New Jersey: ASK6 Mathematics Third Edition by Jonathan D. Kantrowitz and Ralph R. Kantrowitz Edited by Philip W. Sedelnik Item Code • QXP 3007 • Copyright © 2010 Queue, Inc • 80 Hathaway Drive • Stratford CT 06615 Phone 800 232 2224 • Fax 800 775 2729 www.qworkbooks.com Table of Contents Chapter One Number and Numerical Operations ............................................1 Lesson 1: Number Sense ............................................................................1 Lesson 2: Money ........................................................................................10 Lesson 3: Magnitude of Numbers ..............................................................15 Benchmark Quiz #1 ....................................................................................20 Lesson 4: Ratios and Proportions ..............................................................21 Lesson 5: Percents ....................................................................................26 Lesson 6: Equivalent Whole Numbers, Fractions, and Decimals ..............30 Lesson 7: Primes, Factors, and Multiples ..................................................36 Lesson 8: Comparing and Ordering Numbers............................................43 Benchmark Quiz #2 ....................................................................................49 Lesson 9: Operations ................................................................................51 Lesson 10: Methods of Computation..........................................................56 Benchmark Quiz #3 ....................................................................................67 Lesson 11: Division ....................................................................................69 Lesson 12: Selecting Computational Methods ..........................................78 Lesson 13: Squares and Cubes ................................................................81 Lesson 14: Reasonableness of Computations ..........................................84 Lesson 15: Relationships and Properties of Operations ............................87 Lesson 16: Order of Operations ................................................................90 Lesson 17: Estimation Strategies ..............................................................94 Lesson 18: Appropriateness of Estimations ..............................................98 Lesson 19: Accuracy of Estimates ..........................................................100 Benchmark Quiz #4 ..................................................................................103 Chapter Two Geometry and Measurement ..................................................106 Lesson 20: Lines and Angles ..................................................................106 Lesson 21: Polygons and Circles ............................................................112 Lesson 22: Similar Figures ......................................................................122 Lesson 23: Congruent Figures ................................................................126 Lesson 24: Three-Dimensional Shapes ..................................................131 Lesson 25: Projections ............................................................................136 Lesson 26: Nets........................................................................................142 Benchmark Quiz #5 ..................................................................................148 Lesson 27: Transformations ....................................................................154 Lesson 28: Geometry in Everyday Life ....................................................160 Lesson 29: Coordinate Grids....................................................................166 Lesson 30: Units of Measure....................................................................172 Lesson 31: Scales and Proportions..........................................................176 Benchmark Quiz #6 ..................................................................................180 Lesson 32: Conversion Units....................................................................182 Lesson 33: Equivalent Measures ............................................................186 Benchmark Quiz #7 ..................................................................................190 Lesson 34: Measuring Angles ..................................................................191 Lesson 35: Perimeter and Area................................................................195 Lesson 36: Surface Area and Volume ......................................................203 Lesson 37: Area and Perimeter Relationships ........................................211 Lesson 38: Approximating Measures ......................................................215 Benchmark Quiz #8 ..................................................................................218 Chapter Three Patterns and Algebra ..............................................................220 Lesson 39: Number Patterns....................................................................220 Lesson 40: Graphs of Functions ..............................................................230 Lesson 41: Modeling ................................................................................238 Lesson 