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a comprehensive approach to balanced mathematics mathematics planning for seventh grade 2010 edition

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teaching with impact mathematics as you move through this document and the impact materials you will note many recurring themes and underlying programmatic structures that will support your classroom teaching a the grades 6 through 8 program is a comprehensive curriculum that completes a full year of algebra by the end of grade 8 b impact mathematics is a standards-based integrated curriculum that includes strands on number and operations proportional reasoning geometry probability and data with a focus on the development of algebraic thinking c there is a balance of basic skills and conceptual understanding students build new mathematical ideas and at the same time practice needed procedures d the curriculum is centered around problem sets that students work on individually or in groups many of the problems are open-ended allowing students to choose or develop solution strategies e students are asked to make conjectures based on patterns they observe and to develop convincing mathematical arguments f impact mathematics provides opportunities for students to reflect upon critique and communicate their ideas g the concepts in each chapter connect to and build on concepts developed in earlier chapters and courses h there is an emphasis on a variety of mathematical representations as well as modeling i informal to formal development of concepts makes mathematics accessible and appropriate for middle grades students j there is strong content progress from grade to grade with minimal reteaching of topics important topics are revisited in greater depth and formality k the contexts used for developing concepts and practicing skills include real-world applications as well as mathematical settings l to maintain students ongoing interest in all areas of mathematics impact mathematics uses narrative and realistic contexts personalization in the form of cartoons in which middle grades students explain how they approach problems and opportunities for students to choose or create their own problems m manipulatives and calculators are used to support the content learning only when appropriate students need and gain experiences with pencil and paper along with graphing technology n the teaching process is designed around a three-step instructional cycle introduce develop and assign assess o the curriculum balances structured learning direct instruction and creative problem-solving student discovery plays as significant a role in the learning process as teacher-directed instruction p assessment tools are broad encompassing the processes of problem solving reasoning communication connections concepts applications representational strategies and procedures impact mathematics preliminary pacing calendar p 1

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 1 expressions algebraic representations tables and graphs develop algebraic reasoning patterns and numeric forms develop properties and rules develop functions and relations linear expressions equations develop algorithms and operations fractions review and extend administer course 2 pretest crm chapter 1 pp 38-42 1.1 variables and expressions · to match expressions and situations · to understand the order of operations · to use formulas and evaluate expressions · solve equations using backtracking suggested per period pacing 1 t&d p 4 investigation 1:d&u:a p 5 ex p 5 d&u:b p 6 for students who have difficulty with course 2 pretest refer to course 2 pretest auxiliary support materials found on page 2 of this book for additional practice or homework qr 1.3 order of operations p 74 5.1 writing expressions and equations p 228 5.2 simplifying expressions p 242 5.3 evaluating expressions and formulas p.244 5.4 solving linear equations p 250 crm course pretest pp 3-6 leveled lesson resources pp 21-25 problem solving strand students will build new mathematical knowledge through problem solving 7.ps.3 understand and demonstrate how written symbols represent mathematical ideas students will solve problems that arise in mathematics and in other contexts 7.ps.6 represent problem situations verbally numerically algebraically and graphically students will apply and adapt a variety of appropriate strategies to solve problems 7.ps.9 work backwards from a solution number sense and operations strand students will understand meanings of operations and procedures and how they relate to one another 7.n.11 simplify expressions using order of operations note expressions may include absolute value and/or integral exponents greater than 0 continued impact mathematics preliminary pacing calendar lp course 1 3.2 patterns pp 120-125 3.3 translate words into symbols pp 163-165 7.1 squares pp 402-404 9.2 backtracking investigation 1 pp 547-549 investigation 2 pp 550-551 lc the case of the mystery weekend by david connell week 1-2 2 3 4 5 6 d&u:c pp.7-8 s&s p 8 investigation 2 :d&u:a p 9 d&u:b pp.10-11 s&s p 12 investigation 3 t&d pp 13-14 d&u:a p 14 ex p 15 d&u:b p 15 d&u:c p 16 s&s p 17 investigation 4 d&u:a pp.17-19 d&u:b p 19 d&u:c p 20 s&s p 20 iyow p 29 #38 qq p 29 te continued 7 p 2

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections week 1-2 continued note the recommended pacing is based on the mandated 375 minutes or seven to eight 45-60 minute periods per week note quick quizzes and pre-chapter assessments can be found in impact assessment resources volumes a and b algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 7.a.1 translate two-step verbal expressions into algebraic expressions 7.a.8 create algebraic patterns using charts/tables graphs equations and expressions impact mathematics preliminary pacing calendar p 3

