Number Sense And Numeration In grades 9-10 students should be given opportunities to read, write, and use real numbers.

Size: px

Start display at page:

Download "Number Sense And Numeration In grades 9-10 students should be given opportunities to read, write, and use real numbers."

Juliana Daniel
5 years ago
Views:

1 7-10 Mathematics Addendum Content Strands (Grades 9-10) NUMBERS, NUMERATION, OPERATIONS, and NUMBER THEORY Today's mathematics program must be rich in experiences that go far beyond the traditional emphasis on number and operation. Number Sense And Numeration In grades 9-10 students should be given opportunities to read, write, and use real numbers. Have students use Venn diagrams or concept maps to illustrate the relationships among natural numbers, integers, rational numbers, irrational numbers, and real numbers. Given a set of real numbers, students should be able to order them from least to greatest. Students should begin to explore imaginary and complex numbers and their relationship to the set of real numbers. SE/TE: 4-10, 24, 48, 50 Workbook 1-1; Spanish Practice Workbook 1-1; Reading and Math Literacy 1A; Spanish Reading & Literacy 1A SE/TE: 6-10, 24, 48, 50 Workbook 1-1; Spanish Practice Workbook 1-1; Reading and Math Literacy 1A; Spanish Reading & Literacy 1A SE/TE: 255, , 276, 295, 296 Workbook 5-6; Spanish Practice Workbook 5-6; Reading and Math Literacy 5C; Spanish Reading & Literacy 5C; Hands-On Activities 42 Concepts Of Number Operations In Grades 9-10 Students should model the addition and subtraction of polynomials using a concrete manipulative such as Algebra Tiles or Algeblocks, and connect this to the addition and subtraction of whole numbers, fractions, and decimals. Have students connect the multiplication of polynomials to multiplication of whole numbers and fractions using Algebra Tiles or Algeblocks and the area model. Students should have opportunities to apply the field properties in appropriate situations. SE/TE: , , 472, , 495, 504 SE/TE: , 320, , , 345, 354, 356 Workbook 6-3, 6-4, 6-5; Spanish Practice Workbook 6-3, 6-4, 6-5; Reading and Math Literacy 6B; Spanish Reading & Literacy 6B; Hands-On Activities

2 Have students explore the four basic operations from a functional perspective: = 8 is f(3,5) = 8. SE/TE: , , 320, 354, 356 Workbook 6-1, 6-3; Spanish Practice Workbook 6-1, 6-3; Reading and Math Literacy 6A; Spanish Reading & Literacy 6A Computation In Grades 9-10 Students should have opportunities to evaluate algebraic expressions for real number values of the variables. Have students simplify expressions with grouping symbols using the standard algebraic order of operations by hand and by use of a calculator. Have students apply the properties of a field when simplifying expressions. Provide students opportunities to simplify expressions involving scientific notation. Students should perform simple calculations with imaginary and complex numbers. SE/TE: 12-17, 24, 48, 50 Workbook 1-2; Spanish Practice Workbook 1-2; Hands-On Activities 31 SE/TE: 12-17, 24, 48, 50 Workbook 1-2; Spanish Practice Workbook 1-2; Hands-On Activities 31 SE/TE: Skills Handbook: 854 SE/TE: 255, , 276, 295, 296 Workbook 5-6; Spanish Practice Workbook 5-6; Reading and Math Literacy 5C; Spanish Reading & Literacy 5C; Hands-On Activities 42 Estimation And Mental Calculation In Grades 9-10 Provide opportunities for students to use estimation and mental calculation to determine the reasonableness of answers. Have students select and use appropriate mental calculation and estimation strategies to simplify expressions with real numbers when it is appropriate to do so. Continue to encourage estimations of quantities involving length, area, dry volume, temperature, fluid capacity, and weight in metric and customary English units. SE/TE: 12-17, 24, 48, 50 Workbook 1-2; Spanish Practice Workbook 1-2; Hands-On Activities 31 SE/TE: related material: 847,

