A Correlation of to the South Carolina Academic Standards For Mathematics Grades K-5 T/M-160
Introduction The following correlation demonstrates the alignment of content between Investigations in Number, Data, and Space 2008 to the for Mathematics. This document contains page references to the Curriculum Unit Teachers Editions, Student Math Handbooks, and Student Activity Books. Investigations Online Activities for South Carolina Math Standards and, which are available on Pearson SuccessNet, are also cited by unit number and activity number. These South Carolina Activities were written to give teachers additional support while teaching the for Mathematics. They include a student black line master along with a teacher page that contains support such as directions for the teacher, suggested questions to promote discussion, differentiation support, and examples of student responses. Investigations in Number, Data, and Space 2008 is a Kindergarten through Grade 5 mathematics curriculum designed to engage students in making sense of mathematical ideas. Six major goals guided the development of the Investigation in Number, Data, and Space curriculum. The curriculum is designed to: Support students to make sense of mathematics and learn that they can be mathematical thinkers Focus on computational fluency with whole number as a major goal of the elementary grades Provide substantive work in important areas of mathematics rational numbers, geometry, measurement, data, and early algebra and connections among them Emphasize reasoning about mathematical ideas Communicate mathematics content and pedagogy to teachers Engage the range of learners in understanding mathematics. Underlying these goals are three guiding principals that are touchstones for the Investigations 2008 team as they approach both students and teachers as agents of their own learning: 1. Students have mathematical ideas. 2. Teachers are engaged in ongoing learning about mathematics content, pedagogy and student learning. 3. Teachers collaborate with the students and curriculum materials to create the curriculum as enacted in the classroom. Investigations 2008 is based on experience from research and practice. Based on that extensive classroom testing, the curriculum takes seriously the time students need to develop a strong conceptual foundation and skills based on that foundation. Each curriculum unit focuses on an area of content in depth, providing time for students to develop and practice ideas across a variety of activities and contexts that build on each other. An additional set of online lessons have been developed to address specific state standards. Daily guidelines for time spent on class sessions, Classroom Routines (K-3), and Ten-Minute Math (3-5) reflect the commitment to devoting adequate time to mathematics in each school day.
Table of Contents Kindergarten 1 Grade One 9 Grade Two 17 Grade Three 25 Grade Four 35 Grade Five 45.
to the for Mathematics Kindergarten MATHEMATICAL PROCESSES The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes. Standard K-1:The student will have a basic understanding of the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. The indicators for this standard, which are appropriate for kindergarten through grade two, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students. K-1.1 Apply substantive mathematical problem-solving strategies. Unit 1: 59 60 Unit 2: 83 84, 111, 113 115, 139 Unit 3: 102, 125 126 Unit 4: 77, 78, 96 98, 111 112, 137, 152 Unit 6: 84, 111 112, 120, 124, 129 K-1.2 Generate conjectures and exchange mathematical ideas. Unit 1: 65 66, 97 99, 117 119 Unit 2: 47, 70, 82, 122 123, 134 135 Unit 3: 48 49 Unit 6: 72 73, 108 109, 131 Unit 7: 29 30, 32 33, 103 105 K-1.3 Explain and justify answers to simple problems. Unit 1: 117 119 Unit 2: 49 50, 125 127 Unit 3: 40, 103 Unit 4: 117 1 Kindergarten
K-1.4 Analyze patterns by reasoning systematically. Unit 1: 107, 111, 116 117, 121, 125 Unit 3: 27 28, 41 42, 43 44, 46 47, 48 49, 71, 76 77, 81 82, 93 94, 115 116, 117 118, 122 123, 130, 135 136, 137, 141 142 Unit 7: 63 65, 67 68 K-1.5 Generalize mathematical concepts. Unit 1: 65 66, 97 99, 117 119 Unit 2: 47, 53 54, 66 67, 82, 131 Unit 6: 46, 88, 118 Unit 7: 25 26, 32 33, 54 55 K-1.6 Use a variety of forms of mathematical communication. Unit 1: 65 66, 97 99, 117 119 Unit 2: 68 70, 122 123, 134 135 Unit 3: 48 49 Unit 5: 83 84 Unit 6: 72 73, 108 109, 120, 122, 126 127, 131, 141 142 Unit 7: 29 30 K-1.7 Generalize connections among mathematics, the environment, and other subjects. Unit 1: 33, 83 86, 97 99 Unit 2: 27 Unit 5: 23 24, 24 25, 93 94, 95, 108 110 Unit 6: 51 53 Unit 7: 25 26, 44 K-1.8 Use multiple informal representations to convey mathematical ideas. Unit 1: 83 86, 97 99, 122 123 Unit 2: 35 37 Unit 3: 63 64 Unit 6: 74, 93 94, 120, 122, 126 127, 131 Unit 7: 26 29, 75 2 Kindergarten
NUMBER AND OPERATIONS Standard K-2: The student will demonstrate through the mathematical processes an emerging sense of quantity and numeral relationships, sets, and place values. K-2.1 Recall numbers, counting forward through 99 and backward from 10. Unit 1: 33, 48 49, 59 60, 65 66, 70, 76, 94, 101 102, 106, 114, 124 Unit 2: 92 93 Unit 3: 132 133 Unit 4: 75 Unit 6: 72 73 Unit 6: Activity 30 K-2.2 Translate between numeral and quantity through 31. Unit 1: 101 102 Unit 2: 28 30, 30 31, 40, 68 70 K-2.3 Compare sets of no more than 31 objects by using the terms more than, less than, and the same as. Unit 2: 101 102, 108 109 K-2.4 Represent simple joining and separating situations through 10. Unit 1: pp. 48 49, 116 Unit 4: pp. 59 61, 66 67, 72 73, 73 74, 77, 101 Unit 6: pp. 69 70, 70 72, 75, 113 114, 147 148 K-2.5 Understand that addition results in increase and subtraction results in decrease. Unit 1: pp. 48 49, 65 66, 70 76, 85 86, 101, 116 Unit 4: pp. 59 61, 66 67, 72 73, 73 74, 77, 101 Unit 6: pp. 69 70, 70 72, 75, 113 114, 147 148 K-2.6 Analyze the magnitude of digits through 99 on the basis of their place values. Unit 6: Activity 34 3 Kindergarten
