Prentice Hall Mathematics Course

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1 Prentice Hall Mathematics Grade 8 C O R R E L A T E D T O Grade 8

2 Unit 1: Patterns in Number. This unit begins with a review of operations with integers. Students then explore patterns and use properties of numbers to develop algebraic reasoning and make generalizations. Pre-assess student s ability to compare, order and locate rational and common irrational numbers in addition to assessing their ability to operate with signed numbers. GLE Compare and order rational and common irrational numbers; e.g., -5, 1 16, -4½, 2, pi; and locate them on number lines, scales and coordinate grids. Assess: Have students explain in writing a strategy for finding a number between two given numbers CMT: 4D. Locate points on number lines and scales, including fractions, mixed numbers, decimals and integers CMT: 18C. Locate and draw points on fourquadrant coordinate grids.\ CMT: 4A. Order fractions and decimals including mixed numbers in context CMT: 4B. Describe magnitude or order of mixed numbers, fractions and decimals in context. GLE Compute (using addition, subtraction, multiplication and division) and solve problems with positive and negative rational numbers CMT: 5A. Identify the appropriate operation or equation to solve a story problem CMT: 5B. Write a story problem from an equation CMT: 7A. Add and subtract three-, fourand five-digit whole numbers, money amounts and decimals CMT: 7B. Multiply two- and three-digit whole numbers, money amounts and decimals by one- or two-digit numbers and decimals. Divide two- and three- digit whole numbers, money amounts and decimals by one-digit whole numbers and decimals CMT: 8A. Add and subtract fractions and mixed numbers with reasonable and appropriate denominators CMT: 8B. Multiply whole numbers and fractions by fractions and mixed numbers. SE/TE: T44 SE/TE: 2, 9, 11-13, 45, 50C, 50, 62-65, 99, 212, 438, 440, 629 SE/TE: 13, 50C, 62, SE/TE: 8, 10-11, 12, 15, 17, 18, 20, 63, , 247, , , 295, , 423, 427, , , 463 SE/TE: 104C, , 153, 410 SE/TE: 2, 9, 62-65, 99, 212, 629 SE/TE: 2, 9, 62-65, 99, 212 SE/TE: 50C-50D, 66-69, 71, 72-76, 99, 158, 208, 468 SE/TE: T55, , 263, 278, , 415, 541, 537, 542, 545, 568, 587 SE/TE: 36 SE/TE: T44, 2, 18, 35, 631 SE/TE: T44, 2, 634, 636, 637 SE/TE: T44, 50C, 66-69, 99, 639 SE/TE: 50D, 71, 72-75, 99 1

3 2.2.5 CMT: 8C. Add or multiply positive and negative integers CMT: 9A. Solve multistep problems involving fractions, mixed numbers, decimals and money amounts with or without extraneous information CMT: 9B. Solve multistep problems involving whole numbers, mixed numbers, money amounts and decimals CMT: 9C. Solve multistep problems involving whole numbers, fractions, mixed numbers, decimals or money amounts, and explain how the solution was determined. GLE Solve problems in context that involve repetitive multiplication; e.g., compound interest, depreciation; using tables, spreadsheets and calculators to develop an understanding of exponential growth and decay. Assess: Have students compare investment plans in local banks using appropriate technology and representations CMT: 6B. Multiply two- and three-digit whole numbers, money amounts and decimals by one- or two-digit numbers and decimals. Divide two- and three- digit whole numbers, money amounts and decimals by one-digit whole numbers and decimals. GLE Identify perfect squares and their square roots; e.g., squares 1, 4, 9, 16 to corresponding roots 1, 2, 3, 4 ; and use these relationships to estimate other square roots. GLE Calculate the square roots of positive integers using technology. GLE Use the rules for exponents to multiply and divide with powers of 10 and extend to other bases = 10 5 Add exponents = 2-2 Subtract exponents Assess: Have students explain in writing why n 0 = CMT: 6C. Multiply and divide whole numbers and decimals by 10, 100, 1,000, 0.1 and SE/TE: 2C-2D, 16, 18-19, 20-23, 34, 39, 45, 50, 258 SE/TE: 258C, , 294 SE/TE: 258C, , 294 SE/TE: , 294 SE/TE: , 570 SE/TE: 600 SE/TE: T44, 2, 634, 636, 637 SE/TE: 104C, , 152, T643 SE/TE: 107, 109 SE/TE: 558C-558D, , 575, , 591 SE/TE: 558D, , 591 SE/TE: 91, 635 2