3 GEOMETRY, MEASUREMENT and TRIGONOMETRY Geometry helps students describe the world in which they live and serves as a natural link to the integration of mathematics across the curriculum. Students need to investigate, experiment, and explore geometric properties using both technology and hands-on materials. Geometry lends itself to having students work in groups; we encourage you to use group work extensively (Davidson, 1990). Geometry And Spatial Sense In Grades 9-10 Have students represent and solve real world problems with two- and three-dimensional geometric models. Using technology, manipulatives, and/or coordinate geometry, have students explore, deduce, and explain the properties of geometric figures. For example, have students explore the relationships among the diagonals in the family of quadrilaterals or the concurrence of the medians, perpendicular bisectors, altitudes, and angle bisectors in a triangle. Provide activities for students to deepen their understanding of congruence and similarity. Have students further explore the basic transformations and extend the work to include dilations and glide reflections; explore the compositions of these transformations. Students should further apply the Pythagorean relationship to the solution of problems. Have students explore short deductive sequences and write simple proofs. SE/TE: 10-16, 17-22, 25-33, 51-58, , , , , , , , , See Prentice Hall Geometry: SE/TE: 36-39, 62, 63, , 257, 281, 296, 298, 304, 311, 340, 350, 621, 631 SE/TE: 100, , 195, 227, 230 SE/TE: , 207, 226, 228, , 581, 582 Workbook 4-4; Spanish Practice Workbook 4-4; Technology Activities 13 SE/TE: 4, 271, 856 TR: Practice, Reteaching, Enrichment See Prentice Hall Geometry: SE/TE: 99, 102, 132, 187, 203, 207, 212, 217, 218, 219, 222, 225, 248, 269, 271, 273, 274, 275, 278, 294, 295, 304, 305, 312, 313, 317, 321, 322, 324, 334, 335, 336, 337, 384, 433, 441, 446, 450, 451, 591, 595, 599, 603, 604, 608, 609, 612, 615 Measurement In Grades 9-10 Students should use appropriate measurements to solve problems. Students should convert commonly used measurements to equivalent ones within a measurement system and find and use appropriate conversion rules between systems when needed. See Prentice Hall Geometry: SE/TE:

4 Students should use dimensional analysis in the solution of real-life problems. Dimensional analysis is a powerful technique which is also used in the science classroom. Students should apply the Pythagorean theorem to solve measurement problems. Have students select appropriate procedures to determine a measure when a direct measurement cannot be made. Have students use ratio and proportion to find the measures of all sides of similar figures; apply this technique to problem solving situations. SE/TE: SE/TE: , 195, 228, 230 SE/TE: Pythagorean Theorem: 4, 271, 856 TR: Practice, Reteaching, Enrichment SE/TE: , 195, 228, 230 SE/TE: , 195, 228, 230 Trigonometry In Grades 9-10 Explore the basic trigonometric ratios of sine, cosine, and tangent with students. Students should use the basic trigonometric ratios to solve real world problems. Have students use technology to investigate periodic phenomenon and relate to sine and cosine functions. SE/TE: , 785, 814, 816 Workbook 14-3; Spanish Practice Workbook 14-3; Reading and Math Literacy 14B; Spanish Reading & Literacy 14B SE/TE: , 785, , , 806, 814, 816 Workbook 14-3, 14-4, 14-5; Spanish Practice Workbook 14-3, 14-4, 14-5; Reading and Math Literacy 14B; Spanish Reading & Literacy 14B - 4 -

