Prentice Hall : Connected 2, 6th Grade Units 2006 Strand 1: Number Sense and Operations Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). PO 2. Compare two proper fractions, improper fractions, or mixed numbers. SE: Bits and Pieces I Investigation 2 (24) TG: Bits and Pieces I Investigation 2 (57-62) TR: Bits and Pieces I Transparencies; Labsheets; PO 3. Order three or more proper fractions, improper fractions, or mixed numbers. PO 4. Determine the equivalency between and among fractions, decimals, and percents in contextual situations. SE: Bits and Pieces I Investigation 2 (22-23), Investigation 3 (38-39, 39-40, 41-42, 43-44), Investigation 4 (58-59, 59-60) TG: Bits and Pieces I Investigation 2 (51-56), Investigation 3 (79-84, 85-90, 91-96, 97-100), Investigation 4 (125-128, 129-132) TR: Bits and Pieces I Transparencies 2.2A-B, 3.1A- C, 3.2A-E, 4.3, 4.4; Labsheets 2.2, 3.1, 3.2, 3.3, 4.4; 1
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 5. Identify the greatest common factor for two whole numbers. SE: Prime Time Investigation 3 (38-41), Investigation 4 (53-55) TG: Prime Time Investigation 3 (54-58, 59-62, 63-66, 67-70), Investigation 4 (87-92) TR: Prime Time Transparencies 3.4, 4.3; PO 6. Determine the least common multiple for two whole numbers. PO 7. Express a whole number as a product of its prime factors, using exponents when appropriate. Concept 2: Numerical Operations SE: Prime Time Investigation 3 (38-41), Investigation 4 (53-55) TG: Prime Time Investigation 3 (54-58, 59-62, 63-66, 67-70), Investigation 4 (87-92) TR: Prime Time Transparencies 3.4, 4.3; SE: Prime Time Investigation 4 (50-52) TG: Prime Time Investigation 4 (81-86) TR: Prime Time Transparencies 4.2; Labsheets; Understand and apply numerical operations and their relationship to one another. PO 1. Select the grade-level appropriate operation to solve word problems. SE: Bits and Pieces III Investigation 1 (8-9) TG: Bits and Pieces III Investigation 1 (21-24) TR: Bits and Pieces III Transparencies 1.2; 2
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 2. Solve word problems using gradelevel appropriate operations and numbers. This standard is covered within the in-class problems and the ACE exercises found in each investigation of all student units. A representative citation follows: SE: Bits and Pieces I Investigation 1 (5-18), Investigation 2 (19-34), Investigation 3 (35-53), Investigation 4 (54-68) TG: Bits and Pieces I Investigation 1 (15-43), Investigation 2 (44-76), Investigation 3 (77-111), Investigation 4 (112-135) TR: Bits and Pieces I Transparencies; Labsheets; PO 3. Apply grade-level appropriate properties to assist in computation. This standard is covered within the in-class problems and the ACE exercises found in each investigation of all student units. A representative citation follows: SE: Bits and Pieces I Investigation 1 (5-18), Investigation 2 (19-34), Investigation 3 (35-53), Investigation 4 (54-68) TG: Bits and Pieces I Investigation 1 (15-43), Investigation 2 (44-76), Investigation 3 (77-111), Investigation 4 (112-135) TR: Bits and Pieces I Transparencies; Labsheets; PO 4. Apply the symbols for or SE: Bits and Pieces III Investigation 3 (41-42) to represent repeating decimals and : to represent ratios, superscripts as exponents. TG: Bits and Pieces III Investigation 3 (75-78) TR: Bits and Pieces III Transparencies; 3
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 5. Use grade-level appropriate mathematical terminology. This standard is covered within the in-class problems and the ACE exercises found in each investigation of all student units. A representative citation follows: SE: Bits and Pieces I Investigation 1 (5-18), Investigation 2 (19-34), Investigation 3 (35-53), Investigation 4 (54-68) TG: Bits and Pieces I Investigation 1 (15-43), Investigation 2 (44-76), Investigation 3 (77-111), Investigation 4 (112-135) TR: Bits and Pieces I Transparencies; Labsheets; PO 6. Simplify fractions to lowest terms. PO 7. Add or subtract proper fractions and mixed numbers with unlike denominators with regrouping. PO 8. Demonstrate the process of multiplication of proper fractions using models. SE: Bits and Pieces II Investigation 2 (16-19, 19-21, 22-23) TG: Bits and Pieces II Investigation 2 (35-40, 41-46, 51-54) TR: Bits and Pieces II Transparencies 2.1, 2.2, 2.4A-B; Labsheets 2.1, 2.2; Additional Practice; Assessment Resources SE: Bits and Pieces II Investigation 3 (32-33, 34-35) TG: Bits and Pieces II Investigation 3 (60-64, 65-70) 4
