2027 Mathematics Grade 8

Transcription

1 Instructional Material Bureau Summer 2012 Adoption Review Institute Form F: Publisher Alignment Form & Review Scoring Rubric Publisher information and instructions: Corporation or Publisher: Pearson Education, Inc. Submitted by (name) : Hope Heredia Division or Imprint: Prentice Hall Phone: hope.heredia@pearson.com Title of Student Edition: Pearson digits Grade 8 Student Package ISBN: Lexile Score: 800 Title of Teacher Edition: Pearson digits Grade 8 Teacher Package ISBN: Alignment contact information: Completed by (name): Amelia Zarski amelia.zarski@pearson.com Phone: Date: 5/15/2012 SECTION I (CONTENT STANDARDS) CITATION REQUIREMENTS AND SCORING Enter three (3) citations (one in each cell) for each indicator; enter the page number and the paragraph. (Example: [123-5] would refer the reviewer to Page 123, paragraph 5 to find the evidence of the indicator.) Citations for "Content Standards, Benchmarks & Performance Standards" must refer to the Student Edition. Citations for "Other Relevant Criteria" must refer to the Student Edition or the Teacher Edition. Each citation must address an increasing level of cognition: Citation 1: Cites material that provides an introduction to the content at the basic knowledge and recall level. Citation 2: Cites material that builds on prior knowledge/skills at the comprehension and application level. Citation 3: Cites material that builds on prior knowledge/skills and integrates content to meet the standard at the analysis, synthesis, or evaluation levels. At least two citations must be found satisfactory by the Review Team to meet the requirements of the standard. Scoring will be as follows: Satisfactory citations at the Basic Knowledge level only, or no valid citations, score zero (0) points. Satisfactory citations at both the Basic Knowledge and Application level score a total of six (6) points. Satisfactory citations at all three levels score a total of ten (10) points. SEE THE BEGINNING OF SECTION II FOR REQUIREMENTS AND SCORING OF OTHER RELEVANT CITATIONS THE PAGES OF THIS FORM WILL BE SCANNED. PLEASE FOLLOW THESE GUIDELINES WHEN PREPARING IT FOR SUBMISSION: Use only the original forms provided by the Instructional Material Bureau. Do not modify the form. Do not attempt to recreate the form. Print out the completed form on 20# white 8.5 x 11 office paper ONLY. Do not insert covers, dividers, etc. Do not bind the completed form. Use a single staple in the corner to secure the form. 10 Aug 2011 (lb)

2 Instructional Material Bureau Summer 2011 Adoption Review Institute THIS PAGE FOR REVIEW INSTITUTE STAFF FACILITATOR USE ONLY FINAL SCORE VERIFICATION (TO BE COMPLETED BY THE FACILITATOR) Verified: 90% or Higher Facilitator Signature Verified: 89% or Lower Facilitator Signature Reviewer Name: Reviewer : Date: Facilitator: REVIEWER INSTRUCTIONS For each citation you verify, make a note in the citation cell (Use 4 if the citation was verified or 8 if the citation did not provide evidence). Based on the citations you verified, enter the score in the cell at the end of the row. Every item with an item number in the # column must be scored. Citations that you verify at the Basic Knowledge level only, or no valid citations, score zero (0) points. Citations that you verify at both the Basic Knowledge and Application level score a total of six (6) points. Citations that you verify at all three levels score a total of ten (10) points. At the end of each page, total the scores in the column. Enter the total score in the Page Score box at the bottom of each page. At the end of the section, add up all your Page Score boxes and enter that total in the Reviewers Section I Section Score box POINTS DEFINITION 0 Citations did not meet the requirements of the standard for at least two levels. 6 Citations met the requirements of the standard at two of the levels. 10 Citations met the requirements of the standard at all three levels. 10 Aug 2011 (lb)

3 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS The System 8.NS A. Know that there are numbers that are not rational, and approximate them by rational numbers. 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # SE: Unit A, 1-2, Check, Focus Question SE: Unit A, 1-2, #3 SE: Unit A, 1-2, # Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of, show that is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. SE: Unit A, 1- SE: Unit A, 1- SE: Unit A, 1-5, 2 Expressions and Equations 8.EE B. Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3 3 = 1/3 3 = 1/27. SE: Unit B, SE: Unit B, 3-1, SE: Unit B, 3- SE: Unit B, 3- Check # Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational. SE: Unit B, 3-2, * SE: Unit B, 3-1, Check # Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how SE: Unit B, 4-1, SE: Unit B, 4-1, -5 SE: Unit B, 4-5, 5 pg. 3