K-2.7 Represent the place value of each digit in a two-digit whole number. Unit 6: Activity 34 K-2.8 Identify ordinal positions through 31st. Unit 6: Activity 35 Ordinal positions through 10th are covered by the following: Unit 1: Student Math Handbook Flip Chart, 16 ALGEBRA Standard K-3: The student will demonstrate through the mathematical processes an emerging sense of repeating and growing patterns and classification based on attributes. K-3.1 Identify simple growing patterns. Unit 7: 39 42 Unit 3: Activity 31 K-3.2 Analyze simple repeating and growing relationships to extend patterns. Unit 3: 46 47, 48 49, 59 60, 66 67, 71, 86 87, 90, 95, 97, 101, 104 105, 119, 138, 139 Unit 4: 45, 71, 95, 138, 157 Unit 5: 40, 64, 80, 111, 129 Unit 6: 50, 68, 87, 105, 128, 151 Unit 7: 43, 69, 88, 114 K-3.3 Translate simple repeating and growing patterns into rules. Unit 3: 46 47, 48 49, 59 60, 66 67, 71, 86 87, 90, 95, 97, 101, 104 105, 119, 138, 139 Unit 4: 45, 71, 95, 138, 157 Unit 5: 40, 64, 80, 111, 129 Unit 6: 50, 68, 87, 105, 128, 151 Unit 7: 43, 69, 88, 114 Unit 3: Activity 31 4 Kindergarten
K-3.4 Classify objects according to one or more attributes such as color, size, shape, and thickness. Unit 1: 107, 111, 116 117, 121, 125 Unit 7: 63 65, 67 68 GEOMETRY Standard K-4: The student will demonstrate through the mathematical processes an emerging sense of two- and three-dimensional geometric shapes and relative positions in space. K-4.1 Identify the two-dimensional shapes square, circle, triangle, and rectangle and the three-dimensional shapes cube, sphere, and cylinder. Unit 5: 23 24, 37 39, 99, 100 103,130 131 Unit 7: 78 80 K-4.2 Represent two-dimensional geometric shapes. Unit 5: 41, 41 42, 42 43, 45 K-4.3 Use the positional words near, far, below, above, beside, next to, across from, and between to describe the location of an object. Unit 5: Activity 4 K-4.4 Use the directional words left and right to describe movement. Unit 5: Activity 4 5 Kindergarten
MEASUREMENT Standard K-5: The student will demonstrate through the mathematical processes an emerging sense of coin values and the measurement concepts of length, weight, time, and temperature. K-5.1 Identify a penny, a nickel, a dime, a quarter, and a dollar and the value of each. Unit 4: 66 67 Unit 6: Activity 18 K-5.2 Compare the lengths of two objects, both directly and indirectly, to order objects according to length. Unit 2: 83 84, 89, 106, 106 107 Unit 4: 46 47 K-5.3 Use nonstandard units to explore the measurement concepts of length and weight. Unit 2: 83 84, 89, 106, 106 107 Unit 4: 46 47 Unit 7: Activity 25 K-5.4 Identify rulers, yardsticks, and tape measures as devices used to measure length; scales and balances as devices used to measure weight; calendars and analog and digital clocks as devices used to measure time; and digital and standard thermometers as devices used to measure temperature. Length is covered by the following: Unit 4: 29, 30 31, 34 35, 36 37, 39 40, 41 43, 47, 50 Unit 6: 80, 80 82 Related topics for time are covered by the following: Unit 1: 37 39, 47, 58, 64, 82, 100, 110 Unit 2: 26, 105 Unit 3: 35, 99 Unit 4: 33 Unit 5: 125 Unit 7: Activities 25, 27, and 29 6 Kindergarten
K-5.5 Understand which measure length, weight, time, or temperature is appropriate for a given situation. Related topics for time are covered by the following: Unit 1: 37 39, 47, 58, 64, 82, 100, 110 Unit 2: 26, 105 Unit 3: 35, 99 Unit 4: 33 Unit 5: 125 Related topics for length are covered by the following: Unit 4: 29, 30 31, 34 35, 36 37, 39 40, 41 43, 47, 50 Unit 6: 80, 80 82 Unit 7: Activities 25, 27, and 29 K-5.6 Use analog and digital clocks to tell time to the hour. Related topics are covered by the following: Unit 1: 37 39, 47, 58, 64, 82, 100, 110 Unit 2: 26, 105 Unit 3: 35, 99 Unit 4: 33 Unit 5: 125 Unit 7: Activity 29 K-5.7 Use a calendar to identify dates, days of the week, and months of the year. Related topics are covered by the following: Unit 1: 37 39, 47, 58, 64, 82, 100, 110 Unit 2: 26, 105 Unit 3: 35, 99 Unit 4: 33 Unit 5: 125 K-5.8 Recall equivalencies associated with time: 7 days = 1 week and 12 months = 1 year. Related topics are covered by the following: Unit 1: 37 39, 47, 58, 64, 82, 100, 110 Unit 2: 26, 105 Unit 3: 35, 99 Unit 4: 33 Unit 5: 125 7 Kindergarten
DATA ANALYSIS AND PROBABILITY Standard K-6: The student will demonstrate through the mathematical processes an emerging sense of organizing and interpret data. K-6.1 Organize data in graphic displays in the form of drawings and pictures. Unit 2: 146 149 Unit 7: 92 95, 101 103, 104 105, 106 K-6.2 Interpret data in graphic displays in the form of drawings and pictures. Unit 2: 146 149 Unit 7: 92 95, 101 103, 104 105, 106 8 Kindergarten
to the for Mathematics Grade One MATHEMATICAL PROCESSES The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes. Standard 1-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. The indicators for this standard, which are appropriate for kindergarten through grade two, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students. 1-1.1 Apply substantive mathematical problem-solving strategies. Unit 1: 104 106, 127, 129 130 Unit 3: 42, 46 48, 57, 65, 69 70, 85, 98 99, 108 109, 124 125 Unit 6: 53 54, 74 75, 108, 118 119 1-1.2 Generate conjectures and exchange mathematical ideas. Unit 1: 58 59, 79 81 Unit 3: 52 53, 151 Unit 4: 101 Unit 5: 24, 30, 46 47 Unit 7: 58 1-1.3 Explain and justify answers to simple problems. Unit 1: 79 81, 152 153 Unit 2: 27, 45 47, 52 53, 63 64 Unit 3: 30 31, 151 Unit 5: 24, 30, 76 77 Unit 6: 77, 90 92 9 Grade One
