Prentice Hall Mathematics Course 2, Indiana Edition 2010
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1 Prentice Hall Mathematics Course 2, Grade 7 C O R R E L A T E D T O from March 2009 Grade 7
2 Problem Solving Build new mathematical knowledge through problem solving. Solve problems that arise in mathematics and in other contexts. Apply and adapt a variety of appropriate strategies to solve problems. Monitor and reflect on the process of mathematical problem solving. Reasoning and Proof Recognize reasoning and proof as fundamental aspects of mathematics. Make and investigate mathematical conjectures. Develop and evaluate mathematical arguments and proofs. Select and use various types of reasoning and methods of proof. Communication Organize and consolidate their mathematical thinking through communication. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Analyze and evaluate the mathematical thinking and strategies of others. SE/TE: 6, 56, 108, 150, 197, 240, 286, 326, 359, 398, 444, 474, 516, 558, 604 SE/TE: 4, 99, 133, 190, 212, 247, 282, 319, 375, 397, 474, 517, 583 SE/TE: 24-25, 77, 168, 181, 193, 204, 215, 303, 363, 407, 458, 493, 566 SE/TE: T54-T69, 46, 80-81, 170, 183, 196, 206, 217, 305, 365, 419, , 497, 585 SE/TE: 6, 50, 138, 199, 235, 276, 333, 363, 425, 474, 500, 556, 590 SE/TE: 58, 135, 168, 251, 335, 353, 443 SE/TE: 8, 9, 14, 15, 52, 127, 130, 131, 137, 142, 178, 233, 280, 285, 299, 302, 329, 384, 423, 446, 462 SE/TE: 17, 71, 144, 190, 207, 247, 339, 376, 426, 460, 502, 558, 595, 608 SE/TE: 7, 62, 114, 213, 248, 287, 327, 363, 449, 506, 541, 582, 618 SE/TE: 10, 71, 177, 217, 255, 293, 334, 368, 458, 509, 547, 589, 613 SE/TE: 6, 50, 55, 78, 84, 129, 133, 139, 144, 151, 182, 190, 218, 231, 240, 248, 261, 313, 327, 334, 418, 494, 501, 556 1
3 Use the language of mathematics to express mathematical ideas precisely. Connections Recognize and use connections among mathematical ideas. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Recognize and apply mathematics in contexts outside of mathematics. Representation Create and use representations to organize, record, and communicate mathematical ideas. Select, apply, and translate among mathematical representations to solve problems. Use representations to model and interpret physical, social, and mathematical phenomena. Estimation and Mental Computation Know and apply appropriate methods for estimating the results of computations. SE/TE: 6, 77, 156, 196, 212, 261, 306, 363, 416, 488, 516, 546, 611 SE/TE: 7, 71, 123, 172, 213, 263, 307, 353, 397, 445, 489, 536, 583, 613 SE/TE: 11, 78, 129, 177, 218, 277, 314, 357, 403, 449, 494, 542, 589 SE/TE: 8, 67, 161, 183, 212, 280, 305, 392, 448, 480, 513, 586, 612 SE/TE: 36-37, 86, 125, 258, 278, 329, 335, 393, 404, 426, 585 SE/TE: 48-51, , , , , , , , , , , SE/TE: 19, 43, 125, 135, 140, 179, 199, 258, 278, 379, 393, 404, 426, 441, 585 SE/TE: 4-6, 9, 12, 14, 15, 92, , , , 137, 142, 233, 277, 280, 291, 292, 293, 369 Round numbers to a specified place value. SE/TE: 2, 4, 6, 8, 62, 120, 122, 155, 161, 655, 660 Use estimation to decide whether answers are reasonable. Decide when estimation is an appropriate strategy for solving a problem. Determine appropriate accuracy and precision of measurement in problem situations. SE/TE: 8, 14, 127, 130, 131, 137, 142, 233, 280, 285, 299, 302, 329, 384, 423, 446, 462 SE/TE: 8, 14, 15, 92, , , , 137, 142, 233, 277, 280, 291, 292, 293, 369 SE/TE: , 161 2
4 Use properties of numbers and operations to perform mental computation. Recognize when the numbers involved in a computation allow for a mental computation strategy. Technology Technology should be used as a tool in mathematics education to support and extend the mathematics curriculum. Technology can contribute to concept development, simulation, representation, communication, and problem solving. The challenge is to ensure that technology supports-but is not a substitute for- the development of skills with basic operations, quantitative reasoning, and problem solving skills. o Elementary students should learn how to perform thoroughly the basic arithmetic operations independent of the use of a calculator. o The focus must be on learning mathematics, using technology as a tool rather than as an end in itself. 7.1 Standard 1 Number Sense and Computation Read, write, compare and solve problems using whole numbers in scientific notation Recognize and compute whole number powers of positive integers Recognize the prime factors of a number and find the prime factorization of whole numbers and write the results using exponents Recognize or use prime and composite numbers to solve problems Recognize and use the inverse relationship between squaring and finding the square root of a perfect square integer Identify, write, rename, compare and order rational and common irrational numbers and plot them on a number line Solve problems that involve multiplication and division with integers, fractions, decimals and combinations of the four operations. SE/TE: 9, 10, 12, 15, 16, 23, 48, 49, 50, 55, 62, 78, 93, 129, 133, 139, 143, 184, 202, 246, 268, 282, 286, 306, 448, 506, 512, 517, 522, 588 SE/TE: 9, 10, 12, 15, 16, 23, 48, 49, 50, 55, 62, 78, 93, 129, 133, 139, 143, 184, 202, 246, 268, 282, 286, 306, 448, 506, 512, 517, 522, 588 SE/TE: , 110, 113 SE/TE: 68-71, 112, , 429 SE/TE: 75-78, 112 SE/TE: 74-78, 112 SE/TE: , , 429 SE/TE: 31-34, 61, 87-90, , 113, , 400 SE/TE: 14-17, 20-23, 44-47, 60, , , , 161, , , , , 317 3
