Prentice Hall. Connected Mathematics 2, 7th Grade Units Mississippi Mathematics Framework 2007 Revised, Grade 7

Transcription

1 Prentice Hall Connected Mathematics 2, 7th Grade Units 2006 C O R R E L A T E D T O Mississippi Mathematics Framework 2007 Revised, Grade 7

2 NUMBER AND OPERATIONS 1. Apply concepts of rational numbers and perform basic operations emphasizing the concepts of ratio, proportion, and percent with and without the use of calculators. Objectives Pupil Edition Teacher Edition a. Use the order of operations to simplify and/or evaluate whole numbers (including exponents and grouping symbols). (DOK 1) b. Solve problems involving addition, subtraction, multiplication, and division of rational numbers. Express answers in simplest form. (DOK 2) Properties of Operations (60-75) Similar Figures (34); (24, 27, 29, 32-33, 36); Multiplying and (42-59); Properties of Operations (60-75); Review (78) Properties of Operations (86-102) Similar Figures (52); (36-61); Multiplying and (62-85); Properties of Operations (86-102); Review ( ) 1

3 c. Convert among decimals, fractions, mixed numbers, and percents. (DOK 1) and Scaling Making Comparisons (7); Ratios, Percents, and Fractions (21-23, 26-28, 32); Proportions (57); Review (67) d. Evaluate and estimate powers and square roots of real numbers. (DOK 2) Analyzing Graphs and Tables (43); Rules and Equations (58-59); Calculator Tables and Graphs (64-65, 77); Similar Polygons (56); Accentuate the Properties of Operations (62-63, 69-71); Filling and Cones, Spheres, and Pyramids (54) and Scaling Making Comparisons (19, 21); Ratios, Percents, and Fractions (43-46, 48, 50); Proportions (90); Review (93) Analyzing Graphs and Tables (64); Rules and Equations (83); Investigation 4: Calculator Tables and Graphs (87, 101); Stretching and Similar Polygons (72); Accentuate the Properties of Operations (87-90, ); Filling and Cones, Spheres, and Pyramids (91) 2

4 e. Explain the relationship between standard form and scientific notation. (DOK 1) See the CMP2 Grade 8 Unit, Growing, Growing, Growing. f. Multiply and divide numbers written in scientific notation. (DOK 1) See the CMP2 Grade 8 Unit, Growing, Growing, Growing. g. Solve real-life problems involving unit price, unit rate, sales price, sales tax, discount, simple interest, commission, and rates of commission. (DOK 1) Analyzing Graphs and Tables (31-32, 36-38, 44, 46-47); Rules and Equations (50-57, 59, 61); Calculator Tables and Graphs (70-75, 79); and Scaling and Scaling Rates (33-47); Proportions (52-53, 55, 57); Moving Straight Ahead Exploring Linear Functions With Graphs and Tables (31-37, 40-42); See the CMP2 Grade 8 Unit, Growing, Growing, Growing. See the CMP2 Grade 8 Unit, Growing, Growing, Growing. Analyzing Graphs and Tables (45-50, 59-66); Investigation 3: Rules and Equations (69-84); Calculator Tables and Graphs (95-100); and Scaling and Scaling Rates (51-72); Proportions (79-82, 89-90); Moving Straight Ahead Exploring Linear Functions With Graphs and Tables (61-64); 3

5 h. Solve contextual problems requiring the comparison, ordering, and application of integers. (DOK 2) Continued) Solving Equations (56, 62, 65, 67-68); Exploring Slope (76, 85, 88); Review (94-95); Filling and (43 #24); Scaling Boxes (70 #25) Extending the Number System (5-21); (22-41); Multiplying and (42-59); Properties of Operations (60-75) Continued) Solving Equations (85-88, 91-94); Exploring Slope ( , ); Review (121); Filling and (75); Investigation 5: Scaling Boxes (111) Extending the Number System (13-35); (36-61); Multiplying and (62-85); Properties of Operations (86-102) 4

6 i. Develop a logical argument to demonstrate the denseness of rational numbers. (DOK 3) and Scaling Making Comparisons (14); Accentuate the Extending the Number System (5-7, 10-13, 16-18, 21); (38) and Scaling Making Comparisons (28); Accentuate the Extending the Number System (21-24, 33-35); (59) ALGEBRA 2. Develop and apply the basic operations of rational numbers to algebraic and numerical tasks. Create and apply algebraic expressions and equations. Objectives Pupil Edition Teacher Edition a. Recognize, describe, and state the rule of generalized numerical and geometric patterns using tables, graphs, words, and symbols. (DOK 2) Variables, Tables, and Coordinate Graphs (23); Analyzing Graphs and Tables (35-39, 42-44, 46-47); Rules and Equations (51-62); Calculator Tables and Graphs (66, 71, 73-76, 79); Review (81-82); Variables, Tables, and Coordinate Graphs (40); Analyzing Graphs and Tables (59-66); Rules and Equations (69-85); Calculator Tables and Graphs (86-90, ); Review ( ); 5