1-1.4 Analyze patterns by reasoning systematically. Unit 2: 109, 111 112 Unit 7: 27 28, 30 31, 33 34, 35 36, 38, 40 41, 43 44, 47 51, 62 63, 66 67 75 76, 81 82, 89 91, 93 94 Unit 8: 55, 61 63, 67, 71, 84, 103, 120 1-1.5 Generalize mathematical concepts. Unit 1: 66, 67 68, 110, 127, 175 176 Unit 2: 114 116 Unit 3: 46 48, 85, 87 89, 98 99 Unit 4: 92 93 Unit 5: 76 77 Unit 6: 71 73 Unit 8: 57 58, 122 125 1-1.6 Use a variety of forms of mathematical communication. Unit 1: 101 102, 113 116, 124 125 Unit 3: 65, 67 68, 87 89, 90 92, 169 Unit 4: 81 Unit 6: 59 60, 124 Unit 7: 58 59 Unit 8: 122 124 Unit 9: 51 52, 85 1-1.7 Generalize connections among mathematics, the environment, and other subjects. Unit 2: 26, 31, 114 116 Unit 3: 47, 112 Unit 4: 92 93 Unit 5: 76 77 Unit 9: 75, 81 1-1.8 Use multiple informal representations to convey mathematical ideas. Unit 1: 66, 67 68, 110, 127, 175 176 Unit 3: 46 48, 85, 87 89, 98 99 Unit 4: 63 64, 77 79 Unit 6: 71 73 Unit 8: 57 58, 122 125 10 Grade One
NUMBER AND OPERATIONS Standard 1-2: The student will demonstrate through the mathematical processes a sense of quantity and numeral relationships; the relationships among addition, subtraction, and related basic facts; and the connections among numeric, oral, and written-word forms of whole numbers. 1-2.1 Translate between numeral and quantity through 100. Unit 1: 89 90, 120 121 Unit 8: 44 1-2.2 Use estimation to determine the approximate number of objects in a set of 20 to 100 objects. Unit 1: 28 Unit 8: Activity 51 1-2.3 Represent quantities in word form through ten. Unit 1: 89 90, 120 121 Unit 8: 44 1-2.4 Recognize whole-number words that correspond to numerals through twenty. Unit 1: 89 90, 120 121 Unit 8: 44 1-2.5 Compare whole-number quantities through 100 by using the terms is greater than, is less than, and is equal to. Unit 1: 61, 69 70, 72 73, 89 90, 91 93 Unit 8: 110 111, 118 Unit 8: Activity 28 11 Grade One
1-2.6 Recall basic addition facts through 9 + 9 and corresponding subtraction facts. Unit 1: 108 109, 120 121, 124, 129 130, 138, 139 140 Unit 3: 39 40, 42, 65, 69 70, 81, 82 83, 87, 87 89, 90 92, 98 99, 119 120, 123 125, 130 131 Unit 5: 42 44, 50 51 Unit 6: 37 38, 108, 113, 117, 118 119, 121, 125 126, 130, 132 133 Unit 8: 27 28, 77 78, 97 98 1-2.7 Summarize the inverse relationship between addition and subtraction. Unit 3: 99 Unit 6: 48 Unit 8: Activity 24 1-2.8 Generate strategies to add and subtract without regrouping through twodigit numbers. Unit 8: Activities 30 and 56 1-2.9 Analyze the magnitude of digits through 999 on the basis of their place values. Unit 3: 123 Unit 8: 119 Unit 8: Activity 59 ALGEBRA Standard 1-3: The student will demonstrate through the mathematical processes a sense of numeric patterns, the relationship between addition and subtraction, and change over time. 1-3.1 Analyze numeric patterns in addition and subtraction to develop strategies for acquiring basic facts. Unit 7: 75 76, 89 91 Unit 8: 71, 84, 103, 120 1-3.2 Translate patterns into rules for simple addition and subtraction. Unit 7: 75 76, 89 91 Unit 8: 71, 84, 103, 120 12 Grade One
1-3.3 Illustrate the commutative property based on basic facts. Unit 8: Activity 23 1-3.4 Analyze numeric relationships to complete and extend simple patterns. Unit 7: 75 76, 89 91 Unit 8: 71, 84, 103, 120 1-3.5 Classify a number as odd or even. Unit 7: 79, 94 Student Math Handbook: 58 Unit 7: Activity 55 1-3.6 Classify change over time as quantitative or qualitative. Unit 8: Activity 22 GEOMETRY Standard 1-4: The student will demonstrate through the mathematical processes a sense of two- and three-dimensional geometric shapes, symmetry, and relative positions and directions in space. 1-4.1 Identify the three-dimensional geometric shapes prism, pyramid, and cone. Unit 9: 58 59 Student Math Handbook: 83 88 1-4.2 Analyze the two-dimensional shapes circle, square, triangle, and rectangle. Unit 2: 25 27, 31 32, 70, 78 79, 86 87, 91 92, 96 98 1-4.3 Classify two-dimensional shapes as polygons or nonpolygons. Unit 2: 121 13 Grade One
1-4.4 Identify a line of symmetry. Unit 2: Activity 3 1-4.5 Use the positional and directional terms north, south, east, and west to describe location and movement. Related topics are covered by the following: Unit 9: 93 94 Student Math Handbook: 92 MEASUREMENT Standard 1-5: The student will demonstrate through the mathematical processes a sense of the value of combinations of coins and the measurement of length, weight, time, and temperature. 1-5.1 Use a counting procedure to determine the value of a collection of pennies, nickels, dimes, and quarters totaling less than a dollar. Unit 8: Activities 40 and 41 1-5.2 Represent a nickel, a dime, a quarter, a half-dollar, and a dollar in combinations of coins. Unit 8: Activities 40 and 41 1-5.3 Represent money by using the cent and dollar notations. Student Math Handbook: 20 Unit 8: Activity 52 1-5.4 Use whole-inch units to measure the length of an object. Unit 5: 35, 36 38, 39 1-5.5 Generate common referents for whole inches. Related topics are covered by the following: Unit 5: 35, 36 38, 39 Student Math Handbook: 99 102 14 Grade One
1-5.6 Use common referents to make estimates in whole inches. Related topics are covered by the following: Unit 5: 35, 36 38, 39 Student Math Handbook: 99 102 1-5.7 Use nonstandard units to measure the weight of objects. Unit 8: Activity 18 1-5.8 Use analog and digital clocks to tell and record time to the half hour. A related topic is covered in: Unit 8: 96 Unit 9: 56 Unit 8: Activity 43 1-5.9 Illustrate past and future dates on a calendar. Related topics are covered by the following: Unit 1: 33 34, 119 Unit 2: 113 Unit 3: 28 Student Math Handbook: 18, 19 1-5.10 Represent dates in standard form (June 1, 2007, for example) and numeric form (6-1-2007, for example). Unit 5: Activity 60 Related topics are covered by the following: Unit 1: 33 34, 119 Unit 2: 113 Unit 3: 28 1-5.11 Use Celsius and Fahrenheit thermometers to measure temperature. Unit 8: Activity 45 15 Grade One