4 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS many times as much one is than the other. For example, estimate the population of the United States as and the population of the world as , and determine that the world population is more than 20 times larger. Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. SE: Unit B, 4-1, SE: Unit B, 4- SE: Unit B, 4-5, & 5 6 C. Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distance-time equation to determine which of two moving objects has greater speed. SE: Unit C, 5-1, SE: Unit C, 5- SE: Unit C, 5-2, & Use similar triangles to explain why the slope m is the same between and two distinct points on a nonvertical line in the coordinate plane; derive the equation y=mx+b for a line intercepting the vertical axis at b. SE: Unit E, 10- SE: Unit E, 10- Check Focus Question SE: Unit C, 5-6, 8 D. Analyze and solve linear equations and pairs of simultaneous linear equations. 7. Solve linear equations in one variable. SE: Unit B, 2-1, SE: Unit C, 5- SE: Unit C, 5-7, 9 7. (a) Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation SE: Unit B, 2- SE: Unit B, 2- SE: Unit B, 2- Check #6 10 pg. 4

5 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 7. (b) Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # SE: Unit B, 2- SE: Unit B, 2- SE: Unit B, 2-5, Analyze and solve pairs of simultaneous linear equations 1, -2 5, (a) Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Check Focus Question (b) Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 4, 5, (c) Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 1, Functions 8.F E. Define, evaluate, and compare functions. 1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Note: Function notation is not required in Grade 8.) SE: Unit D, 7-1, SE: Unit D, 7- SE: Unit D, 7-2, Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal SE: Unit C, SE: Unit C, 8-6, SE: Unit C, 8-17 pg. 5

6 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # 3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. SE: Unit D, 8-1, -2 SE: Unit D, 8- Check Focus Question SE: Unit D, 7-4, 18 F. Use functions to model relationships between quantities. 4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. SE: Unit D, 7-2, SE: Unit D, 8-5, SE: Unit D, 8-6, Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. SE: Unit D, 7- SE: Unit D, 7-7, -2 SE: Unit D, 7-6, Geometry 8.G G. Understand congruence and similarity using physical models, transparencies, or geometry software. 1. Verify experimentally the properties of rotations, reflections, and translations: 1, 2, (a) Lines are taken to lines, and line segments to line segments of the same length. 1, 1, 4, 22 pg. 6

7 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # 1. (b) Angles are taken to angles of the same measure. 1, 4, (c) Parallel lines are taken to parallel lines. 3, 5, 5, Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Check, Focus Question 4, Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 1, 2, Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. SE: Unit E, 10-2, SE: Unit E, 10-2, SE: Unit E, 10-2, Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. SE: Unit E, 11-1, -4 SE: Unit E, SE: Unit E, 11- Check #6 28 H. Understand and apply the Pythagorean Theorem. 6. Explain a proof of the Pythagorean Theorem and its converse. SE: Unit E, 12-2, Check, Focus Question SE: Unit E, 12-4, SE: Unit E, pg. 7

8 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. SE: Unit E, 12- SE: Unit E, 12- SE: Unit E, 12-2, Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. SE: Unit E, 12-5, SE: Unit E, 12-5, SE: Unit E, 12-5, 31 I. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems SE: Unit E, 13-6, SE: Unit E, 13-2, SE: Unit E, Statistics and Probability 8.SP J. Investigate patterns of association in bivariate data. 1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. SE: Unit F, 14-2, SE: Unit F, 14-3, SE: Unit F, Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. SE: Unit F, 14-5, -2 SE: Unit F, 14-5, SE: Unit F, 14-5, Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height SE: Unit F, 14-6, -3 SE: Unit F, 14-6, SE: Unit F, 14-6, 35 pg. 8

9 CONTENT STANDARDS, BENCHMARKS & PERFORMANCE STANDARDS 4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Citation 1 Basic Knowledge Citation 2 Application Citation 3 Analysis # SE: Unit F, 15-2, SE: Unit F, 15-5, SE: Unit F, 15- Check, #2 36 Reviewer s Section I s Section Score pg. 9

