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a comprehensive approach to balanced mathematics mathematics planning for eighth grade 2010 edition 8

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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 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mathematics planning guide notes qr pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 1 linear relationships algebraic representations coordinate graphs apply tables and graphs develop algebraic reasoning patterns and numeric forms develop properties and rules apply functions and relations linear expressions/equations develop coordinate geometry coordinate representations develop numbers and number sense signed numbers develop ratios and rates meaning and representations develop proportions develop administer pre-chapter one assessment 1.1 direct variation · represent and interpret linear relationships in multiple ways · understanding the connection between a linear equation in the form y mx b and its graph 1 e p 4 investigation 1 d&u a pp 6-7 d&u:b p 8 d&u:c p 9 s&s p 9 investigation 2 d&u:a pp 10-11 d&u:b p 11 s&s p 12 for additional practice or homework qr 6.4 solving linear equations pp 271-278 6.7 graphing on the coordinate plane pp288-294 6.9 direct variation pp 306308 skills intervention for algebra skill 27 ordered pairs pp 53-54 crm pp 16-20 standardized test review qr 7.8 circles p 359-364 algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 8.a.3 describe a situation involving relationships that match a given graph 8.a.4 create a graph given a description or an expression for a situation involving a linear or nonlinear relationship students will recognize use and represent algebraically patterns relations and functions 8.a.15 understand that numerical information can be represented in multiple ways arithmetically algebraically and graphically 8.a.16 find a set of ordered pairs to satisfy a given linear numerical pattern expressed algebraically then plot the ordered pairs and draw the line 8.a.19 interpret multiple representations using equation table of values and graph may­june in grade 8 continued lp course 2 10.2 proportional relationships pp 505-507 10.2 similarity pp 517-522 lc pythagoras gets the right angle a math adventure by julie ellis the kingdom of infinite numbers by bryan bunch week 1 2 3 note while executing mini-lesson include as do now operations with signed numbers and plotting points continued impact mathematics preliminary pacing calendar p 2

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mathematics planning guide notes qr pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 4 week 1 continued investigation 3 t&d p 12 d&u:a p 13 d&u:b p 14 odd numbers d&u:c p 14 odd numbers d&u d p.15 #19,20 s&s p 15 iyow p 22 #14 qq p 23te geometry strands students will apply coordinate geometry to analyze problem solving situations 8.g.15 graph a line using a table of values 5 note the recommended pacing is based on the mandated 375 minutes or seven to eight 45­60 minute periods per week impact mathematics preliminary pacing calendar p 3

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 1.2 slope · understand slope as the constant rate of change in a line · calculate slope as the ratio of rise/run · understanding and applying the idea of slope suggested per period pacing 6 t&d p 24 investigation 1 d&u:a pp.25-26 d&u:b p 26 7 d&u:c pp 27-28 s&s p 28 investigation 2 e p 29 d&u:a pp 29-30 d&u:b p 30 s&s p 30 iyow p 33 24 qq p 34 te for additional practice or homework qr 6.8 slope and intercept p 295298 skills intervention for algebra skill 32 slope of a line pp 63-64 standardized test review qr 7.1 naming angles p 318 algebra strand students will recognize use and represent algebraically patterns relations and functions 8.a.16 find a set of ordered pairs to satisfy a given linear numerical pattern expressed algebraically then plot the ordered pairs and draw the line geometry strands students will apply coordinate geometry to analyze problem solving situations 8.g.13 determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change 8.g.14 determine the y-intercept of a line from a graph and be able to explain the y-intercept 8.g.16 determine the equation of a line given the slope and the y-intercept 8.g.17 graph a line from an equation in slope-intercept form y mx b lp course 2 8.2 speed and the slope connection e p 389 investigation 1 walking and jogging pp 390-393 slope investigation 4 changing the starting point pp 398-401 week 2 8 graphing calculator is suggested for use in checking answers impact mathematics preliminary pacing calendar p 4