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 1.2 expressions and formulas · to use variables to write expressions and solve problems · to develop and use formulas to find specific quantities suggested per period pacing 8 t&d pp 30-31;investigation 1:d&u:a pp.32-33 9 ex p 33 d&u b pp 33­34 s&s p 34 d&u:b pp.33-34 s&s p 36 for additional practice or homework qr 5.1 writing expressions and equations p 228 5.3 evaluating expressions and formulas p 245 8.4 spreadsheets pp 386-392 crm leveled lesson resources pp 27-32 number sense and operations strand students will understand the meanings of operations and how they relate to one another 7.n.12 add subtract multiply and divide integers geometry strand students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes 7.g.1 calculate the radius or diameter given the circumference or area of a circle students will identify and justify geometric relationships formally and informally 7.g.7 find the missing angle when given angles of a quadrilateral algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 7.a.1 translate two-step verbal expressions into algebraic expressions students will perform algebraic procedures accurately 7.a.6 evaluate formulas for given input values surface area rate and density problems continued lp course 1 3.3 translate words into symbols pp 163-165 9.2 backtracking investigation 2 pp 550-551 investigation 3 pp 552555 week 2-3 10 investigation 2 t&d p 35 ex p 36 d&u:a pp 36-37 11 investigation 2 d&u:b pp 38-39 s&s p 39 12 investigation 3 inquiry pp.40-42 13 iyow p 48 #19 qq p 48 te note computer with spreadsheet software is suggested for the inquiry investigation calculator use is suggested impact mathematics preliminary pacing calendar p 4

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grade 7 impact textbook mathematics planning guide notes quick review math handbook crm chapter resource masters skills intervention qr pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections week 2-3 continued measurement strand students will determine what can be measured and how using appropriate methods and formulas 8.m.1 solve equations/proportions to convert to equivalent measurements within metric and customary measurement systems note also allow fahrenheit to celsius and vice versa this concept is introduced in grade 7 to prepare students for later mastery impact mathematics preliminary pacing calendar p 5

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 1.3 the distributive property to understand and apply the distributive property suggested per period pacing 14 t&d p 49 investigation 1 d&u:a pp 51-52 s&s p 52 15 investigation 2 ex p 54 d&u:a p 55 s&s p 55 16 investigations 3 d&u:a pp 56-57 for additional practice or homework qr 1.1 properties 5.2 simplifying expressions pp 238-240 5.4 solving linear equations p 257 crm leveled lesson resources pp 33-37 standardized test review qr 1.3 factors and multiples pp 76-84 problem solving strand students will monitor and reflect on the process of mathematical problem solving 7.ps.17 evaluate the efficiency of different representations of a problem number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 7.n.8 find the common factors and greatest common factor of two or more numbers students will use representations to model and interpret physical social and mathematical phenomena 7.n.9 determine multiples and least common multiple of two or more numbers algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 7.a.1 translate two-step verbal expressions into algebraic expressions continued lp course 1 9.2 backtracking investigation 1 pp 547-549 n game what s my rule week 3-4 17 ex p 57;ex p 58 d&u p 59 s&s p 59 18 investigation 4 d&u:a pp 60-61 ex p 61 t&d p 61 ex p 62 d&u:b p 62 s&s p 62 19 iyow p 68 45 qq p 68 te impact mathematics preliminary pacing calendar p 6

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grade 7 impact textbook mathematics planning guide notes quick review math handbook crm chapter resource masters skills intervention qr pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections students will perform algebraic procedures accurately 7.a.2 add and subtract monomials with exponents of one 7.a.3 identify a polynomial as an algebraic expression containing one or more terms 7.a.4 solve multi-step equations by combining like terms using the distributive property or moving variables to one side of the equation 7.a.6 evaluate formulas for given input values surface area rate and density problems students will recognize use and represent algebraically patterns relations and functions 7.a.10 write an equation to represent a function from a table of values may­june in grade 7 review and self-assessment suggested per period pacing 20 review and self-assessment pp 69-71 21 continue review and self-assessment chapter 1 test week 4 crm mars assessment differences pp 58-62 impact mathematics preliminary pacing calendar p 7

