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COVER PAGE for MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks

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The purpose of this cover page is to provide support for understanding the Horizontal Alignment Planning Guide fields in order to effectively plan instruction. The HISD philosophy for Horizontal Alignment Planning Guides (HAPG) is to serve as the district guide that outlines the nonnegotiable curriculum objectives, supports meaningful instruction based on promising practices, and serves as the springboard for effective instructional planning. Therefore, HAPGs serve as a framework to support the development of units of instruction. Learning Focus: This field provides a unit title with a brief description of the main idea for a unit of study. Each Learning Focus is numbered indicating the grading cycle followed by the unit of instruction within the learning cycle. Ex. Learning Focus 1.1. Key Concepts: This field provides ideas that assist students with transfer of knowledge from the factual level to the conceptual level and may be used by teachers to write essential understandings. Concepts meet the following criteria: common attributes, timeless, universal, abstract, and broad. In English Language Arts, information under this field may also include words that represent Readers or Writers Craft. One or more concepts will be underlined in the Learning focus to assist teachers in planning a concept-based unit of study. Key Skills: This field identifies processes that represent the ability of the student to use knowledge effectively or to execute a performance. Time Assessment HISD Objectives Instructional Considerations Instructional Strategies Resources Allocation Connections This field This field identifies and describes high-yield This field This field identifies a group of This field provides a variety of information to This field provides provides instructional practices. provides HISD Objectives that define support thoughtful planning. resources, guidance for connections to “what” should be taught within materials, and Title/Name of Strategy recommended some the Learning Focus. HISD All content area documents will provide the technology to Strategies based on the nine categories assessments number of Objectives are aligned to the support following: identified in research by Marzano will appear lessons and (see list below). terminology, skills, and concepts instructional Prerequisites and/or Background Knowledge in bold print. the number of of the Texas Essential planning. for Students District and minutes per Knowledge and Skills (TEKS). Resources and These items identify prior general experiences or Literacy Leads the Way Commitments lesson for the State materials may skills students may need to be successful with a Literacy strategies are denoted with a compass learning include: specific objective in a specified grade level. Assessments: Ê Power Objectives are a icon in all curricular areas. focus. TAKS, subset of HISD Objectives and Background Knowledge for Teacher TPRI/TEJAS • District-wide are denoted with a “P” icon. Instructional Modifications for Diverse Time LEE, Assessing resources such They meet the following criteria: Learners allocations Essential Understandings are two or more Math Concepts, as textbooks endurance, readiness, and support concepts stated as a relationship that transfers TELPAS (ELA), Scholars and Knowledge framework leverage. appropriate student thinking to multiple situations – through PK Literacy • Links to This framework is a K-12 resource for Gifted attention for Assessment Kit, time and across cultures. They reflect the supporting PK-12 English Language and Talented (G/T) instruction which allows deep deeper understandings associated with specific PK Numeracy documents for differentiation. Proficiency Standards (ELPS) instruction on Assessment Kit, factual content. They can be tested against and should be implemented in all Power supported by facts. Fitnessgram. Renzulli Learning super starter projects and • Professional content areas. ELPS are Objectives. unit supplements are aligned to grade level Resources denoted with a hyperlink icon, Guiding Questions are questions at the HISD curriculum HAPGs and to the Texas (journal articles, followed by the ELPS number In addition, analysis level or higher to guide students in Performance Standards Project. books, etc.) and letter code, ELPS allows the The classroom-based recommended discovering meaning and are a powerful tool for teacher to plan for differentiated formative and number of helping students think at more complex levels. See Instructional Considerations • TAKS instruction based on student summative lessons for information needs and learning level. assessments are Special Education each HAPG Denotes additional support for teaching books provided. This Special Education resource supports Information related to English cycle is less ELPS when instruction directly aligns to ELPS differentiated instruction. Language Learners (ELLs) that is than the Sample cited in HISD Objectives column. • Children’s not specifically aligned to ELPS number of formative literature Houston ISD has adopted the National will appear in green text actual days in assessments Vocabulary Geographic ELPS (NGELPS) Teacher’s Edition throughout the document. the grading that can be used ¾ Academic words are more complex, • Internet Safety to assist secondary teachers in implementing the cycle to to monitor frequently occurring words that students will The Texas College and Career English Language Proficiency Standards into all accommodate learning during see and use often in academic settings. • Renzulli Readiness Standards (TxCCRS) core and enrichment courses. differentiated instruction are ¾ Content-specific words are highly specialized Learning login are sponsored by the Texas instruction numbered by words that are related to a specific discipline Higher Education Coordinating Teachers should consistently teach and and extended Learning Focus. and not frequently encountered outside of the Board (THECB) and reflect the model exemplary Internet skills with special learning time. For example: content area. legislative mandate to create emphasis on ethical behavior and safe Formative standards that articulate the practices. Resources for teaching these Assessment 1.1 Performance Expectations add details knowledge and skills students important topics can be found on the HISD pertaining to what students are expected to need to successfully participate Cyber Safety website. perform based on the requirements of the in entry-level college courses. objectives. What is it we want all students to learn?

