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a comprehensive approach to balanced mathematics mathematics planning for sixth grade 2010 edition 6
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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 september 2009 p 1
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 1 polygons angles and circles algebraic representation tables and graphs-develop algebraic reasoning patterns and numeric forms develop properties and rules develop two dimensional shapes polygons quadrilaterals triangles develop measurement perimeter and area-develop administer pre-chapter one assessment 1.1 patterns in geometry identifying naming and classifying polygons suggested per period pacing 1 e p 4 investigation 1 t&d p 4-5 ex p 6 d&u:a p.7 s&s p 8 2 investigation 2 t&d p 10 d&u:a p 10 d&u b p 11 s&s p 11 investigation 3 t&d p 13 d&u:a pp.14-15 s&s p 15 investigation 4 inquiry pp 16-17 iyow p 23 #25 qq p 23 te crm course pretest p 41 chapter 1 pretest p 44-47 for additional practice or homework qr 6.1 naming and classifying angles and triangles pp 257-8 261 6.2 naming and classifying polygons and polyhedrons pp 264-268 crm pp 16-20 algebra strand statistics and probability collection of data students will collect organize display and analyze data 6.s.3 construct venn diagrams to sort data may-june in grade 6 geometric relationships students will identify and justify geometric relationships formally and informally 5.g.6 classify triangles by properties of their angles and sides 5.g.7 know that the sum of the interior angles of a triangle is 180 degrees 5.g.8 find a missing angle when given two angles of a triangle transformational geometry students will apply transformations and symmetry to analyze problem solving situations 5.g.11 identify and draw lines of symmetry of basic geometric shapes lp everyday math grade 5 3.7 properties of polygons 3.9 angles of polygons cc www.learner.org/channel/courses /learningmath/geometry/session2 /index.html lc measurement mania by lynette long measuring penny by loreen leedy week 1 pacing 3 4 5 note the recommended pacing is based on the mandated 375 minutes or seven to eight 45-60 minute periods per week impact mathematics preliminary pacing calendar september 2009 p 2
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grade 6 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 qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mars mathematics assessment resource service mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 1.2 angles measuring angles and drawing angles with given measures suggested per period pacing 6 t&d p 24 investigation 1:t&d pp 26-27 d&u:a p.28 7 8 ex p 28 d&u b,p 29 s&s p 29 investigation 2 d&u:a p 30 t&d p 31 d&u:b p 31 t&d p 32 d&u:c p 33-34 s&s p 34 iyow p 39 #24 qq pp 39 te for additional practice or homework qr 6.1 naming and classifying angles and triangles pp 256-262 skills intervention for middle school skill 42 classifying angles crm p 28-32 problem solving strand students will apply and adapt a variety of appropriate strategies to solve problems 6.ps.11 translate from a picture/diagram to a number or symbolic expression 6.ps.13 model problems with pictures/diagrams physical objects algebra strand students will recognize use and represent algebraically patterns relations and functions 7.a.9 build a pattern to develop a rule for determining the sum of the interior angles of polygons geometry strand students will identify and justify geometric relationships formally and informally 7.g.7 find a missing angle when given angles of a quadrilateral note these concepts are introduced in grade 6 to prepare students for later mastery 8.g.1 8.g.6 identify pairs of vertical angles as congruent calculate the missing angle measurements when given two intersecting lines and an angle lp everyday math grade 5 3.3 exploring angle measures 3.4 using a protractor 3.7 properties of polygons 3.9 angles of polygons cc sum of interior angles of a triangle and polygon video 3 www.learner.org/resouces/series 176.html 9 week 2 note these concepts are introduced in grade 6 to prepare students for later mastery impact mathematics preliminary pacing calendar september 2009 p 3