Data Analysis and Probability Standard 1-6: The student will demonstrate through the mathematical processes a sense of collecting, organizing, and interpreting data and of making predictions on the basis of data. 1-6.1 Use survey questions to collect data. Unit 4: 23 24, 32 33, 53, 57 58, 72 73, 76, 91, 99, 105, 111 Unit 5: 41, 78 Unit 6: 33, 45, 61, 102 Unit 7: 39, 61, 86 Unit 9: 29, 44, 60, 79, 92 1-6.2 Organize data in picture graphs, object graphs, bar graphs, and tables. Unit 4: 23 24, 32 33, 53, 57 58, 72 73, 76, 91, 99, 105, 111 Unit 5: 41, 78 Unit 6: 33, 45, 61, 102 Unit 7: 39, 61, 86 Unit 9: 29, 44, 60, 79, 92 1-6.3 Interpret data in picture graphs, object graphs, bar graphs, and tables by using the comparative terms more, less, greater, fewer, greater than, and less than. Unit 4: 58 1-6.4 Predict on the basis of data whether events are likely or unlikely to occur. Unit 4: Activity 12 16 Grade One
to the for Mathematics Grade Two MATHEMATICAL PROCESSES The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes. Standard 2-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. The indicators for this standard, which are appropriate for kindergarten through grade two, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students. 2-1.1 Apply substantive mathematical problem-solving strategies. Unit 1: 121 122, 139, 152 154, 157, 160 161 Unit 3: 39 40, 65 Unit 6: 28 29, 39 41, 44 47, 66 67, 84 86 Unit 8: 88 91, 115 119, 127 128 2-1.2 Generate conjectures and exchange mathematical ideas. Unit 1: 52, 96 97 Unit 3: 33 34, 163 Unit 4: 46 47, 51 Unit 8: 33, 38, 40 42, 44 45, 46 47 Unit 9: 53 54 2-1.3 Explain and justify answers to simple problems. Unit 1: 52, 55 56, 96 97 Unit 3: 42 44, 163 Unit 8: 33, 40 42, 44 45, 46 47, 97 98 Unit 9: 53 54 17 Grade Two
2-1.4 Analyze patterns by reasoning systematically. Unit 3: 143, 144 145, 148, 177, 179 Unit 5: 38 40, 40 41, 42 43, 47 48, 49 51, 59 60, 62 63, 77 79, 80 81, 85 87, 90 92 Unit 6: 132 133, 138, 141 2-1.5 Generalize mathematical concepts. Unit 1: 53 54, 141 143, 157, 160 161 Unit 3: 101, 135, 158, 181 Unit 4: 80 Unit 5: 32, 33 36 Unit 6: 28 29, 34 36, 39 41, 67 68, 78 81 Unit 7: 50 52 Unit 8: 27 28, 53 55, 71 73, 81 84, 88, 115 119, 142 145 2-1.6 Use a variety of forms of mathematical communication. Unit 1: 48 50, 63 64, 65, 93 94, 66 67, 96 97, 121 122, 139 140, 141 143, 150 151 Unit 2: 30, 41, 49, 78, 88, 103 Unit 3: 42 44, 73 75, 135 136, 193 Unit 4: 46 47, 51 Unit 5: 33 36 Unit 6: 44 47, 73, 114 Unit 8: 27 28, 53 55, 71 73, 81 84, 88 91, 115 119, 142 145 Unit 9: 81 e. Express solutions using pictorial, tabular, graphical, or algebraic methods Unit 1: 65, 139 140, 150 151 Unit 2: Unit 3: 135, 139 Unit 8: 27 28, 53 55, 81 84, 88 91 f. Explain solutions in written form Unit 1: 139 140 Unit 2: 88 Unit 6: 73 g. Ask questions about mathematical ideas or problems Unit 4: 46 47, 51 18 Grade Two
2-1.7 Generalize connections among mathematics, the environment, and other subjects. Unit 1: 91 Unit 3: 150, 151 152, 180 181 Unit 5: 29 31 Unit 6: 134 136, 146 Unit 7: 59 62, 66 67 2-1.8 Use multiple informal representations to convey mathematical ideas. Unit 1: 29 31, 53 54, 78, 96 97 Unit 6: 71, 76 77 NUMBER AND OPERATIONS Standard 2-2: The student will demonstrate through the mathematical processes an understanding of the base-ten numeration system; place values; and accurate, efficient, and generalizable methods of adding and subtracting whole numbers. 2-2.1 Generate estimation strategies to determine the approximate number of objects in a set of no more than 1,000 objects. Unit 1: 91 93, 146, 221 2-2.2 Represent quantities in word form through twenty. Unit 1: 53 54, 78, 96 97 Unit 6: 71, 76-77 2-2.3 Represent multiples of ten in word form through ninety. Unit 1: 53 54, 78, 96 97 Unit 6: 71, 76 77 2-2.4 Compare whole-number quantities through 999 by using the terms is less than, is greater than, and is equal to and the symbols <, >, and =. Unit 1: 146 Unit 6: 56 57 Student Math Handbook: 81 82 Unit 8: Activity 30 19 Grade Two
2-2.5 Interpret models of equal grouping (multiplication) as repeated addition and arrays. Unit 8: Activity 38 2-2.6 Interpret models of sharing equally (division) in as repeated subtraction and arrays. Unit 8: Activities 39 and 40 2-2.7 Generate strategies to add and subtract pairs of two-digit whole numbers with regrouping. Unit 1: 65, 138 Unit 3: 31 33, 39 40, 40 41, 54 56 Unit 6: 25 26, 28 29, 31 33, 34 36, 38 41, 54, 84 86 Unit 8: 79, 99 100, 101 103, 104, 112, 113, 146 2-2.8 Generate addition and subtraction strategies to find missing addends and subtrahends in number combinations through 20. Unit 1: 68, 95, 97 98, 103, 125 126, 130, 131, 131 132, 141 143, 152 154, 155, 162, 170 171 Unit 2: 24, 46 Unit 3: 58 59, 181 Unit 8: 53 55, 57 58, 60 61 2-2.9 Generate strategies to round numbers through 90 to the nearest 10. Unit 1: 146 Unit 6: 56 57 Unit 8: Activity 32 2-2.10 Analyze the magnitude of digits through 9,999 on the basis of their place values. Unit 3: 174 175, 189 190, 192 194 Unit 8: 144 20 Grade Two
ALGEBRA Standard 2-3: The student will demonstrate through the mathematical processes an understanding of numeric patterns and quantitative and qualitative change. 2-3.1 Analyze numeric patterns in skip counting that uses the numerals 1 through 10. Unit 3: 143, 144 145, 148, 177, 179 Unit 6: 132 133, 138, 141 2-3.2 Translate patterns into rules for simple multiples. Student Math Handbook: 35 40 2-3.3 Analyze relationships to complete and extend growing and repeating patterns involving numbers, symbols, and objects. Unit 3: 143, 144 145, 148, 177,179 Unit 5: 38 40, 40 41, 42 43, 47 48, 49 51, 59 60, 62 63, 77 79, 80 81, 85 87, 90 92 Unit 6: 132 133, 138, 141 Student Math Handbook: 100 103 2-3.4 Identify quantitative and qualitative change over time. Unit 9: Activity 62 2-3.5 Analyze quantitative and qualitative change over time. Unit 9: Activity 62 GEOMETRY Standard 2-4: The student will demonstrate through the mathematical processes an understanding of basic spatial reasoning and the connection between the identification of basic attributes and the classification of three-dimensional shapes. 21 Grade Two