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks Learning Focus 2.1 – Exponents and Scientific Notation Students use positive and negative exponents in algebraic representations. They also learn to express very large and very small numbers in scientific notation. Key Concepts: • Representation • Exponent • Scientific Notation Time Assessment HISD Objectives Instructional Considerations Instructional Strategies Allocation Connections TAKS (Obj. 1) Cues, Questions, and Advance Organizers Prerequisites/Background Knowledge for MATH.8.1D Grade 8 Total Students Express numbers in Graphic Organizers 2009: #22 (G) Number of Sixth grade Pre-AP students: scientific notation, As a precursor to scientific notation, review Days for including negative 2006: #13(A) • wrote prime factorizations using exponents; place value and expanded notation using Base Learning exponents, in appropriate 2004: #3(C), and Ten Blocks (Graphic Organizer: Mathematics Focus 2.1: problem situations. #43(C) • simplified expressions involving exponents. Graphic Organizer Templates: Place Value 4 days 1(H), 3(C) Chart – see Resources column). Connections to Future Objectives/ Introduce scientific notation as a TAKS (Obj. 1) Assessments Ê MATH.8.1B Two “shorthand notation” used for very large and Grade 8 • Later in this course and in Algebra I, Select and use 90-minute very small numbers. Discuss vocabulary 2009: #49 (A) students will use exponents in algebraic appropriate forms of lessons involved and where the numbers would fit on 2006: #27(C) expressions and equations and in scientific rational numbers to solve the class number line. Explore a model of an 2004: #40(F) notation. real-world problems or “exponential number line” with examples of • Scientific notation is, from this point forward, including those involving numbers from the real world in scientific the notation used for all very large and very proportional relationships. Four notation (Activity: Exponent Number Line – small numbers in mathematics and science 45-minute see Resources column). 3(C) applications. It is also used extensively in lessons TAKS (Obj. 1) scientific and graphing calculator MATH.8.2A Cooperative Learning Grade 8 applications. Select appropriate In small groups, students use tables and 2009: #6 (F), operations to solve patterns to introduce negative powers of ten. #31 (A) Essential Understandings/Guiding Questions problems involving Be sure to extend the patterns to reinforce the 2008: #1.3(A) Exponents and scientific notation are efficient 0 rational numbers and knowledge that 10 is equivalent to one 2006: #16(H), forms of numeric representation. justify the selections. (Laying the Foundation Activities: Discovery of #47(B) 1. What is the purpose of exponents? 2004: #6(J) 2. How are exponents used to represent positive Patterns with Positive and Negative Exponents, Negative Exponents – see numbers less than one? Resources column). 1(H) 3. How are numbers less than one expressed using scientific notation? Generating and Testing Hypotheses TAKS (Obj. 6) 4. Why are different forms needed to represent MATH.7.13A/ Have students explore and formalize the Grade 7 very large and/or very small numbers? MATH.8.14A “rules” for conversion between standard 2009: #12 (H), Identify and apply notation and scientific notation (Activity: Match #34 (J) Performance Expectations mathematics to everyday ‘Em Up – see Resources column). 2008: #6.1(D) By the end of the learning focus, students will experiences, to activities 2006: #6(J) use positive and negative exponents in algebraic Cooperative Learning in and outside of school, 2004: #3(D), representations, express very large or very small Assign students “values” in scientific and with other disciplines, and #48(H) numbers in scientific notation and identify and standard notation and have them arrange with other mathematical TAKS (Obj. 6) apply mathematics to everyday experiences. themselves in order and have them find their topics. Grade 8 partner, that is, the person with an equivalent 2009: #13 (B), Background Knowledge for Teacher value (Activity: Line ‘Em Up – see Resources #40 (G) Critical Content: column). 2008: #6.1(C) • Use powers and exponents; and 2006: #29(D), Homework and Practice • Use scientific notation. #48(F) Use interactive activities to assist students in 2004: #26(G) their understanding of exponents and scientific This is the first time students work with scientific notation (Activities: Brain POP videos or notation, and they should select and use Understanding Math 2008 – see Resources appropriate forms of rational numbers to solve column). real-world problems (Power Objective 8.1B). What is it we want all students to learn?

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Resources A Place Value Chart is available as a template in Mathematics Graphic Organizer Templates. Clarifying Activity: Exponent Number Line includes a model of an “exponential number line” with examples of numbers from the real world in scientific notation Print Resource: Laying the Foundation, Resource and Strategy Guide, Advanced Placement Strategies, Inc, 2004: • “Discovery of Patterns with Positive and Negative Exponents”, pp. 292 – 296 • “Negative Exponents”, pp. 298 – 303. Clarifying Activities: These manipulatives-based activities include student activity masters and extensive teacher notes. • Match ‘Em Up • Line ‘Em Up. Technology Resources: • BrainPOP videos o Exponents; o Negative Exponents; o Standard and Scientific Notation. • Virtual activities on scientific notation are available as Topic 4 in the Exponents section of Understanding Math 2008 from Neufeld Learning Systems, a software program available on HISD Middle School servers.

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives

Time Allocation

Assessment Connections Formative Assessment 2.1 – Assessment for Multiple Choice Questions Use a graphic organizer to solve multiplechoice problems and analyze answer choices (see notes in the Instructional Strategies and Resources columns).

Instructional Considerations Vocabulary Academic Models Tables

Content-Specific Place Value Expanded Notation Base Ten blocks Negative Exponents Exponential Notation Scientific Notation Vocabulary strategies such as those enumerated in the “Six-Step Process for Teaching Vocabulary” from Marzano Building Background Knowledge for Academic Achievement (2004) include: 1. Explain – provide a student friendly description, definition, or example of the new term. 2. Restate – the definition in the student’s own words. 3. Show – a symbol, picture, or graphic to represent the term. 4. Discuss/Oral practice – in structured ways with all students [pairs, groups] and use words so that students can add to their academic vocabulary. 5. Refine/Reflect – periodically revisit words and ask students to refine their word lists. 6. Apply – using learning games and written text.

Instructional Strategies

Resources

Use multiple-choice questions as formative assessments by having students explain not only the correct answers but also the incorrect answers. Using the graphic organizer provided in the formative assessment attachment, students first answer the question as indicated as if it is an open-ended question. Then students will look at all the possible answer choices. For the correct answer, the student adds justifications for the answer given. For the distracters, students must give reasons for why the answer is incorrect: word clues, process mistakes, or concept mistakes. Students may prove the mistake mathematically or in a written statement.

Formative Assessment 2.1 – Assessment for Multiple Choice Questions contains a Multiple-Choice Item Analysis graphic organizer as well as rubrics for evaluation purposes: • Teacher rubric • 6 – 8 Student rubric

If the formative assessment is given after a multiple choice test has been administered, students may use this process to check and correct their work. Even if the student has the question correct in the original testing, he/she must also prove why the incorrect answers are not possible. Region IV Rubrics are provided for evaluation purposes (Formative Assessment 2.1 – Assessment for Multiple Choice Questions – see Resources column).

Professional Resource: “Six-Step Process for Teaching Vocabulary” from Marzano, R.J. (2004) Building Background Knowledge for Academic Achievement. Alexandria, VA: Association of Supervision and Curriculum Development [ASCD]

Primary Textbook Resource: Glencoe, 2007 Texas Mathematics, Course 3 • TWE/SE, pp. 126 – 133; • Ch. 2 resource masters, pp. 56 – 68.

TAKS Tip At the seventh grade level, students are tested on simplifying numeric expressions involving exponents. Be sure to include practice problems involving this as a part of a lesson on scientific notation.

What is it we want all students to learn?

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks Learning Focus 2.2 – Square Roots and the Pythagorean Theorem Students use mental math and technology to approximate the value of square roots and irrational numbers and use them within the larger context of applying the Pythagorean Theorem and right triangle relationships. Key Concepts: • Exponent • Square root • Real number • Rational number • Irrational number • Pythagorean theorem • Relationship Time Assessment HISD Objectives Instructional Considerations Instructional Strategies Resources Allocation Connections TAKS (Obj. 1) Primary Textbook Resource: Prerequisites/Background Knowledge for Cues, Questions, and Advance Organizers MATH.7.1C Grade 7 Total Glencoe, Texas Students Represent squares & Graphic Organizers 2009: #7 (A) Number of Mathematics, Course 3 Sixth grade Pre-AP students: square roots using Review the real-world number system and its Days for geometric models and 2008: #1.2(D) • TWE/SE, 3-1, 3-2 & 3-4, • represented squares and square roots using components. Ask the students to fill in a Venn Learning use technology to 2006: #39(B) pp. 144 – 151, 155 – 159; geometric models; and Diagram with the subsets of the real-world Focus 2.2: estimate and determine 2004 #33(A), • Chap. 3 resource masters, • compared and ordered integers and positive numbers system (e.g. natural 6 days exact square roots. #42(G) pp. 9 – 22, 27 – 32; rational numbers. numbers, whole numbers, • Graphing Irrational integers, rational numbers, Connections to Future Objectives/ MATH.8.1C TAKS (Obj. 1) Numbers: Lab Activity, and irrational numbers). Assessments 2 days Approximate (mentally Grade 8 p. 172. Later in this course and in high school for this Identifying Similarities and Differences and with calculators) the 2009: #29 (D) • Teaching Math with Geometry, students will apply the Pythagorean cluster of Students use the Venn Diagram to value of irrational 2008: #1.2(D) Manipulatives, pp. 43 – Theorem in algebraic and geometric situations. objectives: compare and contrast the attributes of each numbers (such as pi and 2006: #18(F) 44. subset. 4(J) 2004: #42(G) √2) as they arise from Essential Understandings/Guiding Questions algebraic or geometric Exponents and square roots are related. Clarifying Activities: Nonlinguistic Representations One problem situations. 1. How are roots and powers related? • Activity 7.1C, Mathematics The concepts of squares and square roots 90-minute 2. How is the value of a square root estimated? Toolkit, UT Dana Center may be explored using manipulatives such as MATH.8.1E lesson Real numbers are either rational or irrational. • Activity 8.1C, Mathematics Base Ten tiles, color tiles, Algebra Tiles, or Compare and order real 1. How are the various subsets of the rational Toolkit, geoboards (Activities: Textbook resource, numbers with a or number system related? UT Dana Center Teaching Math with Manipulatives , Activities calculator. 2. How can you tell if a number is irrational? • Modeling Square Roots 7.1C and Activity 8.1C in the Mathematics Two 4(J) Toolkit – see Resources column). • Irrational Numbers on the Performance Expectations 45-minute MATH.7.13D/ Line By the end of the learning focus, students will lessons Cooperative Learning MATH.8.14D • Buffon’s Needle – approximate the value of square roots and Think-Pair-Share Select tools such as realExperiment with a irrational numbers using mental math and The addition of irrational numbers to the world objects, simulation to get an technology and use the Pythagorean Theorem to number system should lead to a discussion manipulatives, approximation of Pi by solve real-world problems in identified (e.g. Think-Pair-Share or Round Robin) of how paper/pencil, and dropping a needle on a appropriate contextual situations. to estimate square roots and where they fit on technology or techniques lined sheet of paper. a number line (Activity: Modeling Square such as mental math, (Interactivate, The Shodor Background Knowledge for Teacher Roots, Irrational Numbers on the Line, estimation, and number Education Foundation, Critical Content: Buffon’s Needle, Textbook Lab Activitysense to solve problems. Inc.) • Explore square roots and irrational numbers; Graphing Irrational Numbers – See and TAKS (Obj. 6) Resources column). Ê MATH.7.14A/ Print Resource: • Estimate square roots. Grade 7 “Minimizing Travel Time” is Homework and Practice 2009: #29 (A), Ê MATH.8.15A This is the first time that students work with an application problem found Students apply the knowledge and skills #42 (G) Communicate irrational numbers and use them in problem in the Laying the Foundation, acquired by completing rigorous applications 2006: #19(C), mathematical ideas using situations. Emphasize the definitions and Resource and Strategy and tasks within real-world contextual #47(B) language, efficient tools, classifications of irrational numbers and the Guide, Advanced Placement problems (LTF Activity: “Minimizing Travel 2004: #10(F), appropriate units, and Square Root Property. Strategies, Inc, 2004, pp. 116 Time” – see Resources column). #23(A) graphical, numerical, – 123. Estimate the value of an irrational number by Grade 8 physical, or algebraic Use interactive activities to assist students in identifying the whole number values between 2009: #38 (G) mathematical models. their understanding of square roots (Brain Technology Resource: which it falls (Power Objective 8.1A). Make a 2006: #6(J) POP video, Square Roots – see Resources Square Roots is a BrainPOP connection to finding square roots on a calculator 2004: #9(B), column). video. at this time (Power Objective 7.14A and 8.15A). #31(D) What is it we want all students to learn? Objective Code Key: T - TAKS © Houston ISD – Curriculum - ELPS (English Language Proficiency Standards) Elementary – Content Area.GradeLevel.Objective (Obj) = TAKS objective tested DRAFT 2010 – 2011 - Literacy Leads the Way Best Practices Page 3 of 11 Secondary – Course.Objective *(x) - Grade level Assessed on TAKS Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives

Time Allocation

MATH.8.7C Use pictures or models to demonstrate the Pythagorean Theorem. 1(A), 2(D)

2 days for this cluster of objectives:

One 90-minute lesson or Two 45-minute lessons

MATH.8.2B Use appropriate operations to solve problems involving rational numbers in problem situations and justify the problemsolving process and the reasonableness of the solution.