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 1.3 measure around · finding and estimating perimeters · understanding pi and the formula for the circumference of a circle suggested per period pacing 10 t&d p 40 investigation 1 d&u:a pp 40-41 11 investigation 1 d&u b p 42 ex p 43 d&u:c p 43 s&s p.44 for additional practice or homework qr 6.4 perimeter p 278 6.8 circles p 295-298 standardized test review qr 7.1 systems of measurement p 304 7.6 size and scale pp 319-321 skills intervention for middle school skill 46 circumference of circles skill 48 area of circles crm pp 35-39 problem solving strand students will solve problems that arise in mathematics and in other contexts 6.ps.6 translate from a picture/diagram to a numeric expression students will apply and adapt a variety of appropriate strategies to solve problems 6.ps.11 translate from a picture/diagram to a number or symbolic expression 6.ps.13 model problems with pictures/diagrams physical objects 6.ps.15 make organized lists or charts to solve numerical problems algebra strand students will perform algebraic procedures accurately 6.a.2 use substitution to evaluate algebraic expressions may include exponents of one two and three 6.a.6 evaluate simple proportions within context continued note additional work needs to be included to practice determining the perimeter of a figure when the figure is located on the coordinate graph week 3 12 investigation 2:t&d p 386 d&u:a p 45 d&u:b p 47 s&s p 47 13 iyow p.51 15 qq p 51 te note when determining the value of formulas that involve use the key on the calculator or write the answer in terms of scientific calculator is suggested impact mathematics preliminary pacing calendar september 2009 p 4
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grade 6 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 qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mars mathematics assessment resource service mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing geometry strand week 3 continued students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes 6.g.5 6.g.6 6.g.7 6.g.9 identify radius diameter chords and central angles of a circle understand the relationship between the diameter and radius of a circle determine the area and circumference of a circle using the appropriate formula understand the relationship between the circumference and the diameter of a circle review and self-assessment suggested per period pacing 14 review and self-assessment pp 52-55 15 chapter 1 test crm pp 48-55 crm mars performance-based assessment merritt bakery pp 61-63 impact mathematics preliminary pacing calendar september 2009 p 5
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 2 fractions and decimals numbers and number sense whole numbers signed numbers develop rationals and irrationals fractions and decimal concepts develop algorithms and operations fractions decimals review extend algebraic reasoning patterns and numeric forms develop administer pre-chapter two assessment 2.1 patterns in fractions finding equivalent fractions and comparing fractions suggested per period pacing 16 ex p 58 investigation 1 d&u:a p 59 ex p 59 d&u:b p 60 s&s p 60 crm chapter 2 pretest p 30-33 for additional practice or homework skills intervention workbook skill 21 simplifying fractions skill 22 mixed numbers and improper fractions qr 2.1 fractions and equivalent fractions p 96-100 2.2 comparing and ordering fractions p 108 2.3 addition and subtraction of fractions p 110-115 crm pp 4-8 representation strand students will use representations to model and interpret physical social and mathematical phenomena 6.r.7 use mathematics to show and understand physical phenomena e.g determine the perimeter of a bulletin board number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.7 express equivalent ratios as a proportion 6.n.14 locate rational numbers on a number line including positive and negative 6.n.15 order rational numbers including positive and negative lp everyday math grade 5 5.4 two rules for finding equivalent fractions 8.1 comparing fractions lc the grapes of math mind stretching math riddles by greg tang sideways arithmetic from wayside school by louis sachar week 4 pacing 17 investigation 2 d&u a p 61 t&d p 62 d&u b p 63 s&s p 63 18 investigation 3 d&u a p 64 t&d p 65 d&u:b p 65 s&s p 65 19 investigation 4 t&d p 66 d&u:a pp 66-67 t&d p 67 d&u:b p 67 s&s p 67 20 iyow p 73 #47 qq p.73 te impact mathematics preliminary pacing calendar september 2009 p 6
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing students will understand meanings of operations and procedures and how they relate to one another 6.n.21 find multiple representations of rational numbers fractions decimals and percents 0 to 100 students will compute accurately and make reasonable estimates 6.n.27 justify the reasonableness of answers using estimation including rounding impact mathematics preliminary pacing calendar september 2009 week 4 continued p 7
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 2.2 patterns in decimals understanding and comparing decimals suggested per period pacing 21 e p 74 investigation 1 ex p 75 d&u:a p 76 22 investigation 1 d&u:b p 77 d&u:c pp 78-79 s&s p 79 23 investigation 2:t&d p 79 d&u:a pp 80-81 s&s p 81 for additional practice or homework skills intervention workbook skill 1 large numbers skill 15 multiplying by powers of ten skill 16 dividing by powers of ten qr 2.5 naming and ordering decimals pp 123-128 7.2 length and distance p 309 standardized test review skills intervention workbook skill 58 metric units of measure skill 59 customary units of measure crm pp 12-16 problem solving strand students will apply and adapt a variety of appropriate strategies to solve problems 6.ps.12 use trial and error and the process of elimination to solve problems number sense and operation strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.1 read and write whole numbers to trillions 6.n.14 locate rational numbers on a number line including positive and negative 6.n.15 order rational numbers including positive and negative students will understand meanings of operations and procedures and how they relate to one another 6.n.21 find multiple representations of rational numbers fractions decimals and percents 0 to 100 lp everyday math grade 5 5.5 fractions and decimals part 1 5.6 fractions and decimals part 2 5.7 fractions and decimals part 3 week 5 24 investigation 3 inquiry pp 82-83 iyow p 85 #27 25 qq p 87 te impact mathematics preliminary pacing calendar september 2009 p 8
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grade 6 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 qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mars mathematics assessment resource service mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 2.3 fraction and decimal equivalents converting decimals to fractions and fractions to decimals suggested per period pacing 26 t&d p.88 investigation 1 d&u:a pp 88-90 d&u:b pp 90-91 s&s p 91 27 investigation 2 d&u:a pp 91-92 d&u:b pp 92-93 s&s p 93 28 investigation 3 t&d p 94 ex p 93 d&u:a pp 94-95 t&d p 95 d&u:b p 96 s&s p 97 29 investigation 4 d&u:a pp 97-98 d&u:b p 99 s&s p 99 30 iyow p 102 34 qq p 104 te for additional practice or homework skills intervention workbook skill 24 changing fractions to decimals qr 2.1 fractions and equivalent fractions p 97 2.9 fraction decimal and percent relationships p 147 149 151 crm pp 20-24 number sense and operations strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.14 locate rational numbers on a number line including positive and negative 6.n.15 order rational numbers including positive and negative students will understand meanings of operations and procedures and how they relate to one another 6.n.20 represent fractions as terminating or repeating decimals 6.n.21 find multiple representations of rational numbers fractions decimals and percents 0 to 100 students will compute accurately and make reasonable estimates 6.n.22 evaluate numerical expressions using order of operations may include exponents of two and three lp everyday math grade 5 5.5 fractions and decimals part 1 5.6 fractions and decimals part 2 5.7 fractions and decimals part 3 review and self-assessment suggested per period pacing 31 review self-assessment pp 105-107 32 chapter 2 test week 6-7 crm mars assessment teaching with purpose sports results pp 49-52 impact mathematics preliminary pacing calendar september 2009 p 9