42: Graphing Information ............................................................243 Benchmark Quiz #9 ..................................................................................248 Lesson 43: Solving Equations ..................................................................252 Lesson 44: Properties of Operations........................................................256 Lesson 45: Evaluating ..............................................................................260 Lesson 46: Inequalities ............................................................................263 Benchmark Quiz #10 ................................................................................266 Chapter Four Data Analysis, Probability, and Discrete Mathematics ............268 Lesson 47: Collecting and Displaying Data..............................................268 Lesson 48: Data Analysis ........................................................................283 Lesson 49: Probability ..............................................................................290 Lesson 50: Determining Probabilities ......................................................295 Lesson 51: Compound Events ................................................................299 Benchmark Quiz #11 ................................................................................303 Lesson 52: Concepts of Probability..........................................................306 Lesson 53: Multiple Outcomes ................................................................309 Lesson 54: Combinations and Permutations............................................317 Benchmark Quiz #12 ................................................................................325 Lesson 55: Strategies and Directions ......................................................328 Lesson 56: Vertex-Edge Graphs ..............................................................331 Lesson 33 4.2.6.D.4 Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). Equivalent Measures Remember what you have learned about estimating the values of numbers. Estimating is very important when converting between metric and customary units. Although it is relatively simple to convert kilometers to meters, you need to understand how to convert kilometers to miles as well. The list below shows some basic conversions between the two different systems of measurements. The ≈ sign means “approximately equal to.” All of these relationships are estimates, not exact calculations. 1 1 1 1 km ≈ 0.6 mile inch ≈ 2.5 centimeters foot ≈ 30 cm meter ≈ 3.25 feet Example 1: Laquisha ran a 10 km race to raise money for a charity. About how many miles are in 10 km? Step 1: Find the approximate conversion factor. 1 km ≈ 0.6 mile Step 2: Use the conversion factor to set up a proportion. 1/10 = .6/? Reproducing copyrighted material is against the law! 186 © 2010 Queue, Inc. All rights reserved. Step 3: Solve the proportion. Since 1 x 10 = 10, the second ratio is greater than the first by a factor of 10. So, multiply the denominator by 10 to find the missing value. 0.6 x 10 = 6 Laquisha ran about 6 miles in her race. Example 2: Rowena is 5.5 feet tall. About how many centimeters is that? Step 1: Find the approximate conversion factor. 1 foot ≈ 30 cm Step 2: Use the conversion factor to set up a proportion. 1/30 = 5.5/? Step 3: Solve the proportion. Since 1 x 5.5 = 5.5, the second ratio is greater than the first by a factor of 5.5. So, multiply the denominator by 5.5 to find the missing value. 30 x 5.5 = 165 Rowena is about 165 cm tall. © 2010 Queue, Inc. All rights reserved. 187 Reproducing copyrighted material is against the law! Example 3: Ned found a worm in his back yard that was 7.5 cm long. About how many inches long is the worm? Step 1: Find the approximate conversion factor. 1 inch ≈ 2.5 cm For this problem, since we start with centimeters, it is best to reverse this approximation. 2.5 cm ≈ 1 inch Step 2: Use the conversion factor to set up a proportion. 2.5 = 7.5 1 x Step 3: Solve the proportion. Cross-multiply to find the ratio. 2.5x = 1 x 7.5 2.5x = 7.5 x=3 x = 3, so the worm must be 3 inches long. Reproducing copyrighted material is against the law! 188 © 2010 Queue, Inc. All rights reserved. Practice Solve the following: 1. 1.2 miles ≈ _____ kilometers 2. 5 centimeters ≈ _____ inches 3. 60 centimeters ≈ _____ feet 4. 6.5 feet ≈ _____ meters 5. 8 meters ≈ _____ feet 6. 8 inches ≈ _____ centimeters 7. 8 feet ≈ _____ centimeters 8. 8 kilometers ≈ _____ miles 9. 1 yard ≈ _____ centimeters ≈ _____ meters 10. A sign in France said the speed limit was 100 km/hour. That is the same as A. B. C. D. 160 m.p.h. 100 m.p.h. 66 m.p.h. 60 m.p.h. © 2010 Queue, Inc. All rights reserved. 189 Reproducing copyrighted material is against the law! Benchmark Quiz #7 1. 60 inches = _________ ft 2. 2 yards = _________ in 3. 10 pounds = _________ ounces 4. 2,000 centimeters = _________ meters 5. 4 gallons = ________ quarts 6. 10 inches equal about _____ centimeters. a. b. c. d. 7. 3.5 2.5 35 25 2 kilometers equal about _______ miles. a. c. c. d. 8. a. b. c. d. 9. .6 6 1.2 12 Reproducing copyrighted material is against the law! 1 kilogram equals about _______ pounds. 1 gallon equals about ________ liters. a. b. c. d. 190 .22 2.2 .45 4.5 4 1 .4 .1 © 2010 Queue, Inc. All rights reserved.