Assessment Connections TAKS (Obj. 3) Grade 8 2009: #32 (G) 2008: #3.4(A); 2006: #22(H) TAKS (Obj. 7) Grade 9 2009: #11 (A) 2008: #7.3(D); 2006: #23(C) Grade 10 2009: #32 (F), #49 (A) 2008: #7.3(C); 2006: #15(D)

TAKS (Obj. 1) Grade 8 2009: #19 (18.75) 2008: #1.4 (128.75) 2006: #11(B) 2004: #35(D), #47(D)

Instructional Considerations Vocabulary Academic Models Estimation Think-Pair-Share Round Robin Graphing

Content-Specific Square roots Rational numbers Irrational numbers Number line Square Root Property

Prerequisites/Background Knowledge for Students Sixth grade Pre-AP students determined the value of square roots by estimation and by using technology.

What is it we want all students to learn?

Resources

Nonlinguistic Representations Geoboard or Grid Paper Activity To begin, illustrate a square placed at right angles with the dots or pins. Students have no problem with finding the area or side length of a construction that is “square” with the grid. However, when the square is “tilted” as shown below, the counting strategy students often use is ineffective (Activities: Teaching Math with Manipulatives, Lab activity in the textbook – see Resources column).

Primary Textbook Resource: Glencoe, Texas Mathematics, Course 3 • TWE/SE, 3-1, 3-2 & 3-4, pp. 144 – 151, 162 – 171; • Lab Activity, p. 161; • Ch. 3 resource masters, pp. 9 – 22, 27 – 45; • Teaching Math with Manipulatives, pp. 43 – 44, 46 – 47; • Mathscape: Roads and Ramps, pp. 236 – 239.

Connections to Future Objectives/ Assessments Students will use the Pythagorean Theorem in algebraic and geometric contexts in this grade and beyond. Essential Understandings/Guiding Questions The Pythagorean Theorem can be used to solve problems involving right triangle relationships. 1. How can the area of a “tilted” square be determined? 2. How is the measure of the hypotenuse of a right triangle related to the measures of the other two sides (legs)? 3. How can models be used to demonstrate the Pythagorean Theorem? Background Knowledge for Teacher Critical Content: • Explore Pythagorean Theorem using models.

MATH.7.15A/ MATH.8.16A Make conjectures from patterns or sets of examples and nonexamples.

Instructional Strategies

The Pythagorean Theorem should be demonstrated using models, both concrete and pictorial. In hands-on activities, be sure that students discover or experience: • that the hypotenuse is always the longest side and its relationship to the placement of the right angle; • that the Pythagorean Theorem is only true of right triangles; • the use of letters other than a, b, and c in examples; • identification of models of examples and nonexamples of the Pythagorean Theorem.

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Cooperative Learning Students work in pairs or small groups to discover a “system” for finding the area of such a tilted square.

Nonlinguistic Representations Think-Aloud Students collect information about the area of squares on the sides of right triangles drawn on dot paper or illustrated on a geoboard. Use a Think-Aloud strategy to relate the information they discovered previously to find the area of the “tilted” square on the hypotenuse of a right triangle as well as those on the legs of the triangle (Activities: Modeling the Pythagorean Theorem, “Pythagorean Theorem Investigation” (LTF activity) – see Resources column).

Clarifying Activity: Modeling the Pythagorean Theorem is a manipulativesbased activity that includes student activity masters and extensive teacher notes.

Print Resource: “Pythagorean Theorem Investigation” is an application problem found in the Laying the Foundation, Resource and Strategy Guide, Advanced Placement Strategies, Inc, 2004, pp. 220 – 224.

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives

Time Allocation

Assessment Connections

Instructional Considerations There are two common solutions for finding the area of a tilted square: • Enclosing the square in a large square and subtracting the “outside” triangular area. • Subdividing the square into small regions and combining their area.

After students have found the area of the squares, they should see how area relates to the side length and how that is connected to the concepts of square root and irrational numbers. For example, the connection between a square 2 of area 5, the formula A = 5 , and the side length of

5 should be made.

A statement of the relationship between the lengths of the sides of a right triangle should be the ultimate goal of an investigation of the model of the squares on those sides. This observation leads to the verbalization of the Pythagorean Theorem.

Instructional Strategies Summarizing and Note Taking Graphic Organizers As students gather data from various right triangles and the squares on their sides, they should be recording their notes and observations using some form of an organizing grid such as a t-chart or table (Activities: Pythagorean Squares and Activity 8.7C in the Mathematics Toolkit – see Resources column).

Nonlinguistic Representations A non-linguistic representation or visual explanation linking the discoveries from the previous activity will help some students understand the essence of the Pythagorean Theorem. 1(A)

a2 + b2 = c2

A demonstration lesson (including video Vocabulary Academic Models

What is it we want all students to learn?

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

Content-Specific Squares Square roots Right triangle properties Area Legs Hypotenuse

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

clips) of the derivation of the Pythagorean Theorem (from Annenberg Media) may be used to help elaborate on their understanding of the concepts behind the Pythagorean Theorem (Geometry: The Pythagorean Theorem – see Resources column.) 2(D)

Resources

Clarifying Activities: The following hands-on manipulatives-based activities include student activity masters and extensive teacher notes: • Pythagorean Squares; • Activity 8.7C, Mathematics Toolkit, UT Dana Center.