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mathematics planning guide notes qr pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 1.3 write equations to recognize and write equations for linear relationships using the method of constant differences suggested per period pacing 9 t&d p 35 investigation 1 t&d p 35 d&u:a p 36 d&u:b pp 36-37 10 d&u:c p 37 ex p 38 s&s p 38 investigation 2 d&u:a pp 38-40 11 d&u:b p 40 s&s p 41 investigation 3:t&d p 42 d&u:a pp 42 s&s 12 investigation 4:e p 44 ex p 45 d&u:a p 45 d&u:b pp 45-46 d&u:c p 46 d&u:d pp 46-47 s&s p 47 13 investigation 5:t&d p 48 d&u:a pp 48-49 t&d p 49 d&u:b p 49 14 d&u:c p 50 d&u:d p 50 s&s investigation 6 inquiry pp 51-52 15 iyow p 59 42 qq 59 te review and self-assessment suggested per period pacing 16 review and self-assessment pp 60-63 17 test chapter 1 for additional practice or homework skills intervention for pre-algebra skill 39 solve equations in two variables pp 77-78 qr 6.1 writing expressions and equations pp 252-257 6.2 simplifying expressions p 259 6.4 solving linear equations pp 271-277 6.8 slope and intercept pp 295-298 crm pp 27-31 algebra strand 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 geometry strand students will apply coordinate geometry to analyze problem solving situations 8.g.14 determine the y-intercept of a line from a graph and be able to explain the y-intercept 8.g.15 graph a line using a table of values week 2-3 lp course 1 3.2 find the rule pp 133-135 3.2 patterns and variables pp 120-135 3.3 variables and rules pp 143-165 9.1 understanding equations pp 534 9.2 backtracking pp 546-554 9.3 guess check and improve pp 560-567 crm mars assessment number pairs pp 52-56 impact mathematics preliminary pacing calendar p 5

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 2 lines and angles algebraic representations coordinate graphs develop tables and graphs develop algebraic reasoning patterns and numeric forms develop functions and relations linear expressions/equations develop geometric relationships congruenc develop data analysis modeling and analysis 2.1 lines administer pre-chapter two assessment · understanding the connection between a linear equation in the form y mx b and its graph · understanding and applying the idea of slope · using a linear graph to gather information · fitting a line to data for additional practice or homework qr 6.7 graphing on the coordinate plane pp 288-290 6.8 slope and intercept p 299 6.4 solving linear equations 271-277 7.1 classifying angles and triangles pp 318-324 crm pp.4-8 standardized test review qr 4.4 statistics pp 201-205 skills intervention for algebra skill 29 graphing functions pp 57-58 algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 8.a.4 create a graph given a description or an expression for a situation involving a linear or nonlinear relationship geometry strands students will apply coordinate geometry to analyze problem solving situations 8.g.17 graph a line from an equation in slopeintercept form y mx b lp course 2 8.3 linear relationships pp 410-422 9.3 solve equations pp 460-465 lc the adventures of penrose the mathematical cat by theoni pappas mathographics by robert dixon week 4-5 suggested per period pacing 18 explore p 66 investigation 1 d&u:a p 67 d&u:b p 68 s&s p 69 19 investigation 2:t&d p 69 d&u:a p 69 d&u:b p 70 s&s p 70 20 investigation 3:inquiry pp 71-73 21 investigation 4:t&d p 74 d&u:a pp 75-76 d&u:b pp 77-78 d&u:c p 78 s&s p 78 22 iyow p 85 #29 qq p 86 te graphing calculator is suggested impact mathematics preliminary pacing calendar p 6

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mathematics planning guide notes qr pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 2.2 angle relationships · identify and determine the measure of supplementary angles complementary angles and vertical angles · explore angle relationships for parallel lines cut by a transversal suggested per period pacing 23 investigation 1 t&d pp 87-88 d&u:a p 88 ex p 89 d&u:b p 89 #4-7 24 d&u:b p 90 #8-10 d&u:c p 90 s&s p 90 25 investigation 2:e p 91 d&u:a pp 9192 d&u:b pp 92-93 s&s p 93 26 iyow p 94 16 qq p 95 te for additional practice or homework qr 7.1 classifying angles and triangles pp 319-321 crm pp 15-19 geometry strands students will apply coordinate geometry to analyze problem solving situations 8.g.0 construct using a straight edge and compass segment congruent to a segment angle congruent to an angle perpendicular bisector and angle bisector may-june in grade 8 8.g.1 identify pairs of vertical angles as congruent 8.g.2 identify pairs of supplementary and complementary angles 8.g.3 calculate the missing angle in a supplementary or complementary pair 8.g.4 determine angle pair relationship when given two parallel lines cut by a transversal 8.g.5 calculate the missing angle measurements when given two parallel lines cut by a transversal 8.g.6 calculate the missing angle measurements when given two intersecting lines and an angle lp course 1 1.1 investigation 2 pp 8-11 1.2 angles pp 24-34 review and self-assessment suggested per period pacing 26 review and self assessment pp 107-109 27 continue review and test week 5-6 crm mars assessment pentagons pp 40-44 impact mathematics preliminary pacing calendar p 7

