Connected Mathematics 2, 7th Grade Units 2009 Correlated to: Washington Mathematics Standards for Grade 7

Transcription

1 Grade 7 Connected Mathematics 2, 7th Grade Units Core Content: Rational numbers and linear equations (Numbers, Operations, Algebra) 7.1.A Compare and order rational numbers using the number line, lists, and the symbols <, >, or =. 7.1.B Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically. 7.1.C Fluently and accurately add, subtract, multiply, and divide rational numbers. 7.1.D Define and determine the absolute value of a number. SE: Accentuate the Negative Investigation (5-11), 16-19, 72 #30 TG: Accentuate the Negative (15-24, 33-34, 100) SE: Accentuate the Negative Investigation (12-15), Investigation (22-30), Investigation 3 (42-49) Additional citations: Accentuate the Negative Investigation 4 (60-68), (72-73 #32) TG: Accentuate the Negative (4-6, 25-32, 36-52, 62-80) Additional citations: Accentuate the Negative (86-98, ) SE: Accentuate the Negative Investigation (22-30), 52-55; Filling and Wrapping (44-45) Additional citations: Accentuate the Negative Investigation 1.3 (12-13), Investigation 1.4 (14-15), Investigation 3 (42-44), Investigation 4 (60-68); Variables and Patterns (60-62); Stretching and Shrinking (88-89); Comparing and Scaling (56-57); Filling and Wrapping (16-17, 27, 57-58); Data Distribution (21) TG: Accentuate the Negative (3-6, 36-52, 81-84); Filling and Wrapping (76) Additional citations: Accentuate the Negative (25-28, 29-32, 62-80, 86-98); Variables and Patterns (84-85); Stretching and Shrinking ( ); Comparing and Scaling (89-90); Filling and Wrapping (34, 52, 92-93); Data Distribution (40) SE: Accentuate the Negative Investigation 2.2 (24-27) TG: Accentuate the Negative (41-44) 7.1.E Solve two-step linear equations. SE: Variables and Patterns Investigation (52-54); Moving Straight Ahead Investigation (52-54), Investigation 4.4 (76-77) (82); Moving Straight Ahead Investigation 1.3 (8-9), Investigation 1.4 (10-11), Investigation 2 (25-30) 1

2 7.1.F Write an equation that corresponds to a given problem situation, and describe a problem situation that corresponds to a given equation. 7.1.G Solve single- and multi-step word problems involving rational numbers and verify the solutions. TG: Variables and Patterns (73-80); Moving Straight Ahead (77-84, ) (103); Moving Straight Ahead (25-30, 31-34, 41-60) SE: Variables and Patterns Investigation 3 (49-54); Moving Straight Ahead Investigation (46-53), Accentuate the Negative (58 #35) (57); Comparing and Scaling Investigation 3.1 (33-34), Investigation 3.3 (36-37), 45 #32; Moving Straight Ahead Investigation 1 (5-11), Investigation 2 (25-30), Investigation 4.4 (76-77) TG: Variables and Patterns (68-80); Moving Straight Ahead (67-80); Accentuate the Negative (45) (82-83); Comparing and Scaling (51-53, 61-62, 72); Moving Straight Ahead (15-34, 41-60, ) SE: Variables and Patterns Investigation (52-54); Moving Straight Ahead Investigation 4.4 (76-77); Filling and Wrapping Investigation 5.2 (62-65) (82); Accentuate the Negative Investigation 4.2 (64-65), Investigation 4.3 (66-68); Moving Straight Ahead Investigation 1.3 (8-9), Investigation 2 (25-30), Investigation 3.3 (52-53) TG: Variables and Patterns (73-80); Moving Straight Ahead ( ); Filling and Wrapping (95-108) (103); Accentuate the Negative (91-94, 95-98); Moving Straight Ahead (25-30, 41-60, 77-80) 7.2. Core Content: Proportionality and similarity (Operations, Geometry/Measurement, Algebra) 7.2.A Mentally add, subtract, multiply, and divide simple fractions, decimals, and percents. SE: Stretching and Shrinking (15 #14-16), (85); Comparing and Scaling Investigation 1 (5-7) Additional citations: (can be developed from the Grade 6 units: Bits and Pieces II: 5-7, 36-37; Bits and Pieces III: 5-7, 24-25, 33, 38-39, 51-54) 2

3 7.2.B Solve single- and multi-step problems involving proportional relationships and verify the solutions. 7.2.C Describe proportional relationships in similar figures and solve problems involving similar figures. 7.2.D Make scale drawings and solve problems related to scale. 7.2.E Represent proportional relationships using graphs, tables, and equations, and make connections among the representations. TG: Stretching and Shrinking (30, 103); Comparing and Scaling (14-26, 30) Additional citations: (see Grade 6 units: Bits and Pieces II: 20-22, 71-72; Bits and Pieces III: 16-17, 47-48, 59, 65-67, 89-90, 93-94) SE: Comparing and Scaling Investigation 3 (33-39), Investigation 4 (48-54); Stretching and Shrinking Investigation 5 (78-83); Investigation 3.3 (42-43), Investigation 4 (58-65); Filling and Wrapping Investigation 5 (62-66) TG: Comparing and Scaling (4-7, 51-68, 73-88); Stretching and Shrinking (90-102) (65-68, 75-86); Filling and Wrapping (95-108) SE: Stretching and Shrinking Investigation 4 (58-65), Investigation 5 (78-83); Comparing and Scaling Investigation 4.2 (52-53) Investigation 1-3 (5-56); Comparing and Scaling (58 #22, 61 #27); Filling and Wrapping Investigation 5 (62-66) TG: Stretching and Shrinking (3-7, 74-86, ); Comparing and Scaling (79-82) (14-73); Comparing and Scaling (91); Filling and Wrapping (95-108) SE: Stretching and Shrinking Investigation 2 (21-27), Investigation 3 (38-43); Filling and Wrapping Investigation 5 (62-65) (34 #19), Investigation 4.3 (64-65) TG: Stretching and Shrinking (32-48, 54-68); Filling and Wrapping (95-108) (52, 83-86) SE: Variables and Patterns Investigation 3.1 (49-51); Comparing and Scaling 41 #9); Moving Straight Ahead Investigation 1.2 (6-7) (29 #22), Investigation 3 (33-39), Investigation 4 (48-54); Moving Straight Ahead Investigation 1.1 (5-6) 3

4 7.2.F Determine the slope of a line corresponding to the graph of a proportional relationship and relate slope to similar triangles. 7.2.G Determine the unit rate in a proportional relationship and relate it to the slope of the associated line. 7.2.H Determine whether or not a relationship is proportional and explain your reasoning. 7.2.I Solve single- and multi-step problems involving conversions within or between measurement systems and verify the solutions. TG: Variables and Patterns (69-72); Comparing and Scaling (70); Moving Straight Ahead (4-5, 19-24) (49, 51-68, 73-88); Moving Straight Ahead 16-18) SE: Comparing and Scaling Investigation 3.3 (36-37); Moving Straight Ahead Investigation (70-74), Additional citations: Moving Straight Ahead Investigation 1.2 (6-7) TG: Comparing and Scaling (61-62); Moving Straight Ahead (3-5, , ) Additional citations: Moving Straight Ahead (19-24) SE: Comparing and Scaling Investigation 3.3 (36-37); Moving Straight Ahead Investigation 2.1 (6-7), Investigation (70-74) (47) TG: Comparing and Scaling (61-62); Moving Straight Ahead (3-5, 19-24, ) (72) SE: Comparing and Scaling (46 #33); Stretching and Shrinking Investigation (58-63), 76 #38 (57 #18) TG: Comparing and Scaling (72); Stretching and Shrinking (75-82, 89) (90) SE: Filling and Wrapping (28 #18, 29 #23-24, 39 #7, 70 #20-23); Moving Straight Ahead (88 #47) (45 #26) TG: Filling and Wrapping (52-54, 111); Moving Straight Ahead (120) (71) 4

5 7.3. Core Content: Surface area and volume (Geometry/Measurement) 7.3.A Determine the surface area and volume of cylinders using the appropriate formulas and explain why the formulas work. 7.3.B Determine the volume of pyramids and cones using formulas. 7.3.C Describe the effect that a change in scale factor on one attribute of a two- or threedimensional figure has on other attributes of the figure, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure. 7.3.D Solve single- and multi-step word problems involving surface area or volume and verify the solutions Core Content: Probability and data (Data/Statistics/Probability) 7.4.A Represent the sample space of probability experiments in multiple ways, including tree diagrams and organized lists. 7.4.B Determine the theoretical probability of a particular event and use theoretical probability to predict experimental outcomes. SE: Filling and Wrapping Investigation (34-36) TG: Filling and Wrapping (5, 61-68) SE: Filling and Wrapping Investigation 4.2 (50-52), Investigation 4.3 (52-53) TG: Filling and Wrapping (5-6, 83-86, 87-90) SE: Stretching and Shrinking Investigation 3 (38-43); Filling and Wrapping (44 #27), Investigation 5 (62-66) Investigation 1.3 (10-11), 13 #5, Investigation 2.3 (25-27); Filling and Wrapping Investigation 2.1 (20), Investigation 2.2 (21) TG: Stretching and Shrinking (54-68); Filling and Wrapping (6, 75-76, ) (25-28, 29, 43-48); Filling and Wrapping (37-42, 43-46) SE: Filling and Wrapping Investigation 2 (19-23), Investigation 3.4 (37), Investigation 4.3 (52-53) Additional citations: Filling and Wrapping Investigation 1 (5-9), Investigation 5 (62-66) TG: Filling and Wrapping (36-50, 69-72, 87-90) Additional citations: Filling and Wrapping (13-30, ) SE: What Do You Expect? Investigation 1 (5-9) Additional citations: (taught in Grade 6 unit: How Likely Is It?: 24-26) TG: What Do You Expect? (4-7, 17-32) Additional citations: (see Grade 6 unit: How Likely Is It?: 4-6, 45-46) SE: What Do You Expect? Investigation 1 (5-9), 17 Additional citations: (taught in Grade 6 unit: How Likely Is It?: 21-27) 5

6 7.4.C Describe a data set using measures of center (median, mean, and mode) and variability (maximum, minimum, and range) and evaluate the suitability and limitations of using each measure for different situations. 7.4.D Construct and interpret histograms, stemand- leaf plots, and circle graphs. 7.4.E Evaluate different displays of the same data for effectiveness and bias, and explain reasoning Additional Key Content (Numbers, Algebra) 7.5.A Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane. TG: What Do You Expect? (4-7, 17-32, 35) Additional citations: (see Grade 6 unit: How Likely Is It?: 3-7, 36-52) SE: Data Distributions Investigation (12-15), Investigation 2 (28-43), Investigation 3 (55-61) Additional citations: Data Distributions Investigation 4 (74-77) TG: Data Distributions (3-10, 29-36, 46-66, 74-92) Additional citations: Data Distributions (97-114) SE: Comparing and Scaling (60 #26); Data Distributions (21-23), 80; Additional citations: Data Distributions Investigation 2 (28-43), 51, 72; (taught in Grade 6 units: Bits and Pieces III: 66; Data About Us: 14-20, 23, 30-33, 44; Grade 8 unit: Samples and Populations: 5-11) TG: Comparing and Scaling (91); Data Distributions (40-41, 116) Additional citations: Data Distributions (46-66, 70, 96); (see Grade 6 units: Bits and Pieces III: 109; Data About Us: 31-40, 43, 47-52, 69; Grade 8 unit: Samples and Populations: 7, 20-30) SE: Variables and Patterns (19 #6); Comparing and Scaling (44); Moving Straight Ahead (20 #8) Investigation 1.4 (12-13); Comparing and Scaling(60 #26) TG: Variables and Patterns (44); Comparing and Scaling (71); Moving Straight Ahead (39) (29-32); Comparing and Scaling (91) SE: Variables and Patterns Investigation 1 (5-14); Stretching and Shrinking Investigation (21-25); Accentuate the Negative Investigation 2.5 (30-31) (36-37); Stretching and Shrinking (29); Comparing and Scaling (29 #22, 41-42); Moving Straight Ahead (14-15); Data Distributions (53) 6

7 7.5.B Write the prime factorization of whole numbers greater than 1, using exponents when appropriate Core Processes: Reasoning, problem solving, and communication 7.6.A Analyze a problem situation to determine the question(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution to a problem. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. TG: Variables and Patterns (15-36); Stretching and Shrinking (33-42); Accentuate the Negative (53-56); (59-60); Stretching and Shrinking (50); Comparing and Scaling (49, 70); Moving Straight Ahead (36-37); Data Distributions (70-71) SE: (taught in Grade 6 unit: Prime Time: 50-55) TG: (see Grade 6 unit: Prime Time: 5, 7-9, 81-89) SE: Moving Straight Ahead Investigation 2.4 (29-30), Investigation 3.1 (46-48); Filling and Wrapping Investigation 4.3 (52-53) Additional citations: Filling and Wrapping Investigation 3.4 (37); What Do You Expect? Investigation 1.3 (9) TG: Moving Straight Ahead (55-60, 67-70); Filling and Wrapping (87-90) Additional citations: Filling and Wrapping (69-72); What Do You Expect? (27-32) SE: Variables and Patterns Investigation 1.5 (14); Filling and Wrapping Investigation 3.4 (37), 42 #22 Additional citations: Moving Straight Ahead Investigation 3.1 (46-48) TG: Variables and Patterns (33-36); Filling and Wrapping (69-72) Additional citations: Moving Straight Ahead (67-70) SE: Comparing and Scaling Investigation (18-21); Moving Straight Ahead Investigation 2.2 (25-26); Stretching and Shrinking Investigation 5.2 (80-81) Investigation 3.4 (37-39), Investigation 4.3 (53-54); Moving Straight Ahead (34) TG: Comparing and Scaling (32-42,); Moving Straight Ahead (47-50); Stretching and Shrinking (95-98) (65-66, 83-85); Moving Straight Ahead (62) 7

8 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. SE: Moving Straight Ahead Investigation 2.1 (24-25), Investigation3.2 (50-51); Comparing and Scaling Investigation 4.3 (53-54) (84 #3); Filling and Wrapping (79) TG: Moving Straight Ahead (42-46, 71-76); Comparing and Scaling (83-85) (103); Filling and Wrapping (113) SE: Filling and Wrapping Unit Project (76-77); Data Distributions (86); Accentuate the Negative Unit Project (76-77) Unit Project (94-95); Comparing and Scaling Unit Project (63-64) TG: Filling and Wrapping ( ); Data Distributions ( ); Accentuate the Negative ( ) ( ); Comparing and Scaling (94-98) SE: Stretching and Shrinking Unit Project (94-95); What Do You Expect? (63); Comparing and Scaling Investigation 4.3 (53-54) TG: Stretching and Shrinking ( ); What Do You Expect? (94-95); Comparing and Scaling (83-85) SE: Data Distributions Investigation 1.4 (13-15); Moving Straight Ahead Investigation 1.2 (6-7); Variables and Patterns (20-21) Investigation 2.1 (30-31); Stretching and Shrinking Investigation 2 (21-27); Comparing and Scaling Investigation 2.1 (18-19), (30 #23); Filling and Wrapping (28 #22) TG: Data Distributions (33-36); Moving Straight Ahead (19-24); Variables and Patterns (39-40) (45-50); Stretching and Shrinking (32-48); Comparing and Scaling (32-36, 50); Filling and Wrapping (53) SE: Filling and Wrapping Investigation 2.2 (21); Comparing and Scaling Unit Project (63-64); Moving Straight Ahead (84 #31) Investigation 1.1 (5-7); Filling and Wrapping Investigation 3.1 (32-33) 8

9 TG: Filling and Wrapping (43-46); Comparing and Scaling (94-98); Moving Straight Ahead (118) (16-20); Filling and Wrapping (57-60) Units Used: Grade 7: Variables and Patterns, Stretching and Shrinking, Comparing and Scaling, Accentuate the Negative, Moving Straight Ahead, Filling and Wrapping, What Do You Expect, Data Distributions 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. 9