Math Skill Builder Program, 6th Grade Units 2007 Correlated to: Pennsylvania Assessment Anchors and Eligible Content (Grade 5)

Transcription

1 ANCHORS AND ASSESSMENT ANCHOR M5.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M5.A.1.1 Express numbers in equivalent forms. Reference: A SE: Unit 1: Skill 7 (13-14); Unit 2: Skill 4 (7-8); Skills (21-26); Skill 14 (29-30) TG: Unit 1: Skill 7 (11); Unit 2: Skill 4 (41); Skills (49-51); Skill 14 (53) M5.A Use expanded notation to represent whole numbers or decimals (whole numbers less than 10,000,000 and decimals through hundredths). M5.A.1.2 Demonstrate understanding of place value of whole numbers and decimals. Reference: I SE: Unit 1: Skill 1 (1-2) TG: Unit 1: Skill 1 (5) M5.A Match the standard form to the word form of decimal numbers through the hundredths. SE: Unit 1: Skill 1 (1-2) TG: Unit 1: Skill 1 (5) M5.A Identify the place value of a digit (from millions through hundredths). SE: Unit 1: Skill 1 (1); Skill 3 (5-6) TG: Unit 1: Skill 1 (5); Skill 3 (7) M5.A.1.3 Compare quantities or magnitudes of numbers. Reference: A SE: Unit 1: Skill 2 (3-4); Skill 20 (43-44); Unit 2: Skill 15 (31-32) TG: Unit 1: Skill 2 (6); Skill 20 (28); Unit 2: Skill 15 (54) 1

2 ANCHORS AND M5.A Compare whole numbers through 9 digits using the words more, less, equal, least, most, greater than, less than or the symbols <, >, =. SE: Unit 1: Skill 20 (43-44) TG: Unit 1: Skill 20 (28) M5.A Compare and/or order decimals through the hundredths (Limit sets for ordering to no more than 4 numbers.) SE: Unit 1: Skill 2 (3-4) TG: Unit 1: Skill 2 (6) M5.A Compare proper fractions through 16ths with like and unlike denominators. SE: Unit 2: Skill 15 (31-32) TG: Unit 2: Skill 15 (54) M5.A.1.4 Use simple applications of negative numbers (number line, counting, temperature). Reference: F SE: Unit 1: Skills (41-44) TG: Unit 1: Skills (27-28) M5.A Locate/Identify integers on a number line (greater than or equal to -20). SE: Unit 1: Skill 19 (41-42) TG: Unit 1: Skill 19 (27) 2

3 ANCHORS AND M5.A Identify negative temperatures on a thermometer (through -20 C or F). M5.A.1.5 Use or develop models to represent fractions and/or mixed numbers. Reference: D SE: Unit 2: Skill 8(17-18); Skill 13(27-28) TG: Unit 2: Skill 8(47); Skill 13(52) M5.A Use or develop regions and/or sets (e.g., circle graph, base ten blocks) to model fractions and mixed numbers through hundredths (may include reducing the fractions). SE: Unit 2: Skill 8(17-18); Skill 13(27-28) TG: Unit 2: Skill 8(47); Skill 13(52) M5.A.1.6 Apply number theory concepts (i.e., primes, factors, multiples, composites). Reference: E SE: Unit 2: Skills 1-3(1-6); Skill 5(9-10) TG: Unit 2: Skills 1-3(38-40); Skill 5(42) M5.A Define/list/identify prime and composite numbers less than or equal to 100. SE: Unit 2: Skills 2-3(3-6) TG: Unit 2: Skills 2-3(39-40) M5.A Define/list/identify factors and/or multiples of a given whole number less than or equal to 50. SE: Unit 2: Skill 1(1-2); Skill 3(5-6) TG: Unit 2: Skill 1(38); Skill 3(40) 3