10 PUBLISHER: SECTION II CITATION REQUIREMENTS AND SCORING Citations for "Other Relevant Criteria" will usually refer to the Teacher Edition, but may refer to the Student Edition. Enter three (3) citations (one in each cell) for each indicator; enter the page number and the paragraph. Example: [123-5] would refer the reviewer to +Page 123, paragraph 5 to find the evidence of the indicator. All three citations must be found satisfactory by the Review Team to meet the requirements of the standard. REVIEWER: USE THE TEACHER'S EDITION AND THE STUDENT EDITION TO CONDUCT THIS PORTION OF THE REVIEW For each citation you verify, make a note in the citation cell (Use 4 if the citation was verified or 8 if the citation did not provide evidence). Every item with an item number in the # column must be scored. All three citations must be verified in order to receive points. Based on the citations you verified, enter the score in the cell at the end of the row. At the end of each page, total the scores in the column. Enter the total score in the Page Score box at the bottom of each page. At the end of the section, add up all your Page Score boxes and enter that total in the Reviewers Section II Section Score box KEY: 0 = Citations did not meet the requirements of the standard. 5 = Citations met the requirements of the standard. GENERAL A. The textbook provides pictorials, graphics, and illustrations that represent diversity of cultures, race, color, creed, national origin, age, gender, language or disability. SE: Unit B, 2-5, SE: Unit B, 4-2, SE: Unit E, 10-1, 1 B. The textbook provides a variety of cultural perspectives used within the lesson content to account for various cultural/background experiences. SE: Unit E, 13-7, #3 SE: Unit E, 13-4, Check Focus Question SE: Unit B, 2-1, 2 pg. 10

11 C. The textbook provides assignments with activities requiring student responses that promote respect for all people regardless of race, color, creed, national origin, age, gender, language or disability. SE: Unit B, 2-1, #2 SE: Unit D, 7-1, SE: Unit B, 4-5, & Reflect 3 D. The textbook presents appropriate role models within content rather than an oversimplified standardized image of a person or group; avoids stereotyping. SE: Unit B, 2-5, SE: Unit B, 4-2, SE: Unit E, 10-1, 4 E. At the beginning of each unit, chapter or lesson there is a list of content and mathematical practice standards covered within the unit, chapter and/or lesson. TE: Unit B, 3-2, Preparation Notes TE: Unit C, 6-5, Preparation Notes TE: Unit E, 9-3, Preparation Notes 5 F. The textbook provides an introduction to the lesson including the comprehension questions (i.e. focus questions or guiding questions) the student will be expected to answer at the conclusion of the classroom instruction. SE: Unit B, 3-2,, Focus Question 5, Check, Focus Question SE: Unit E, 10-2,, Focus Question 6 G. The textbook integrates appropriate mathematical vocabulary into each lesson. SE: Unit B, 4-1, #6 SE: Unit C, 11-1, Check #6 SE: Unit F, 15-1 #4 7 H. The textbook provides visual representations such as pictorial models, tables, graphs, manipulatives and number lines to assist students comprehension. SE: Unit B, 3-5, SE: Unit C, 5-6, 4, 8 I. The textbook provides extensive and varied opportunities to practice lesson objectives using higher order thinking skills. SE: Unit B, 3-2, #5-6 SE: Unit C, 5-3, SE: Unit E, 10-1, #4 9 pg. 11

12 J. The textbook provides the student with ongoing review and practice for the purpose of retaining previously acquired knowledge. SE: Unit B, 4-5, #6 7, SE: Unit E, 11-6, #3 10 K. The textbook provides activities for students to make interdisciplinary connections to social studies, science, language arts, music, art and sports plus connections with their personal experiences. SE: Unit F, 14-7, SE: Unit E, 10-3, SE: Unit B, 4-2, #3 11 L. The textbook provides field activities for students. TE: Unit C, TE: Unit D, TE: Unit E, 12 M. The textbook incorporates increasingly complex tasks within lessons requiring analysis, evaluation and synthesis. SE: Unit A, 1-4, #4 2, SE: Unit D, 7-1, #5 13 N. The textbook provides cognitively demanding activities that elicit critical thinking and reasoning. SE: Unit A, 1-2, # SE: Unit C, 5-1, Close & Check #4 SE: Unit F, 15-5, #4 14 O. The textbook incorporates the use of appropriate technology and manipulatives by students. Area Models Algebra Tiles Pan Balance 15 P. The textbook provides references to support student learning such as a glossary and word lists. TE: Unit B, 2-2, Lesson Vocabulary TE:Unit C, 5-3, Lesson Vocabulary TE: Unit F, 14-3, Lesson Vocabulary 16 Q. The Teacher s Edition presents learning progressions to provide an overview of the scope and sequence of skills and concepts. TE: Project Overview, p30 TE: Project Overview, p31 TE: Project Overview, p32 17 R. Within each lesson of the Teacher s Edition, there are clear measurable learning objectives and opportunities for differentiated instruction. TE: Unit B, 2-2, Preparation Notes TE: Unit C, 5-7, Preparation Notes TE: Unit E, 10-2, Preparation Notes 18 pg. 12