Prentice Hall : Connected 2, 6th Grade Units 2006 TR: Bits and Pieces II Transparencies 3.2; Labsheets 3.1; Additional Practice; Notebook Resources PO 9. Multiply proper fractions. SE: Bits and Pieces II Investigation 3 (32-33, 34-35) TG: Bits and Pieces II Investigation 3 (60-64, 65-70) TR: Bits and Pieces II Transparencies 3.2; Labsheets 3.1; Additional Practice; Notebook Resources PO 10. Multiply mixed numbers. SE: Bits and Pieces II Investigation 3 (36-37, 37-38) Bits and Pieces III Investigation 2 (21-23) TG: Bits and Pieces II Investigation 3 (71-74, 75-80) Bits and Pieces III Investigation 2 (37-42) TR: Bits and Pieces II Transparencies 3.3, 3.4; Bits and Pieces III Transparencies 2.1; Labsheets; PO 11. Demonstrate that division is the SE: Bits and Pieces II Investigation 4 (53-54) inverse of multiplication of proper fractions. TG: Bits and Pieces II Investigation 4 (109-114) 5
Prentice Hall : Connected 2, 6th Grade Units 2006 TR: Bits and Pieces II Transparencies 4.4; PO 12. Divide proper fractions. PO 13. Divide mixed numbers. SE: Bits and Pieces II Investigation 4 (52-53) TG: Bits and Pieces II Investigation 4 (103-108) TR: Bits and Pieces II Transparencies; Labsheets; PO 14. Solve problems involving fractions SE: Bits and Pieces I Investigation 4 (57) Bits and or decimals (including money) in contextual Pieces II Investigation 2 (16-21) Bits and Pieces situations. III Investigation 1 (10-11) TG: Bits and Pieces I Investigation 4 (119-124) Bits and Pieces II Investigation 2 (35-40, 41-46) Bits and Pieces III Investigation 1 (25-28) TR: Bits and Pieces I Transparencies; Labsheets; Bits and Pieces II Transparencies 2.1, 2.2; Labsheets 2.1, 2.2; Bits and Pieces III Transparencies 1.3; Labsheets; PO 15. Simplify numerical expressions using the order of operations with gradeappropriate operations on number sets. Concept 3: Estimation Use estimation strategies reasonably and fluently. 6
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 1. Solve grade-level appropriate problems using estimation. SE: Bits and Pieces I Investigation 4 (54-56) Bits and Pieces II Investigation 1 (8-9) TG: Bits and Pieces I Investigation 4 (113-118) Bits and Pieces II Investigation 1 (25-30) TR: Bits and Pieces I Transparencies 4.1A-B; Labsheets 4.1; Additional Practice; Notebook Resources Bits and Pieces II Transparencies; PO 2. Use estimation to verify the SE: Bits and Pieces II Investigation 3 (33) reasonableness of a calculation (e.g., Is 5/9 x 3/7 more than 1?). TG: Bits and Pieces II Investigation 3 (60-64) TR: Bits and Pieces II Transparencies; Labsheets 3.1; PO 3. Round to estimate quantities in contextual situations (e.g., round up or round down) SE: Bits and Pieces III Investigation 1 (5-7) TG: Bits and Pieces III Investigation 1 (16-20) TR: Bits and Pieces III Transparencies 1.1; PO 4. Estimate and measure for the area and perimeter of polygons using a grid. SE: Covering and Surrounding Investigation 5 (70-71) 7
Prentice Hall : Connected 2, 6th Grade Units 2006 TG: Covering and Surrounding Investigation 5 (110-114) TR: Covering and Surrounding Transparencies 5.1; Labsheets 5.1; Additional Practice; Notebook Resources PO 5. Verify the reasonableness of estimates made from calculator results within a contextual situation. Strand 2: Data Analysis, Probability, and Discrete Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization and representation to analyze and sort data. PO 1. Formulate questions to collect data in contextual situations. PO 2. Construct a histogram, line graph, scatter plot, or stem-and-leaf plot with appropriate labels and title from organized data. SE: Data About Us Investigation 2 (30-33, 36-38) TG: Data About Us Investigation 2 (47-52, 57-62) PO 3. Interpret simple displays of data including double bar graphs, tally charts, frequency tables, circle graphs, and line graphs. TR: Data About Us Transparencies 2.1A-C, 2.3A- B; Labsheets; Additional Practice; Notebook Resources SE: Data About Us Investigation 2 (34-35) TG: Data About Us Investigation 2 (53-56) 8