4 ANCHORS AND ASSESSMENT ANCHOR M5.A.2 Understand the meanings of operations, use operations and understand how they relate to each other. M5.A.2.1 Solve problems involving decimals, fractions and/or whole numbers (straight computation or word problems). Reference: A, B, C, I SE: Unit 1: Skills 5-6 (9-12); Skills 8-11 (17-24); Skill 13 (27-28); Unit 2: Skills (41-44); Skill 22 (47-48) TG: Unit 1: Skills 5-6 (9-10); Skills 8-11 (14-17); Skill 13 (19); Unit 2: Skills (60-61); Skill 22 (63) M5.A Solve problems involving addition, subtraction, multiplication and division of whole numbers (multipliers up to 2 digits divisors one digit) and decimals including money (answer through hundredths no division with decimals). SE: Unit 1: Skill 8 (17-18); Skills (21-24); Skill 13 (27-28) M5.A Solve problems involving addition and subtraction of fractions (through 16ths like and unlike denominators for unlike denominators, the LCD must be one of the given denominators). TG: Unit 1: Skill 8 (14); Skills (16-17); Skill 13 (19) SE: Unit 2: Skills (41-44); Skill 22 (47-48) TG: Unit 2: Skills (60-61); Skill 22 (63) M5.A Choose the correct operation(s) to solve a problem (no more than 2 operations). SE: Unit 1: This Assessment Anchor is addressed on the second page of Skills 4-6, 8-18, 21-24; Unit 2: This Assessment Anchor is addressed on the second page of Skills 7, 18, 20-21, 23-33; Unit 3: This Assessment Anchor is addressed on the second page of Skills 10, 13-15; Unit 4: This Assessment Anchor is addressed on the second page of Skills 10-14,

5 ANCHORS AND TG: Unit 1: Skills 4-6 (8-10); Skills 8-18 (14-24); Skills (29-32); Unit 2: Skill 7 (44); Skill 18 (59); Skills (61-62); Skills (64-76); Unit 3: Skill 10 (92); Skills (97-99); Unit 4: Skills ( ); Skills ( ) ASSESSMENT ANCHOR M5.A.3 Compute accurately and fluently and make reasonable estimates. M5.A.3.1 Apply estimation strategies to a variety of problems. Reference: D, E, G SE: Unit 1: Skill 12 (25-26); Skill 18 (37-38); Unit 2: Skill 9 (19-20); Skill 18 (39-40); Skill 25 (55-56); Skill 29 (63-64) TG: Unit 1: Skill 12 (18); Skill 18 (24); Unit 2: Skill 9 (48); Skill 18 (59); Skill 25 (68); Skill 29 (72) M5.A Round whole numbers through millions and decimals through hundredths. M5.A Use estimation to solve problems involving whole numbers and/or decimals (up to 2- digit multipliers, single-digit divisors or multiples of 10; whole numbers through thousands and decimals through hundredths). SE: Unit 1: Skill 3 (5-6) TG: Unit 1: Skill 3 (7) SE: Unit 1: Skill 4 (7-8); Skill 12 (25-26); Unit 2: Skill 9 (19-20); Skill 18 (39-40) TG: Unit 1: Skill 4 (8); Skill 12 (18); Unit 2: Skill 9 (48); Skill 18 (59) M5.A.3.2 Compute accurately without the use of a calculator (straight computation or 1 operation word problems). Reference: A SE: Unit 1: Skills 5-6 (9-12); Skills 8-10 (17-22); Skills (45-52) 5

6 ANCHORS AND TG: Unit 1: Skills 5-6 (9-10); Skills 8-10 (14-16); Skills (29-32) 6

7 ANCHORS AND M5.A Use addition, subtraction, multiplication and division to compute accurately without a calculator (multipliers up to 2 digits, single-digit divisors or multiples of 10 whole numbers through thousands and decimals through hundredths- no division with decimals). SE: Unit 1: Skills 5-6 (9-12); Skills 8-11 (17-24); Skill 13 (27-28) TG: Unit 1: Skills 5-6 (9-10); Skills 8-11 (14-17); Skill 13 (19) ASSESSMENT ANCHOR M5.B.1 Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement. M5.B.1.1 Select appropriate units (customary or metric) to measure specific attributes of objects. Reference: A SE: Opportunities to address this standard are found throughout the Unit 4 text. TG: Unit 4: M5.B Select the appropriate unit for measuring weight (mass), capacity, length, perimeter and area. SE: This content is embedded within the exercises of Unit 4/Section B (Skills 9-17) M5.B.1.2 Solve problems using simple conversions and/or add and subtract measurements. Reference: D, E TG: Unit 4: Skills 9-17 ( ) SE: Unit 1: Skill 6 (12); Skill 21 (46); Unit 2: Skill 18 (40); Skill 20 (44); Skill 21 (46); Skill 23 (50); Unit 3: Skill 4 (8); Unit 4: Skill 9 (19-20) TG: Unit 1: Skill 6 (10); Skill 21 (29); Unit 2: Skill 18 (59); Skill (61-62); Skill 23 (64); Unit 3: Skill 4 (84); Unit 4: Skill 9 (112) 7