2-4.1 Analyze the three-dimensional shapes spheres, cubes, cylinders, prisms, pyramids, and cones according to the number and shape of the faces, edges, corners, and bases of each. Unit 2: 28, 41 42, 112 113 Student Math Handbook: 122 125 2-4.2 Identify multiple lines of symmetry. Related topic is covered by the following: Unit 2: 121 122, 128, 131 Unit 7: 23 2-4.3 Predict the results of combining and subdividing polygons and circles. Unit 7: 23 Student Math Handbook: 100 MEASUREMENT Standard 2-5: The student will demonstrate through the mathematical processes an understanding of the value of combinations of coins and bills and the measurement of length, weight, time, and temperature. 2-5.1 Use a counting procedure to determine the value of a collection of coins and bills. Unit 6: 69 Student Math Handbook: 19 21 Unit 8: Activity 42 2-5.2 Use coins to make change up to one dollar. Unit 8: Activity 44 2-5.3 Use appropriate tools to measure objects to the nearest whole unit: measuring length in centimeters, feet, and yards; measuring liquid volume in cups, quarts, and gallons; measuring weight in ounces and pounds; and measuring temperature on Celsius and Fahrenheit thermometers. Student Math Handbook: 146 147, 153 157 Unit 9: Activities 49, 51, and 53 22 Grade Two
2-5.4 Generate common measurement referents for feet, yards, and centimeters. Unit 9: 60 62, 83, 88, 89, 97 98 2-5.5 Use common measurement referents to make estimates in feet, yards, and centimeters. Unit 9: 63 64, 89, 99 100, 102 2-5.6 Predict whether the measurement will be greater or smaller when different units are used to measure the same object. Unit 9: 102 104 2-5.7 Use analog and digital clocks to tell and record time to the nearest quarter hour and to the nearest five-minute interval. Related topic is covered in: Unit 6: 82, 142 Classroom Routines Units 1-9: What Time Is It? Unit 9: Activity 61 2-5.8 Match a.m. and p.m. to familiar situations. Unit 9: 111 114, 117 120, 122 125, 127 132, 135 138, 139 141, 143 145 2-5.9 Recall equivalencies associated with length and time: 12 inches = 1 foot, 3 feet = 1 yard, 60 minutes = 1 hour, and 24 hours = 1 day. Unit 9: 88, 113 Student Math Handbook: 132 133, 136, 153 154 DATA ANALYSIS AND PROBABILITY Standard 2-6: The student will demonstrate through the mathematical processes an understanding of creating questions to collect data, organizing data, describing trends of a data set, and making predictions based on data. 2-6.1 Create survey questions to collect data. Unit 4: 26, 38 40, 46 47, 51, 91 2-6.2 Organize data in charts, pictographs, and tables. Unit 4: 93 94 Student Math Handbook: 106 111 Unit 4: Activities 56 and 58 23 Grade Two
2-6.3 Infer trends in a data set as increasing, decreasing, or random. Unit 5: 37 41, 42 43, 45 51, 54 60, 62 68, 70 72 2-6.4 Predict on the basis of data whether events are more likely or less likely to occur. Unit 4: Activity 16 24 Grade Two
to the for Mathematics Grade Three MATHEMATICAL PROCESSES The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes. Standard 3-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. The indicators for this standard, which are appropriate for grades three through five, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students. 3-1.1 Analyze information to solve increasingly more sophisticated problems. Unit 1: 126 Unit 3: 131 135, 157 Unit 5: 36 37, 122 Unit 6: 80 3-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships. Unit 2: 138 139, 149 Unit 3: 55 56, 60 Unit 7: 98 99 Unit 8: 68, 69 71 Unit 9: 44 45 25 Grade Three
3-1.3 Explain and justify answers on the basis of mathematical properties, structures, and relationships. Unit 1: 29, 38 39, 46, 81 84, 103 104, 127 Unit 2: 86 87, 93 96, 151 153 Unit 3: 73 74, 109 110, 158 159 Unit 5: 29 30, 41 Unit 8: 48 51 Unit 9: 83 84 3-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects. Unit 1: 29, 38 39, 46, 81 84, 103 104, 127 Unit 2: 138 139, 149 Unit 3: 55 56, 73 74, 109 110, 158 159 Unit 5: 128 Unit 8: 68, 69 71 Unit 9: 44 45 3-1.5 Use correct, complete, and clearly written and oral mathematical language to pose questions, communicate ideas, and extend problem situations. Unit 1: 37 39, 86 87, 93 96, 151 153 Unit 2: 118 119 Unit 3: 38 39, 101 102 Unit 4: 97 Unit 5: 29 30, 41, 51 Unit 8: 112 115, 143 144 Unit 9: pp. 83 84 3-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered. Unit 1: 49 50, 103 106, 114 115 Unit 2: 118 119, 125 Unit 5: 60 62, 65 66 Unit 8: 56 58, 138 139 Unit 9: 51, 86 3-1.7 Use flexibility in mathematical representations. Unit 1: 27 31, 37 39, 45 48, 81 84 Unit 3: 52 53, 73 74 26 Grade Three
3-1.8 Recognize the limitations of various forms of mathematical representations. Unit 1: 27 31, 37 39, 45 48, 81 84 Unit 3: 52 53, 73 74 NUMBER AND OPERATIONS Standard 3-2: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts. 3-2.1 Compare whole-number quantities through 999,999 by using the terms is less than, is greater than, and is equal to and the symbols <, >, and =. Unit 1: 65, 71 Unit 3: 31 33, 36 37, 38-39, 123 124 3-2.2 Represent in word form whole numbers through nine hundred ninetynine thousand. Unit 8: Activity 80 Related topics are covered by the following: Unit 3: 31 32, 47 Unit 4: 22, 29, 37, 45, 50, 81, 110, 129, 134 Unit 8: 30 Unit 9: 22, 28, 32, 37, 42 3-2.3 Apply an algorithm to add and subtract whole numbers fluently. Unit 1: 29 31, 37 39, 45 49, 53 54, 97 99, 125, 133 Unit 3: 72 74, 76 77, 88 89, 92 93, 97 98, 109 111, 173 174, 176 179 Unit 8: 31 33, 73 75, 86 87, 92 94, 118 122, 134 136 Unit 8: Activity 61, Activity 62 27 Grade Three