7 b. Solve equations that represent algebraic and real-world problems using multiple methods including the real number properties. (DOK 1) Moving Straight Ahead Investigation 1: Walking Rates (9-15, 18, 20); Exploring Linear Functions With Graphs and Tables (26, 31, 34-38, 40-42); Solving Equations (65-68); Exploring Slope (76-78, 84-85); Unit Project (90-93); Review (94-96) Moving Straight Ahead Investigation 3: Solving Equations (46-69) Moving Straight Ahead Investigation 1: Walking Rates (25-39); Exploring Linear Functions With Graphs and Tables (47-50, 61-64); Solving Equations (93-94); Exploring Slope ( , ); Review ( ); Unit Project ( ) Moving Straight Ahead Investigation 3: Solving Equations (66-94) 6

8 c. Formulate algebraic expressions, equations, and inequalities to reflect a given situation and vice versa. (DOK 2) Rules and Equations (49-54, 56-58, 60-62); Accentuate the Extending the Number System (12-13); (34); Investigation 3: Multiplying and (58); Investigation 4: Properties of Operations (65) Rules and Equations (68-85); Extending the Number System (25-28); (43); Investigation 3: Multiplying and (85); Investigation 4: Properties of Operations (94) 7

9 d. Complete a function table based on a given rule and vice versa. (DOK 1) Variables, Tables, and Coordinate Graphs (7); Analyzing Graphs and Tables (36-37, 39, 43, 46); Rules and Equations (50-51, 53-54, 56, 58, 60-62); Calculator Tables and Graphs (64-66, 71-72, 74-76); Review (82); Accentuate the Multiplying and (54) Variables, Tables, and Coordinate Graphs (19-20); Analyzing Graphs and Tables (59-67); Rules and Equations (68-85); Calculator Tables and Graphs (86-102); Review ( ); Multiplying and (83) 8

10 e. Identify the following properties using variables and apply them in solving problems: (DOK 1) Zero property of multiplication Inverse properties of addition/subtraction and multiplication/division Commutative and associative properties of addition and multiplication Identity properties of addition and multiplication Distributive properties of multiplication over addition and subtraction Extending the Number System (24, 27); (30, 36); Multiplying and (45, 48, 51-52, 57-58); Properties of Operations (64-70, 73-75) f. Predict the shape of a graph from a function table. (DOK 2) Moving Straight Ahead Investigation 1: Walking Rates (10, 15-16, 18, 20-21); Exploring Linear Functions With Graphs and Tables (29, 31, 34-35, 41, 43); Solving Equations (61) Extending the Number System (40, 42, 44); (49-52, 59); Multiplying and (62, 63-76, 81-82, 84-85); Investigation 4: Properties of Operations (91-102) Moving Straight Ahead Investigation 1: Walking Rates (31-34, 37-39); Exploring Linear Functions With Graphs and Tables (51-54, 61-62, 64); Solving Equations (92) 9

11 GEOMETRY 3. Apply geometric relationships of angles, two- and three-dimensional shapes, and transformations. Objectives Pupil Edition Teacher Edition a. Classify and compare three-dimensional shapes using their properties. (DOK 1) Filling and Building Boxes (7, 10); (32-33, 36-37, 40-42); Cones, Spheres, and Pyramids (48-53, 55, 57, 60-61); Scaling Boxes (71) b. Construct two-dimensional representations of three-dimensional objects. (DOK 2) Filling and Building Boxes (5-18); Designing Rectangular Boxes (19-31); (32-47); Cones, Spheres, and Pyramids (48-61); Scaling Boxes (62-75) Filling and Building Boxes (23-26, 31); (57-60, 65-72, 74-75); Cones, Spheres, and Pyramids (79-90, 92-94); Investigation 5: Scaling Boxes (111) Filling and Building Boxes (13-35); Designing Rectangular Boxes (36-54); (55-77); Cones, Spheres, and Pyramids (78-94); Scaling Boxes (95-112) 10

12 c. Justify the congruency or symmetry of two figures. (DOK 2) Similar Figures (21-22, 24-33, 35, 37); Similar Polygons (38-42, 44-48, 53-54, 57); (61, 63, 66-67, 71, 74, 76); Using Similar Triangles and Rectangles (82, 86-87, 89-90); Unit Project (94-97); Review (98-100); Filling and Scaling Boxes (63-71, 74) d. Perform transformations (rigid and non-rigid motions) on two-dimensional figures using the coordinate plane. (DOK 2) e. Create an argument using the Pythagorean Theorem principles to show that a triangle is a right triangle. (DOK 2) Similar Figures (22-25, 28-29, 31-36); Review (98-100) See the 8th Grade CMP2 Unit, Looking for Pythagoras. Similar Figures (33-53); Similar Polygons (55-73); (75-82, 87-89); Using Similar Triangles and Rectangles (99-104); Review (105); Unit Project ( ) Filling and Scaling Boxes (96-112) Similar Figures (33-42, 49-52); Review (105) See the 8th Grade CMP2 Unit, Looking for Pythagoras. 11