Prentice Hall : Connected 2, 6th Grade Units 2006 TR: Data About Us Transparencies 2.2; PO 4. Answer questions based on simple SE: Data About Us Investigation 1 (7-9, 14-17, 18- displays of data including double bar 20) Data Distributions Investigation 1 graphs, tally charts, frequency tables, circle graphs, and line graphs. TG: Data About Us Investigation 1 (17-20, 31-36, 37-40) Data Distributions Investigation 1 TR: Data About Us Transparencies 1.1A-B, 1.4A- C, 1.5A-B; Labsheets; Additional Practice; Assessment Resources Data Distributions Transparencies; Labsheets; Additional Practice; Assessment Resources PHSchool.com, Web Code amk-5500, ank-5500; LessonLab PO 5. Find the mean, median (odd number of data points), mode, range, and extreme values of a given numerical data set. SE: Data About Us Investigation 1 (9-11, 12-13), Investigation 3 (50-51, 52-53, 54-55) TG: Data About Us Investigation 1 (21-26, 27-30), Investigation 3 (74-80, 81-86, 87-90) TR: Data About Us Transparencies 1.2A-B, 1.3, 3.1A-B, 3.2A-B, 3.3A-B; Labsheets; Additional Practice; Notebook Check; Self-Assessment; Spanish Assessment Resources PO 6. Identify a trend (variable increasing, decreasing, remaining constant) from displayed data. PO 7. Compare trends in data related to the same investigation. 9
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 8. Solve contextual problems using bar graphs, tally charts, and frequency tables. Concept 2: Probability Understand and apply the basic concepts of probability. PO 1. Name the possible outcomes for a probability experiment. SE: How Likely Is It? Investigation 1 (8-10), Investigation 2 (24-26) TG: How Likely Is It? Investigation 1 (25-28), Investigation 2 (45-48) TR: How Likely Is It? Transparencies 2.3; PO 2. Express probabilities of a single event as a decimal. PO 3. Predict the outcome of a grade-level appropriate probability experiment. PO 4. Record the data from performing a grade-level appropriate probability experiment. SE: How Likely Is It? Investigation 1 (6-7, 7-8, 8-10), Investigation 2 (24-26) What Do You Expect? Investigations 1, 2, and 3 TG: How Likely Is It? Investigation 1 (15-20, 21-24, 25-28), Investigation 2 (45-48) What Do You Expect? Investigations 1, 2, and 3 TR: How Likely Is It? Transparencies 1.1A-B, 2.3; Labsheets 1.1; Additional Practice; Notebook Resources What Do You Expect? Transparencies; PHSchool.com, Web Code amk-5500, ank-5500; LessonLab 10
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 5. Compare the outcome of an experiment to predictions made prior to performing the experiment. SE: What Do You Expect? Investigation 3 TG: What Do You Expect? Investigation 3 TR: What Do You Expect? Transparencies; PHSchool.com, Web Code ank-5500; LessonLab PO 6. Make predictions from the results of student-generated experiments using objects (e.g., coins, spinners, number cubes, cards). SE: How Likely Is It? Investigation 1 (6-7, 7-8), Investigation 3 (39-40) What Do You Expect? Investigations 2 and 4 TG: How Likely Is It? Investigation 1 (15-20, 21-24), Investigation 3 (59-62) What Do You Expect? Investigations 2 and 4 TR: How Likely Is It? Transparencies 1.1A-B, 3.1A- C; Labsheets 1.1, 3.1; Additional Practice; Assessment Resources What Do You Expect? Transparencies; Labsheets; Additional Practice; Assessment Resources PHSchool.com, Web Code amk-5500, ank-5500; LessonLab PO 7. Compare the results of two repetitions of the same grade-level appropriate probability experiment. SE: How Likely Is It? Investigation 4 (60-61) TG: How Likely Is It? Investigation 4 (83-86) TR: How Likely Is It? Transparencies 4.3; Labsheets 4.3; Additional Practice; Notebook Resources 11
Prentice Hall : Connected 2, 6th Grade Units 2006 Concept 3: Discrete Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1. Determine all possible outcomes involving a combination of three sets of three items, using a systematic approach (e.g., 3 different shirts, 3 different pairs of pants, and 3 different belts). PO 2. Determine all possible arrangements given a set with four or fewer objects using a systematic list, table or tree diagram when order is not important. Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. PO 1. Find the shortest route on a map from one site to another (vertex-edge graph). Strand 3: Patterns, Algebra, and Functions PO 1. Communicate a grade-level appropriate recursive pattern, using symbols or numbers. PO 2. Extend a grade-level appropriate iterative pattern. PO 3. Solve grade-level appropriate iterative pattern problems. SE: How Likely Is It? Investigation 2 (24-26) What Do You Expect? Investigation 2 TG: How Likely Is It? Investigation 2 (45-48) What Do You Expect? Investigation 2 TR: How Likely Is It? Transparencies 2.3; What Do You Expect? Transparencies; Labsheets; PHSchool.com, Web Code amk-5500, ank-5500; LessonLab Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically. 12
