Connected Mathematics 2, 6 th and 7th Grade Units 2009 Correlated to: Washington Mathematics Standards for Grade 5
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1 Grade Core Content: Multi-digit division (Operations, Algebra) 5.1.A Represent multi-digit division using place value models and connect the representation to the related equation. 5.1.B Determine quotients for multiples of 10 and 100 by applying knowledge of place value and properties of operations. 5.1.C Fluently and accurately divide up to a four-digit number by one- or two-digit divisors using the standard long-division algorithm. 5.1.D Estimate quotients to approximate solutions and determine reasonableness of answers in problems involving up to two-digit divisors. 5.1.E Mentally divide two-digit numbers by onedigit divisors and explain the strategies used. 5.1.F Solve single- and multi-step word problems involving multi-digit division and verify the solutions. SE: Bits and Pieces II Investigation 1 (48); Bits and Pieces III Investigation 3.1 (36-37), Investigation 3.2 (38-39), Investigation 3.3 (40, 44) TG: Bits and Pieces II (11-12, 90-94); Bits and Pieces III (60-64, 65-67, 71-72, 80) SE: Prime Time (18 #34, 37), Investigation 3.1 (37-38) TG: Prime Time (32-33, 54-55) SE: Prime Time Investigation 4.2 (50-52) TG: Prime Time (81-83) SE: Bits and Pieces III Investigation 3.1 (36-37), Investigation 3.2 (38-39), Investigation 3.3 (40, 44) TG: Bits and Pieces III (5-6, 60-64, 65-67, 71-72, 80) SE: Prime Time Investigation 1.1 (6-9), Investigation 1.2 (9-10), Investigation 4.2 (50-52); Bits and Pieces I (15 #20, 21) TG: Prime Time (17-18, 21-22, 81-83); Bits and Pieces I (42) SE: Prime Time Investigation 3.4 (41), 58 #31 TG: Prime Time (67-68, 94) 5.2. Core Content: Addition and subtraction of fractions and decimals (Numbers, Operations, Algebra) 5.2.A Represent addition and subtraction of SE: Bits and Pieces II Investigation 2 (16-23) fractions and mixed numbers using visual and numerical models, and connect the representation to the related equation. TG: Bits and Pieces I (5-6); Bits and Pieces II (5-6, 35-54) 5.2.B Represent addition and subtraction of SE: Bits and Pieces III Investigation 1 (5-12) decimals using place value models and connect the representation to the related equation. TG: Bits and Pieces I (6); Bits and Pieces III (15-32) 5.2.C Given two fractions with unlike denominators, rewrite the fractions with a common denominator. SE: Bits and Pieces I Investigation 1.2 (7), Investigation 2.1 (19-21), Investigation 2.2 (21-23), Investigation 2.5 (25-27); Bits and Pieces II Investigation 2 (16-23) 1
2 5.2.D Determine the greatest common factor and the least common multiple of two or more whole numbers. 5.2.E Fluently and accurately add and subtract fractions, including mixed numbers. 5.2.F Fluently and accurately add and subtract decimals. 5.2.G Estimate sums and differences of fractions, mixed numbers, and decimals to approximate solutions to problems and determine reasonableness of answers. TG: Bits and Pieces I (23-25, 46-48, 51-54, 67-69); Bits and Pieces II (35-54) SE: Prime Time Investigation 3 (37-41), Investigation 4 (49-55); Bits and Pieces I Investigation 2.2 (21-23) TG: Prime Time (9, 53-70, 74-92); Bits and Pieces I (51-53) SE: Bits and Pieces II Investigation 2 (16-23, 29 #48-50) TG: Bits and Pieces II (5-6, 35-54, 57) SE: Bits and Pieces III Investigation 1.2 (8-9), Investigation 1.3 (10-11), Investigation 1.3 (12) TG: Bits and Pieces III (21-22, 25-26, 29-30) SE: Bits and Pieces II Investigation 1.1 (5-7), Investigation 1.2 (8-9, 11 #27-30); Bits and Pieces III Investigation 1.1 (5-7) TG: Bits and Pieces II (5, 20-22, 25-28, 32); Bits and Pieces III (16-17) 5.2.H Solve single- and multi-step word SE: Prime Time Investigation 3 (37-41); Bits problems involving addition and subtraction of and Pieces I Investigation 3.4 (43-44), whole numbers, fractions (including mixed Investigation 3.5 (45-46, 51 #51); Bits and numbers), and decimals, and verify the Pieces II Investigation 2.1 (17-19), solutions. Investigation 2.2 (19-21, 29 #48-50); Bits and Pieces III Investigation 1 (5-12, 14 #20-22) TG: Prime Time (53-70); Bits and Pieces I (97-98, , 110); Bits and Pieces II (35-37, 41-43, 57); Bits and Pieces III (15-32, 33) 5.3. Core Content: Triangles and quadrilaterals (Geometry/Measurement, Algebra) 5.3.A Classify quadrilaterals. SE: Shapes and Designs Investigation 1.1 (7-11), Investigation 4.3 (74-75, 77) TG: Shapes and Designs (4, 18-22, 91-94, 96) 5.3.B Identify, sketch, and measure acute, right, and obtuse angles. 