student understands that different forms of numbers are appropriate for different situations. (8.1) 117 133 132 131 222 The student selects and uses appropriate operations to solve problems. (8.2) Supporting TEKS The student identifies proportional or nonproportional linear relationships in problem situations and solves problems. (8.3) 1& 2 Homework Practice: Holt: Practice Workbook p. 32 # 1-20 Centers: Building Arrays MGA2 Equivalent Fraction Array (Page 106) Extension: Holt: pp.224-227 Dimensional Analysis 2 days DRAFT 8th Grade Page 1 of 6 11/7/2009 MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series Austin Independent School District Austin ISD Instructional Planning Guide – Mathematics Six Weeks IPG- October 5th – November 6th, 24 days; (2 days for 6 weeks review/test) 8th Grade Major Concept #1: Proportional Reasoning Overarching Idea Teacher Guiding Questions Matrix # Matrix Strand Recognizing, understanding, and applying proportional reasoning to ratios, rates, and percents.   11 DAYS How can using ratio tables help students understand relationships between proportional quantities? How are applications involving percents connected to proportional reasoning? How can using ratio tables help students understand percents? Student Expectation The student is expected to select and use appropriate forms of rational numbers to solve real-life problems involving proportional relationships. (8.1B) TEKS Knowledge & Skill TAKS OBJ Resource Time/ Pace Teacher Tools Vocabulary: rate, unit rate, unit price, ratio tables, constant factor Numbers and Operations and Algebraic Thinking And Patterns Generalizations, Relationships, Proportional Reasoning and Making Predictions The student understands that different forms of numbers are appropriate for different situations. (8.1) Foundation Activity: HOM Developing the ratio concept and equivalent ratios or proportions (Pages 69-74) Core Lesson (s): APIE 119-125 Munchie Math NCTM: Navigating through Numbers and Operations; Using Unit Rate to Solve Problems pp. 147-149 NCTM: Activities for Middle School Math – pp.125-129 Ratio Tables MIC: Revisiting Numbers pp. 1-8 Classroom Practice: 8th Sense Student pages 123-125 Munchie Math Homework Practice: Holt: Practice Workbook p. 35 Holt: Lab Manual; p. PS32 Holt Textbook: pp.222 #114 NCTM: Teaching in Middle School Mathematics (August 2008) – Ratio Triples pp12-17 TAKS Information: The students will be expected to compare and contrast proportional and non-proportional linear relationships and estimate and found solutions to application problems involving percents and other proportional relationships such as similarity and rates. 8th Sense Teacher notes for Munchie Math Lesson: The student is expected to select appropriate operations to solve problems involving rational numbers and justify the selections. (8.2A) The student uses appropriate operations to solve problems involving rational numbers and justify the selections. (8.2B) The student is expected to use multiplication by a constant factor (unit rate) to represent proportional relationships. (8.2D) The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. (8.3B) The student is expected to predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations (8.5A)      HOM use integer chip counters for introduction activity Lesson 8.2D and Munchie Math have students figuring how much items are at their unit cost. Allow students to make their own posters for Munchie Math. Bring in empty boxes of cereal for students. Bring in adds from newspaper for students to figure the unit price of items. 117 133 132 131 220 242 The student selects and uses appropriate operations to solve problems. (8.2) The student identifies proportional or nonproportional linear relationships in problem situations and solves problems. (8.3) 1& 2 3 days NCTM Activities Teacher Notes and Differentiation ideas      For the NCTM navigating lesson, be sure to read the teacher notes pp. 104-109 on proportional reasoning It is best to have discussion (such as the Re-teach: Ratios, Rates and Unit Rates) before beginning the NCTM Activity of Ratio Triples Density, which involves unit rate, is taught in Science class. Have a discussion with your science teacher about finding unit rates and there could be some reteach in the science class. The ratio triples includes task cards and prior reading for the teacher. Have students go grocery shopping with their parents/guardian and bring back the pricing information that compared different brands of the same item. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. (8.5) DRAFT 8th Grade Page 2 of 6 11/7/2009 MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series Austin Independent School District Austin ISD Instructional Planning Guide – Mathematics Six Weeks IPG- October 5th – November 6th, 24 days; (2 days for 6 weeks review/test) 8th Grade Major Concept #1: Proportional Reasoning Overarching Idea Teacher Guiding Questions Matrix # Matrix Strand 11 DAYS Recognizing, understanding, and applying proportional reasoning to ratios, rates, and percents.   