8 ANCHORS AND M5.B Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below use a conversion chart or a hint with problems e.g., hint: 16oz = 1lb). Metric using mm, cm, m and km; ml and L; g and kg Customary using cup, pint, quart, gallon; in, ft, yd; oz, lb. SE: Opportunities to address this standard are found throughout the Unit 4 text. The referenced units are used in many activities. TG: Unit 4: M5.B Add or subtract linear measurements, (feet and inches) or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form). SE: Unit 1: Skill 5 (10); Skill 6 (12); Skill 21 (46); Unit 2: Skill 18 (40); Skill 20 (44); Skill 21 (46); Skill 23 (50); Unit 4: Skill 9 (19-20) TG: Unit 1: Skill 5 (9); Skill 6 (10); Skill 21 (29); Unit 2: Skill 18 (59); Skill (61-62); Skill 23 (64); Unit 4: Skill 9 (112) M5.B.1.3 Estimate and/or compare the perimeters or areas of 2 figures without computation. Reference: E, C M5.B Estimate which polygon (shown on a grid) has a greater perimeter or area (compare either area to area or perimeter to perimeter). SE: Opportunities to address this standard can be found on: Unit 4: Skills 9-12 (19-26); Skills (29-32) M5.B Estimate the area of an irregular figure shown on a grid. TG: Unit 4: Skills 9-12 ( ); Skills ( ) SE: Opportunities to address this standard can be found on: Unit 4: Skill 15 (31-32) TG: Unit 4: Skill 15 (120) 8

9 ANCHORS AND 9

10 ANCHORS AND ASSESSMENT ANCHOR M5.B.2 Apply appropriate techniques, tools and formulas to determine measurements. M5.B.2.1 Use appropriate tools to determine measurements. Reference: B SE: Unit 4: Skill 10 (22); Skill 16 (34); Skill 18 (40) TG: Unit 4: Skill 10 (115); Skill 16 (121); Skill 18 (125) M5.B Use a ruler to measure to the nearest 1/8 inch or centimeter. SE: Unit 4: Skill 10 (22); Skill 16 (34); Skill 18 (40) TG: Unit 4: Skill 10 (115); Skill 16 (121); Skill 18 (125) M5.B.2.2 Solve problems involving length, time, weight (mass), capacity, temperature, perimeter and/or area. Reference: A, B SE: Unit 4: Skills 9-12 (19-26); Skills (29-32); Skill 17 (35-36) TG: Unit 4: Skills 9-12 ( ); Skills ( ); Skill 17 (122) M5.B Find the perimeter of a figure drawn and labeled (with the same units throughout). SE: Unit 4: Skill 9 (19-20) TG: Unit 4: Skill 9 (114) M5.B Find the area of a square or rectangle (with the same units throughout - whole numbers only). SE: Unit 4: Skill 10 (21-22) TG: Unit 4: Skill 10 (115) 10

11 ANCHORS AND M5.B Solve problems involving weight, time, temperature, length and capacity (limited to 3 digits) (With the same units throughout). SE: Unit 4: Skills 9-12 (19-26); Skills (29-32); Skill 17 (35-36) TG: Unit 4: Skills 9-12 ( ); Skills ( ); Skill 17 (122) ASSESSMENT ANCHOR M5.C.1 Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships. M5.C.1.1 Define and/or use basic properties of SE: Unit 4: Skills 5-8 (9-16); Skill 13 (27-28); quadrilaterals (parallelograms, squares, rectangles, Skill 23 (49-50) trapezoids, rhombi), triangles, circles, pyramids, cubes, and/or prisms. Reference: B, C, F, A TG: Unit 4: Skills 5-8 ( ); Skill 13 (118); Skill 23 (130) M5.C Identify, and/or classify cubes, rectangular prisms or pyramids using faces, vertices and edges. SE: Unit 4: Skill 23 (49-50) TG: Unit 4: Skill 23 (130) M5.C Identify and/or describe properties of all types of quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid). SE: Unit 4: Skills 7-8 (13-16) TG: Unit 4: Skills 7-8 ( ) M5.C.1.2 Represent and/or use properties of lines, line segments, rays, points and planes. Reference: I SE: Unit 4: Skill 3 (5-6); Skill 22 (47-48) 11

