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Mississippi Table of Contents Correlation Chart Mississippi Competencies, Objectives, and Depth of Knowledge Levels Letter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Letter to the Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Mississippi Correlation Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Chapter 1 Number and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Lesson 1 Powers and Square Roots . . . . . . . . . . . . . . . .12 1d (DOK 2) Lesson 2 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . .17 1e, 1f (DOK 1) Lesson 3 Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 1b (DOK 2) Lesson 4 Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 1b (DOK 2) Lesson 5 Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . .33 1b (DOK 2) Lesson 6 Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 1b (DOK 2) Lesson 7 Relate Decimals, Fractions, and Percents . . . .46 1c, 1i (DOK 1, 3) Lesson 8 Rates and Proportions . . . . . . . . . . . . . . . . . . .52 1g, 4d (DOK 1, 2) Lesson 9 Applications of Percents . . . . . . . . . . . . . . . . . .57 1g (DOK 1) Lesson 10 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 1b, 1h (DOK 2) Lesson 11 Order of Operations . . . . . . . . . . . . . . . . . . . . .70 1a (DOK 1) Lesson 12 Number Properties . . . . . . . . . . . . . . . . . . . . . .80 2e (DOK 1) Lesson 13 Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86 2a (DOK 2) Lesson 14 Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 2a, 2d, 2f (DOK 1, 2) Lesson 15 Expressions, Equations, and Inequalities . . . . .95 2b, 2c (DOK 1, 2) Lesson 16 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106 3f (DOK 2) Lesson 17 Congruence and Similarity . . . . . . . . . . . . . . .111 3c (DOK 2) Lesson 18 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . .115 3c (DOK 2) Chapter 1 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . . 74 Chapter 2 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Chapter 2 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 100 Chapter 3 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Duplicating any part of this book is prohibited by law. 76MS_Mth_G7_SE_pdf.indd 3 3 8/20/07 4:42:16 PM Mississippi MCT2 Coach, Gold Edition, Mathematics, Grade 7 Lesson 19 Translations, Reflections, and Rotations . . . . .120 3d (DOK 2) Lesson 20 Dilations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128 3d (DOK 2) Lesson 21 Pythagorean Theorem . . . . . . . . . . . . . . . . . . .133 3e (DOK 2) Lesson 22 Three-Dimensional Figures . . . . . . . . . . . . . . .137 3a, 3b (DOK 1, 2) Lesson 23 Units of Measure . . . . . . . . . . . . . . . . . . . . . . .148 4a (DOK 2) Lesson 24 Perimeter and Circumference . . . . . . . . . . . . .154 4b (DOK 2) Lesson 25 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158 4b (DOK 2) Lesson 26 Surface Area and Volume . . . . . . . . . . . . . . . .164 4c (DOK 3) Lesson 27 Measures of Central Tendency . . . . . . . . . . . .176 5b (DOK 2) Lesson 28 Frequency Tables and Scatter Plots . . . . . . . .181 5c (DOK 2) Lesson 29 Box-and-Whisker Plots and Histograms . . . .186 5a, 5c (DOK 2) Lesson 30 Line Graphs and Circle Graphs . . . . . . . . . . . .191 5a, 5c (DOK 2) Lesson 31 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . .197 5d (DOK 2) Chapter 3 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 142 Chapter 4 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Chapter 4 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 170 Chapter 5 Data Analysis and Probability . . . . . . . . . . . . . . . . . . . . . 175 Chapter 5 MCT2 Review . . . . . . . . . . . . . . . . . . . . . . . 203 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 4 76MS_Mth_G7_SE_pdf.indd 4 Duplicating any part of this book is prohibited by law. 8/9/07 5:11:53 PM 1 Powers and Square Roots 1d (DOK 2) Getting the Idea When you multiply a number by itself, the product is called the square of the number. 