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STUDY LINK 21 Large Numbers 41 4 Name Date Time Copyright © Wright Group/McGraw-Hill ,,,, 100,000,000,000,000 10,000,000,000,000 1,000,000,000,000 100,000,000,000 10,000,000,000 1,000,000,000 100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1 trillions billions millions thousands ones 1. Write the digit in each place of the number 6,812,507,439. a. millions b. hundred thousands c. ten millions d. billions e. hundred millions f. ten thousands 2. Write each of the following numbers in standard form. a. four hundred thirty thousand b. ninety million, one hundred five thousand c. one hundred seventy million, sixty-five d. nine billion, five hundred million, two hundred forty-three thousand 3. Write each number in expanded form.Example:235 (2 º 100) (3 º 10) (5 º 1) a. 321,000 b. 7,300,000,000,000 c. 2,510,709 4. Use extended facts to complete the following. a. 1 million 1,000 º b. 1 billion 1,000 º c. 1 trillion 1,000 ºSTUDY LINK 21 Large Numbers continued Copyright © Wright Group/McGraw-Hill 42 Name Date Time ,,,, trillion billion million thousand Because the orbits of the planets are elliptical in shape, the distance between two planets changes over time. The least distances of Mercury, Venus, Saturn, and Neptune from Earth appear in the table at the right. The distances are approximations. 5. Write each planet’s least distance from Earth in number-and-word notation. a. Mercury b. Venus c. Saturn d. Neptune 6. Write the following numbers in standard notation. a. 44.3 billion b. 6.5 trillion c. 0.9 million d. 0.7 hundred Least Distance from Earth Planet Distance (in miles) Mercury 48,000,000 Venus 25,700,000 Saturn 850,000,000 Neptune 2,680,000,000 Round each number to the given place. 7. 416,254; hundreds 8. 234,989; ten thousands 9. 1,857,000; hundred thousands 10. 6,593,278; millions Practice
LESSON 21 Name Date Time Walking Away with a Billion Dollars 43 Copyright © Wright Group/McGraw-Hill Suppose you inherit one billion dollars. The bank pays you the entire amount of money in $100 bills. About how much will your payment weigh in tons? Use the information below to solve the problem. Show all your work. Write an explanation that is clear and easy to follow. You can cover a sheet of paper with about six $100 bills. There are 500 sheets in a ream of paper. There are 10 reams in 1 carton of paper. One ream of paper weighs about 5 pounds. One ton equals 2,000 pounds.
STUDY LINK 22 Writing Decimals Copyright © Wright Group/McGraw-Hill 44 26 –28 Name Date Time 1. Build a numeral. Write: 2. Build a numeral. Write: 9 in the thousandths place, 3 in the tenths place, 4 in the tenths place, 6 in the ten-thousandths place, 8 in the ones place, 4 in the hundredths place, 3 in the tens place, and 0 in the thousandths place, and 6 in the hundredths place. 1 in the ones place. Answer: Answer: .. Write the following numbers in words. 3. 0.8 4. 0.95 5. 0.05 6. 0.067 7. 4.0802 Write a decimal place value in each blank space. 8. Bamboo grows at a rate of about 0.00004, or four , kilometer per hour. 9. The average speed that a certain brand of catsup pours from the mouth of the bottle is about 0.003, or three , mile per hour. 10. A three-toed sloth moves at a speed of about 0.068 to 0.098, or sixty-eight to ninety-eight , mile per hour.