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grade 7 impact textbook mathematics planning guide notes quick review math handbook crm chapter resource masters skills intervention qr pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 2 exponents algebraic reasoning patterns and numeric forms develop properties and rules­develop functions and relations linear expressions/equations­apply numbers and number sense whole numbers develop exponents and roots­develop administer pre-chapter two pretest 2.1 factors and multiples understanding and applying concepts related to factors and multiples suggested per period pacing 22 t&d p 74 investigation 1 d&u:a p.75 d&u:b p 76 d&u:c p 76 s&s p 77 23 investigation 2 d&u a pp 77-78 ex p 78 d&u b p 79 s&s p 79 24 investigation 3 e p 80 d&u:a p 81 ex p 81:d&u:b p 82 s&s p 82 25 investigation 4 d&u:a p 83 ex p 83 d&u:b p 84 26 d&u:c pp 84-85 s&s p 85 iyow p 91 #40 qq p 91 te crm chapter 2 pretest pp 23-26 for additional practice or homework skills intervention workbook skill 17 pp 33­40 qr 1.4 factors and multiples pp 76-82 crm leveled lesson resources pp 37 number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 7.n.8 find the common factors and greatest common factors of two or more numbers 7.n.9 determine multiples and least common multiple of two or more numbers 7.n.10 determine the prime factorization of a given number and write in exponential form lp everyday math,grade 5 1.9 factor strings and prime factorizations 12.1 factor trees lp impact math course 1 3.1 investigation 2 pp 113-116 lc math curse by jon scieszka and lane smith week 5-6 impact mathematics preliminary pacing calendar p 8

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 2.2 exponent machines · to model the behavior of exponents using stretching and shrinking machines · to understand and apply the product laws of exponents suggested per period pacing 27 t&d p.92 investigation 1:d&u:a p 93 d&u:b p 94 d&u c p 95 s&s p 96 28 investigation 2 t&d p 96 ex p 97 d&u:a p.97 ex p 98 d&u:b p b 29 ex p 99 d&u:c p 100 s&s p 100 30 investigation 3 d&u:a pp 100-101 ex p 101 d&u:b p 102 d&u:c p 103 s&s p 103 iyow p 106 #46 qq p.106 te for additional practice or homework qr 3.1 powers and exponents p.160 crm leveled lesson resources pp 13-17 number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 7.n.4 develop the laws of exponents for multiplication and division students will understand meanings of operations and procedures and how they relate to one another 7.n.11 simplify expressions using order of operations lp course 1 3.2 investigation 4 find the rule pp 133-135 week 6 impact mathematics preliminary pacing calendar p 9

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 2.3 more exponent machines · to model the behavior of exponents using division machines with exponents · to understand and apply the quotient laws of exponents · to understand and apply the power of a power law of exponents suggested per period pacing 31 t&d p 107 investigation 1 d&u:a pp 107-108 s&s p 108 standardized test review skills intervention for pre-algebra skill 8 prime factorization pp 15-16 qr 3.1 powers and exponents p 160 crm leveled lesson resources pp 18-22 problem solving strand students will build new mathematical knowledge through problem solving 7.ps.3 understand and demonstrate how written symbols represent mathematical ideas reasoning and proof strand students will select and use various types of reasoning and methods of proof 7.rp.6 support an argument by using a systematic approach to test more than one case number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 7.n.4 develop the laws of exponents for multiplication and division students will understand meanings of operations and procedures and how they relate to one another 7.n.14 develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals lp course 1 3.1 investigation 2 exponents pp 113-116 week 7-8 32 investigation 2 ex p 109 d&u:a p 109 33 ex p 110 d&u:b p 110 s&s p 110 34 investigation 3 t&d p 111 d&u:a pp 111-112 ex p 112 d&u:b p 113 s&s p 113 35 suggested investigation 4 inquiry pp 114-116 iyow p 119 #50 qq p 119 te review and self-assessment suggested per period pacing 36 review and self-assessment pp 120-123 37 continue review and self-assessment chapter 2 test crm mars assessment aunt mabel pp 37-39 impact mathematics preliminary pacing calendar p 10