5.3.C Identify, describe, and classify triangles by angle measure and number of congruent sides. 5.3.D Determine the formula for the area of a parallelogram by relating it to the area of a rectangle. 5.3.E Determine the formula for the area of a triangle by relating it to the area of a parallelogram. 5.3.F Determine the perimeters and areas of triangles and parallelograms. SE: Shapes and Designs Investigation 2.1 (24-28), Investigation 2.3 (32-35, 41-44, 84) TG: Shapes and Designs (36-40, 45-46, 57-58, 97) SE: Shapes and Designs Investigation 1.1 (7-11, 63 #10) TG: Shapes and Designs (4, 18-22, 79) SE: Covering and Surrounding Investigation (53-57) TG: Covering and Surrounding (4-7, 87-96) SE: Covering and Surrounding Investigation (37-43) TG: Covering and Surrounding (4-7, 60-78) SE: Covering and Surrounding Investigation 3 (37-43), Investigation 4 (53-59) 2
3 5.3.G Draw quadrilaterals and triangles from given information about sides and angles. 5.3.H Determine the number and location of lines of symmetry in triangles and quadrilaterals. 5.3.I Solve single- and multi-step word problems about the perimeters and areas of quadrilaterals and triangles and verify the solutions Core Content: Representations of algebraic relationships (Operations, Geometry/Measurement, Algebra) 5.4.A Describe and create a rule for numerical and geometric patterns and extend the patterns. 5.4.B Write a rule to describe the relationship between two sets of data that are linearly related. TG: Covering and Surrounding (4-7, 60-82, ) SE: Shapes and Designs Investigation 4 (70-77, 80); Covering and Surrounding Investigation 3.4 (43), Investigation 4.3 (57) TG: Shapes and Designs (82-96); Covering and Surrounding (79-80, 97-98) SE: Shapes and Designs Investigation 1.2 (12-13, 21) TG: Shapes and Designs (5, 23-26, 33-34) SE: Covering and Surrounding Investigation 1 (5-9), Investigation 2 (19-25), (50 #34), Investigation 4.4 (58-59, 63 #20) TG: Covering and Surrounding (17-32, 37-54, 85, , 106) SE: Prime Time Investigation 2.2 (24-26), Investigation 3.1 (37-38), Investigation 3.2 (39-40, #41-42); Variables and Patterns (23 #16-17) TG: Prime Time (41-42, 54-55, 59, 72-73); Variables and Patterns (40) SE: Variables and Patterns Investigation 3 (49-54) TG: Variables and Patterns (7, 69-80) 5.4.C Write algebraic expressions that represent SE: Bits and Pieces II Investigation 2.1 (16- simple situations and evaluate the expressions, 19); Covering and Surrounding Investigation using substitution when variables are involved. 1.3 (8-9); Variables and Patterns Investigation 3 (49-54, 56) TG: Bits and Pieces II (35-37); Covering and Surrounding (5-9, 27-29); Variables and Patterns (69-80, 82) 5.4.D Graph ordered pairs in the coordinate SE: Variables and Patterns Investigation 1.2 plane for two sets of data related by a linear rule (7-9), (36 #3, 37 #4, 38), Investigation 3 (49- and draw the line they determine. 54) TG: Variables and Patterns (4-7, 21-22, 59-61, 69-80) 5.5. Additional Key Content (Numbers, Data/Statistics/Probability) 5.5.A Classify numbers as prime or composite. SE: Prime Time (15 #15), Investigation 2.1 (22-24), Investigation 2.3 (27-29) TG: Prime Time (5-8, 31, 36-38, 45-46) 5.5.B Determine and interpret the mean of a SE: Data About Us Investigation 3.1 (49-51) small data set of whole numbers. TG: Data About Us (74-77) 5.5.C Construct and interpret line graphs. SE: Variables and Patterns Investigation 1.2 (7-9), Investigation 1.3 (10-11), Investigation 1.4 (12-13) 3