4 GLE Read and represent whole numbers and those between zero and one in scientific notation (and vice versa) and compare their magnitudes CMT: 1A. Identify alternative forms of expressing numbers using scientific notation. GLE Develop and use strategies for multiplying and dividing with numbers expressed in scientific notation using the commutative and associative properties. SE/TE: 50D, 92-96, 99 SE/TE: 50D, 92-96, 99 SE/TE: 558C-558D, 572, 573, 575, 582, , 591 Unit 2: Patterns in Algebra. This unit connects the idea of number patterns to representations with algebraic expressions and equations and leads to furthering students ability to write and solve equations while using their knowledge of number and order of operations from Unit 1. GLE Generalize the relationships in patterns in a variety of ways including recursive and explicit descriptions; e.g., the pattern 1, 4, 7, 10 is represented as follows: recursively as add 3 to the previous number explicitly as 3n + 1 See model lesson CMT: 22A. Identify the missing terms in a pattern, or identify rules for a given pattern using numbers and attributes CMT: 22B. Extend or complete patterns and state rules for given patterns using numbers and attributes. GLE Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations CMT: 23E. Write an expression or equation to represent a situation CMT: 23C. Evaluate expressions or solve equations and use formulas. GLE Write and solve multistep equations using various algebraic methods including the distributive property, e.g., 3 (x + 2) =10), combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions CMT: 23A. Solve simple equations, including two-step equations. SE/TE: , SE/TE: 85, 91, 130, 149, 195, 287, 302, 323, 397, 431, 489, , 552, 570 SE/TE: 85, 91, 130, 149, 195, 287, 302, 323, 397, 431, 489, , , 552, 570 SE/TE: 2C-2D, 4-8, 21-23, 33-36, 39-41, 44, 45, 73, 75, 81-85, 88, 89, 99, 100, 104, 107, 116, 258, 261, 258C, 262, 265, , , 295, 300D, 300, 328, 329, , 347, 369, 370, 376, 405, 470, 504, 558 SE/TE: 2C, 4-8, 44, 560 SE/TE: 2C-2D, 4-8, 21-23, 33-36, 39-41, 44, 45, 73, 75, 81-85, 88, 89, 99, 100, 104, 107, 116, 258, 261, 258C, 262, 265, , , 295, 300D, 300, 328, 329, , 347, 369, 370, 376, 405, 470, 504, 558 SE/TE: 258C, , 295 SE/TE: 2D, 33-36, 38-41, 45, 73, 75, 208, 258C, , 294, 300 3

5 CMT: 23B. Solve multistep problems using algebraic concepts. Assess students ability to write and solve an equation: doc SE/TE: 258C, , 295 SE/TE: Assessments from text: 46, 287, 296 Unit 3: Side and Angle Relationships. This unit relies on students to use previous knowledge to make and test conjectures about side and angle relationships in polygons to formalize their understanding of geometry and connect to algebra. Pre-assess students knowledge of the polygons and their properties. GLE Determine the effect of scale factors (resulting in similar figures) on the perimeters and areas of two-dimensional shapes and the surface areas and volumes of three-dimensional solids CMT: 16A. Measure and determine perimeters, areas and volumes. Explain or show how the solution was determined. GLE Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations CMT: 15A. Estimate lengths, areas, volumes and angle measures. GLE Make and test conjectures about the angle and side relationships to determine that similar figures have congruent angles and corresponding sides proportional and congruent figures have congruent angles and sides CMT: Identify, describe and classify twoand three-dimensional geometric shapes and figures CMT: 17B. Draw, describe and classify two- and three-dimensional geometric shapes and figures. (Connected only.) CMT: 18A. Identify congruent and similar figures CMT: 18B. Draw, classify, describe and/ or explain why figures are similar. GLE Use a coordinate plane to make and test conjectures about changes in the coordinates of the vertices of polygons as a result of a transformation (translation and/or reflection) and describe the results in writing CMT: 17A. Identify, describe and classify two- and three-dimensional geometric shapes and figures. SE/TE: 300 SE/TE: 185 SE/TE: 82, 85, 111, 121, 185, , 347, 352, , , 405 SE/TE: 402, 461 SE/TE: 121, 169, 198, 335, 378, 381, 382, 385, 390, 461, 640 SE/TE: 158C-158D, , 185, 191, 196, , 203, 300C, , 347 SE/TE: 300C-300D, , , , , 347, 352C, , 404 SE/TE: 300D, , , 347, 352C, , 404 SE/TE: , , 347 SE/TE: , 203 SE/TE: 104D, , , , 153 SE/TE: 300C-300D, , , , , 347, 352C, , 404 4