2 For example, the square of 3 is 9, because 3 3 9. It can also be written as 3 . The 3 is called the base, which is the factor being multiplied. The 2 is called the exponent, 2 which is the number of times you are multiplying the base. 3 can be referred to as three squared or 3 to the 2nd power, where “2nd power” refers to the exponent 2. The square of a whole number is called a perfect square. The perfect squares are 0, 1, 4, 9, 16, 25, and so on. Do you see the pattern? These numbers are simply 2 2 2 2 2 2 0 , 1 , 2 , 3 , 4 , 5 , and so on. EXAMPLE 1 2 What is 15 ? STRATEGY Multiply the base by itself. 15 15 225 SOLUTION 15 225 2 EXAMPLE 2 What is 73? STRATEGY STEP 1 Show the complete multiplication and do the math. Show the multiplication. Use 7 as a factor 3 times. 73 7 7 7 STEP 2 Do the math. 7 7 7 49 7 343 SOLUTION 12 76MS_Mth_G7_SE_pdf.indd 12 3 7 343 Duplicating any part of this book is prohibited by law. 8/9/07 5:12:18 PM Lesson 1: Powers and Square Roots What number would you have to square (multiply by itself) to get 9? Another way to ask this question is: What is the__square root of 9? The answer is 3, because 3 3 9. The square root of 9 is written as √ 9 . So, the square of 3 is 9 and the square root of 9 is 3. Because a perfect square is the square of a whole number, the square root of a perfect square must be a whole number. EXAMPLE 3 ___ What is √ 36 ? STRATEGY Which number, when squared, equals 36? 6 6 6 36 2 SOLUTION ___ √ 36 6 Sometimes, you need to estimate the square root of a number that is not a perfect square. To do this, find the two consecutive whole numbers that the square root falls between. EXAMPLE 4 ____ Between which two whole numbers is √ 139 ? STRATEGY Use guess-and-test. ____ STEP 1 Compare √ 139 to the squares of 10 and 20. 10 10 100 20 20 400 ____ Since 139 is between 100 and 400, √ 139 is between 10 and 20. STEP 2 Find the squares of numbers between ____ 10 and 20 until you find the two consecutive whole numbers that √ 139 falls between. Since 139 is closer to 100 than 400, start with 11. 11 11 121 12 12 144 ____ Since 139 is between 121 and 144, √ 139 is between 11 and 12. SOLUTION ____ √ 139 lies between 11 and 12. Duplicating any part of this book is prohibited by law. 76MS_Mth_G7_SE_pdf.indd 13 13 8/9/07 5:12:24 PM Mississippi MCT2 Coach, Gold Edition, Mathematics, Grade 7 COACHED EXAMPLE What is 24? THINKING IT THROUGH The base is __________ and the exponent is __________. Use the number __________ as a factor __________ times. 24 __________ __________ __________ __________ Simplify. 24 __________ 14 76MS_Mth_G7_SE_pdf.indd 14 Duplicating any part of this book is prohibited by law. 8/9/07 5:12:25 PM Lesson 1: Powers and Square Roots Lesson Practice Choose the correct answer. 1. 5. A. 9–10 What is 172? B. 8–9 A. 219 C. 7–8 B. 239 D. 6–7 C. 269 D. 289 2. 6. Which number is a perfect square? A. 49 B. 56 D. 88 7. ___ What is √ 64 ? A. 6 B. 7 D. 9 What is 53? A. 15 B. 25 C. 53 A. 5 B. 9 C. 49 4 What is 4 ? A. 16 B. 44 C. 256 D. 4,444 C. 8 4. 2 Which is the best estimate of (3.07) ? D. 327 C. 72 3. ___ √ 77 is between which two numbers? ____ 8. What is √ 441 ? A. 19 B. 21 C. 23 D. 27 D. 125 Duplicating any part of this book is prohibited by law. 76MS_Mth_G7_SE_pdf.indd 15 15 8/9/07 5:12:26 PM Mississippi MCT2 Coach, Gold Edition, Mathematics, Grade 7 OPEN-ENDED QUESTION 9. The_____ distance from the northeast corner to the southwest corner of a rectangular swimming pool is √ 1,764 feet. Part A: What is the distance in feet from the northeast corner to the southwest corner, written as a whole number? Part B: Explain how you found your answer. 16 76MS_Mth_G7_SE_pdf.indd 16 Duplicating any part of this book is prohibited by law. 8/9/07 5:12:27 PM