Technology Resources: • A demonstration lesson (including video clips) is available at Learning Math, Geometry: The Pythagorean Theorem, Annenberg Media. • BrainPOP movie: Pythagorean Theorem; • Arcytech.org: The Pythagorean Theorem; • National Library of Virtual Manipulatives: Pythagorean Theorem. • Interactivate, The Shodor Education Foundation, Inc.) o Pythagorean Theorem (Lesson); o Pythagorean Explorer (Activity); o Squaring the Triangle (Activity). • Virtual activities on the Pythagorean Theorem are available as Topic 6 in the Understanding Graphing section of Understanding Math 2008 from Neufeld Learning Systems.

Homework and Practice Use technology-based or interactive activities to assist students in their explanations of the concepts learned in this learning focus (Activities: Brain POP movie: Pythagorean Theorem, Arcytech.org, National Library of Virtual Manipulatives, Interactivate, Understanding Math 2008 – see Resources column). - ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives

Ê MATH.8.9A Identify appropriate contextual situations for the use of the Pythagorean Theorem and use the Pythagorean Theorem to solve realworld problems.

Time Allocation 2 days for this cluster of objectives:

One 90-minute lesson or

MATH.8.2B Use appropriate operations to solve problems involving rational numbers in problem situations and justify the problemsolving process and the reasonableness of the solution.

Two 45-minute lessons

MATH.7.15A/ MATH.8.16A Make conjectures from patterns or sets of examples and nonexamples.

Assessment Connections TAKS (Obj. 4) Grade 8 2009: #24 (H) 2008: #4.2(A); 2006: #33(C), #45(C) TAKS (Obj. 8) Grade 9 2009: #29 (C) 2008: #8.2(A); 2006: #35(B) Grade 10 2009: #19 (20) 2008: #8.3(A); 2006: #53(C) TAKS (Obj. 1) Grade 8 2009: #19 (18.75) 2008: #1.4 (128.75) 2006: #11(B); 2004: #35(D), #47(D) TAKS (Obj. 6) Grade 7 2009: #15 (D) 2006: #2(J) 2004: #13(C) Grade 8 2009: #10 (G), #26 (H) 2006: #9(B), #37(C); 2004: #10(F) Formative Assessment 2.2 - In the Rafters applies the Pythagorean Theorem in an architecture situation (see notes in the Instructional Strategies and Resources columns).

What is it we want all students to learn?

Instructional Considerations Prerequisites/Background Knowledge for Students This is the first formal work with the Pythagorean Theorem. Previously, students identified right triangles and their properties. Connections to Future Objectives/ Assessments In Geometry, students will derive, extend, and use the Pythagorean Theorem. Essential Understandings/Guiding Questions The Pythagorean Theorem can be used to solve problems involving right triangle relationships. 1. How can the Pythagorean Theorem be used to find a missing side of a right triangle? 2. How is the Pythagorean Theorem used to determine if a triangle is a right triangle? 3. What kinds of real-world problems can be solved using the Pythagorean Theorem? Background Knowledge for Teacher Critical Content: • Apply the Pythagorean Theorem

After discovering the Pythagorean Theorem through exploration, students should apply it in numerous application situations (Power Objective 8.9A). Vocabulary Academic Models

Content-Specific Right triangle relationships Legs Hypotenuse Pythagorean Theorem Pythagorean Triples

TAKS Tips Illustrate the power of the Pythagorean Theorem using contextual problems that apply the theorem in various situations. For example, a common application used in testing situations is finding distances on maps or in illustrated situations. In working with the Pythagorean Theorem, students should: • use a calculator (Obj. 8.1E) • estimate solutions; • solve application problems that: o include fields such as art and architecture; o involve finding a leg when given the length of a leg and the hypotenuse of the triangle; o include multi-step solutions; and • evaluate solutions for reasonableness.

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Instructional Strategies Homework and Practice Rubrics Use a rubric as an evaluation tool for openended problems used as problem-solving opportunities or as formative assessments (Region IV Benchmark Assessments, Middle School Mathematics Assessments – see Resources column).

Sample problem: How much farther does Kris walk if she walks from her house to school and then to the bookstore than if she walks from her house to the bookstore? Justify your answer.

Homework and Practice Use graphing calculator activities to assist students in their exploration of these concepts and their applications (Graphing calculator activities at TI Activities Exchange – see Resources column).

Formative Assessment 2.2 - In the Rafters (see Resources column) is an activity that applies the Pythagorean Theorem to an architectural situation and integrates vocabulary that foreshadows the algebraic concept of slope (i.e. rise and run) from Middle School Mathematics Assessments.

Resources

Assessment Resources: Use the following openended problems as problemsolving opportunities or as formative assessments. • Region IV Benchmark Assessments; • Middle School Mathematics Assessments, Ch 3 UT Dana Center. Austin, TX. Technology Resources: Graphing calculator activities are available at TI Activities Exchange: • Walking the Fence Line, Then the Hypotenuse; • Right Triangles are Cool Because of Pythag's Rule; • Exploring the Pythagorean Theorem and its Applications. Primary Textbook Resource: Glencoe, Texas Mathematics, Course 3: • TWE/SE, 3-5 & 3-6, pp. 162 – 171; • Math Lab: The Pythagorean Theorem, pp. 160 – 161; • Chap. 3 res. masters, pp. 33 – 45; • Teaching Math with Manipulatives, pp. 45 – 47; • Application Activity: Distance on the Coordinate Plane: pp. 173 – 178. (Resource masters: pp. 46 – 52).

Formative Assessment 2.2 In the Rafters is an activity involving the Pythagorean Theorem from Middle School Mathematics Assessments. - ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks Learning Focus 2.3 – Equations and Algebraic Reasoning Students solve equations in which model real-world problems involving patterns and algebraic relationships. They also generate and use multiple representations of the same data in tables, graphs, verbal descriptions, and as symbols. Key Concepts: • Representation • Relationship • Pattern • Sequence • Expression • Table • Graph • Symbol • Verbal description • Equation • Operation • Property • Real-world problem HISD Objectives MATH.7.2E Describe the order of operations in a given numerical expression and simplify numerical expressions involving order of operations and exponents. MATH.8.4A Generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). 4(F) MATH.8.5B Write and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change) and identify the appropriate algebraic expression given terms in a sequence. 3(J)

Time Allocation Total Number of Days for Learning Focus 3.2: 12 days

Assessment Connections TAKS (Obj. 1) Grade 7 2009: #26 (H) 2008: #1.4(54) 2006: #44 (G); 2004: #30(G)

2 days for this cluster of objectives:

TAKS (Obj. 2) Grade 8 2009: #23 (D), #42 (F) 2008: #2.3(B) 2006: #3(B), #32(J) 2004: #7(A), #19(D)

One 90-minute lesson or Two 45-minute lessons

Ê MATH.7.14A/ Ê MATH.8.15A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

What is it we want all students to learn?