6 3.2.5 CMT: 17B. Draw, describe and classify two- and three-dimensional geometric shapes and figures CMT: 18D. Identify geometric transformations (reflections, rotations and translations) CMT: 18E. Draw geometric transformations (reflections, rotations and translations). GLE Construct and/or examine right triangles and make and test conjectures about the relationships of the angles and sides and develop the Pythagorean theorem. GLE Apply side and angle relationships in geometric figures to solves problems including the Pythagorean theorem and similar figures. Assess: Give students a picture of a right triangle with one leg measuring 8 cm and one angle marked with 45 degrees and ask students to write everything they know about the triangle CMT: 25A. Solve extended numerical and statistical problems. SE/TE: 300D, , , 347, 352C, , 404 SE/TE: 104D, , , , 153 SE/TE: 104D, , 140, , 145, , 153 SE/TE: 104C, 111, , 153 SE/TE: 104C, 111, , , , 153, , 185, 186, , 191, 196, , 201, 203 SE/TE: Similar problems: 111, , , SE/TE: 111, , , , 153, , 185, 186, , 191, 196, , 201, 203 Unit 4: Ratio, Proportion and Percentage. This unit focuses on the application of rational numbers and operations to solve practical problems. These GLEs could be presented in a thematic unit such as personal finance, sports, statistics, community planning, etc. GLE Represent fractions, decimals, mixed numbers and percentages in equivalent forms CMT: 3A. Rename fractions and mixed numbers as equivalent decimals and vice versa CMT: 3B. Rename fractions and decimals as equivalent percents and vice versa CMT: 3C. Identify and/or shade decimals, fractions or percents of regions or sets. GLE Use proportional reasoning to write and solve problems in context CMT: 12A. Solve problems involving ratios CMT: 12B. Solve problems involving proportions in context CMT: 12C. Solve multistep problems involving ratio or proportion, and explain how the solution was determined. SE/TE: 50C, 57-60, 61, 104, 158, 208C, , 252 SE/TE: 50C, 57-60, 61, 104 SE/TE: 208C, , 252 SE/TE: 73, 78, SE/TE: 158C-158D, , 164, , , , 185, , , 196, , 201, 203, 208, SE/TE: , 185, 202, , 587 SE/TE: 158C-158D, , 164, , , , 185, , , 196, , 201, 203, 208, SE/TE: , 164, , , , 185, , , 196, , 201, , 208, , 587 5

7 GLE Solve customary or metric measurement problems in context using Dimensional Analysis (The Unit Factor Method) and justify the results in writing. Performance Task: Kilometers per Mile Problem: palm.sri.com/tasks/6-8/kilometers/index.html CMT - 16C. Solve problems involving conversions and/or operations within customary or metric units of measure. GLE Solve a variety of problems in context involving percents, including the following: Percentage of a number, e.g., If 65 percent of the 250 applicants will be accepted to the Arts Magnet School, how many students will be accepted? The percentage one number is of another number, e.g., Find the percent of students who play soccer if 39 students play soccer out of a total of 387 students. The percentage of a missing amount, e.g., 5 percent of the money from a fundraiser will be donated to a charity. If $25 is donated to the charity, how much money was made from the fundraiser? Percentage increase/decrease, e.g., the number of music downloads have increased from 1,345 per minute to 1,567 per minute. What is the percentage increase? Assess with these percentage problems: In a school poll, 23 percent of the girls voted in favor of a new schedule and 29 percent of the boys voted in favor of a new schedule. If everyone voted, did a majority of people vote in favor of the new schedule? Explain your reasoning and show your work. Or This shopping problem, which compares a discount taken on a discount to just adding the two discounts: CMT: 13A. Find percents of whole numbers or the percent a given number is of another number.13b. Solve problems involving percents in context. SE/TE: 158C, , 202 SE/TE: Similar problems: 158C, , 164, 202 SE/TE: 158C, , 202 SE/TE: 208C-208D, , , , SE/TE: 208C-208D, , , ,