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 3 percents and proportions rationals and irrationals fraction and decimal concepts-apply meaning and representation develop ratio and rates meaning and representation develop proportion develop algorithms and operations fractions and decimals apply administer pre-chapter three assessment 3.1 understand percents · recognize percents as ratios with a common scale of 100 · recognize percents as a convenient way to compare ratios · solve percent problems using proportions suggested per period pacing 28 investigation 1 t&d p 112 d&u:a p 113 d&u:b pp 114-115 s s p 115 29 investigation 2 d&a p 116 d&u:a p 116 t&d p.117 d&u:b pp 117118 s&s p 118 qq p 122 te iyow p 122 for additional practice or homework qr 2.6 meaning of percents pp 123-129 2.7 using and finding percents p 130-134 crm pp 3-7 number sense and operations students will understand meanings of operations and procedures and how they relate to one another 8.n.3 read write and identify percents less than 1 and greater than 100 8.n.4 apply percents to tax percent increase/decrease simple interest sale price commission interest rates and gratuities lp course 1 6.1 use percents pp 348-361 6.2 a percent of a quantity pp 368-375 6.3 percents as whole pp 380389 lc erin mcewen your days are numbered by alan ritchie week 6 impact mathematics preliminary pacing calendar p 8

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mathematics planning guide notes qr pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 3.2 work with percents · to calculate percent increase and percent decrease · to interpret comparisons that use ratios and percentages 30 investigation 1 t&d p 123 d&u:a pp 124-125 d&u:b p 125 d&u:c p 126 s&s p 126 31 investigation 2 t&d p 127 d&u:a pp 127-128 d&u:b p.129 s&s p 129 32 investigation 3 d&u:a p 130 d&u:b p 131 s&s p 131 33 inquiry investigation 4 pp 132-133 iyow p 139 qq p.139 te for additional practice or homework qr 2.7 using finding percents pp 135-141 number sense and operations students will understand meanings of operations and procedures and how they relate to one another 8.n.4 apply percents to tax percent increase/decrease simple interest sale price commission interest rates and gratuities lp course 1 6.1 use percents pp 348-361 6.2 a percent of a quantity pp 368-375 6.3 percents as whole pp 380389 review and self-assessment suggested per period pacing 34 review and self assessment pp 140-141 test-taking practice p 143 35 continue review and test week 7 crm mars assessment number pairs impact mathematics preliminary pacing calendar p 9

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 4 exponents and exponential variation algebraic reasoning patterns and numeric forms develop properties and rules develop functions and relations quadratic expressions/equations develop coordinate geometry coordinate representations develop numbers and number sense exponents and roots develop rationals and irrationals fraction and decimal concepts apply administer pre-chapter four assessment 4.1 exponents · calculate values of expressions with positive and negative integer exponents · to raise positive and negative including fractional bases to powers · to understand and use laws of exponents · to use scientific notation suggested per period pacing 36 ex p 146 investigation 1 d&u:a p 147 d&u:b p.147 1-11 37 investigation 1 d&u:b p 148 1216 d&u:c p 148 s&s p 149 38 investigation 2 t&d p.149 ex p 149 d&u:a p 150 t&d p 151 d&u:b p 151 d&u:c p 152 s&s p 152 39 investigation 3 example p 153 d&u:a p 154 d&u:b pp 154-155 d&u,c p 155 s&s p 155 40 investigation 4 d&u:a pp 156-158 d&u:b p 158 s&s p 158 41 inquiry investigation 5 pp 159-161 iyow p 167 58 qq p 168 te impact mathematics preliminary pacing calendar p 10 for additional practice or homework qr 3.1 powers exponents pp 146-155 3.3 scientific notation pp 161-166 3.4 laws of exponents pp 167-171 crm pp 4-11 number sense and operations students will understand meanings of operations and procedures and how they relate to one another 8.n.1 develop and apply the laws of exponents for multiplication and division 8.n.2 evaluate expressions with integral exponents web resources www.ex.ac.uk/mirrors/nineplanets www.nineplanets.org www.ex.ac.uk/mirrors/nineplanets www.nineplanets.org lp course 2 3.1 stretching and shrinking machines pp 146-159 2.3 more exponent machines pp 107-116 lc king s chessboard by david birch anno s mysterious multiplying jar week 8-9

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mathematics planning guide notes qr pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 4.2 exponential relationships · to develop a sense of exponential growth and exponential decay · to describe examples of exponential growth with other kinds of growth · to represent exponential growth and exponential decay relationships with algebraic expressions for additional practice or homework qr 3.1 powers exponents pp 146-155 3.4 laws of exponents pp 167171 crm pp 12-16 week 9 number sense and operations students will understand meanings of operations and procedures and how they relate to one another 8.n.1 develop and apply the laws of exponents for multiplication and division 8.n.2 evaluate expressions with integral exponents lp course 2 4.1 scientific notation pp 174184 42 ex p 169 investigation 1 d&u:a p 170 d&u:b p 171 ss p 171 43 investigation 2 t&d p 172 d&u:a p 173 d&u:b p 174 s&s p 175 44 investigation 3 t&d p 175 d&u:a pp 176-177 d&u:b p 177-178 45 s&s p 178 iyow p 184 #29 qq p 184 te impact mathematics preliminary pacing calendar p 11