TAKS (Obj. 2) Grade 8 2009: #8 (J), #30 (G) 2008: #2.4(B) 2006: #10(H), #24(J) 2004: #32(G), #39(C)

TAKS (Obj. 6) Grade 7 2009: #29 (A), #42 (G) 2006: #19(C), #47(B) 2004: #10(F), #23(A) Grade 8 2009: #38 (G) 2006: #6(J) 2004: #9(B), #31(D)

Instructional Considerations Prerequisites/Background Knowledge for Students Sixth-grade Pre-AP students used words and symbols to describe the terms in an arithmetic sequence (with a constant rate of change) and their positions in a sequence; and represented those sequences using a variety of strategies (including concrete models, tables, algebraic rules, and graphs).

Instructional Strategies Nonlinguistic Representations

Engage students by using manipulatives such as geoboards, color tiles, pattern blocks, or graph paper to create concrete and pictorial representations of visual patterns that are then “translated” into the other representations (Activities: Borders, Cutting a Pizza, Graphs of a Sequence – see Resources column). 4(F)

Connections to Future Objectives/ Assessments In this course and in Algebra I, students write and solve equations given other representations of data.

Essential Understandings/Guiding Questions Patterns and sequences help to discover, analyze, describe, extend, and formulate understandings of mathematical relationships and real-world phenomena. 1. How do patterns and sequences occur in the real world? 2. How can we use patterns and sequences to solve real-world problems? Patterns and algebraic relationships can be represented with multiple representations (e.g. tables, graphs, symbols, and verbal descriptions). 1. How can patterns, represented either concretely or pictorially, be described with words and symbols? with tables and graphs? 2. Why are patterns and relationships represented in multiple ways? Expressions and equations are algebraic representations of patterns or sequences. 1. How can a pattern in a table or chart be recognized? 2. How can an expression or equation represent a relationship from the everyday world?

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Generating and Testing Hypotheses Students should connect models of arithmetic sequences (as in the example above) to their algebraic representations by: • predicting a rule for a model and justifying the answer; • writing a verbal description of a model that relates the figure number to the model; and • building tables that include a process column to explain the relationship between the figure number and its value (Activity 8.5B in the Mathematics Toolkit, Virtual Lesson: Junior High Math Interactives: Patterns – see Resources column).

Resources

Clarifying Activities: The following activities involve multiple hands-on opportunities. • Borders; • Cutting a Pizza; • Graphs of a Sequence; • Activity 8.5B, Mathematics Toolkit, UT Dana Center; • Junior High Math Interactives: Patterns; and • Guess My Rule.

Primary Textbook Resource: Glencoe, Texas Mathematics, Course 3: • TWE/SE, pp. 544-548; • Ch. 10 resource masters, pp. 28 – 33.

Nonlinguistic Representations Play “Guess My Rule” situations in concrete, pictorial, and symbolic situations (Activity: Guess My Rule – see Resources column). 3(J)

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives

Time Allocation

Assessment Connections

Instructional Considerations

Instructional Strategies

Resources

Performance Expectations By the end of this learning focus, students will generate and use multiple representations of the same data, solve equations that model real – world problems involving patterns and algebraic representations and predict, find, and justify solutions to application problems involving data displayed in various ways.

Summarizing and Note-Taking Two-Column Notes Function machines are a logical extension of patterning activities. Interactive virtual function machines are very helpful visual representations that allow students to make connections between “input” and “output” and relate these to other vocabulary such as “independent” and “dependent.” The actions that function machines simulate also help students formalize the use of function rules. Use a two-column note-taking strategy to create t-charts for the input and output values of the function machines with a summary box used for recording the formula rule in both verbal and symbolic forms.(Virtual Activities: Function Machine, Introduction to Functions, Introduction to Linear Functions, Understanding Math 2008 – see Resources column).

Technology Resources: • Function Machine at National Library of Virtual Manipulatives • Interactivate, The Shodor Education Foundation, Inc.) • Introduction to Functions • Introduction to Linear Functions • Patterns and sequences are found in Topics 1 and 3 of Understanding Algebra in Understanding Math 2008, Neufeld Learning Systems

Background Knowledge for Teacher Critical Content: • Write a rule for an informal pattern represented concretely or pictorially; and • Write a rule (expression) for function relationships presented in tables or as verbal descriptions.

Objectives 8.4A and 8.5B involve informal patterns and the multiple representations of the functions behind them. Power Objectives 7.14A and 8.15A references the use of these multiple representations at the application level. Begin by introducing familiar arithmetic sequences of numbers (constant rate of change) in t-charts and relating them back to concepts previously covered on proportionality (e.g. independent and dependent relationships, proportional vs. non-proportional relationships, ordered pairs, linear relationships).

Cooperative Learning In small groups, students elaborate on and apply the knowledge and skills acquired by completing rigorous applications and tasks within real-world contextual problems (Laying the Foundation Activity: “The Best Payment Plan” – see Resources column).

Print Resource: “The Best Payment Plan – Using Sequences” is an application problem found in the Laying the Foundation, Resource and Strategy Guide, pp. 182 – 188.

Move to formalizing relationships observed in the t-charts using finite differences and introduce the function rule for the relationship observed. Vocabulary Academic Models Patterns Input Output Function

Content-Specific Sequences Rate of change Finite Differences Function machines Independent variables Dependent variables

TAKS Tips At the seventh grade level, students are expected to be able to: • write an expression to find the nth term where n represents the position of the term in the arithmetic sequence; and • identify the expression when given terms in and arithmetic sequence, and vice versa. What is it we want all students to learn?