Prentice Hall : Connected 2, 6th Grade Units 2006 Concept 2: Functions and Relationships Describe and model functions and their relationships. PO 1. Describe the rule used in a simple grade-level appropriate function (e.g., T- chart, input/output model). PO 1. Evaluate expressions involving the four basic operations by substituting given fractions for the variable (e.g., n +3, when n = ½ ). PO 2. Use variables in contextual situations. PO 3. Translate a written phrase to an algebraic expression (e.g., The quotient of m and 5 is m/5 or m 5 PO 4. Translate a phrase written in context into an algebraic expression (e.g., Write an expression to describe the situation: John has x pieces of candy and buys three more x + 3) PO 5. Solve one-step equations with one variable represented by a letter or symbol, using inverse operations with whole numbers. Concept 4: Analysis of Change Analyze change in a variable over time and in various contexts. PO 1. Identify values on a given line graph or scatter plot (e.g., Given a line showing wages earned per hour, what is the wage at five hours?). Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. SE: Data About Us Investigation 2 (38-39) TG: Data About Us Investigation 2 (63-66) TR: Data About Us Transparencies 2.4; Labsheets 2.4; 13
Prentice Hall : Connected 2, 6th Grade Units 2006 Strand 4: Geometry and Measurement Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional shapes and develop mathematical arguments about their relationships. PO 1. Classify polygons by their attributes (e.g., number of sides, length of sides, angles, parallelism, perpendicularity). SE: Shapes and Designs Investigation 1 (7-11, 12-13), Investigation 4 (74-75) TG: Shapes and Designs Investigation 1 (18-22, 23-26), Investigation 4 (91-94) TR: Shapes and Designs Transparencies 1.1A-E, 1.2A-C; Labsheets Shapes Set, 4.3; Additional Practice; Notebook Check; Self-Assessment; Spanish Assessment Resources PO 2. Draw a geometric figure showing specified properties, such as parallelism and perpendicularity. SE: Shapes and Designs Investigation 4 (72) TG: Shapes and Designs Investigation 4 (87-90) TR: Shapes and Designs Transparencies; Labsheets Shapes Set, 4.2; Additional Practice; Assessment Resources PO 3. Classify prisms, pyramids, cones, and cylinders by base shape and lateral surface shape. PO 4. Classify 3-dimensional figures by their attributes. PO 5. Compare attributes of 2-dimensional figures with 3-dimensional figures. 14
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 6. Draw triangles with appropriate labels. PO 7. Identify supplementary or complementary angles. PO 8. Identify the diameter, radius, and circumference of a circle or sphere. SE: Covering and Surrounding Investigation 5 (72-73) TG: Covering and Surrounding Investigation 5 (115-118) TR: Covering and Surrounding Transparencies 5.2A-B; Labsheets; Additional Practice; Notebook Resources PO 9. Draw a 2-dimensional shape with a given number of lines of symmetry. Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. PO 1. Identify reflections and translations using pictures. SE: Kaleidoscopes, Hubcaps, and Mirrors Investigations 1 & 2 TG: Kaleidoscopes, Hubcaps, and Mirrors Investigations 1 & 2 TR: Kaleidoscopes, Hubcaps, and Mirrors Transparencies; Labsheets; Additional Practice; Assessment Resources PHSchool.com, Web Code apk-5500; LessonLab PO 2. Perform elementary transformations to create a tessellation. SE: Kaleidoscopes, Hubcaps, and Mirrors Investigation 2 TG: Kaleidoscopes, Hubcaps, and Mirrors Investigation 2 15