13 S. The Teacher s Edition provides tiered activities for differentiated instructional to meet the needs of all students including below proficiency and advanced learners. T. The Teacher s Edition provides instructional strategies, resources, and language development support for English language learners (sheltered instruction). TE: Unit B, Topic 4, Readiness Lesson r4 TE: Project Overview, p112 TE: Unit D, Topic 7, Readiness Lesson r7 TE: Project Overview, p113 TE: Unit F, Topic 14, Readiness Lesson r14 19 TE: Project Overview, p115 U. The Teacher s Edition includes content and information that support a variety of approaches to instruction, including (score each item separately): Writing activities where students explain their mathematical thinking. TE: Unit A, 2. Project-based learning assignments TE: Unit B, 3. Interdisciplinary instruction TE: Unit A, 4. Cooperative learning strategies TE: UA, 5. Early and effective intervention instructional strategies V. The Teacher s Edition provides the teacher with instructional strategies for every lesson. TE: Unit B, Topic 3, Readiness Lesson r3 TE: Unit B, 4-2, Preparation Notes TE: Unit C, TE: Unit D, TE: Unit B, TE: UC, TE: Unit D, Topic 6, Readiness Lesson r6 TE: Unit D, 7-5, Preparation Notes TE: Unit E, 21 TE: Unit F, 22 TE: UF, 23 TE: Unit E, 24 TE: Unit E, Topic 10, Readiness Lesson r10 25 TE: Unit F, 12-2, Preparation Notes 26 pg. 13

14 W. The Teacher s Edition and resources provide instructional support for developing both student conceptual understanding and procedural fluency. TE: Unit C, 5-3, #5 TE: Unit C, 5-4, TE: Unit C, 6-3, 27 X. The Teacher s Edition and resources provide various assessments (e.g., pre- and post-tests, self-assessments, written reflections, mid-unit quizzes, quick checks for understanding of the key concepts, etc.) that address lesson and/or chapter objectives. TE: Unit B, Readiness Assessment TE: Unit C: Progression Monitoring, Unit C Test TE: Unit F: Topic 15 Test 28 Y. The Teacher s Edition and resources provide student assessments that are accompanied by student work exemplars and score identification of concepts and skills to support further instruction, differentiation, remediation or acceleration. TE: Unit A, TE: Unit C, TE: Unit F, 29 Z. The Teacher s Edition provides opportunities for student presentations and projects using technology. TE: Unit A, TE: Unit B, TE: Unit C, 30 STANDARDS FOR MATHEMATICAL PRACTICE AA. Make sense of problems and persevere in solving them: 1. The lesson activities and assessments require students to make conjectures about the form and meaning of their solution strategies and plan a solution strategy rather than jumping into solution attempts. 6, #5 SE: Unit B, 4-5, Check #6 1, #3 31 pg. 14

15 2. The lesson activities require students to communicate their understanding of the approaches of others in solving problems and to identify correspondences between different approaches. SE: Unit B, 2-5, #4 SE: Unit B, 3-3, Check #7 6, #4 32 BB. Reason abstractly and quantitatively: 1. The lesson activities and assessments require students to make sense of quantities and their relationships in problem situations. 2. The lesson activities and assessments require students to decontextualize mathematical problem situations by abstracting the situation, representing it symbolically, and manipulating the representing symbols to solve problems. 3. The lesson activities and assessments require students to pause during manipulation of numbers and symbols to contextualize mathematical expressions and equations, create coherent representations, consider the units involved, and attend to the meaning of quantities within a context. SE: Unit B, 3-1, #6 SE: Unit B, 2-5, #1-3 SE: Unit C, 5-4, CC. Construct viable arguments and critique the reasoning of others: SE: Unit B, 4-2, 7, SE: Unit C, 5-7, SE: Unit D, 8-2, #5 33 SE: Unit D, 7-2, SE: Unit C, 14-4, The lesson activities and assessments require students to understand and use stated assumptions, definitions, and previously established results in constructing mathematical arguments. SE: Unit E, 12-1, SE: Unit E, 12-1, SE: Unit E, 12-4,, Focus Question 36 pg. 15