STUDY LINK 22 Writing Decimals continued 45 Name Date Time Copyright © Wright Group/McGraw-Hill Write each of the following numbers in expanded notation. Example:2.756 (2 º 1) (7 º 0.1) (5 º 0.01) (6 º 0.001) 11. 0.013 12. 109.3527 13. Using the digits 0, 3, 6, and 8, write the greatest decimal number possible. . 14. Using the digits 0, 3, 6, and 8, write the least decimal number possible. . 100 10 1 0 0 0 0 0 0 ones tens hundreds thousandths hundredths tenths millionths hundred-thousandths ten-thousandths . .1 .01 .001 .0001 .00001 .000001 and Try This Name the point on the number line that represents each of the following numbers. 15. 0.66 16. 0.6299 17. 0.6 18. 0.695 19. Refer to the number line above. Round 0.6299 to the nearest hundredth. 0.60.7 0.65 CA D B 20. 0.01 0.006 0.0008 21. 0.7 0.04 0.0002 22. 40 5 0.009 23. 0.50 0.080 0.00010 Practice
LESSON 22 Name Date Time Modeling and Comparing Decimals 46 Copyright © Wright Group/McGraw-Hill One way to compare decimals is to model them with base-10 grids. The flat is the whole, or 1.0.The long is wor th 0.1.The cube is wor th 0.01.The fractional part of the cube is wor th 0.001. Another way to compare decimals is to draw pictures. 1. Use decimal models to complete the following. 1.0 0.10 º 0.10 0.01 º 0.01 0.001 º Model the decimal numbers in each pair. Draw a picture to record each model. Then compare the decimal numbers using , , or . 2. 3. 0.3 0.14 1.56 1.562 4. 5. Model and record a decimal number that is between 0.41 and 0.42. 0.2 0.025 0.41 0.42 The flat is the whole, or 1.0.The long is wor th 0.1.The cube is wor th 0.01.The fractional part of the cube is wor th 0.001.
Copyright © Wright Group/McGraw-Hill Solve. 1. The fastest winning time for the New York Marathon (Tesfay Jifar of Ethiopia, 2001) is 2 hours, 7.72 minutes. The second fastest time is 2 hours, 8.017 minutes (Juma Ikangaa of Tanzania, 1989). How much faster was Jifar’s time than Ikangaa’s? 2. In the 1908 Olympic Games, Erik Lemming of Sweden won the javelin throw with a distance of 54.825 meters. He won again in 1912 with a distance of 60.64 meters. How much longer was his 1912 throw than his 1908 throw? 3. Driver Buddy Baker (Oldsmobile, 1980) holds the record for the fastest winning speed in the Daytona 500 at 177.602 miles per hour. Bill Elliott (Ford, 1987) has the second fastest speed at 176.263 miles per hour. How much faster is Baker’s speed than Elliott’s? 4. The highest scoring World Cup Soccer Final was in 1954. Teams played 26 games and scored 140 goals for an average of 5.38 goals per game. In 1950, teams played 22 games and scored 88 goals for an average of 4 goals per game. What is the difference between the 1954 and the 1950 average goals per game? 5. 46.09 123.047 Estimate 6. 0.172 4.5 Estimate 46.09 123.047 0.172 4.5 STUDY LINK 23 Name Date Time Sports Records 47 31–33 257 Solve mentally. 7. $0.36 $0.29 $0.64 $2.00 8. 7.03 14.05 13.07 35 9. 9.225 8.5 5.775 25 10. $3.69 $8.31 $6.25 $25 Practice
LESSON 23 Name Date Time Modeling Subtraction of Decimals 48 Copyright © Wright Group/McGraw-Hill You can model subtraction of decimals using base-10 grids or pictures. For example, to solve 1.237 – 0.645, first represent 1.237, adjust by trading, and then subtract. Use base-10 grids or pictures to find each difference. Show your work. 1. 3.6 2.973 2. 2.0 0.761 3. 1.7 0.083 1s 0.1s 0.01s 0.001s 1s 0.1s 0.01s 0.001s • • • • • • • • • 1s 0.1s 0.01s 0.001s 0.592 left trade trade Subtract 0.645
49 Name Date Time Copyright © Wright Group/McGraw-Hill Multiply. 1. 4.9 º 0.001 2. 7.8 º 0.01 3. 30 º 10 1 4. 7 º 10 2 5. 0.15 º 10 3 6. 1.9 º 100 7. 37.6 º 10 2 8. 42.8 º 10 3 9. Mathematician Edward Kasner asked his 9-year-old nephew to invent a name for the number represented by 10 100 . The boy named it a googol.Later, an even larger number was named—a googolplex.This number is represented by 10 googol , or 10 10100. a. How many zeros are in the standard form of a googol, or 10 100 ? b. One googolplex is 1 followed by how many zeros? 10. The speed of computer memory and logic chips is measured in nanoseconds. A nanosecond is one-billionth of a second, or 10 9 second. Write this number in standard form. 11. Light travels about 1 mile in 0.000005 seconds. If a spacecraft could travel at this speed, it would travel almost 10 6miles in 5 seconds. About how far would this spacecraft travel in 50 seconds?miles STUDY LINK 24 Multiplying by Powers of 10 Some Powers of 10 10 4 10 3 10 2 10 1 10 0 . 10 1 10 2 10 3 10 4 10 º 10 º 10 º 10 10 º 10 º 10 10 º 10 10 1 . 11 0 11 0º11 0 11 0º11 0º11 0 11 0º11 0º11 0º11 0 10,000 1,000 100 10 1 . 0.1 0.01 0.001 0.0001 Mentally calculate your change from $10. 12. Cost: $4.75; Change: 13. Cost: $3.98; Change: 14. Cost: $0.89; Change: 15. Cost: $8.46; Change: Practice
LESSON 24 Name Date Time “What’s My Rule?” 50 Copyright © Wright Group/McGraw-Hill For each problem, complete the table and find the rule. Use Problem 4 to write your own “What’s My Rule?” problem. 1. Rule: 2. Rule: in out $10 $100 $25 $1,450 $7,985 $2,300,000 in out $0.10 $3.00 $30.00 $500.00 $88.50 $235.75 in out $0.90 $0.09 $5.00 $0.50 $2.00 $760 $1,000 in out 3. Rule: 4. Rule:
STUDY LINK 25 51 37 38 Name Date Time Copyright © Wright Group/McGraw-Hill Multiply. 1. 23 2. 56 3. 124 º87 º 23 º 96 4. Use your answer for Problem 1 5. Use your answer for Problem 3 to place the decimal point in to place the decimal point in each product. each product. a. 2.3 º 8.7 a. 124 º 9.6 b. 23 º 0.87 b. 1.24 º 9.6 c. 2.3 º 87 c. 12.4 º 0.96 Two new U.S. nickels were issued in 2004. A likeness of Thomas Jefferson remained on the front of the nickels. The reverse side featured images commemorating either the Louisiana Purchase or the Lewis and Clark expedition. 6. A U.S. nickel is 1.95 mm thick. a. Estimate the height of a stack of 25 nickels. Estimate mm b. Calculate the actual height of the stack in mm. mm c. How much is a stack of 25 nickels worth? Multiplying Decimals: Part 1 Multiply by 0.10 to find 10% of each number. 7. 10% of $50.00 8. 10% of $110.00 9. 10% of 345 10. 10% of 0.70 Practice
LESSON 25 Name Date Time Estimating and Calculating Cost 52 Copyright © Wright Group/McGraw-Hill Suppose you have $25.00 to spend on snacks for your basketball team. You need to purchase 25 pieces of fruit and 25 beverages. The table below shows the food items available and the cost of each item. 1. Make a table of the items you will buy, how many of each item, and the cost. Remember that you can spend up to $25.00 but not more than $25.00. Your table might have four columns with these headings: Food Item, Number of Items, Cost per Item, and Subtotals. 2. Explain how you decided which items to buy and how many of each item. Fruit Cost Beverages Cost Banana $0.42 Fruit punch $0.65 Apple $0.28 Orange juice $0.50 Orange $0.41 Bottled water $0.75
LESSON 25 Name Date Time Whole Number Multiplication 53 Copyright © Wright Group/McGraw-Hill Use your favorite multiplication algorithm to find the following products. Show your work in the computation grid below or on a separate sheet of paper. 1. 16 º 17 2. 32 º 45 3. 4 º 186 4. 89 º 51 5. 724 º 6 6. 26 º 32 7. 9 º 5,668 8. 37 º 487