8 GLE Estimate reasonable answers and solve problems in context involving rational and common irrational numbers, ratios and percentages (including percentage of increase and decrease) and justify solutions in writing CMT: 4C. Round mixed numbers, fractions and decimals in context CMT: 11A. Determine a reasonable estimate, and describe the strategy used to arrive at the estimate CMT: 11B. Given an estimate as a solution for problems involving whole numbers, mixed numbers, decimals and percents, judge its reasonableness and justify the decision. Performance Task: Solar Elements at doc SE/TE: 24, 34, 35, 68, 73, 80, 116, 161, 167, 175, 179, 198, , 220, 224, , , , 272, 279, 289, 370, 381, 385, 394, 454 SE/TE: 80, 630 SE/TE: 74, 80, 121, 169, , 252, 262, 263, 335, 372, 378, 381, 382, 385, 390, 630 SE/TE: 80 SE/TE: Similar problems: 2, 62-65, 629 Unit 5: Surface Area and Volume. This unit also relies on students prior knowledge to extend and formalize their understanding of two- and three-dimensional measurement. Students make connections to algebra by moving from concrete understandings to the application of formulas. GLE Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids CMT: 18F. Relate two- and threedimensional representations and vice versa CMT: 16A. Measure and determine perimeters, areas and volumes. Explain or show how the solution was determined CMT: 25A. Solve extended numerical and statistical problems. GLE Develop formulas using measurement strategies and concrete models; and use formulas to determine the volumes of pyramids, cones and spheres. GLE Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context. GLE Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations CMT: 15A. Estimate lengths, areas, volumes and angle measures CMT: 25A. Solve extended numerical and statistical problems. SE/TE: 352C-352D, 367, , 373, , , 461 SE/TE: 363, , 362, , 409 SE/TE: 81-83, 85, 111, 121, 185, , , , 347, 352D, 352, 379, , 386, 387, , , 397, 405 SE/TE: Sample problems: 85, 111, 185, , , 352, 380, 386, , SE/TE: 81-84, 99, , 387, , , 405 SE/TE: 352C-352D, 367, , 373, , 379, , , 387, , , , 409, 461 SE/TE: 402, 461 SE/TE: 121, 169, 198, 335, 378, 381, 382, 385, 390, 461, 640 SE/TE: Sample problems: 81-84, 99, 121, 169, 373, , 387, , , 405 7

9 Unit 5 Assess: Have students select from select from three to four odd shapes objects and create a package that would hold of them. Students should determine the type and amount of material used to create the package, the cost and the amount of space that would be left over after, including the items. Have students justify why their design is the best and show all calculations. SE/TE: Similar problem: 601 Unit 6: Patterns and Functions. This unit focuses on the nature of linear relationships. Students compare situations and their tables and graphs to write and manipulate equations and vice versa. A formal understanding of slope, intercepts and graphing lines from equations should be developed. GLE Determine whether relationships are linear or nonlinear. GLE Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible) CMT: 23D. Represent situations with algebraic expressions or equations CMT: 23E. Write an expression or equation to represent a situation. GLE Examine and make comparisons in writing between linear and non-linear mathematical relationships including y = mx, y = mx 2 and y = mx 3 using a variety of representations. Assess: Have students compare and contrast linear and nonlinear situations, tables, graphs and equations. GLE Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx) CMT: 12C. Solve multistep problems involving ratio or proportion, and explain how the solution was determined. GLE Determine the constant rate of change in a linear relationship and recognize this as the slope of a line. GLE Compare and contrast the slopes and the graphs of lines that have a positive slope, negative slope, zero slope, undefined slope, slopes greater than one and slopes between zero and one. SE/TE: 104C, , 510D, , 553 SE/TE: 104C, , 153, 510D, 527, , 532, 533, , , , , 553 SE/TE: T55, 4-8, 35, 40, 44, , 226, 241, 263, 278, , 415, 454, , 553, 541, 542, 560, 568, SE/TE: T55, 4-8, 35, 40, 44, , 226, 241, 263, 278, , 415, 454, , 553, 541, 542, 560, 568, SE/TE: 546, 548 SE/TE: 546, 548 SE/TE: SE/TE: , 164, , , , 185, , , 196, , 201, , 208, , 587 SE/TE: 510C-510D, , 553 SE/TE: 510C-510D, , 532, 553 8