5 DATA ANALYSIS, STATISTICS, AND PROBABILITY Collecting, organizing, displaying, and interpreting data, as well as using that information to make predictions and decisions, are extremely important in today's society. However, before collecting data, students need to clearly define the problem and decide what information they will collect in order to solve the problem. Data collection and analysis lend themselves to small group work. Statistical instruction should be investigative and explorative in nature, so that students can answer questions about data. Probability should also be active and engaging, with students experimenting and modeling situations. Students need to investigate fairness, chances of winning, and uncertainty. Technology is an integral tool when students work with data and chance. In Grades 9-10 Have students construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations. Students should use tables, box-and-whisker plots, and stem-and-leaf graphs to analyze data. Have students collect ordered pairs of data, and make a scatter plot. Have students use different linear regression techniques such as the median-median line and other curve fitting techniques to predict trends from data. Have students make use of the several technologies that are available to help do this. Students should understand, find (using technology), and apply measures of central tendency, variability, and correlation. Explore sampling techniques and have students recognize its role in statistical claims. Provide opportunities for students to design statistical experiments to study problems, conduct experiments, and interpret and communicate the outcomes. SE/TE: , 655, 688, 690 Workbook 12-3; Spanish Practice Workbook 12-3; Reading and Math Literacy 12B; Spanish Reading & Literacy 12B SE/TE: 80, 108 SE/TE: 80, 85, 236, 240, 302, 430 SE/TE: 80, 85, 236, 240, 302, 430 SE/TE: , 655, 688, 690 Workbook 12-3; Spanish Practice Workbook 12-3; Reading and Math Literacy 12B; Spanish Reading & Literacy 12B SE/TE: , 677, 689, 690 Workbook 12-5; Spanish Practice Workbook 12-5 SE/TE: , , 655, , , , 677, , , 690 Workbook 12-1, 12-2, 12-4, 12-5, 12-6, 12-7; Spanish Practice Workbook 12-1, 12-2, 12-4, 12-5, 12-6, 12-7; Reading and Math Literacy 12A, 12C; Spanish Reading & Literacy 12A, 12C; Hands-On Activities 55,

6 Have students explore counting principles and tree diagrams as they apply to a sample space. Provide class time to discuss equally likely outcomes and outcomes that are not equally likely and their relationship to probability. Have students conduct experiments and simulations to assign probabilities to events which are not equally likely. Have students explore real world probability situations, such as lotteries and medical testing. Have students interpret real world probabilities and odds, and their relationship. Students should use spreadsheets and statistical graphing software to explore how the same data may be represented through many different kinds of graphs or charts. Discuss how the choice of graph affects the interpretation of the data. SE/TE: , 345, 355, 356 Workbook 6-7; Spanish Practice Workbook 6-7; Reading and Math Literacy 6C; Spanish Reading & Literacy 6C SE/TE: , , 655, 688, 690 Workbook 12-1, 12-2; Spanish Practice Workbook 12-1, 12-2; Reading and Math Literacy 12A; Spanish Reading & Literacy 12C; Hands-On Activities 55 SE/TE: , , 655, 688, 690 Workbook 12-1, 12-2; Spanish Practice Workbook 12-1, 12-2; Reading and Math Literacy 12A; Spanish Reading & Literacy 12C; Hands-On Activities 55 SE/TE: 39-45, 49, 50, , , 655, 688, 690 Workbook 1-6, 12-1, 12-2; Spanish Practice Workbook 1-6, 12-1, 12-2; Reading and Math Literacy 12A; Spanish Reading & Literacy 12C; Technology Activities 36; Hands-On Activities 32, 55 SE/TE: 39-45, 49, 50, , , 655, 688, 690 Workbook 1-6, 12-1, 12-2; Spanish Practice Workbook 1-6, 12-1, 12-2; Reading and Math Literacy 12A; Spanish Reading & Literacy 12C; Technology Activities 36; Hands-On Activities 32, 55 SE/TE: 25, 253, 396, 618 SE/TE: , 655, 688, 690 Workbook 12-3; Spanish Practice Workbook 12-3; Reading and Math Literacy 12B; Spanish Reading & Literacy 12B - 6 -