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives MATH.7.2E Describe the order of operations in a given numerical expression and simplify numerical expressions involving order of operations and exponents.

MATH.8.4A Generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description).

Time Allocation 2 days for this cluster of objectives:

Assessment Connections TAKS (Obj. 1) Grade 7 2009: #26 (H) 2008: #1.4(54) 2006: #44 (G); 2004 #30(G)

One 90-minute lesson or Two 45-minute lessons

TAKS (Obj. 2) Grade 8 2009: #23 (D), #42 (F) 2008: #2.3(B) 2006: #3(B), #32(J) 2004: #7(A), #19(D)

MATH.8.5B Write and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change) and identify the appropriate algebraic expression given terms in a sequence.

TAKS (Obj. 2) Grade 8 2009: #8 (J), #30 (G) 2008: #2.4(B) 2006: #10(H), #24(J) 2004: #32(G), #39(C)

Ê MATH.7.14A/ Ê MATH.8.15A

TAKS (Obj. 6) Grade 7 2009: #29 (A), #42 (G) 2006: #19(C), #47(B) 2004: #10(F), #23(A) Grade 8 2009: #38 (G) 2006: #6(J) 2004: #9(B), #31(D)

Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 1(E)

What is it we want all students to learn?

Instructional Considerations

Instructional Strategies

Prerequisites/Background Knowledge for Students Sixth-grade grade Pre-AP students wrote problem situations when given a simple equation and wrote equations when given a problem situation.

Cues, Questions, and Advance Organizers KWL To help students recall the order of operations, use an acronym such as GEMDAS (Grouping Symbol – Exponent – Multiplication – Division – Addition – Subtraction). This cue is different from that which most students are familiar in that the G stands for “grouping symbols.” Use a KWL graphic organizer to help students connect to their prior knowledge.

Connections to Future Objectives/ Assessments In this course, students write and solve equations given other representations of data. Essential Understandings/Guiding Questions Equations express relationships between two algebraic representations or expressions. 1. How are expressions simplified? 2. How is an equation different from an expression? 3. What does the “=” in an equation mean? Background Knowledge for Teacher Critical Content: • Order of operations; • Evaluate expressions; and • Write equations.

Objectives 8.4A and 8.5B involve informal patterns and the multiple representations of the functions behind them. Power Objective 8.15A references the use of these multiple representations at the application level. If students have had little or no previous exposure to algebraic models (e.g. Algebra Tiles), spend time discussing what each type of tile represents when introducing the models. Provide time for the students to practice using the models, both determining what a given tile arrangement represents and using the tiles to model a given expression.

As an important step in transitioning to the abstract level, students should be “recording” their steps first in pictorial form as they use the concrete manipulatives and then move to the symbolic recording process (Power Objectives 7.14A and 8.15A). 1(E) Vocabulary Academic Evaluate Patterns Models

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

Content-Specific Order of operations Algebraic expressions Equations Algebra Tiles

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Nonlinguistic Representations Write an algebraic expression such as 2 (4 + 1) – 6 – 3 + 5 on the board and ask the students to create index cards with each symbol and number. They then rearrange the cards to create new expressions that: • changes the numbers in order to have a greater or lesser value; • changes the grouping symbols in order to have a greater or lesser value; • change the operations in order to have a greater or lesser value; • change a combination of the grouping and operations to have a greater or lesser value.

Have students also (using their cards) model the largest and smallest value (Activity 7.2E in the Mathematics Toolkit – see Resources column). Cooperative Learning Group students in pairs or small groups to explore algebraic models such as Algebra Tiles or cups and counters to model representing expressions and equations concretely (Textbook, Teaching Mathematics with Manipulatives, pp. 36 – 37). Homework and Practice Use interactive virtual videos/activities to assist students in their conceptual understanding (Activities: BrainPOP movie “Order of Operations” and Understanding Math 2008 – see Resources column).

Resources

Clarifying Activity: Activity 7.2E, Mathematics Toolkit (UT Dana Center) includes a hands-on activity as well as scaffolding questions and assessment connections. Primary Textbook Resource: Glencoe, Texas Mathematics, Course 3 • TWE/SE, 1-2: pp. 29 – 34; 1-7: pp. 57 – 61; • Ch. 1 resource masters, pp. 15 – 20, 48 – 53; • Teaching Mathematics with Manipulatives, pp. 36 – 37; • Mathscape: Exploring the Unknown, pp. 182-185. Supplemental Textbook Resource: Glencoe, Texas Mathematics, Course 2 • TWE/SE, 1-4: pp. 38 – 41; • Ch. 1 resource masters, pp. 29 – 34. Technology Resources: • Order of Operations is a BrainPOP movie available online. • Virtual activities about the order of operations are available as Topic 9 in the Understanding Whole Numbers and Integers section of Understanding Math 2008 from Neufeld Learning Systems.

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives MATH.7.5A Use concrete and pictorial models to represent and solve equations involving rational numbers, use pictures and symbols to record the steps of the solution process, and verify the solution using substitution. 2(E)

Ê MATH.8.5A Predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations.

Time Allocation 8 days for this cluster of objectives:

Assessment Connections TAKS (Obj. 2) Grade 7 2009: #28 (J) 2008: #2.3(A) 2006: #11(A) 2004: #44(J)

Four 90-minute lessons

TAKS (Obj. 2) Grade 8 2009: #37 (C), #48 (G) 2006: #21 (244.5), #38(H), #46(G) 2004: #1(B), #14(F)

MATH.8.4A Generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). 3(E)

TAKS (Obj. 2) Grade 8 2009: #23 (D), #42 (F) 2008: #2.3(B) 2006: #3(B), #32(J) 2004: #7(A), #19(D)

Ê MATH.7.14A/ Ê MATH.8.15A

TAKS (Obj. 6) Grade 7 2009: #29 (A), #42 (G) 2006: #19(C), #47(B) 2004: #10(F), #23(A) Grade 8 2009: #38 (G) 2006: #6(J) 2004: #9(B), #31(D)

Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. 4(I)

What is it we want all students to learn?