12 ANCHORS AND TG: Unit 4: Skill 3 (106); Skill 22 (129) M5.C Identify, draw and/or label points, lines, line segments and rays. SE: Unit 4: Skill 3 (5-6) TG: Unit 4: Skill 3 (106) ASSESSMENT ANCHOR M5.C.2 Identify and/or apply concepts of transformations or symmetry. M5.C.2.1 Analyze transformations and/or use symmetry to analyze mathematical situations. Reference: K, L SE: Unit 4: Skills (43-46) TG: Unit 4: Skills ( ) M5.C Draw or identify a translation (slide), reflection (flip) or rotation (turn) of a 2- dimensional shape. SE: Unit 4: Skill 20 (43-44) TG: Unit 4: Skill 20 (127) M5.C Identify the number of lines of symmetry and/or draw all lines of symmetry in a two-dimensional polygon. SE: Unit 4: Skill 21 (45-46) TG: Unit 4: Skill 21 (128) ASSESSMENT ANCHOR M5.C.3 Locate points or describe relationships using the coordinate plane. Assessed in Grade 4 and Grades 6 and higher with negative numbers. ASSESSMENT ANCHOR M5.D.1 Demonstrate an understanding of patterns, relations and functions. 12

13 ANCHORS AND M5.D.1.1 Create or extend patterns. Reference: A SE: Unit 3: Skill 7 (16) TG: Unit 3: Skill 7 (89) M5.D Extend or find a missing element in a numerical or simple geometric pattern (+, -, x or of whole numbers). Pattern must show 3 repetitions. SE: Unit 3: Skill 7 (16) TG: Unit 3: Skill 7 (89) M5.D Create or replicate a numerical or geometric pattern showing 3 repetitions of that pattern (+, -, x or of whole numbers may be used). M5.D.1.2 Analyze patterns. Reference: C M5.D Form a rule based on a given pattern, or illustrate a pattern based on a given rule (+, -, x or of whole numbers may be used). Patterns must show 3 repetitions. ASSESSMENT ANCHOR M5.D.2 Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs. M5.D.2.1 Select and/or use appropriate strategies, including concrete materials, to solve or represent expressions or number sentences. Reference: G, F SE: Unit 3: Skill 7 (15-16); Skill 9 (19-20) TG: Unit 3: Skill 7 (89); Skill 9 (91) 13

14 ANCHORS AND M5.D Solve for a missing number (blank, question mark, variable) in an equation involving a single operation whole numbers only. SE: Unit 3: Skill 10 (21-22) TG: Unit 3: Skill 10 (92) M5.D Match a realistic situation to an equation, expression, inequality (<, >, =), table or graph (variable must be isolated, e.g., = n). SE: Unit 3: Skill 9 (20); Skill 10 (22) TG: Unit 3: Skill 9-10 (91-92) ASSESSMENT ANCHOR M5.D.3 Analyze change in various contexts. M5.D.3.1 Describe the relationship between rate of change and another variable (e.g., time, temperature). Reference: D ASSESSMENT ANCHOR M5.D.4 Describe or use models to represent quantitative relationships. Not assessed at Grade 5. ASSESSMENT ANCHOR M5.E.1 Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data. M5.E.1.1 Organize, display and/or interpret data using pictographs, tallies, tables, charts, line, bar graphs. Reference: A M5.E Display and/or interpret data shown in tallies, tables, charts, pictographs, bar graphs, line graphs and using a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs. ASSESSMENT ANCHOR M5.E.2 Select and/or use appropriate statistical methods to analyze data. 14

15 ANCHORS AND M5.E.2.1 Describe data sets using mean, median, mode and/or range. Reference: B 15

16 ANCHORS AND M5.E Determine the mean/average (answer is a whole number), median (answer is a whole number or average of 2 numbers) and range of data (up to 10 numbers). M5.E Identify the mode in a set of data (up to 10 numbers). ASSESSMENT ANCHOR M5.E.3 Understand and/or apply basic concepts of probability or outcomes. M5.E.3.1 Predict or determine all possible combinations, outcomes and/or calculate the probability of a simple event. Reference: E, H, J M5.E Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (information could be represented by pictographs,, bar graphs, charts, tables and/or spinners). M5.E Determine the probability of an outcome (e.g., a coin toss, a roll of a number cube) and express as a fraction without reduction. ASSESSMENT ANCHOR M5.E.4 Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays. Not assessed at Grade 5. 16