STUDY LINK 26 Copyright © Wright Group/McGraw-Hill 54 37–39 Name Date Time Place a decimal point in each problem. 1. 2 4 3 º 7.06 171.558 2. 16.4 º 0.7 1 1 4 8 3. 8 2 7 º 9.5 7.8565 4. 7 5 6 3 º 5.1 3,857.13 Multiply. Show your work on a separate sheet of paper or on the back of this page. 5. 2.28 º 7.9 6. 49.7 º 0.6 7. 3.84 º 13 8. 0.19 º 53.9 Solve each problem. Then write a number model. (Hint: Change fractions to decimals.) 9. Janine rides her bike at an average speed of 11.8 miles per hour. At that speed, about how many miles can she ride in 6 1 2hours? Number Model 10. Kate types at an average rate of 1.25 pages per quarter hour. If she types for 2 3 4hours, about how many pages can she type? Number Model 11. Find the area in square meters of a rectangle with length 1.4 m and width 2.9 m. Number Model Multiplying Decimals: Part 2 Multiply mentally by 0.10 to find 10%. Then mentally calculate the percent that has been assigned to each number. 12. 20% of $80.00 13. 5% of $220.00 14. 15% of 640 15. 30% of 80 = Practice
LESSON 26 Name Date Time A Mental Multiplication Strategy 55 Copyright © Wright Group/McGraw-Hill The same strategy was used to solve both example problems below. This strategy can also be used to multiply numbers mentally. 1. Explain the strategy. 2. Use the strategy to solve the problems below. Show your work. a. 16 º 1.5 b. 18 º 3.5 c. 20 º 0.75 d. 0.125 º 16 3. Solve these problems mentally. a. 8 º 7.5 b. 24 º 1.25 4. Make up two problems that can be solved using a mental multiplication strategy. a. b. ➤ ➤ ➤ ➤ 16 º 2.5 16 / 2 2.5 º 2 8º 5 ➤ ➤ 72 º 0.125 72 / 2 0.125 º 2 36 º 0.25 36 / 2 0.25 º 2 18 º 0.50 Example 1: Example 2: 16 º 2.5 8 º 5 40 72 º 0.125 18 º 0.50 9
LESSON 26 Name Date Time Modeling Decimal Multiplication 56 Copyright © Wright Group/McGraw-Hill You can use an area model to find a product. Example:0.3 º 0.5 Shade 0.3 of Next, shade 0.5 of The product is the area that is the grid this way: the grid this way: double-shaded this way: Since 0.15 of the grid is double-shaded, 0.3 º 0.5 0.15. 0.3 0.30.5 Shade each factor. Then find the product. 1. 0.9 º 0.4 2. 0.7 º 0.6 0.9 º 0.4 0.7 º 0.6 3. 0.5 º 0.5 4. Write your own problem. 0.5 º 0.5 º
STUDY LINK 2 7 57 42–43 Name Date Time Copyright © Wright Group/McGraw-Hill 3 Ways to Write a Division Problem 246 12 ∑ 20 R6 122 46 ∑ 20 R6 246 / 12 ∑ 20 R6 2 Ways to Express a Remainder 122 46 ∑ 20 R6 122 46 20 16 2, or 20 1 2 When estimating quotients, use “close” numbers that are easy to divide. Example:346 / 12 Estimate How I estimated: 1. 234 / 6 Estimate How I estimated: 2. 659 / 12 Estimate How I estimated: 3. 512 / 9 Estimate How I estimated: 4. 1,270 / 7 Estimate How I estimated: 5. 728 / 34 Estimate How I estimated: Solve using a division algorithm. Show your work on a separate sheet of paper or a computation grid. 6. 85 34 7. 976 / 15 8. 98020 9. 468 43 10. 6,024 / 38 11. 5,58644 350 / 10 = 35 35 Dividing Numbers Multiply mentally. 12. 2 notebooks at $1.99 each 13. 4 pens at $2.96 each 14. 3 books at $24.98 each 15. 5 gifts at $99.99 each Practice
STUDY LINK 28 Dividing Decimals Copyright © Wright Group/McGraw-Hill 58 Name Date Time For each problem, follow the steps below. Show your work on a separate sheet of paper or a computation grid. Estimate the quotient. Use numbers that are close to the numbers given and that are easy to divide. Write your estimate. Then write a number sentence to show how you estimated. Ignore any decimal points. Divide as if the numbers were whole numbers. Use your estimate to insert a decimal point in the final answer. 1. 19.76 8 Estimate How I estimated Answer 2. 78.8 / 4 Estimate How I estimated Answer 3. 85.8 / 13 Estimate How I estimated Answer 4. 51.8 / 7 Estimate How I estimated Answer 5. Find 17 6. Give the answer as a decimal with 2 digits after the decimal point. 6. Five people sent a $36 arrangement of flowers to a friend. Divide $36 into 5 equal shares. How much is 1 share, in dollars and cents? Divide mentally to find the price for 1 pound (lb). 7. $3.98 for 2 lb $ per 1 lb 8. $16.88 for 4 lb $ per 1 lb 9. $45.80 for 5 lb $ per 1 lb 10. $299.10 for 10 lb $ per 1 lb Practice 42–45
STUDY LINK 29 Using Scientific Notation 59 Name Date Time Copyright © Wright Group/McGraw-Hill Write each number in standard notation. 1. 1.24 º 10 4 2. 3.5 º 10 3 3. 8 º 10 6 4. 7.061 º 10 8 Change the numbers given in standard notation to scientific notation. Change the numbers given in scientific notation to standard notation. 5. Light travels about 11,802,000,000, or , inches per second. 6. A bacterium can travel across a table at a speed of 1.6 º 10 4 , or , km per hour. 7. One dollar bill has a thickness of 0.0043, or , inches. 8. The mass of 1 million pennies is approximately 2.835 º 10 6, or , grams. Use , , or to compare each pair of numbers. 9. 10 2 10 3 10. 1.23 º 10 3 11 ,0.2 03 0 11. 9.87 º 10 5 1.2 º 10 6 12. 5.4 º 10 1 9.6 º 10 4 13. Explain how you can tell whether a number written in scientific notation is less than 1. Solve mentally. 14. 3,625 3,999 15. 8.7 4.99 16. 4 º 225 17. 100,000 / 500 18. 683 298 19. 387 499 Practice 78
LESSON 29 Name Date Time Ground Areas of Buildings 60 Copyright © Wright Group/McGraw-Hill The approximate ground areas of some famous buildings are given below in scientific notation. To the left of the photograph of each building is its ground plan. Convert the scientific notation to standard notation. 1. Great Pyramid of Giza (Egypt; c. 2580 B.C.)º 5.7 º 10 5, or , ft 2 2. Roman Colosseum (Rome, Italy; 70–224) º 2.5 º 10 5, or , ft 2 3. St. Peter’s Basilica (Vatican City; 1506–1626) º 3.9 º 10 5, or , ft 2 4. Taj Mahal (Agra, India; 1636–1653) º 9.8 º 10 4, or , ft 2 ºLocation and date(s) of construction
LESSON 29 Name Date Time 61 Copyright © Wright Group/McGraw-Hill Ground Areas of Buildings continued 5. Pentagon (Arlington, Virginia, United States; 1941–1943) º 1.3 º 10 6, or , ft 2 º Location and dates of construction Source: Comparisons 6. Use the information in Problems 1–5 to write two comparisons. a. Ratio comparison (The area of one building is xtimes larger [or smaller] than the area of another building.) b. Difference comparison (The area of one building is xsquare feet more [or less] than the area of another building.) 7. Try to find out the ground area of a large building, such as your school, a shopping mall, an historic landmark, a sports arena, or a factory. How does that building’s ground area compare to the ground area of each building pictured in Problems 1– 5?
LESSON 29 Name Date Time Patterns and Powers of 10 62 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Use any patterns you notice to fill in the blanks. 10 510 01 1010,000 10 1 0.1 10 31,000 10 0.01 10100 10 3 10 110 0.0001 What do you notice about the number of digits after the decimal point and the negative powers of 10? LESSON 29 Name Date Time Patterns and Powers of 10 Use any patterns you notice to fill in the blanks. 10 510 01 1010,000 10 1 0.1 10 31,000 10 0.01 10100 10 3 10 110 0.0001 What do you notice about the number of digits after the decimal point and the negative powers of 10?
STUDY LINK 210 Exponential Notation 63 Name Date Time Copyright © Wright Group/McGraw-Hill Use your calculator to write each number in standard notation. 1. 72 2. (0.25) 2 3. 43 4. (0.41) 3 5. 10 5 6. (2.5) 3 Use digits to write each number in exponential notation. 7. three to the ninth power 8. eight to the seventh power 9. eleven to the negative third power 10. five-tenths to the negative sixth power Write each number as a product of repeated factors. Example:5 35 º 5 º 5 11. (1 2)5 12. 10 2 13. 10 6 14. You can find the total number of different 4-digit numbers that can be made using the digits 1 through 9 by raising the number of choices for each digit (9) to the number of digits (4), or 9 4. Based on this pattern, how many different 5-digit numbers could you make from the digits 1 through 8? Solve mentally. 15. 15.321.88 16. 7,200 / 90 17. 4.983.99 18. 8 º 525 Practice 6
LESSON 210 Name Date Time Binary Numbers 64 Copyright © Wright Group/McGraw-Hill The table below shows how to write whole numbers 1 through 10 as binary numbers. A binary number is written with a subscripted twoto distinguish it from a base-ten number. To write a binary number as a base-ten number, first write the binary number in expanded notation. Then convert to standard form. Example:11111 two (1 º 2 4)(1 º 2 3) (1 º 2 2) (1 º 2 1) (1 º 2 0) (1 º 16) (1 º 8) (1º4)(1º2)(1º1) 16 84 2 1 31 Use the table and example above to write each binary number as a base-ten number. 1. 1011 two 2. 101110 two 3. 1110101 two 4. 111101 two 5. 1000001 two 6. 1111111 two Powers of 2 26 25 24 23 22 21 20 Base-Ten Number Binary Number64 32 16 8 4 2 1 11 two 1 º 2 0 210 two 1 º 2 1 0 º 2 0 311 two 1 º 2 1 1 º 2 0 4 100 two 1 º 2 2 0 º 2 1 0 º 2 0 5 101 two 1 º 2 2 0 º 2 1 1 º 2 0 6 110 two 1 º 2 2 1 º 2 1 0 º 2 0 7 111 two 1 º 2 2 1 º 2 1 1 º 2 0 8 1000 two 1 º 2 3 0 º 2 2 0 º 2 1 0 º 2 0 9 1001 two 1 º 2 3 0 º 2 2 0 º 2 1 1 º 2 0 10 1010 two 1 º 2 3 0 º 2 2 1 º 2 1 0 º 2 0 Try This Use patterns in the table to write the binary number for each number. 7. 21 8. 68 9. 100
STUDY LINK 211 Scientific Notation 65 Name Date Time Copyright © Wright Group/McGraw-Hill Write the following numbers in scientific notation. 1. 0.0036 2. 0.0007 3. 80,000 4. 600 thousand Write the following numbers in standard notation. 5. 5 º 10 4 6. 4.73 º 10 9 7. 4.81 º 10 7 8. 8.04 º 10 2 Write the next two numbers in each pattern. 9. 1 º 10 1 ; 0.1; 1 º 10 2 ; 0.01; ; 10. 0.01, 0.002, 0.0003, , Solve the following problems. Write each answer in scientific notation. 11. (4 º 10 3) 10 2 12. 10 3(2 º 10 1) 13. (5 º 10 1 ) 0.02 14. (7 º 10 4) 10 3 15. Use a calculator to complete the table. Find the missing digits to complete each number sentence. 16. , 63 – 3,9 9 2,83 17. 71, 4 – 4,8 6 6 ,270 Problem Calculator Display Scientific Notation Standard Notation 5,000,000 2 90 4300 2 20 330 2 10 4 º10 4 520 / 5 16 Practice 78
LESSON 211 Name Date Time Practicing Calculator Skills 66 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill 66 Use your calculator to complete the table. LESSON 211 Name Date Time Practicing Calculator Skills Use your calculator to complete the table. Problem Scientific Notation Standard Notation 100,000 3 1 º 10 15 1,000,000,000,000,000 20,000 5 30 830 8 800 4400 2 10 7º 10 7 7 70 0 1 42 Problem Scientific Notation Standard Notation 100,000 3 1 º 10 15 1,000,000,000,000,000 20,000 5 30 830 8 800 4400 2 10 7º 10 7 7 70 0 1 42