Prerequisites/Background Knowledge for Students Sixth grade Pre-AP students: • used concrete and pictorial models to solve equations; and • simplified numerical expressions involving order of operation. Connections to Future Objectives/ Assessments In this course and in Algebra I, students write and solve linear equations given other representations of data.

or Eight 45-minute lessons

Instructional Considerations

Essential Understandings/Guiding Questions Inverse operations and the property of equality are used to solve algebraic equations. 1. How are inverse operations used to solve equations? 2. How are mathematical properties used to solve equations? Graphs of equations are visual representations of the algebraic relationships involved in real-world problems. 1. How does a graph of an equation relate to the equation? 2. What are the advantages of using a graph to represent an algebraic equation? Background Knowledge for Teacher Critical Content: • Solve addition and subtraction equations; • Solve multiplication and division equations; • Solve equations with rational numbers; • Simplify algebraic expressions; • Solve two-step equations; • Write two-step equations; and • Solve equations with variables on each side.

Students continue their study of Power Objective 8.5A by solving algebraic equations and applying them in various situations. Power Objectives 7.14A and 8.15A encourage students to communicate mathematically by generating multiple representations of their solutions (tabular, graphic, and algebraic) to problems.

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Instructional Strategies Nonlinguistic Representation Students begin their explorations with algebraic reasoning on the concrete and pictorial levels and move to the abstract only after they have an understanding of the processes involved in solving equations (Activities: Texas Mathematics, Course 2: Algebra Lab: Solving Equations using Models, pp. 182 – 183 or Activity 7.5A in the Mathematics Toolkit). 2(E)

Cues, Questions, and Advance Organizers Graphic Organizers When students move to the abstract level in application problems, help students relate the step-by-step process back to the concrete or pictorial level. Students explain their reasoning by creating a chart with columns entitled “verbal description,” “equation,” and “picture.” Give students information in one column and ask them to generate the corresponding information in the other two columns.

Cooperative Learning Students work with a partner in a concentration-style activity to explain their understanding of the multiple representations of algebraic situations (tabular, graphic, and symbolic) (Activity: Algebraic Concentration – see Resources column). 3(E), 4(I) Cooperative Learning In small groups, students apply the knowledge and skills acquired by completing rigorous applications and tasks within realworld contextual problems (Laying the Foundation Activities – see Resources column).

Resources

Primary Textbook Resource: Glencoe, Texas Mathematics, Course 3 • TWE/SE, 1-9 & 1-10: pp. 65 – 73; 2-7: pp. 119 – 123; 528 – 556; • Ch. 1 resource masters, pp. 58 – 69; • Ch. 2 resource masters, pp. 45 – 50; • Ch. 10 resource masters, pp. 15 – 39; • Teaching Math with Manipulatives, pp. 36 – 37, 94 – 97. Supplemental Textbook Resource: Glencoe, Texas Mathematics, Course 2 • TWE/SE, Algebra Lab: Solving Equations using Models, pp. 182 – 183; • Teaching Math with Manipulatives, pp. 51 – 54. Clarifying Activities: • Activity 7.5A, Mathematics Toolkit, UT Dana Center. • Algebraic Concentration is a hands-on manipulativesbased activity that includes extensive teacher notes. Print Resource: Laying the Foundation, Resource and Strategy Guide includes: • Functions – Show the Graph, pp. 42 – 45; • Interpreting Distance Graphs, pp. 46 – 49; • Interpreting Rate Graphs, pp. 50 – 57; • Linear Functions, pp. 58 – 65; • Limits of Numbers, pp. 128 – 136; • Goodyear Walks Using the Rule of Four, p. 168.

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective

MATHEMATICS GRADE 7 PRE-AP Horizontal Alignment Planning Guide (HAPG) Second Six-Weeks HISD Objectives

Time Allocation

What is it we want all students to learn?

Assessment Connections Formative Assessment 2.3 – Solving Problems Using Multiple Representations Students solve real-world application problems, use graphing calculators, and complete a selfevaluation of their solutions (see notes in the Instructional Strategies and Resources columns).

Instructional Considerations

Graphing calculators are excellent tools to reinforce these different representations. The software program TI-SmartView is a calculator emulator program that allows the students to view representations simultaneously. Use this program with a computer, a LCD projector, or an Interactive whiteboard. Vocabulary Academic Representations Graph

Content-Specific Equations Inverse operations

TAKS Tips Students should: • solve equations and o estimate solutions; o determine the exact solution (using concrete models if necessary); o justify the solution; • match equations to solution strategies; • use an equation to generate a problem situation and related data with a verbal description, a table, and a graph; • create a scenario, a data table, and a graph for a given equation; and • solve problems using tables, graphs, and equations.

Objective Code Key: Elementary – Content Area.GradeLevel.Objective Secondary – Course.Objective

T - TAKS (Obj) = TAKS objective tested *(x) - Grade level Assessed on TAKS

Instructional Strategies Homework and Practice Use interactive virtual activities/videos to assist students in their understanding of the concepts in this learning focus (Activities: BrainPOP movies, Understanding Math 2008 – see Resources column).

In small groups, students solve open-ended items as formative assessments (Activities: Region IV Benchmark Assessments, and Formative Assessment 2.3 – Solving Problems Using Multiple Representations – see Resources column).

Resources

Technology Resources: • BrainPOP movies: o Simple Equations; o Solving Equations; o Two-Step Equations Equations with Variables. • Understanding Equations section of Understanding Math 2008 from Neufeld Learning Systems.

Assessment Resources: • Region IV Benchmark Assessments; • Formative Assessment 2.3 – Solving Problems Using Multiple Representations includes the following problems and evaluation documents from Middle School Mathematics Assessments, UT Dana Center o “City in Space”, pp. 67 – 73; o “Fast Food Workout”, pp. 103 – 107; o “Global Warming”, pp. 109 – 114; and o Middle School Mathematics Assessment Solution Guide, which is a selfassessment instrument for student use that may be used when solving application problems.

- ELPS (English Language Proficiency Standards) - Literacy Leads the Way Best Practices Ê - Power Objective