How can using ratio tables help students understand relationships between proportional quantities? How are applications involving percents connected to proportional reasoning? How can using ratio tables help students understand percents? TEKS Knowledge & Skill Student Expectation TAKS OBJ Resource Core Lesson (s): APIE: (1) RIV Unit 2 Lesson 3 TE P. 92-104 SE P. 46-53 (2) RIV Unit 3 Lesson 2 TE P. 125-145 SE P. 64-72 (3) RIV Unit 3 Lesson 3 TE P. 146 - 159 SE P. 73-81 Classroom/Homework: RIV Student Edition Unit 2 Lesson 3 (pages 46-53) Unit 3 Lesson 2 (pages 64-72) Unit 3 lesson 3 (pages 73-81) Additional Classroom Practice Lessons: Holt - Lab manual: Alternate Openers/ Exploration: p. E40 and E43 Holt: Lesson 6-1, 6-3, 6-4, 6-5, 6-6 and 6-7 Holt: Are you Ready? Skills 2629 pp. 123-150 Centers: Super Source- Number Foreign Currency Exchange Super Source- Number From Head to Toe Extension: NCTM – Numbers and Operations Buying Pizza (page 85-89) student page 131 Exchanging Currency (page 9092) student pages 132-133 8th Grade Page 3 of 6 Time/ Pace Teacher Tools Vocabulary: proportional, non-proportional, rate, ratio TAKS Information: The students will be expected to compare and contrast proportional and non-proportional linear relationships and estimate and found solutions to application problems involving percents and other proportional relationships such as similarity and rates. Teacher Notes:  Unit 3 Lesson 2 – Each group will need paper clips and a ruler. Review measuring using customary units of a ruler before the activity.  Pesky Patterns - Activity master is found on CD for RIV. Each group gets a different pattern and creates a graph. Make a carousel activity to answer questions about patterns.  Unit 3 Lesson 3 – Before starting lesson review proportional relationships. Have students make a T-chart and list things they know about proportional and non-proportional relationships.  Foreign Currency Exchange – Make sure you relate exchange rates to proportions and show how to use them to find new exchange rates. Review changing fractions to decimals.  From Head to Toe – Demonstrate measuring with snap cubes. Vertical measurements should be made instead of measuring along the contour.  Percent Increase and Decrease should be at least 2 days. Differentiation Strategies from Holt for each lesson:  Reading Strategies and Re-teach resources  Power point presentations  Have students make flash cards of vocabulary – can be found through Holt on-line Additional Differentiation Strategies:  Use the Frayer Model for vocabulary in section 9 of the curriculum notebooks – post select quality student sheets.  Bring in clippings from the newspaper – particularly Wednesday - to get real-life practice in using percent off/increase. Include coupons such as Jiffy Lube and such that offer percent off. 11/7/2009 Numbers and Operations and Algebraic Thinking And Patterns Generalizations, Relationships, Proportional Reasoning and Making Predictions The student understands that different forms of numbers are appropriate for different situations. (8.1) Compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals. (8.1A) The student is expected to select and use appropriate forms of rational numbers to solve real-life problems involving proportional relationships. (8.1B) The student is expected to use multiplication by a constant factor (unit rate) to represent proportional relationships. (8.2D) The student is expected to compare and contrast proportional and nonproportional linear relationships (8.3A) 110 117 131 222 220 The student selects and uses appropriate operations to solve problems. (8.2) 1 and 2 3 days The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. (8.3) The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. (8.3B) DRAFT MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series Austin Independent School District Austin ISD Instructional Planning Guide – Mathematics Six Weeks IPG- October 5th – November 6th, 24 days; (2 days for 6 weeks review/test) 8th Grade Major Concept #1: Proportional Reasoning Overarching Idea Teacher Guiding Questions Matrix # Matrix Strand 11 DAYS Recognizing, understanding, and applying proportional reasoning to ratios, rates, and percents.   