67 Copyright © Wright Group/McGraw-Hill STUDY LINK 212 Unit 3: Family Letter Name Date Time Variables, Formulas, and Graphs In Unit 3, students will be introduced to variables—symbols such as x, y,andm—that stand for a specific number or any number in a range of values. The authors of Everyday Mathematicsbelieve that work with variables is too important to be delayed until high- school algebra courses. The problem “Solve 3x4052” might be difficult for some high-school students because they see it as merely symbol manipulation. Problems such as these are posed to Everyday Mathematicsstudents as puzzles that can be unraveled by asking, “What number makes the equation true?” I need to add 12 to 40 to get 52. Three times what number yields 12? The answer is x4. In addition to being used in algebraic equations, variables are also used to describe general patterns, to form expressions that show relationships, and to write rules and formulas. Unit 3 will focus on these three uses of variables. In this unit, your child will work with “What’s My Rule?” tables like the one below (introduced in early grades of Everyday Mathematics). He or she will learn to complete such tables following rules described in words or by algebraic expressions. Your child will also determine rules or formulas from information given in tables and graphs. xy 517 2 0 37 Rule: y(4 º x) 3 Total Total 1 2 3 4 5ABCDEF ln addition, your child will learn how to name cells in a spreadsheet and write formulas to express the relationships among spreadsheet cells. If you use computer spreadsheets at work or at home, you may want to share your experiences with your child. The class will playSpreadsheet Scramble,in which students practice computation and mental addition of positive and negative numbers. Encourage your child to play a game at home. See the Practice through Gamessection of this letter for some suggestions. Please keep this Family Letter for reference as your child works through Unit 3.
Copyright © Wright Group/McGraw-Hill 68 Math Tools Your child will be using spreadsheets,a common mathematics tool for the computer. The spreadsheet, similar to the one shown here, gets its name from a ledger sheet for financial records. Such sheets were often large pages, folded or taped, that were spread out for examination. algebraic expression An expression that contains a variable. For example, if Maria is 2 inches taller than Joe, and if the variable mrepresents Maria’s height, then the algebraic expression m2 represents Joe’s height. cell In a spreadsheet, a box formed where a column and a row intersect. A columnis a section of cells lined up vertically. A rowis a section of cells lined up horizontally. general pattern InEveryday Mathematics,a num- ber model for a pattern or rule. special case InEveryday Mathematics, a specific example of a general pattern. For example, 6 6 12 is a special case of yy2yand 9 = 4.5 º2 is a special case of A = l º w. Same as instance of a pattern. time graph A graph representing a story that takes place over time. For example, the time graph below shows the trip Mr. Olds took to drive his son to school. The line shows the increases, decreases, and constant rates of speed that Mr. Olds experienced during the 13-minute trip. variable A letter or symbol that represents a number. A variable can represent one specific number, or it can stand for many different numbers. Vocabulary Important terms in Unit 3: A 1234 56 78 91011 B C Class picnic ($$) budget for class picnic quantity food items unit price 6 5 3 quarts of macaroni salad 44.50 1.6913.50 6.76 bottles of soft drinks1.29 6.45 packages of hamburger buns 3 3.12 9.36bags of potato chips packages of hamburgers2.79 16.74 D cost subtotal 52.81 8% tax 4.23 total 57.04 1 2 3 4ABCD cell row column 0 021436587 Time (min) Speed (mph) 91110 1312 10 20 30 40 formula A general rule for finding the value of something. A formula is often written using letters, calledvariables,that stand for the quantities involved. For example, the formula for the area of a rectangle may be written as Abºh,whereA represents the area of the rectangle, brepresents its base, and hrepresents its height. Unit 3: Family Letter cont. STUDY LINK 212