7 FUNCTIONS, RELATIONS, and ALGEBRA One of the central themes of mathematics is the study of patterns, relations, and functions. This study requires students to recognize, describe, and generalize patterns and build mathematical models to predict the behavior of real-world phenomenon that exhibit the observed pattern. This study of patterns leads to an exploration of functions, a concept which is an important unifying idea in all aspects of mathematics. Functional relationships are of primary importance in many other disciplines such as the natural sciences, business [compound interest], the social sciences, and psychology [learning curves]. Functions And Relations In Grades 9-10 Students should represent and analyze relationships using tables, charts, verbal rules, graphs, and equations. Have students show how the change in one variable affects the value of the other variable in a relationship. Provide opportunities for students to identify relationships that are functions and explain why a relationship is or is not a function. Have students regularly translate among tables, equations, verbal rules, and graphs. Students should recognize when a table, equation, rule, or graph represents the same data and describes the same relationship. SE/TE: 55-61, 86-90, , , , , , Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Spanish Practice Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Reading and Math Literacy 2A; Spanish Reading & Literacy 2A; Technology Activities 5, 9; Hands-On Activities 33 SE/TE: 55-61, 77, 108, 110 Workbook 2-1; Spanish Practice Workbook 2-1; Reading and Math Literacy 2A; Spanish Reading & Literacy 2A; Hands-On Activities 33 SE/TE: 55-61, 86-90, , , , , , Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Spanish Practice Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Reading and Math Literacy 2A; Spanish Reading & Literacy 2A; Technology Activities 5, 9; Hands-On Activities 33 SE/TE: 55-61, 86-90, , , , , , Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Spanish Practice Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Reading and Math Literacy 2A; Spanish Reading & Literacy 2A; Technology Activities 5, 9; Hands-On Activities

8 Students should use functions and relations to predict the outcome of an unobserved value of a variable in a function; apply to statistical prediction. SE/TE: , 719, 758, 760 Workbook 13-1; Spanish Practice Workbook 13-1; Reading and Math Literacy 13A; Spanish Reading & Literacy 13A; Hands-On Activities 63 Algebra In Grades 9-10 Students should solve linear equations and inequalities in one unknown. Have students graph linear equations and inequalities in two unknowns. Have students model division and factoring of polynomials using Algebra Tiles and Algeblocks. Provide students opportunities to discuss the results of doing addition and subtraction of polynomials and connect the adding of like terms to the distributive property. Provide students the opportunity to discuss the use of the distributive property in the process of multiplying two polynomials. Have students explore the sum, difference, product and quotient of two polynomials under various constraints, such as adding or multiplying two polynomials of degree one; students should formulate conjectures about the answers and defend their conjectures. Students should have opportunities to perform the four basic operations on polynomials. SE/TE: 26-31, 38, 50, 62-70, 77, , , 110 Workbook 1-4, 2-2, 2-7; Spanish Practice Workbook 1-4, 2-2, 2-7; Technology Activities 1, 2, 3, 27; Hands-On Activities 34 SE/TE: , , 320, , 345, 354, 356 Workbook 6-2, 6-3, 6-4; Spanish Practice Workbook 6-2, 6-3, 6-4; Reading and Math Literacy 6B; Spanish Reading & Literacy 6B; Hands-On Activities 43 SE/TE: 853 SE/TE: 853 SE/TE: , 320, 354, 356 Workbook 6-3; Spanish Practice Workbook 6-3; Reading and Math Literacy 6B; Spanish Reading & Literacy 6B; Hands-On Activities 43 SE/TE: , 320, 354, 356, 853 Workbook 6-3; Spanish Practice Workbook 6-3; Reading and Math Literacy 6B; Spanish Reading & Literacy 6B; Hands-On Activities