10 Assess students as they solve a problem involving two cars traveling at various speeds: doc. GLE Compare and contrast the slopes and graphs of lines to classify lines as parallel, perpendicular or intersecting. GLE Interpret and describe slope and y- intercepts from contextual situations, graphs and linear equations. Performance Task: Height of the bounce of a ping-pong ball: GLE Examine systems of two linear equations in context that have a common solution, i.e. point of intersection, using tables, graphs and substitution and interpret the solution CMT: 25A. Solve extended numerical and statistical problems. Unit 6 Performance Task - This activity highlights the "real world" interpretation of graphs: ml. SE/TE: Similar problems: 135, 510C, , 522 SE/TE: 532, 544 SE/TE: 510C-510D, 527, , 532, , 553 SE/TE: Similar problems: 135, 510C, SE/TE: 151, 532, 544 SE/TE: Sample problems: 4-8, 164, , 185, , 196, , 201, , SE/TE: Similar problems: 135, 510C, , 522 Unit 7: Making Decisions with Statistics: This unit focuses on analyzing sets of data and statistical claims as related to real world contexts. GLE Collect, organize and display data using an appropriate representation (including box-and-whisker plots, stem and leaf plots, scatter plots, histograms) based on the size and type of data set and purpose for its use CMT: 19B. Create graphs from data in tables and charts CMT: 24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams, combinations, permutations and transitive reasoning questions. GLE Explain the effects of sample size and sampling techniques (convenience sampling, voluntary response sampling, systematic sampling and random sampling) on statistical claims. SE/TE: 410C-410D, , 423, 426, 428, 432, , , 442, , 448, 449, 453, 455, , , 538, 620, 621 SE/TE: 527, , , 550 SE/TE: 56, 68, 76, 83, 191, 193, 221, 315, 323, 340, 367, 373, , 427, 455, 463, 464, , , 499, 501, 505, 508, 512, 550, 556, 620, 621 SE/TE: 468C, , 505 9

11 GLE Describe in writing the accuracy of statistical claims, e.g., 4 out of 5 dentists prefer Brand X toothpaste, by recognizing when a sample is biased or when data is misrepresented. Assess: Have students compare and write about two graphs. Or compare two graphs at stage_g/10ag2.pdf. GLE Use descriptive statistics, including range, mode, median, mean, quartiles and outliers to describe data and support conclusions in writing CMT: 20C. Solve problems involving means, medians, modes and ranges of sets of data. GLE Identify where measures of central tendency and spread are found in graphical displays including box-and-whisker plots, stem and leaf plots, scatter plots and histograms CMT: 19A. Identify correct information from tables, graphs and charts. GLE Use appropriate representations to compare and analyze large data sets. GLE Make observations and inferences and evaluate hypotheses based on collected and/or experimental data. Performance Task: Predator/Prey Relationships 6-8/ME406/index.html CMT: 20B. State a conclusion and explain why an answer is or is not reasonable based on the data. GLE Make predictions from scatter plots by using or estimating a line-of-best-fit CMT: 20A. Draw reasonable conclusions from data in tables, graphs and charts CMT 25A. Solve extended numerical and statistical problems. SE/TE: SE/TE: Similar problems:432, , , 463 SE/TE: 410C-410D, , 417, , 462 SE/TE: 410C-410D, , 417, 462 SE/TE: , 417, , 442, 462 SE/TE: 223, 427, , 463 SE/TE: 223, 427, , 463 SE/TE: 468C, , 474, , 462 SE/TE: Similar problem: 602 SE/TE: 454 SE/TE: 410D, , 463 SE/TE: 410D, , 463, 468C, , 474, , 462 SE/TE: , 463, , 474, ,

12 Unit 8: Permutations and Combinations. This unit focuses on the exploration of openended problems involving permutations and combinations in order to determine outcomes and probabilities. Suggestions would include spending no more than two weeks on this unit or embedding the concepts into contextual problems that could be solved in previous units. GLE Determine when a situation is a permutation (changing the order results in a different outcome) or a combination (changing the order does not result in a different outcome) CMT: 24A. Solve problems involving the organization of data. GLE Use tree diagrams, lists or the Counting Principle to determine all possible outcomes in permutations and combinations CMT: 24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams, combinations, permutations and transitive reasoning questions. GLE Apply permutations and combinations to predict possible outcomes and find probabilities to solve problems in a variety of contexts CMT: 21A. Identify correct solutions to problems involving elementary notions of probability and fairness expressed as fractions, decimals or percents CMT: 21B. Solve problems involving elementary notions of probability and fairness expressed as fractions, decimals or percents and justify solutions CMT: 21C. Solve problems involving expected outcomes or predictions and justify solutions CMT: 25A. Solve extended numerical and statistical problems. Unit 8 Assess: Have students complete this task on pizza topping combinations at 74.doc. SE/TE: 468D, , , , 505 SE/TE: 410D, , 463, 468C, , 474, , 462 SE/TE: , 474, SE/TE: 56, 68, 76, 83, 191, 193, 221, 315, 323, 340, 367, 373, , 427, 455, 463, 464, , , 499, 501, 505, 508, 512, 550, 556, 620, 621 SE/TE: , 468D, 474, , , 505 SE/TE: 468C, , 474, 504 SE/TE: 468C, , 474, 504 SE/TE: 223, 245, 323, , , 448, , 505 SE/TE: Sample problems: 83, 191, 245, , 323, , , 448, , 505 SE/TE: Similar problem:

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

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