3-2.4 Apply procedures to round any whole number to the nearest 10, 100, or 1,000. Unit 8: Activity 51 Related topics are covered by the following: Unit 1: 48, 109, 110 111, 116, 121, 125, 138, 139 Unit 2: 24, 33 Unit 8: 41 43 3-2.5 Understand fractions as parts of a whole. Unit 7: 25 26, 27 28, 30 31, 37 38 3-2.6 Represent fractions that are greater than or equal to 1. Unit 7: 25 26, 27 28, 30 31, 37 38 Student Math Handbook: 61 62 3-2.7 Recall basic multiplication facts through 12 x 12 and the corresponding division facts. Unit 5: 31 32, 50, 61, 66, 68, 98 99, 101 103, 108 109, 119, 138 139 Unit 5: Activity 34 3-2.8 Compare the inverse relationship between multiplication and division. Unit 5: 122 124, 126, 140 3-2.9 Analyze the effect that adding, subtracting, or multiplying odd and/or even numbers has on the outcome. Unit 5: Activity 70 Readiness for this topic is covered by the following: Unit 5: 50, 54 3-2.10 Generate strategies to multiply whole numbers by using one single-digit factor and one multidigit factor. Unit 5: 31 33, 36 38, 60 61, 102 103, 104 105, 135 136, 138 139 28 Grade Three
3-2.11 Use basic number combinations to compute related multiplication problems that involve multiples of 10. Unit 3: 55, 161 Student Math Handbook: 43 3-2.12 Analyze the magnitude of digits through 999,999 on the basis of their place value. Unit 1: 30, 135 Unit 3: 38 39, 58 60, 70 ALGEBRA Standard 3-3: The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time. 3-3.1 Create numeric patterns that involve whole-number operations. Unit 5: 48, 49 50, 51, 53, 54 55, 56 57, 59, 64, 66 68, 71 Unit 8: 28, 29 30, 36, 47, 55 3-3.2 Apply procedures to find missing numbers in numeric patterns that involve whole-number operations. Unit 5: 48, 49 50, 51, 53, 54 55, 56 57, 59, 64, 66 68, 71 Unit 8: 28, 29 30, 36, 47, 55 3-3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction, or multiplication equation. Unit 1: 40 Unit 3: 138, 149 150, 157 161 Unit 5: 37 3-3.4 Illustrate situations that show change over time as increasing. Unit 6: 27 29, 34 38, 40 43, 45 47, 49 51, 79 83, 86 91, 93 96, 98 101, 104 106, 109 111 29 Grade Three
GEOMETRY Standard 3-4: The student will demonstrate through the mathematical processes an understanding of the connection between the identification of basic attributes and the classification of two-dimensional shapes. 3-4.1 Identify the specific attributes of circles: center, radius, circumference, and diameter. Unit 4: 51 Unit 4: Activity 22 3-4.2 Classify polygons as either triangles, quadrilaterals, pentagons, hexagons, or octagons according to the number of their sides. Unit 4: 105 106, 108 109, 111, 112 113 3-4.3 Classify lines and line segments as either parallel, perpendicular, or intersecting. Related topics are covered by the following: Unit 4: 109, 121, 124 126, 131 133 Unit 4: Activity 18 3-4.4 Classify angles as either right, acute, or obtuse. Unit 4: 109, 121, 124 126 3-4.5 Classify triangles by the length of their sides as either scalene, isosceles, or equilateral and by the size of their angles as either acute, obtuse, or right. Unit 4: 108 109 Unit 4: Activity 21 3-4.6 Exemplify points, lines, line segments, rays, and angles. Unit 4: 109, 121, 124 126, 131 133 Unit 4: Activity 17 30 Grade Three
3-4.7 Analyze the results of combining and subdividing circles, triangles, quadrilaterals, pentagons, hexagons, and octagons. Unit 4: 53 55, 62, 74, 94, 104, 116, 123 3-4.8 Predict the results of one transformation either slide, flip, or turn of a geometric shape. Unit 4: 64 65, 76 77 Student Math Handbook: 117, 124 MEASUREMENT Standard 3-5: The student will demonstrate through the mathematical processes an understanding of length, time, weight, and liquid volume measurements; the relationships between systems of measure; accurate, efficient, and generalizable methods of determining the perimeters of polygons; and the values and combinations of coins required to make change. 3-5.1 Use the fewest possible number of coins when making change. Unit 4: Activity 77 3-5.2 Use appropriate tools to measure objects to the nearest unit: measuring length in meters and half inches; measuring liquid volume in fluid ounces, pints, and liters; and measuring mass in grams. Unit 2: 127 128, 134 135, 144 145 Student Math Handbook: 105 109 Unit 5: Activities 30, and 31 Unit 6: Activity 38 31 Grade Three
3-5.3 Recognize the relationship between meters and yards, kilometers and miles, liters and quarts, and kilograms and pounds. Unit 4: Activity 78, Activity 79 Unit 6: Activity 38 Related topics are covered by the following: Unit 2: pp. 127 128, 134 135, 144 145 Student Math Handbook: 107 3-5.4 Use common referents to make comparisons and estimates associated with length, liquid volume, and mass and weight: meters compared to yards, kilometers to miles, liters to quarts, and kilograms to pounds. Unit 4: Activity 78, Activity 79 Unit 6: Activity 38 Related topics are covered by the following: Unit 2: pp. 127 128, 134 135, 144 145 Student Math Handbook: 105 106 3-5.5 Generate strategies to determine the perimeters of polygons. Unit 4: 34 35, 47 49 Student Math Handbook: 110 113 3-5.6 Use analog and digital clocks to tell time to the nearest minute. Unit 3: 108, 113 114, 115, 122, 128, 136, 141 Unit 5: 24, 28, 34, 82, 87, 92, 116, 121, 125, 129, 133, 137, 141 Unit 7: 47, 90 3-5.7 Recall equivalencies associated with time and length: 60 seconds = 1 minute and 36 inches = 1 yard. Unit 8: Activity 58 Unit 2: 126 127, 133 134, 142 143 Unit 4: 23 24 Related topics for time are covered by the following: Unit 3: 108, 113 114, 115, 122, 128, 136, 141 Unit 5: 24, 28, 34, 82, 87, 92, 116, 121, 125, 129, 133, 137, 141 Unit 7: 47, 90 32 Grade Three
DATA ANALYSIS AND PROBABILITY Standard 3-6: The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability. 3-6.1 Apply a procedure to find the range of a data set. Unit 2: 85, 86, 92, 130, 163, 166, 167 3-6.2 Organize data in tables, bar graphs, and dot plots. Unit 1: 33 34 Unit 2: 26 27, 50 51, 71, 83 85, 104 105, 83 86, 90, 90 91, 104 105, 130 131, 146, 150 3-6.3 Interpret data in tables, bar graphs, pictographs, and dot plots. Unit 2: 28, 34, 44 48, 50 51, 60, 71, 85 86, 90 92, 93 97, 111 112, 115, 130 131, 146, 150 3-6.4 Analyze dot plots and bar graphs to make predictions about populations. Related topics are covered in the following: Unit 1: 33 34 Unit 2: 26 27, 50 51, 71, 83 85, 104 105, 83 86, 90, 90 91, 104 105, 130 131, 146, 150 3-6.5 Compare the benefits of using tables, bar graphs, and dot plots as representations of a given data set. Related topics are covered by the following: Unit 1: 33 34 Unit 2: 26 27, 50 51, 71, 83 85, 104 105, 83 86, 90, 90 91, 104 105, 130 131, 146, 150 33 Grade Three