9 Have students discuss and write about the connections between concrete representations with manipulatives (Algebra Tiles or Algeblocks) and the abstract, symbolmanipulating techniques of more traditional algebraic methods. Provide opportunities for students to solve systems of linear equations in two and three unknowns and linear inequalities in two unknowns. Students should represent situations that involve variable quantities using expressions, equations, inequalities, and matrices. Have students develop, construct, and evaluate formulas to solve a variety of real world and mathematical problems. Provide opportunities for students to develop an understanding of the value, importance, and power of abstraction and symbolism. SE/TE: 78-80, 85, 108, 240, 302, 308, , 545, 551, 724 TR: Practice, Reteaching, Enrichment SE/TE: , , , 134, , , , 147, 158, 160 Workbook 3-1, 3-2, 3-3, 3-4, 3-5, 3-6; Spanish Practice Workbook 3-1, 3-2, 3-3, 3-4, 3-5, 3-6; Reading and Math Literacy 3A; Spanish Reading & Literacy 3A; Technology Activities 4; Hands-On Activities 36 SE/TE: 12-17, 18-24, 26-31, 33-37, 62-70, , , , , , , , , , , , Workbook 1-2, 1-3, 1-4, 1-5, 2-2, 2-7, 3-1, 3-3, 5-4, 5-5, 6-4, 7-1, 7-2, 7-3, 7-5, 8-5, 9-6; Spanish Practice Workbook 1-2, 1-3, 1-4, 1-5, 2-2, 2-7, 3-1, 3-3, 5-4, 5-5, 6-4, 7-1, 7-2, 7-3, 7-5, 8-5, 9-6; Reading and Math Literacy 1B, 1C; Spanish Reading & Literacy 1B, 1C; Hands-On Activities 31 SE/TE: 19, 25, 64, , 295, , , , 590, 595, 599, 601, 629, 614, 616, 657, , Workbook 8-5, 14-4, 14-5; Spanish Practice Workbook 8-5, 14-4, 14-5; Reading and Math Literacy 8C; Spanish Reading & Literacy 8C; Technology Activities 12; Hands-On Activities 48 SE/TE:

10 Have students explore non-linear functions that arise from problem situations (quadratic, step, and exponential, for example). Provide opportunities for students to solve linear, quadratic, polynomial, exponential, and other equations using graphing calculators to explore the relationships between the solution of the equations and the zeros of the function. SE/TE: , , , , 417, 418, , 437, , 498, 528, 530 Workbook 5-1, 6-1, 7-7, 8-2, 9-3; Spanish Practice Workbook 5-1, 6-1, 7-7, 8-2, 9-3; Reading and Math Literacy 5A, 6A, 8B; Spanish Reading & Literacy 5A, 6A, 8B; Technology Activities 5, 9, 30, 33 SE/TE: 55-61, 86-90, , , , , 417, 418, , 437, , 498, 528, 530 Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Spanish Practice Workbook 2-1, 2-5, 5-1, 6-1, 7-7, 7-8, 8-2, 9-3; Reading and Math Literacy 2A; Spanish Reading & Literacy 2A; Technology Activities 5, 9; Hands-On Activities 33 MATHEMATICS OF CHANGE All natural phenomena are characterized by change, and mathematics is one of the primary tools used for representing and describing change. Understanding rates of change is a preliminary precursor to the more formal ideas of calculus. Through investigations and explorations of patterns, tables, graphs, and functions which focus on the nature of change, the representation, understanding, and recognition of types of change can be promoted. Real-world examples of change such as unit pricing, rates of speed, and averages should be explored. Fractions, decimals, percents, proportional reasoning, and slopes of lines are integral to this process. In Grades 9-10 Provide opportunities for students to use proportional reasoning and/or dimensional analysis to solve algebraic problems about rates of change. Have students explore number and geometric patterns and predict the tenth, hundredth, and nth terms in the pattern using words and symbols. Students need opportunities to discuss rates of change of functions in graphs, such as the slope of a line or the curvature of a parabola. SE/TE: , , , 605, , , 619, , 632 Workbook 11-1, 11-2, 11-3, 11-4, 11-5; Spanish Practice Workbook 11-1, 11-2, 11-3, 11-4, 11-5; Reading and Math Literacy 11A, 11B, 11C; Spanish Reading & Literacy 11A, 11B, 11C; Technology Activities 35; Hands- On Activities 57, 58 SE/TE: 62-70, , 554, 580, 582 Workbook 2-2, 10-2; Spanish Practice Workbook 2-2, 10-2; Technology Activities 1, 2, 3, 27, 29; Hands-On Activities,