13 f. Construct and classify angles. (DOK 2) Similar Polygons (50-51); (74); Filling and Building Boxes (15, ACE 25) Similar Polygons (69-70); (89); Filling and Building Boxes (33) MEASUREMENT 4. Apply appropriate techniques, tools, and formulas to determine measurements with a focus on real-world problems. Recognize that formulas in mathematics are generalized statements about rules, equations, principles, or other logical mathematical relationships. Objectives Pupil Edition Teacher Edition a. Convert from one unit to another, perform basic operations, and solve real-world problems using standard (English and metric) measurements within the same system. (DOK 2) Enlarging and Reducing Shapes (13); Investigation 2: Similar Figures (34); and Scaling and Scaling Rates (45); Filling and (39, ACE 7); Scaling Boxes (70 - ACE 20-23, 72 - ACE 29) Enlarging and Reducing Shapes (29); Investigation 2: Similar Figures (52); and Scaling and Scaling Rates (71); Filling and (73); Investigation 5: Scaling Boxes (111) 12

14 b. Use formulas and strategies, such as decomposition, to compute the perimeter and area of triangles, parallelograms, trapezoids, the circumference and area of circles, and find the area of more complex shapes. (DOK 2) c. Develop and justify geometric formulas for volume and surface area of cylinders, pyramids, and prisms. (DOK 3) Enlarging and Reducing Shapes (9, 11-19); Investigation 2: Similar Figures (29, 31-33, 35); Similar Polygons (39-42, 45-49, 54, 56-57); (65, 68-69, 71); Using Similar Triangles and Rectangles (86-87, 89); Unit Project (95); Review (98-100) Filling and Building Boxes (5-13, 16-18); Designing Rectangular Boxes (19-31); (32-47); Cones, Spheres, and Pyramids (48-61); Scaling Boxes (62-75) Enlarging and Reducing Shapes (14-31); Similar Figures (32-53); Similar Polygons (54-72); (74-89); Using Similar Triangles and Rectangles (90-105) Filling and Building Boxes (13-35); Designing Rectangular Boxes (36-54); (55-77); Cones, Spheres, and Pyramids (78-94); Scaling Boxes (95-112) 13

15 d. Solve problems involving scale factors using ratios and proportions. (DOK 2) Similar Figures (25-29, 31-37); Similar Polygons (39-49, 51-57); (58-77); Using Similar Triangles and Rectangles (78-93); Unit Project (94-95); Review (98-100); and Scaling Proportions (51, 58-59, 61-62) Similar Figures (43-53); Similar Polygons (33-72); (74-89); Using Similar Triangles and Rectangles (90-104); Review (105); Unit Project ( ); and Scaling Proportions (74-78, 91-92) 14

16 DATA ANALYSIS & PROBABILITY 5. Organize and interpret data. Analyze data to make predictions. Objectives a. Use proportions, estimates, and percentages to construct, interpret, and make predictions about a population based on histograms or circle graph representations of data from a sample. (DOK 2) Pupil Edition Data Distributions Variability (5-16, 18-19, 22); Measures of Center (30, 36-38, 48, 50); Distributions: Equal Numbers of Data Values (56-59, 62, 66-69, 71-72); Distributions: Unequal Numbers of Data Values (75, 78, 80, 82-83) b. Determine how outliers affect mean, median, mode, or range. (DOK 2) Data Distributions Variability (12, 15, 17, 25); Distributions: Equal Numbers of Data Values (70) Teacher Edition Data Distributions Variability (19-40); Measures of Center (46-50, 55-60, 69); Distributions: Equal Numbers of Data Values (74-82, 93-96); Distributions: Unequal Numbers of Data Values (99-102, ) Data Distributions Variability (29-32, 36, 38, 41); Distributions: Equal Numbers of Data Values (95) 15

17 c. Construct and interpret line graphs, frequency tables, circle graphs, box-and-whisker plots, and scatter plots to generalize trends from given data. (DOK 2) Data Distributions Variability (5-20, 22-27); Measures of Center (30, 33-43, 45-48, 50-54); Investigation 3: Distributions: Equal Numbers of Data Values (55-69, 71-73); Distributions: Unequal Numbers of Data Values (75-80, 82-85) Data Distributions Variability (19-42); Measures of Center (44-71); Distributions: Equal Numbers of Data Values (72-96); Distributions: Unequal Numbers of Data Values (97-118) 16

18 d. Determine probabilities through experimentation, simulation, or calculation. (Note: Make and test conjectures and predictions by calculating the probability of an event.) (DOK 2) Variables, Tables, and Coordinate Graphs (24); Calculator Tables and Graphs (78-79); (72); What Do You Expect? Evaluating Games of Chance (5-19); Analyzing Situations Using an Area Model (20-37); Expected Value (38-49); Binomial Outcomes (50-60); Data Distributions Distributions: Equal Numbers of Data Values (70) Variables, Tables, and Coordinate Graphs (40-41); Calculator Tables and Graphs (102); (88); What Do You Expect? Evaluating Games of Chance (17-35); Analyzing Situations Using an Area Model (37-58); Expected Value (59-76); Binomial Outcomes (78-94); Data Distributions Distributions: Equal Numbers of Data Values (95) 17