4 TG: Variables and Patterns (4-7, 21-22, 25-26, 29-30) 5.6. Core Processes: Reasoning, problem solving, and communication 5.6.A Determine the question(s) to be answered given a problem situation. 5.6.B Identify information that is given in a problem and decide whether it is essential or extraneous to the solution of the problem. 5.6.C Determine whether additional information is needed to solve the problem. 5.6.D Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem. 5.6.E Select and use one or more appropriate strategies to solve a problem, and explain the choice of strategy. 5.6.F Represent a problem situation using words, numbers, pictures, physical objects, or symbols. 5.6.G Explain why a specific problem-solving strategy or procedure was used to determine a solution. 5.6.H Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. SE: Prime Time Investigation 5.1 (61-64); Data About Us Investigation 1.1 (6-9); Variables and Patterns Investigation 2.1 (30-31) TG: Prime Time (96-98); Data About Us (17-18); Variables and Patterns (45-50) SE: Bits and Pieces II Investigation 2.2 (19-21); Covering and Surrounding Investigation 2.1 (19-21); Data About Us Investigation 1.4 (14-17); Variables and Patterns Investigation 1.5 (14) TG: Bits and Pieces II (41-46); Covering and Surrounding (38-42); Data About Us (31-33); Variables and Patterns (33-36) SE: Prime Time (72 #4); Data About Us Investigation 1.4 (14-17) TG: Prime Time (103); Data About Us (31-33) SE: Prime Time Investigation 3.4 (41), Investigation 5.1 (61-64); Bits and Pieces II Investigation 2.4 (23) TG: Prime Time (67-68, 96-98); Bits and Pieces II (51-52) SE: Prime Time Investigation 5.1 (61-64); Bits and Pieces II Investigation 2.1 (16-19); Covering and Surrounding (14 #24, 91) TG: Prime Time (96-98); Bits and Pieces II (35-37); Covering and Surrounding (34-35, 132) SE: Prime Time Investigation 2.1 (22-24), Investigation 3.1 (38), Investigation 5.1 (61-64); Bits and Pieces II Investigation 2.1 (16-19); Data About Us Investigation 3.1 (49-51) TG: Prime Time (36-38, 54-55, 96-98); Bits and Pieces II (35-40); Data About Us (74-77) SE: Prime Time Investigation 2.1 (22-24); Bits and Pieces II Investigation 2.2 (19-21) TG: Prime Time (36-38); Bits and Pieces II (41-43) SE: Prime Time Investigation 3.3 (40); Bits and Pieces II (24 #1): Data About Us (25 #26-31) TG: Prime Time (63-64); Bits and Pieces II (55); Data About Us (43-44) 4
5 5.6.I Summarize mathematical information, draw conclusions, and explain reasoning. 5.6.J Make and test conjectures based on data (or information) collected from explorations and experiments. SE: Prime Time Investigation 2.1 (22-24); Covering and Surrounding Investigation 2.1 (20-21), Investigation 2.3 (24); Data About Us (24 #22-24), Investigation 2.3 (36-38), Unit Project (5, 64); Variables and Patterns (36 #9) TG: Prime Time (36-40); Covering and Surrounding (38-42, 47-50); Data About Us (43, 57-59, ); Variables and Patterns (39-40) SE: Prime Time Investigation 2.2 (24-26), (35 #38) Investigation 5.1 (61-64); Shapes and Designs Investigation 2.5 (39) TG: Prime Time (41-42, 51, 96-98); Shapes and Designs (53-56) Units Used: Grade 6: Prime Time, Bits and Pieces I, Shapes and Designs, Bits and Pieces II, Covering and Surrounding, Bits and Pieces III, Data About Us Grade 7: Variables and Patterns Note: The ACE (Application, Connection, Extension) problems at the end of each investigation and problems from Additional Practice and Skills Workbook are not cited in the document. These problems are the practice of the standards taught in the investigations as well as extension problems for advanced students. The Special Needs Handbook has modified problems to meet special individual needs. The Assessment Resource book contains quizzes, tests, and question banks for assessment use. Note: Multi-digit division is not a concept taught in 6 th grade CMP2 units except to the extent that it is used in division of decimals. 5
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