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 3 signed numbers algebraic representations coordinate graphs develop tables and graphs develop algebraic reasoning patterns and numeric forms develop number and number sense whole numbers signed numbers apply rationals and irrationals fraction and decimal concepts-apply algorithms and operations fractions decimals signed numbers apply administer chapter three pre-test 3.1 add and subtract negative numbers to add and subtract signed numbers suggested per period pacing 38 p 218 t&d p 127 investigation 1 t&d p 128 d&u:a pp 128-129 ex p 129 d&u:b p 130 ex p.130 39 d&u:c p.130 s&s p 130 inquiry investigation 2 pp 131-133 crm chapter 3 pre-test pp 21-24 for additional practice or homework qr 1.5 integer operations p 85 5.6 inequalities p 266 skills intervention for pre-algebra skill 5 integers pp 9-10 skill 6 adding and subtracting integers pp 11-12 crm leveled lesson resources pp 6-10 number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 7.n.3 place rational and irrational numbers approximations on a number line and justify the placement of the numbers students will understand meanings of operations and procedures and how they relate to one another 7.n.12 add subtract multiply and divide integers 7.n.13 add and subtract two integers with and without the use of a number line students will comopute accurately and make reasonable estimates 7.n.19 justify the reasonableness of answers using estimation continued lp course 1 4.1 adding and subtracting fractions pp 198-210 9.1 celsius to kelvin temperature conversion p 545 #33 qr book 1 2.6 decimal operations lc the man who counted a collection of mathematical adventures by malba tahan week 8-9 40 investigation 3 134-136 t&d p 136 d&u:a p 137 ex p 138 d&u:b p 139 s&s p 139 41 investigation 4 t&d p 140 d&u:a pp 140-141 t&d:b p 142 s&s p 142 42 investigation 5 d&u:a pp 143-144 d&u:b p 144 43 t&d p 145 d&u:c p 145 s&s p 145 investigation 6 d&u:a p 146 44 d&u:b pp 146-147 s&s p 147 iyow p 153 68 qq p 153 te impact mathematics preliminary pacing calendar p 11

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grade 7 impact textbook mathematics planning guide notes quick review math handbook crm chapter resource masters skills intervention qr pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections expand the amount of work done involving inequalities week 8-9 continued algebra strand students will perform algebraic procedures accurately 7.a.5 solve one-step inequalities positive coefficients only geometry strand students will apply coordinate geometry to analyze problem solving situations 7.g.10 graph the solution set of an inequality positive coefficients only on a number line impact mathematics preliminary pacing calendar p 12

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grade 7 impact textbook mathematics planning guide notes qr quick review math handbook crm chapter resource masters skills intervention pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 3.2 multiply and divide with negative numbers to multiply and divide with signed numbers suggested per period pacing 45 ex p 154 investigation 1 d&u:a p 155 t&d p 243;d&u:b odd numbers p 155 d&u:c odd numbers p 156 46 d&u:b even numbers p 155 d&u:c even numbers p 156 s&s p 156 investigation 2 d&u:a p 157 for additional practice or homework qr 1.5 integer operations p 92 4.4 statistics p 210 skills intervention for pre-algebra skill 7 multiplying and dividing integers pp 13-14 crm leveled lesson resources pp 19-23 suggested test review qr 3.2 square root p 166 number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 7.n.1 distinguish between the various subsets of real numbers counting/natural numbers whole numbers integers rational numbers and irrational numbers 7.n.2 recognize the difference between rational and irrational numbers e.g explore different approximations of students will understand meanings of operations and procedures and how they relate to one another 7.n.12 add subtract multiply and divide integers 7.n.15 recognize and state the value of the square root of a perfect square up to 225 7.n.17 classify irrational numbers as nonrepeating/non-terminating decimals students will compute accurately and make reasonable estimates 7.n.19 justify the reasonableness of answers using estimation continued lp course 1 4.2 multiplying and dividing with fractions pp 216-233 4.3 multiplying and dividing with decimals pp 242-257 week 9-10 47 t&d p 157 d&u:b p 158 ex p 158 d&u:c p 159 s&s p 159 48 investigation 3 d&u:a p 160 t&d p 160 d&u:b p 161 s&s p 161 49 investigation 4 t&d p 162 d&u:a pp 162-163 d&u:b p 163 50 t&d pp 163-164 s&s p.164 iyow p 168 #60 qq p 168 note to meet standards 7.n.1 and 7.n.2 page 160 te must be done and extended to include all the subsets of numbers listed in 7.n.1 and to classify irrational numbers as non-repeating non-terminating decimals calculator use is suggested impact mathematics preliminary pacing calendar p 13

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grade 7 impact textbook mathematics planning guide notes quick review math handbook crm chapter resource masters skills intervention qr pacing d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections week 9-10 continued algebra strand students will perform algebraic procedures accurately 7.a.4 solve multi-step equations by combining like terms using the distributive property or moving variables to one side of the equation 7.a.6 evaluate formulas for given input values surface area rate and density problems statistics and probability strand students will collect organize display and analyze data 7.s.4 calculate the range for a given set of data review and self-assessment suggested per period pacing 50 review and self-assessment pp 169-171 51 continue review and self-assessment chapter 3 test crm mars assessment integers pp 35-38 impact mathematics preliminary pacing calendar p 14

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