16 2. The lesson activities and assessments require students to provide a justification for their solutions, communicate their mathematical reasoning to others and respond to arguments of others. SE: Unit B, 3-2, #5 SE: Unit D, 7-2, SE: Unit E, 10-2, # The lesson activities and assessments require students to compare the effectiveness of two plausible arguments; distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument, explain what it is. SE: Unit E, 10-1, #4 SE: Unit C, 5-3, Check #6 5, # The lesson activities and assessments provide opportunities for students to explore examples and counter examples. SE: Unit B, 3-2, #6 2, SE: Unit E, 10-2, #4 39 DD. Model with mathematics: 1. The lesson activities and assessments require students to apply the mathematics they know to solve problems arising in everyday life, society and the workplace. SE: Unit E, 10-1, SE: Unit B, 3-3, SE: Unit B, 4-5, The lesson activities and assessments require students to apply what they know to breakdown and simplify complicated situations. SE: Unit B, 3-3, #5 1, SE: Unit E, 13-3, The lesson activities and assessments require students to interpret their mathematical results in the context of the situation, reflect on whether the results make sense, and reflect on how well their model has supported their problem solving. SE: Unit C, 5-5, SE: Unit C, 8-5, SE: Unit D, 8-6, 42 pg. 16

17 EE. Use appropriate tools strategically: 1. The lesson activities and assessments require students to use a variety of tools and manipulatives to solve various problems. Algebra Tiles Data & Graphs Grids & Organizers The lesson activities and assessments require students to make sound decisions about choosing appropriate tools. Place Value Blocks Area Models Integer Chips The lesson activities and assessments require students to use estimation to detect possible errors. SE: Unit A, 1-3, #3 SE: Unit A, 1-1, SE: Unit A, 1-5, The lesson activities and assessments require students to use technology to explore and deepen their understanding of concepts. SE: Unit C, 5-1, SE: Unit C, 5-7, 3, 46 FF. Attend to precision: 1. The lesson activities and assessments require precise communication among students (e.g., using clear definitions, stating the meaning of symbols, specifying units of measure.) SE: Unit B, 3-1, #6 SE: Unit C, 4-4, SE: Unit D, 8-5, # The lesson activities and assessments require students to answer with a degree of precision appropriate for the problem s context. SE: Unit B, 4-5, #5 2, SE: Unit E, 10-2, #2 48 GG. Look for and make use of structure: pg. 17

18 1. The lesson activities and assessments require students to look closely to discern a pattern or structure through opportunities provided. HH. Look for and express regularity in repeated reasoning: SE: Unit B, 3-5, SE: Unit D, 7-4, SE: Unit D, 8-1, # The lesson activities and assessments require students to notice if calculations are repeated, and look both for general methods and for shortcuts. SE: Unit B, 4-2, SE: Unit B, 4-3, SE: Unit B, 4-4, The lesson activities and assessments require students to maintain oversight of the process, while attending to the details. SE: Unit B, 2-1, SE: Unit B, 2-2 SE: Unit B, 2-3, The lesson activities and assessments require students to continually evaluate the reasonableness of their intermediate results. SE: Unit B, 2-5, SE: Unit B, 3-2, SE: Unit B, 3-7, 52 II. The Teacher s Edition provides scaffolded curriculum maps. TE: Project Overview, p30 TE: Project Overview, p31 TE: Project Overview, p32 53 TECHNOLOGY KNOWLEDGE AND SKILLS (GRADES 6-8) JJ. Provides students with opportunities to: 1. Demonstrate keyboarding proficiency in technique and posture while building speed. N/A N/A N/A Refine their selection and use of appropriate search strategies. TE: Unit A, TE: Unit B, TE: Unit E, 55 pg. 18

19 3. Expand their use of word processing, graphics, databases, spreadsheets, simulations, multimedia, and telecommunications. TE: Unit A, TE: Unit B, TE: Unit F, Become fluent in using multiple software applications and applying them across the curriculum. Area Models 2-D Geometry Data & Graphs 57 Section Score Reviewer s Section II Review Score Reviewer s Grand pg. 19