How can using ratio tables help students understand relationships between proportional quantities? How are applications involving percents connected to proportional reasoning? How can using ratio tables help students understand percents? TEKS Knowledge & Skill Student Expectation Select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships. (8.1B) The student is expected to select appropriate operations to solve problems involving rational numbers and justify the selections. (8.2A) The student uses appropriate operations to solve problems involving rational numbers and justify the selections. (8.2B) 1 and 6 The student is expected to use multiplication by a constant factor (unit rate) to represent proportional relationships. (8.2D) The student is expected to compare and contrast proportional and nonproportional linear relationships (8.3A) The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity rates. (8.3B) TAKS OBJ Resource Core Lesson: APIE: RIV Unit 2 Lesson 2 Unit 2 Lesson 1 8th Sense Lesson 8.3B (Pages 139 – 145) Holt 6-7 Classroom Practice: RIV Student Edition 2-2 (pages 39-45) 2-1 (pages 32-37) Percent/Proportion Foldable Lesson 8.3B (pages 143-145) Holt (pages 302-305) Homework Practice: Holt: Practice Workbook: pp. 40-46 and Lab Manual (Problems Solving) pp. PS40PS46 Centers: HOM Relate functions, decimals and percents. Activity 1: Renaming The Blocks (page 62-63) Activity 2: Picturing Equivalent Forms (pages 63-65) Activity 3: Peculiar Percents (Pages 66-68) 3 days Time/ Pace Teacher Tools Numbers, Operations, and quantitative reasoning The student understands that different forms of numbers are appropriate for different situations. (8.1) Vocabulary: percent, percent increase, percent decrease, commission, interest, principal, simple interest, sales tax, discount, sales price, commission, markup, markdown TAKS Information: The students will be expected to compare and contrast proportional and non-proportional linear relationships and estimate and found solutions to application problems involving percents and other proportional relationships such as similarity and rates. Teacher Notes:  2-2 – Review measuring with a metric ruler before starting activity. Review benchmarks of percent bars.  After using percent bars, model how to setup proportions based on bars.  Review finding percents of numbers with your class by using a percent bar. Use benchmark numbers and percents.  Complete foldable before Unit 2 Lesson 1 and Lesson 8.3B. Ask students guiding questions to learn how to use the foldable.  Review simple interest through Holt 6-7. Make sure that students recognize the simple interest formula on the Mathematics Chart.  Create a bulletin board with advertisements involving percents. Allow students to model application problems using the advertisements from the bulletin board. 117 133 132 131 The student selects and uses appropriate operations to solve problems. (8.2) The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. (8.3) DRAFT 8th Grade Page 4 of 6 11/7/2009 MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series Austin Independent School District Austin ISD Instructional Planning Guide – Mathematics Six Weeks IPG- October 5th – November 6th, 24 days; (2 days for 6 weeks review/test) 8th Grade Major Concept #2: Similarity Figures and Indirect Measurement Overarching Idea Teacher Guiding Questions 11 DAYS Recognizing, understanding, and applying proportional reasoning to Similar Figures; Indirect Measurement; Scale Drawings, Scale Models and Dilations    How does the concept of ratios and similarity connect to proportionality? How are applications involving percents connected to proportional reasoning? How are two-dimensional shapes affected by the absolute and relative change of their dimensions? Matri x# Matrix Strand TEKS Knowledge & Skill The student understands that different forms of numbers are appropriate for different situations. (8.1) The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. (8.3) The student uses graphs, tables, and algebraic representations to make predictions and solve problems. (8.5) The student uses transformational geometry to develop spatial sense. (8.6) The student uses indirect measurement to solve problems. (8.9) Student Expectation TAKS OBJ Resource Time/ Pace Teacher Tools Patterns Relationships and Algebraic Thinking Geometry Measurement Target TEKS Student Expectations The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity rates. (8.3B) The student is expected to generate similar figures using dilations including enlargements and reductions. (8.6A) The student is expected to use proportional relationships in similar twodimensional figures or similar three-dimensional figures to find missing measurements. (8.9B) Supporting TEKS Student Expectations (8.1B) (8.5A) (8.15A) (8.16B) Foundation Activity: HOM Enlarging Shapes (pages 267269) Core Lesson (s): APIE: RIV Unit 3 Lesson 1 (pages 109124) 8th Sense Lesson 8.9B (pages 281-291) Holt 5-7 (pages 248-249) Holt Math In Context: It’s all the Same P. 27-34 Student Activity Sheet 4 TE p. 78. Holt Math In Context: Section D Similar