3-6.6 Predict on the basis of data whether events are likely, unlikely, certain, or impossible to occur. Unit 2: Activity 9 3-6.7 Understand when the probability of an event is 0 or 1. Unit 2: Activity 75 34 Grade Three
to the for Mathematics Grade Four MATHEMATICAL PROCESSES The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes. Standard 4-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. The indicators for this standard, which are appropriate for grades three through five, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students. 4-1.1 Analyze information to solve increasingly more sophisticated problems. Unit 1: 27 Unit 5: 133 134 Unit 7: 65 Unit 8: 107 Unit 9: 36 38 4-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships. Unit 1: 51 52, 77 78, 97 98, 102 103, 106 107, 108 110 Unit 2: 34, 44, 53 54, 72 73, 76 77, 82 83, 88 90, 117, 122, 137 140 Unit 3: 83 Unit 4: 103 104, 119 120 Unit 6: 59 60 Unit 7: 38 39, 41 Unit 9: 62 64, 101 102 35 Grade Four
4-1.3 Explain and justify answers to problems on the basis of mathematical properties, structures, and relationships on mathematical properties, structures, and relationships. Unit 1: 28 29, 48, 89 90, 92 93, 98 101, 108 110 Unit 3: 81 83, 89 91, 120, 125 126, 132 134 Unit 4: 44 46, 99 101, 129 130, 133 134, 136 137 Unit 5: 44, 47 48, 68, 80 81, 81 83, 133 134, 152 154 Unit 6: 90 91, 96 97, 117 118, 123 124 Unit 8: 36 38, 41 44 Unit 9: 66, 82, 101 102, 117 118 4-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects. Unit 1: 108 110 Unit 3: 89 91, 120 Unit 4: 99 101, 129 130, 136 137 Unit 5: 133 134 4-1.5 Use correct, complete, and clearly written and oral mathematical language to pose questions, communicate ideas, and extend problem situations. Unit 1: 51 52, 106 107 Unit 2: 74, 89 90 Unit 3: 66 68, 81 83, 112 113, 119 Unit 4: 62, 106 107 Unit 5: 47 48, 64 65, 67 69, 124 Unit 6: 26 27 Unit 8: 29 30, 55 57, 94 95 Unit 9: 66, 82 4-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered. Unit 2: 83 86 Unit 3: 29 30, 35 38, 66 67, 97 98, 106 107, 117 118, 137 140 Unit 4: 82 Unit 6: 34 36 Unit 8: 29 30 Unit 9: 125 126 36 Grade Four
4-1.7 Use flexibility in mathematical representations. Unit 1: 98 101, 108 110 Unit 3: 47 48, 49 50, 53, 85 86, 89 91 Unit 8: 36 38 Unit 9: 47 49 4-1.8 Recognize the limitations of various forms of mathematical representations. Unit 1: 98 101, 108 110 Unit 3: 47 48, 49 50, 53, 85 86, 89 91 Unit 8: 36 38 Unit 9: 47 49 NUMBER AND OPERATIONS Standard 4-2: The student will demonstrate through the mathematical processes an understanding of decimal notation as an extension of the place-value system; the relationship between fractions and decimals; the multiplication of whole numbers; and accurate, efficient, and generalizable methods of dividing whole numbers, adding decimals, and subtracting decimals. 4-2.1 Recognize the period in the place-value structure of whole numbers: units, thousands, millions, and billions. Related topics are covered by the following: Unit 5: 29, 34 35, 37, 38 39, 45, 52 53, 60, 79, 86, 105 106, 113 114, 117, 122, 144, 150, 155 Unit 6: 24, 33, 37, 41, 47, 52, 58 Student Math Handbook: 7 4-2.2 Apply divisibility rules for 2, 5, and 10. Unit 8: 91 92, 100 Unit 3: Activity 12 37 Grade Four
4-2.3 Apply an algorithm to multiply whole numbers fluently. Unit 1: 27, 43 45, 61, 65 66, 78 79, 81 Unit 3: 29 30, 32 33, 39 41, 49 50, 52 53, 106 108, 112 113, 117 118, 130 131, 137 140 Unit 8: Activities 48 and 60 4-2.4 Explain the effect on the product when one of the factors is changed. Related topics are covered by the following: Unit 1: 27, 43 45, 61, 65 66, 78 79, 81 Unit 3: 29 30, 32 33, 39 41, 49 50, 52 53, 106 108, 112 113, 117 118, 130 131, 137 140 4-2.5 Generate strategies to divide whole numbers by single-digit divisors. Unit 3: 61 62, 63, 66 68, 78 79, 81 83, 125 126 Unit 8: 95 98, 100, 103 Unit 8: Activities 49 and 61 4-2.6 Analyze the magnitude of digits through hundredths on the basis of their place value. Unit 5: 31, 53 4-2.7 Compare decimals through hundredths by using the terms is less than, is greater than, and is equal to and the symbols <, >, and =. Unit 6: 104, 111, 112 113, 114 115, 116, 120, 127, 132, 135 Unit 7: 33, 55, 60, 76 Student Math Handbook: 68 69 4-2.8 Apply strategies and procedures to find equivalent forms of fractions. Unit 6: 36, 73 4-2.9 Compare the relative size of fractions to the benchmarks 0, 2 1, and 1. Unit 6: 50, 79 81, 84 85, 89 90, 91 93 Student Math Handbook: 60 61 38 Grade Four
4-2.10 Identify the common fraction/decimal equivalents 2 1 =.5, 4 1 =.25, 4 3 =.75, 1 2 1 1!.33,!.67, multiples of, and multiples of. 3 3 10 100 Unit 6: 36, 73 4-2.11 Represent improper fractions, mixed numbers, and decimals. Unit 6: 70 72, 104, 105 108, 109 110, 111, 114 115, 116, 120, 127, 132, 135 Unit 7: 33, 55, 60, 76 4-2.12 Generate strategies to add and subtract decimals through hundredths. Unit 6: 104, 111, 116, 117 118, 120, 123 124, 125 126, 127, 132, 135 Unit 7: 33, 55, 60, 76 ALGEBRA Standard 4-3: The student will demonstrate through the mathematical processes an understanding of numeric and nonnumeric patterns, the representation of simple mathematical relationships, and the application of procedures to find the value of an unknown. 4-3.1 Analyze numeric, nonnumeric, and repeating patterns involving all operations and decimal patterns through hundredths. Unit 1: 89 90 Unit 3: 46, 60, 65 Unit 9: Activities 57 and 58 4-3.2 Generalize a rule for numeric, nonnumeric, and repeating patterns involving all operations. Unit 1: 89 90 Unit 3: 46, 60, 65 Unit 9: 73 74, 94 95, 98 100 Unit 9: Activities 57 and 58 4-3.3 Use a rule to complete a sequence or a table. Related topic is covered by the following: Unit 9: 55 58 39 Grade Four