Prentice Hall : Connected 2, 6th Grade Units 2006 TR: Kaleidoscopes, Hubcaps, and Mirrors Transparencies; Labsheets; Additional Practice; Assessment Resources PHSchool.com, Web Code apk-5500; LessonLab Concept 3: Coordinate Geometry Specify and describe spatial relationships using coordinate geometry and other representational systems. PO 1. Graph a polygon in the first quadrant using ordered pairs. PO 2. State the missing coordinate of a given figure in the first quadrant of a coordinate grid using geometric properties (e.g., Find the coordinates of the missing vertex of a rectangle when two adjacent sides are drawn.). Concept 4: Measurement - Units of Measure - Geometric Objects Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 1. Determine the appropriate measure of accuracy within a system for a given contextual situation (e.g., Would you measure the length of your bedroom wall using inches or feet?). PO 2. Determine the appropriate tool needed to measure to the needed accuracy. PO 3. Determine a linear measurement to the appropriate degree of accuracy. PO 4. Measure angles using a protractor. SE: Shapes and Designs Investigation 2 (32-35) TG: Shapes and Designs Investigation 2 (45-48) TR: Shapes and Designs Transparencies 2.3; 16
Prentice Hall : Connected 2, 6th Grade Units 2006 PO 5. Convert within a single measurement system (U.S. customary or metric) (e.g., How many ounces are equivalent to 2 pounds?). PO 6. Solve problems involving the perimeter of polygons. SE: Covering and Surrounding Investigation 1 (5-6, 6-7), Investigation 2 (20-21, 22-23), Investigation 3 (38-39), Investigation 4 (54-55) TG: Covering and Surrounding Investigation 1 (18-22, 23-26), Investigation 2 (38-42, 43-46), Investigation 3 (61-68), Investigation 4 (88-92) TR: Covering and Surrounding Transparencies 1.1, 1.2, 2.1A-B, 2.2, 3.1A-C, 4.1A-B; Labsheets 1.2, 2.1, 3.1, 4.1; Additional Practice; Notebook Resources PO 7. Determine the area of triangles. SE: Covering and Surrounding Investigation 3 (38-39, 40-41, 42-43) TG: Covering and Surrounding Investigation 3 (61-68, 69-74, 75-78) TR: Covering and Surrounding Transparencies 3.1A-C, 3.2, 3.3; Labsheets 3.1, 3.2A-B; PO 8. Distinguish between perimeter and area in contextual situation. SE: Covering and Surrounding Investigation 1 (5-6, 6-7), Investigation 3 (43), Investigation 4 (57) TG: Covering and Surrounding Investigation 1 (18-22, 23-26), Investigation 3 (79-82), Investigation 4 (97-100) 17
Prentice Hall : Connected 2, 6th Grade Units 2006 TR: Covering and Surrounding Transparencies 1.1, 1.2; Labsheets 1.2; Additional Practice; Assessment Resources PO 9. Solve problems for the areas of parallelograms (includes rectangles). PO 10. Identify parallelograms having the same perimeter or area. SE: Covering and Surrounding Investigation 1 (6-7, 8-9), Investigation 2 (24), Investigation 4 (54-55, 56-57) TG: Covering and Surrounding Investigation 1 (23-26, 27-32), Investigation 2 (47-50), Investigation 4 (88-92, 93-96) TR: Covering and Surrounding Transparencies 1.2, 1.3A-C, 2.3A-B, 4.1A-B, 4.2; Labsheets 1.2, 1.3, 2.3, 4.1, 4.2A-B; Additional Practice; Assessment Resources SE: Covering and Surrounding Investigation 1 (5-6, 6-7), Investigation 2 (20-21) TG: Covering and Surrounding Investigation 1 (18-22, 23-26), Investigation 2 (38-42) TR: Covering and Surrounding Transparencies 1.1, 1.2, 2.1A-B; Labsheets 1.2, 2.1; Additional Practice; Notebook Check; Self-Assessment; Spanish Assessment Resources PO 11. Determine the actual measure of objects using a scale drawing or map. 18
Prentice Hall : Connected 2, 6th Grade Units 2006 Strand 5: Structure and Logic Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems in contextual situations. PO 1. Discriminate necessary information from unnecessary information in a given grade-level appropriate word problem. PO 2. Analyze algorithms for computing with decimals. SE: Bits and Pieces III Investigation 1 (12), Investigation 2 (26-27) TG: Bits and Pieces III Investigation 1 (29-32), Investigation 2 (51-56) TR: Bits and Pieces III Transparencies 2.4; Labsheets 2.4; Additional Practice; Notebook Resources Concept 2: Logic, Reasoning, Arguments, and Mathematical Proof Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications. PO 1. Solve a simple logic problem from given information (e.g., Which of three different people live in which of three different colored houses?). 19