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 3 patterns numbers and rules algebraic reasoning patterns and numeric forms develop properties and rules-develop algebraic representation tables and graphs develop functions and relations linear expressions equations-develop two-dimensional shapes polygons develop measurement perimeter and area develop numbers and number sense whole numbers signed numbers develop exponents and roots-develop algorithms and operations fractions review extend data analysis modeling and analysis develop administer pre-chapter three assessment 3.1 number sense suggested per period pacing 33 t&d p 110 investigation 1 t&d p 111 d&u a pp 111-112 t&d p 112 d&u pp 112-113 s&s p 113 crm chapter 3 pretest p 30-33 for additional practice or homework qr 1.1 place value of whole numbers p 68 3.1 powers and exponents p 158 skills intervention for pre-algebra skill 54 metric units of measure pp 107-108 crm p 6-10 number sense and operation strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.1 read and write whole numbers to trillions students will understand meanings of operations and procedures and how they relate to one another 6.n.23 represent repeated multiplication in exponential form 6.n.24 represent exponential form as repeated multiplication lp everyday math grade 5 1.7 square numbers 1.8 unsquaring numbers 1.9 factor strings lp course 1 2.2 patterns in decimals pp 74-87 lc how much is a million by david schwartz if you made a million by david schwartz pacing week 7 34 investigation 2 d&u:a p 114 d&u:b p 115 d&u c pp 115-116 s&s p 116 35 iyow p 119 qq p 119 scientific calculator is suggested impact mathematics preliminary pacing calendar september 2009 p 10
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 3.2 patterns recognizing describing and extending numeric and visual patterns suggested per period pacing 36 explore p.120 investigation 1 d&u:a pp 121-122 t&d p 126 37 d&u:b pp 123-125 s&s p 125 38 investigation 2 d&u:a p 127 d&u:b p 128 d&u:c p 129 s&s p 129 for additional practice or homework qr 1.3 order of operations p 76 1.4 factors and multiples pp 78-80 skills intervention workbook pp 175-176 crm pp 11-15 number sense and operation strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.4 define and identify the identity and inverse properties of addition and multiplication students will understand meanings of operations and procedures and how they relate to one another 6.n.22 evaluate numerical expressions using order of operations may include exponents of two and three 6.n.23 represent repeated multiplication in exponential form 6.n.25 evaluate expressions having exponents where the power is an exponent of one two or three geometry strand students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes 6.g.2 determine the area of triangles and quadrilaterals squares rectangles rhombi and trapezoids and develop formulas lp course 1 2.2 patterns in decimals pp 74-87 lc how much is a million by david schwartz if you made a million by david schwartz week 8 39 investigation 3 t&d p 130 d&u:a pp 130-131 d&u:b pp 131-132 s&s p 132 40 investigation 4 ex p 133 d&u:a p 134 t&d p 134 d&u:b p 135 s&s p 135 41 iyow p 139 #41 qq p 142 te scientific calculator is suggested impact mathematics preliminary pacing calendar september 2009 p 11
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 3.3 variables and rules · writing and interpreting rules for sequences and input/output tables · showing that two rules for a sequence are equivalent suggested per period pacing 42 t&d p 143;investigation 1:d&u:a pp 144-146 d&u:b p 146 11-14 43 d&u:b pp.147-148 15-18 s&s p 148 44 investigation 2:d&u:a pp 149-150 d&u:b p 151 s&s p 152 45 investigation 3 t&d p 152 ex p 153 d&u:a pp 154-156 s&s p 156 46 investigation 4 inquiry pp.157-159 47 investigation 5:t&d p 160 d&u:a p 161 d&u:b p 161 48 d&u:c p 162 s&s p 162 investigation 6 t&d p 163 d&u:a p 164 49 d&u:b p 165 s&s p 165 iyow p 173 #34 qq p 173te for additional practice or homework qr patterns pp 61-63 1.3 order of operations pp 76-77 6.1 writing expressions and equations pp 210 227 6.2 simplifying expressions pp 216-221 crm pp 19-23 skills intervention for middle school mathematics skill 88 look for a pattern pp 175-176 standardized test review math skills maintenance workbook using order of operations pp 52-57 skills intervention for middle school mathematics skill 8 order of operations pp 15-16 number sense and operation strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.5 define and identify the zero property of multiplication students will understand meanings of operations and procedures and how they relate to one another 6.n.22 evaluate numerical expressions using order of operations may include