4-3.4 Translate among, letters, symbols, and words to represent quantities in simple mathematical expressions or equations. Unit 1: 32, 64 Unit 8: 106, 110 Unit 9: 93 95, 98 100, 101 102 Student Math Handbook: 86 4-3.5 Apply procedures to find the value of an unknown letter or symbol in a whole-number equation. Unit 3: 79 Unit 5: 135 Unit 9: 93 95, 98 100, 101 102 4-3.6 Illustrate situations that show change over time as either increasing, decreasing, or varying. Unit 4: 27 32, 35 39, 47 52, 55 59, 62 67, 69 74, 91 95, 107 113, 115 118, 119 123, 125 128 GEOMETRY Standard 4-4: The student will demonstrate through the mathematical processes an understanding of the relationship between two- and three-dimensional shapes, the use of transformations to determine congruency, and the representation of location and movement within the first quadrant of a coordinate system. 4-4.1 Analyze the quadrilaterals squares, rectangles, trapezoids, rhombuses, and parallelograms according to their properties. Unit 4: 55 59, 61 65, 69 71, 75 79, 81 83 4-4.2 Analyze the relationship between three-dimensional geometric shapes in the form of cubes, rectangular prisms, and cylinders and their twodimensional nets. Unit 7: 28 30, 35 37, 42 43 40 Grade Four
4-4.3 Predict the results of multiple transformations of the same type translation, reflection, or rotation on a two-dimensional geometric shape. Related content is covered by the following: Unit 4: 35 36 Unit 4: Activity 21 4-4.4 Represent the two-dimensional shapes trapezoids, rhombuses, and parallelograms and the three-dimensional shapes cubes, rectangular prisms, and cylinders. Unit 4: 11, 61 64, 95 96, 118 120, 155, Unit 7: 23, 24 4-4.5 Use transformation(s) to prove congruency. Unit 4: 130 Unit 4: Activity 21 4-4.6 Represent points, lines, line segments, rays, angles, and polygons. Unit 4: 70, 77 79, 95 96, 99 101, 103 104, 124 Unit 9: 94 Student Math Handbook: 111 113 Unit 4: Activities 14 4-4.7 Represent with ordered pairs of whole numbers the location of points in the first quadrant of a coordinate grid. Unit 9: 27 Unit 2: Activity 8 4-4.8 Illustrate possible paths from one point to another along vertical and horizontal grid lines in the first quadrant of the coordinate plane. Related topics are covered by the following: Unit 9: 27 Unit 2: Activity 7 41 Grade Four
MEASUREMENT Standard 4-5: The student will demonstrate through the mathematical processes an understanding of elapsed time; conversions within the U.S. Customary System; and accurate, efficient, and generalizable methods of determining area. 4-5.1 Use appropriate tools to measure objects to the nearest unit: measuring length in quarter inches, centimeters, and millimeters; measuring liquid volume in cups, quarts, and liters; and measuring weight and mass in pounds, milligrams, and kilograms. Length is covered by the following: Unit 2: 31 32, 37 Unit 4: 23, 24 26, 37 40, 42 43 Unit 8: Activities 51, 52, 53, 54 4-5.2 Compare angle measures with referent angles of 45 degrees, 90 degrees, and 180 degrees to estimate angle measures. Unit 4: 70, 77 79 4-5.3 Use equivalencies to convert units of measure within the U.S. Customary System: converting length in inches, feet, yards, and miles; converting weight in ounces, pounds, and tons; converting liquid volume in cups, pints, quarts, and gallons; and converting time in years, months, weeks, days, hours, minutes, and seconds. Length is covered by the following: Unit 2: 31 32, 37 Unit 4: 23, 24 26, 37 40, 42 43 Unit 4: Activities 27 and 28 Unit 8: Activities 51, 52, 53, 54, 55, and 56 4-5.4 Analyze the perimeter of a polygon. Related topic is covered in: Unit 4: 67 69 Student Math Handbook: 104 105 42 Grade Four
4-5.5 Generate strategies to determine the area of rectangles and triangles. Related topic is covered by the following: Unit 4: 114 115, 117 119, 125, 138, 142 Unit 4: Activity 25 4-5.6 Apply strategies and procedures to determine the amount of elapsed time in hours and minutes within a 12-hour period, either a.m. or p.m. Unit 8: Activity 55 4-5.7 Use Celsius and Fahrenheit thermometers to determine temperature changes during time intervals. Unit 5: Activity 34 4-5.8 Recall equivalencies associated with liquid volume, time, weight, and length: 8 liquid ounces = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon; 365 days = 1 year, 52 weeks = 1 year; 16 ounces = 1 pound, 2,000 pounds = 1 ton; and 5,280 feet = 1 mile. Unit 2: 31 32, 37 Unit 4: 23, 24 26, 37 40, 42 43 Unit 4: Activity 27 and 28 Unit 8: Activities 51, 53, 55, and 56 4-5.9 Exemplify situations in which highly accurate measurements are required. Related topics are covered by the following: Unit 2: 31 32, 37 Unit 4: 23, 24 26, 37 40, 42 43 Student Math Handbook: 103 43 Grade Four
DATA ANALYSIS AND PROBABILITY Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event. 4-6.1 Compare how data-collection methods impact survey results. Unit 2: 57 60 4-6.2 Interpret data in tables, line graphs, bar graphs, and double bar graphs whose scale increments are greater than or equal to 1. Unit 9: 27 29, 30, 108 109, 114 4-6.3 Organize data in tables, line graphs, and bar graphs whose scale increments are greater than or equal to 1. Unit 9: 27 29, 30, 108 109, 114 4-6.4 Distinguish between categorical and numerical data. Unit 2: 57 61 Unit 4: 53, 130 Student Math Handbook: 87 4-6.5 Match categorical and numerical data to appropriate graphs. Unit 2: 57 61 Unit 4: 53, 130 Student Math Handbook: 88 91 4-6.6 Predict on the basis of data whether events are likely, unlikely, certain, impossible, or equally likely to occur. Unit 2: 95 100 Student Math Handbook: 98 4-6.7 Analyze possible outcomes for a simple event. Unit 2: 102 105, 108 112, 114 116 Student Math Handbook: 99 100 44 Grade Four