Problems P. 55-44 Student Activity Sheet 38 TE p. 78. Classroom/Homework Practice: RIV Student Edition 3-1 (pages 54-63) Lesson 8.9B 287-291 Extension: NCTM Geometry Indirect Measurement (page 77 and 118) Vocabulary: similar, congruent angles, corresponding angles, corresponding sides, indirect measurement, scale drawing, scale, scale model, scale factor TAKS Information:  Students will find and apply scale factor in problem solving situations  Match a 2 dimensional representation of a solid with a three dimensional representation of the same solid using the top, front and/or side views of the solid  Use proportional relationships in similar two=dimensional figures or similar three-dimensional figures to find missing measurements. Teacher Notes:  Enlarging shapes activity can be revisited or extended to compare areas of enlarged shapes.  Remind students of the meaning of similar shapes as defined by the activity Enlarging Shapes.  RIV 3-1 – Activity master is found on the CD. Have students make posters of their rectangles, and questions. Use this activity to define scale-factor.  Holt Math In Context: Every AISD Middle School Classroom should have a classroom set of the Math In Context books. If you do not have this student and teacher resource, please contact your department chair or campus textbook administrator for the classroom set of these student and teacher books. We are providing copies of the pages in the notebook, however, to save paper, please use the student books in the room. 220 242 313 419 610 613 2, 3, and 4 7 days DRAFT 8th Grade Page 5 of 6 11/7/2009 MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series Austin Independent School District Austin ISD Instructional Planning Guide – Mathematics Six Weeks IPG- October 5th – November 6th, 24 days; (2 days for 6 weeks review/test) 8th Grade Major Concept #2: Similarity Figures and Indirect Measurement Overarching Idea Teacher Guiding Questions 11 DAYS Recognizing, understanding, and applying proportional reasoning to Similar Figures; Indirect Measurement; Scale Drawings, Scale Models and Dilations    How does the concept of ratios and similarity connect to proportionality? How are applications involving percents connected to proportional reasoning? How are two-dimensional shapes affected by the absolute and relative change of their dimensions? Matri x# Matrix Strand TEKS Knowledge & Skill The student uses transformational geometry to develop spatial sense. (8.6) The student uses geometry to model and describe the physical world. (8.7) The student communicates about Grade 8 math through informal and mathematical language, representations, and models. (8.15) The student uses logical reasoning to make conjectures and verify conclusions. (8.16) Student Expectation Target TEKS Student Expectations The student is expected to generate similar figures using dilations including enlargements and reductions. (8.6A) The student is expected to graph dilations, reflections, and translations on a coordinate plane. (8.6B) The student is expected to locate and name points on a coordinate plane using ordered pairs of rational numbers. (8.7D) Supporting TEKS Student Expectations The student is expected to communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. (8.15A) The student is expected to validate his/her conclusions using mathematical properties and relationships. (8.16B) TAKS OBJ Resource Time/ Pace Teacher Tools Core Lesson (s): APIE: RIV Unit 5 Lesson 2 (Pages 225-248) TAKS Math Preparation RIV Coordinate Dilation Lesson (Pages 173-185) Holt: Hands-On Lab (Pgs. 242243) Classroom or Homework Practice: RIV Student Edition 5-2 (pages 112-124) Extension: 8th Sense Lesson 8.6A (pages 187-197) Vocabulary: dilation, scale factor, coordinate grid, ordered pair, transformations, enlargement, reduction, y-axis, x-axis, prime (‘) TAKS Information:  Students will find and apply scale factor in problem solving situations  Match a 2 dimensional representation of a solid with a three dimensional representation of the same solid using the top, front and/or side views of the solid  Graph points on coordinate grid using all four quadrants. 4 days Teacher Notes and Differentiation ideas:  Transformations end the second 6-weeks and begin the third 6-weeks. Reflection and translation will be taught at the beginning of the third 6-weeks.  RIV 5-2 – Activity master is on CD. Relate dilations with scale factor and proportions.  My Dilation activity – allow students to work in small groups and create posters of their different dilated characters.  Make a Venn Diagram that compares reductions to enlargements and how it relates to scale factor. 313 314 312 610 613 Geometry Underlying Processes and Tools 3 and 6 DRAFT 8th Grade Page 6 of 6 11/7/2009 MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series