5 7.1.8 Solve problems involving percents. Find the whole given a part and the percentage Find percentage increase or decrease Solve problems involving ratios and proportions. Express one quantity as a fraction of another, given their ratio, and vice versa. Find how many times one quantity is as large as another, given their ratio, and vice versa. Express one quantity as a fraction of another given the two quantities. Find the whole, or one part, when a whole is divided into parts in a given ration. Solve problems involving two pairs of equivalent ratios. 7.2 Standard 2 Algebra and Functions Use variables and appropriate operations to write an expression, equation or inequality that represents a verbal description Write and solve two-step linear equations and inequalities in one variable Evaluate numerical expressions and simplify algebraic expressions involving rational and irrational numbers Solve an equation or formula with two variables for a particular variable Find the slope of a line from its graph and relate the slope of a line to similar triangles Draw the graph of a line given its slope and one point on the line or two points on the line Identify situations that involve proportional relationships, draw graphs representing these situations and recognize that these situations are described by a linear function in the form y = mx where the unit rate m is the slope of the line. 7.3 Standard 3 Geometry and Measurement Identify and use basic properties of angles formed by transversals intersecting pairs of parallel lines Identify, describe, and use transformations (translations, rotations, reflections and simple compositions of these transformations) to solve problems. SE/TE: , , , 302, , , 317 SE/TE: , , 236, , 242, 243, , 249, , , 266, 267 SE/TE: , 174, 182, 183, , 204, , 220, 221, 434, 457, 484 SE/TE: , 213, 218, 221 SE/TE: , 174, , 220 SE/TE: , , , , , , , 428, 429, , , 479 SE/TE: , 525 SE/TE: , 525 SE/TE: , 479, , 525 Related material: SE/TE: SE/TE: 509, , , 518, , 525 4
6 7.3.3 Draw two-dimensional patterns (nets) for three-dimensional objects, such as right prisms, pyramids, cylinders and cones Recognize, describe, or extend geometric patterns using tables, graphs, words, or symbols Identify, describe, and construct similarity relationships and solve problems involving similarity (including similar triangles) and scale drawings by using proportional reasoning Solve simple problems involving distance, speed and time. Understand concepts of speed and average speed. Understand the relationship between distance, time and speed. Find speed, distance or time given the other two quantities. Write speed in different units (km/h, m/s, cm/s, mi/hr, ft/sec). Solve simple problems involving speed and average speed. 7.4 Standard 4 Data Analysis and Probability Create, analyze and interpret data sets in multiple ways using bar graphs, frequency tables, line plots, histograms and circle graphs. Justify the choice of data display Make predictions from statistical data and use proportions to make estimates about a population based on a sample Describe how additional data, particularly outliers, added to a data set may affect the mean, median and mode Analyze data displays, including ways that they can be misleading. Analyze ways in which the wording of questions can influence survey results Understand that when all outcomes of an experiment are equally likely, the theoretical probability of an event is the fraction of outcomes in which the event occurs. Use theoretical probability and proportions to make approximate predictions. SE/TE: 409, , 429 SE/TE: 419, 441, , SE/TE: 251, , 256, 258, , 264, 267 SE/TE: 264, , , SE/TE: , , , 572, 573, , 367 SE/TE: , , 573, 596 SE/TE: 53-57, 61 SE/TE: 549, , , 573 SE/TE: , 584, 596, 616 5
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This unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.
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The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
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Mathematics Instructional Materials SAS#.1 (one per pair of students) SAS#.2 (one per pair of students) TIS#.1 (transparency) TIS#.2 (transparency) TIS#.3 (Journal prompt) Isometric Dot Paper Isometric