exponents of two and three 6.n.25 evaluate expressions having exponents where the power is an exponent of one two,or three algebra strand students will represent and analyze algebraically a wide variety of problem solving situations 6.a.1 translate two-step verbal expressions into algebraic expressions students will perform algebraic procedures accurately 6.a.2 use substitution to evaluate algebraic expressions may include exponents of one two and three 6.a.3 translate two-step verbal sentences into algebraic equations 6.a.6 evaluate formulas for given input values circumference area volume distance temperature interest etc lp everyday math grade 5 10.3 algebraic expressions 10.4 rules tables and graphs part 1 10.5 american tour old faithful s next eruption 10.6 rules tables and graphs part 2 impact mathematics preliminary pacing calendar september 2009 week 9-10 p 12
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grade 6 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 qr quick review math handbook crm chapter resource masters inrj investigation notebook and reflection journal mars mathematics assessment resource service mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections pacing 3.4 apply properties 50 e p 174 investigation 1:t&d p 175 d&u:a p 175 d&u:b p 176 51 e p 176 t&d p 177 d&u:c p 178 d&u:d p 178 for additional practice or homework qr 1.2 properties pp 72-75 5.2 simplifying expressions p 223 standardized test review qr 1.4 factors and multiples pp 81-85 crm pp 24-28 52 investigation 2 d&u:a pp 179-180 t&d p 181 ex p 181 d&u:b p 182 53 d&u:c p 183 s&s p 183 53 investigation 3 d&u:a p 184 d&b:b p 185 d&b:c p 186 s&s p 186 iyow p 190 #37 qq p 190 te number sense and operation strand students will understand numbers multiple ways of representing numbers relationships among numbers and number systems 6.n.2 define and identify the commutative and associative properties of addition and multiplication 6.n.3 define and identify the distributive property of multiplication over addition 6.n.4 define and identify the identity and inverse properties of addition and multiplication review and self-assessment suggested per period pacing 54 review self-assessment pp 191-195 55 chapter 3 test week 11 crm mars assessment design a logo pp 49-52 impact mathematics preliminary pacing calendar september 2009 p 13
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grade 6 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 mars mathematics assessment resource service qr mathematics planning guide notes new york state mathematics standards n lp lc cc notes links to the past literature connections computer connections chapter 4 fraction and decimal operations rationals and irrationals fractions and decimal concepts develop algorithms and operations fractions decimals review extend data analysis:graphs and displays develop statistical measures-review and extend administer pre-chapter four assessment 4.1 add and subtract fractions adding and subtracting fractions and mixed numbers suggested per period pacing 56 t&d p 198 investigation 1 ex p 199 d&u:a p.199 d&u:b pp 200-201 s&s p 201 for additional practice or homework skills intervention workbook skill 21 simplifying fractions p 41 skill 26 adding fractions pp 51-52 skill 27 subtracting fractions pp 53-54 qr 2.3 addition and subtraction of fractions pp 110-115 skills maintenance workbook p 71 crm pp 4-16 number sense and operations strand students will understand meanings of operations and procedures and how they relate to one another 6.n.16 add and subtract fractions with unlike denominators 6.n.18 add subtract multiply and divide mixed numbers with unlike denominators lp everyday math grade 5 5.2 mixed numbers 6.8 using a slide rule to add and subtract fractions 8.2 adding mixed numbers 8.3 subtracting mixed numbers lc the number devil by hans magnus enzenberger more sideway arithmetic from wayside school by louis sachar pacing week 12 57 investigation 2 e p 201 d&u:a p 202 d&u:b p 202 58 ex p 203 d&u:c pp 203-204 d&u:d p 204 s&s p 204 59 investigation 3 all 60 investigation 4 inquiry pp 208-209 iyow p 214 53 qq p 215 te note inquiry investigation provides practice in using a scientific calculator scientific calculator suggested impact mathematics preliminary pacing calendar september 2009 p 14
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