11 Have students recognize and describe different types of change: e.g., arithmetic, geometric, periodic, oscillating, etc. Provide opportunities for students to describe change from both continuous and discrete contexts. Have students analyze and interpret information about change in familiar contexts: e.g., percent of change, average change, or distance per unit of time. Relate ratios and rate of change to concepts from other disciplines: e.g., science (density), social studies (population growth), language arts (sentence complexity or reading level). SE/TE: 62-70, 77, 108, 110, , 554, 580, 582 Workbook 2-2, 10-2; Spanish Practice Workbook 2-2, 10-2; Technology Activities 1, 2, 3, 27, 29; Hands-On Activities, 34 SE/TE: 62-70, 77, 108, 110, , 554, 580, 582 Workbook 2-2, 10-2; Spanish Practice Workbook 2-2, 10-2; Technology Activities 1, 2, 3, 27, 29; Hands-On Activities, 34 SE/TE: 62-70, 77, 108, 110, , 554, 580, 582 Workbook 2-2, 10-2; Spanish Practice Workbook 2-2, 10-2; Technology Activities 1, 2, 3, 27, 29; Hands-On Activities, 34 SE/TE: 62-70, 77, 108, 110, , 554, 580, 582 Workbook 2-2, 10-2; Spanish Practice Workbook 2-2, 10-2; Technology Activities 1, 2, 3, 27, 29; Hands-On Activities, 34 DISCRETE MATHEMATICS Discrete Mathematics is defined as the study of topics which involve items that can be counted rather than continuous quantities which can only be measured. Discrete mathematics is actually an umbrella term which can include such topics as counting techniques, sets, relations, functions, logic, reasoning, and algorithms. Information and communication continue to impact the modern world and require the understanding of topics in discrete mathematics. Decision-making, involving sets and systems having a countable number of elements, needs to be integrated throughout the curriculum. Students should have experience with finite graphs, matrices, sequences, recursion, and the development and testing of algorithms. In Grades 9-10 Have students represent data and solve problems using graphs, trees, and matrices. Provide opportunities for students to use algebraic and geometric iteration to explore patterns and solve problems. SE/TE: , , , 605, , , 619, , 632 Workbook 11-1, 11-2, 11-3, 11-4, 11-5; Spanish Practice Workbook 11-1, 11-2, 11-3, 11-4, 11-5; Reading and Math Literacy 11A, 11B, 11C; Spanish Reading & Literacy 11A, 11B, 11C; Technology Activities 35; Hands- On Activities 57,

12 Students should use combinations and permutations to solve complex counting problems. Have students create their own algorithms to solve optimization problems. Encourage students to create and interpret discrete probability distributions using technology whenever appropriate. Have students explore the use of linear programming to solve problems. Continue to explore elementary logic notions relating to and, or, and ;not statements and relate them to Venn diagrams. Students should explore the relation among an if-then statement and its converse, inverse, and contrapositive statement. Provide opportunities for students to write simple computer programs to solve problems. SE/TE: , 345, 355, 356 Workbook 6-7; Spanish Practice Workbook 6-7; Reading and Math Literacy 6C; Spanish Reading & Literacy 6C SE/TE: , 345, 355, 356 Workbook 6-7; Spanish Practice Workbook 6-7; Reading and Math Literacy 6C; Spanish Reading & Literacy 6C SE/TE: 39-45, 49, 50, , , 655, 688, 690 Workbook 1-6, 12-1, 12-2; Spanish Practice Workbook 1-6, 12-1, 12-2; Reading and Math Literacy 12A; Spanish Reading & Literacy 12C; Technology Activities 36; Hands-On Activities 32, 55 SE/TE: , 141, 147, 159, 160 Workbook 3-4; Spanish Practice Workbook 3-4 SE/TE: 9, 79, 120, 175, 241, 284, , 343, 346, 383, 450, 497, 547, 553, 576, 607, 615, 667, 705, 718, 720, 737, 753, 754, 755, 778, 783, 792, 804, 805 TR: Practice, Reteaching, Enrichment See Prentice Hall Geometry: SE/TE: 82-87, 88, 106, 108, , 283, 284 SE/TE: related material: 25, 141, 177, 253, 396, 407, 430, 542, 618, 622,

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic