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

Transcription

1 Grade 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 1.1 (5-9), Investigation 1.2 (10-11), (16-19), (72 #30) TG: Accentuate the Negative (15-20, 21-24, 33-34, 100) SE: Accentuate the Negative Investigation 1.3 (12-13), Investigation 1.4 (14-15), Investigation (22-30), Investigation 3 (42-49), Investigation 4 (60-68), (72-73 #32), TG: Accentuate the Negative (4-6, 25-28, 29-32, 36-52, 62-80, 86-98, ) SE: Variables and Patterns (60-62); Stretching and Shrinking (88-89); Comparing and Scaling (56-57); Accentuate the Negative Investigation 1.3 (12-13), Investigation 1.4 (14-15), Investigation (22-30), Investigation 3 (42-44), (52-55), Investigation 4 (60-68); Filling and Wrapping (16-17, 27, 44-45, 57-58); Data Distribution (21) TG: Variables and Patterns (84-85); Stretching and Shrinking ( ); Comparing and Scaling (89-90); Accentuate the Negative (3-6, 25-28, 29-32, 36-52, 62-80, 81-84, 86-98); Filling and Wrapping (34, 52, 76, 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 3.2 (52-53), Investigation 3.3 (54), (82); Moving Straight Ahead Investigation 1.3 (8-9), Investigation 1.4 (10-11), Investigation 2 (25-30), Investigation 3.3 (52-53), Investigation 3.4 (53-54), Investigation 4.4 (76-77) TG: Variables and Patterns (73-76, 77-80, 103); Moving Straight Ahead (25-30, 31-34, 41-60, 77-80, 81-84, ) 7.1.F Write an equation that corresponds to a given problem situation, and describe a problem situation that corresponds to a given equation. SE: Variables and Patterns Investigation 3 (49-54), (57); Comparing and Scaling Investigation 3.1 (33-34), Investigation 3.3 (36-37), 45 #32; Accentuate the Negative (58 #35); Moving Straight Ahead Investigation 1 (5-11), Investigation 2 (25-30), Investigation 3.3 (52-53), Investigation 4.4 (76-77) 1

2 7.1.G Solve single- and multi-step word problems involving rational numbers and verify the solutions. TG: Variables and Patterns (68-80, 82-83); Comparing and Scaling (51-53, 61-62, 72); Accentuate the Negative (45); Moving Straight Ahead (15-34, 41-60, 77-80, ) SE: Variables and Patterns Investigation 3.2 (52-53), Investigation 3.3 (54),(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), Investigation 4.4 (76-77); Filling and Wrapping Investigation 5.2 (62-65) TG: Variables and Patterns (73-76, 77-80, 103); Accentuate the Negative (91-94, 95-98); Moving Straight Ahead (25-30, 41-60, 77-80, ); Filling and Wrapping (95-108) 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. 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. SE: Stretching and Shrinking (15 #14-16); Comparing and Scaling Investigation 1 (5-7); (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) TG: Stretching and Shrinking (30); Comparing and Scaling (14-26, 30); (see also: Bits and Pieces II: 20-22, 71-72; Bits and Pieces III: 16-17, 47-48, 59, 65-67, 89-90, 93-94) 3.3 (42-43), Investigation 4 (58-65), Investigation 5 (78-83); Comparing and Scaling Investigation 3 (33-39), Investigation 4 (48-54); Filling and Wrapping Investigation 5 (62-66) TG: Stretching and Shrinking (65-68, 75-86, ); Comparing and Scaling (4-7, 51-68, 73-88); Filling and Wrapping (95-108) 1-5 (5-92); Comparing and Scaling Investigation 4.1 (49-51), Investigation 4.2 (52-53), (58 #22, 61 #27); Filling and Wrapping Investigation 5 (62-66) TG: Stretching and Shrinking (3-7, ); Comparing and Scaling (74-78, 79-82, 91); Filling and Wrapping (95-108) 2.3 (25-27), (34 #19), Investigation 3 (38-43), Investigation 4.3 (64-65); Filling and Wrapping Investigation 5 (62-65) 2

3 7.2.E Represent proportional relationships using graphs, tables, and equations, and make connections among the representations. 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 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. TG: Stretching and Shrinking (43-48, 52, 54-68, 83-86); Filling and Wrapping (95-108) SE: Variables and Patterns Investigation 3.1 (49-51); Comparing and Scaling (29 #22), Investigation 3 (33-39), (41 #9), Investigation 4 (48-54); Moving Straight Ahead Investigation 1.1 (5-6), Investigation 1.2 (6-7) TG: Variables and Patterns (69-72); Comparing and Scaling (49, 51-68, 70, 73-88); Moving Straight Ahead (4-5, 16-18, 19-24) SE: Comparing and Scaling Investigation 3.3 (36-37); Moving Straight Ahead Investigation 1.2 (6-7), Investigation (70-74), (86-87) TG: Comparing and Scaling (61-62); Moving Straight Ahead (3-5, 19-24, , ) SE: Comparing and Scaling Investigation 3.3 (36-37), (47); Moving Straight Ahead Investigation 2.1 (6-7), Investigation (70-74) TG: Comparing and Scaling (61-62, 72); Moving Straight Ahead (3-5, 19-24, ) SE: Stretching and Shrinking (76 #38); Comparing and Scaling (46 #33, 57 #18) TG: Stretching and Shrinking (89); Comparing and Scaling (72, 90) SE: Comparing and Scaling (45 #26); Moving Straight Ahead (88 #47); Filling and Wrapping (28 #18, 29 #23-24, 39 #7) TG: Comparing and Scaling (71); Moving Straight Ahead (120); Filling and Wrapping (52, 53-54) 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) 1.3 (10-11), (13 #5), Investigation 2.3 (25-27), Investigation 3 (38-43); Filling and Wrapping Investigation 2.1 (20), Investigation 2.2 (21), (44 #27), Investigation 5 (62-66) TG: Stretching and Shrinking (25-28, 29, 43-48, 54-68); Filling and Wrapping (6, 37-42, 43-46, 75-76, ) 3

4 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. 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. SE: Filling and Wrapping Investigation 1 (5-9), Investigation 2 (19-23), Investigation 3.4 (37), Investigation 4.3 (52-53), Investigation 5 (62-66) TG: Filling and Wrapping (13-30, 36-50, 69-72, 87-90, ) SE: What Do You Expect? Investigation 1 (5-9); (taught in How Likely Is It?: 24-26) TG: What Do You Expect? (4-7, 17-32); (How Likely Is It?: 4-6, 45-46) SE: What Do You Expect? Investigation 1 (5-9, 17); (taught in How Likely Is It?: 21-27) TG: What Do You Expect? (4-7, 17-32, 35); (How Likely Is It?: 3-7, 36-52) SE: Data Distributions Investigation 1.3 (12-13), Investigation 1.4 (13-15), Investigation 2 (28-43), Investigation 3 (55-61), Investigation 4 (74-77) TG: Data Distributions (3-10, 29-32, 33-36, 46-66, 74-92, ) SE: Comparing and Scaling (60 #26); Data Distributions (21-23), Investigation 2 (28-43), (51), (72), (80); (taught in Bits and Pieces III: 66; Data About Us: 14-20, 23, 30-33, 44; Samples and Populations: 5-11) TG: Comparing and Scaling (91); Data Distributions (40-41, 46-66, 70, 96, 116); (Bits and Pieces III: 109; Data About Us: 31-40, 43, 47-52, 69; Samples and Populations: 7, 20-30) SE: Variables and Patterns Investigation 1.4 (12-13), (19 #6); Comparing and Scaling (44), (60 #26); Moving Straight Ahead (20 #8) TG: Variables and Patterns (29-32, 44); Comparing and Scaling (71, 91); Moving Straight Ahead (39) SE: Variables and Patterns Investigation 1 (5-14), (36-37); Stretching and Shrinking Investigation 2.1 (21-23), Investigation 2.2 (24-25), (29); Comparing and Scaling (29 #22), (41-42); Accentuate the Negative Investigation 2.5 (30-31); Moving Straight Ahead (14-15); Data Distributions (53) 4

5 7.5.B Write the prime factorization of whole numbers greater than 1, using exponents when appropriate. TG: Variables and Patterns (15-36, 59-60); Stretching and Shrinking (33-38, 39-42, 50); Comparing and Scaling (49,70); Accentuate the Negative (53-56); Moving Straight Ahead (36-37); Data Distributions (70-71) SE: (taught in Prime Time: 50-55) TG: (Prime Time: 5, 7-9, 81-89) 7.6. 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. 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. SE: Moving Straight Ahead Investigation 2.4 (29-30); Filling and Wrapping Investigation 3.4 (37), Investigation 4.3 (52-53); What Do You Expect? Investigation 1.3 (9) TG: Moving Straight Ahead (55-60); Filling and Wrapping (69-72, 87-90); What Do You Expect? (27-32) SE: Variables and Patterns Investigation 1.5 (14); Moving Straight Ahead Investigation 3.1 (46-48); Filling and Wrapping Investigation 3.4 (37), (42 #22) TG: Variables and Patterns (33-36); Moving Straight Ahead (67-70); Filling and Wrapping (69-72) 5.2 (80-81); Comparing and Scaling Investigation 2.1 (18-19), Investigation 2.2 (20-21), Investigation 3.4 (37-39), Investigation 4.3 (53-54); Moving Straight Ahead Investigation 2.2 (25-26), (34) TG: Stretching and Shrinking (95-98); Comparing and Scaling (32-36, 39-40, 65-66, 83-85); Moving Straight Ahead (47-50, 62) SE: Stretching and Shrinking (84 #3); Comparing and Scaling Investigation 4.3 (53-54); Moving Straight Ahead Investigation 2.1 (24-25), Investigation3.2 (50-51); Filling and Wrapping (79) TG: Stretching and Shrinking (103); Comparing and Scaling (83-85); Moving Straight Ahead (42-46, 71-76); Filling and Wrapping (113) SE: Stretching and Shrinking Unit Project (94-95); Comparing and Scaling Unit Project (63-64); Accentuate the Negative Unit Project (76-77); Filling and Wrapping Unit Project (76-77); Data Distributions (86) 5

6 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. TG: Stretching and Shrinking ( ); Comparing and Scaling (94-98); Accentuate the Negative ( ); Filling and Wrapping ( ); Data Distributions ( ) SE: Stretching and Shrinking Unit Project (94-95); Comparing and Scaling Investigation 4.3 (53-54); What Do You Expect? (63) TG: Stretching and Shrinking ( ); Comparing and Scaling (83-85); What Do You Expect? (94-95) SE: 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); Moving Straight Ahead Investigation 1.2 (6-7); Filling and Wrapping (28 #22); Data Distributions Investigation 1.4 (13-15) TG: Variables and Patterns (39-40, 45-50); Stretching and Shrinking (32-48); Comparing and Scaling (32-36, 50); Moving Straight Ahead (19-24); Filling and Wrapping (53); Data Distributions (33-36) SE: Variables and Patterns Investigation 1.1 (5-7); Comparing and Scaling Unit Project (63-64); Moving Straight Ahead (84 #31); Filling and Wrapping Investigation 2.2 (21), Investigation 3.1 (32-33) TG: Variables and Patterns (16-20); Comparing and Scaling (94-98); Moving Straight Ahead (118); Filling and Wrapping (43-46, 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. 6