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 4.3 radicals · to simplify radical expressions · to understand that irrational numbers cannot be expressed as the ratio of two integers · to determine whether simple radicals are rational or irrational numbers suggested per period pacing 46 ex p 185 investigation 1 pp 185186 d&u:a p 186 d&u:b p 187 47 investigation 1 d&u:c p 187 s&s p 188 48 investigation 2 d&u:a p 188-190 49 investigation 2 d&u:b p 190-191 d&u:c p 191 s&s p 192 50 investigation 3 t&d p.192 d&u:a p 193 d&u:b p 194 s&s p 194 51 iyow p 198 qq p 199 te quiz lesson 4.3 for additional practice or homework qr 3.1 powers exponents pp 146-155 3.2 squares and cube roots pp 156-160 number sense and operations students will understand meanings of operations and procedures and how they relate to one another 8.n.1 develop and apply the laws of exponents for multiplication and division 8.n.2 evaluate expressions with integral exponents week 10-11 lp course 2 7.3 pythagorean theorem pp 343-350 7.3 inquiry investigation 3 distance formula pp 351354 10.3 percents and proportions pp 530-536 10.4 rates pp 540-546 lc what s your angle pythagoras by julie ellis mathematicians are people too by lyetta reimer and wilbert reimer review and self-assessment suggested per period pacing 52 review and self assessment pp 200-202 test-taking practice p 203 53 continue review and test mars assessment sequences and graphs pp 38-42 impact mathematics preliminary pacing calendar p 12

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 5 algebraic expressions algebraic reasoning patterns and numeric forms develop properties and rules apply numbers and number sense whole numbers apply administer pre-chapter five assessment 5.1 rearrange algebraic expressions · use geometric models in illustrating the distributive property to expand expressions of the form ab+c · represent algebraic expressions using rectangle models · simplify expressions by combining like terms · write and solve simple linear equations related to angle measures suggested per period pacing 54 t&d p 206 investigation 1 d&u:a pp 207-208 d&u:b p 208-209 5 6 7 55 d&u:b p 209 8 9 s&s p 209 t&d pp 210-211 investigation 2 d&u:a pp 211-212 56 d&u:b pp 212-213 s&s p 213 57 inquiry investigation 3 pp 214-215 58 investigation 4 t&d p 216 d&u:a pp 216-217 t&d p 217 d&u:b pp 217-218 s&s p 218 iyow p 220 #8 qq p 222 te for additional practice or homework qr 6.2 simplifying expressions pp 259-261 crm pp 3-7 algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 8.a.5 use physical models to perform operations with polynomials 8.a.7 add and subtract polynomials integer coefficients 8.a.12 apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines lp course 1 2.1 patterns in fractions pp 58-67 course 2 1.3 the distributive property pp 52-68 3.1 adding and subtracting with negative numbers pp 126147 8.2 speed and the slope connection pp 389-401 8.3 recognize linear relationships pp 410-422 9.1 find a solution method revisited pp 436-443 9.2 a model for solving equations pp 446-454 9.3 solve equations pp 460468 10.1 ratios and rates pp 494499 lc jayden s rescue by vladmir tumanov week 11-12 impact mathematics preliminary pacing calendar p 13

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grade 8 impact textbook d&u develop understand e explore ex example iyow in your own words ps problem set qq quick quiz s&s share and summarize mathematics planning guide notes qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal pacing new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections 5.2 monomials binomials and trinomials · to multiply and divide an expression by a monomial · to use geometric models to multiply binomials · to multiply binomials using the distributive property suggested per period pacing 59 t&d p 224 investigation 1 d&u:a p 225-226 d&u:b p 226 d&u:c p 227 s&s p 227 60 investigation 2 d&u:a p 227-228 s&s p 228 61 investigation 3 d&u:a p 230-231 s&s p.231 62 investigation 4 ex p 231 t&d p 232 d&u:a p 232 d&u:b p 232 s&s p 233 63 investigation 5 d&u:a p 234 t&d pp 234-235 d&u:b p 235 t&d p 235 64 d&u:c p 236 s&s p 236 iyow p 241 #50 qq p 243 te for additional practice or homework qr 6.1 writing expressions pp 252258 6.2 simplifying expressions pp 259-266 6.3 evaluating expressions formulas pp 267-270 6.4 solving linear equations pp 271-278 crm pp 10-14 algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 8.a.5 use physical models to perform operations with polynomials 8.a.6 multiply and divide monomials 8.a.8 multiply a binomial by a monomial or a binomial integer coefficients 8.a.9 divide a polynomial by a monomial integer coefficients course 1 3.3 variables and rules pp 143-156 course 2 1.1 variables and expressions pp 4-17 1.3 the distributive property pp 49-62 week 12-13 impact mathematics preliminary pacing calendar p 14

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