69 Copyright © Wright Group/McGraw-Hill Do-Anytime Activities Try these ideas to help your child with the concepts taught in this unit. 1.If you are planning to paint or carpet a room, consider having your child measure and calculate the area using the area formula for rectangular surfaces: Area baseºheight. If the room is irregular in shape, divide it into rectangular regions, find the area of each region, and add all the areas to find the total area. If a room has a cathedral ceiling, imagine a line across the top of the wall to form a triangle. Your child can use the area formula for triangles: Area 1 2º(baseºheight), to calculate the area of the triangle. 2.If you use a spreadsheet program on a home computer, help your child learn how to use it. You might help your child set up a spreadsheet to keep track of his or her math scores and to figure out the mean. 3.Practice renaming fractions, which is a prerequisite skill for Unit 4. Examples: Rename as Fractions Rename as Mixed or Whole Numbers 31 2 3 53 8 1 3 2 55 5 6 base height 7 2 2 35 3 5 Unit 3: Family Letter cont. STUDY LINK 212 The concepts learned in Unit 3 will be reinforced through several math games included in this unit that are fun to play in class and at home. Detailed game instructions for all sixth-grade games are available in the games section of the Student Reference Book.Here is a list and a brief description of some of the games in this unit: Getting to OneSeeStudent Reference Book,page 321 Two players can play this game using a calculator. The object of the game is to divide a number by a mystery number and to find the mystery number in as few tries as possible. Players apply place-value concepts of decimal numbers to determine which numbers to play. Division Top-It(Advanced Version)SeeStudent Reference Book,page 336 Two to four people can play this game using number cards 1 through 9. Players apply place-value concepts, division facts, and estimation strategies to generate whole-number division problems that will yield the largest quotient. Building Skills through Games
Copyright © Wright Group/McGraw-Hill 70 As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. Some of the answers listed below will guide you through the unit’s Study Links. Study Link 3 1 Sample answers (1–7): 1. a. The sum of any number and 0 is equal to the original number. b. 36.09036.09; 52 052 2. (2º24)243º24; (2 º10)103º10 3. 1000.250.25100; 0.50.250.250.5 4. x2ºx 3x 5 5. sº0.1 1s 0 6. m01 7. 10 8. 100, 0.25 9. 20 10. 75, 100 11. 80, 0.80 12. 70, 0.70 Study Link 3 2 Sample answers (1–7): 1. (6º2)º36º(2º3); (6º1)º56º(1º5) 2. 12( 6 2)(2º12)6; 10( 4 2)(2º10)4 3. 1 5010º 1 5;3 43º 1 4 4. a–ba(–b) 5. m n m nº º3 3 6. s t s t 22 7. dcº 1 2 dcº º1 2 8. 2.5 9. 1.06 10. 1.00 Study Link 3 3 1. x– 7 2. d2.5 3. c 12,c12, or 1 12c 4. 2ºh,or 2h; 8 5. 3r8, or (3 ºr)8; 44 6. 275 7. 35 8. 0.5 Study Link 3 4 1. a. Subtract 0.22 from m. b. nm– 0.22 2. a. Multiplyrby 1 2or divide rby 2. b. rº0.5t 3. q(2ºp)2 4. 15 5. 210 6. 1,760 7. 29,040 Study Link 3 5 1. in:6 1 2;out:10 1 2, 9 1 2, 3, – 1 2 2. in:6, 1 4;out:48, 1.2, 2 3. in:7, 0; out:0, 18 4. Divide the innumber by 3; db3 5. Answers vary. 6. –3 7. –12 8. –3 9. 10 Study Link 3 6 1. Perimeter (in.): 4, 8, 12, 16, 20; Area (in. 2): 1, 4, 9, 16, 25 3. 10 in. 4. 17 in. 6. 21 4in. 2 7. 10 1 2in. 2 8. 54.45 9. 4.2 Study Link 3 7 1. January 2. $115.95 3. A5 4. C3 5. Column E: $118.75; $152.95; $2,625.00 6. E3B3C3D3 7. E5B5C5D5 8. $128.75 9. 144 10. 9 11. 73.96 12. 17 Study Link 3 8 1. –6 2. 4 3. 1 4. 6 5. 8 6. 2 7. 15 8. 5 9. 13 10. 12 11. 0,2,9 a. Sample answer: Add 6 to x. b. x(6)y 12. a. 25 b. 32 c. 50 d. 19 13. a. 11 0 b. 1 2 c. 2 d. 9 Study Link 3 9 1. Sample answer: People are getting on the Ferris wheel. 2. 125 sec 3. 170 sec 4. 4 times 5. 40 sec Study Link 3 10 1. Jenna’s Profit: $3, $6, $9, $12, $15; Thomas’s Profit: $6, $8, $10, $12, $14 2. $18, $16 3. Jenna 4. Jenna’s 5. $3, $2 6. (4,12) 7. a. 81 b. 8,000 c. 76 d. 875 e. 3 Unit 3: Family Letter cont. STUDY LINK 212