STRATEGIES ACHIEVE MATHEMATICS SUCCESS

Transcription

1 STAMS SERIES D STRATEGIES TO ACHIEVE MATHEMATICS SUCCESS PROVIDES INSTRUCTIONAL ACTIVITIES FOR 12 MATHEMATICS STRATEGIES USES A STEP-BY-STEP APPROACH TO ACHIEVE MATHEMATICS SUCCESS PREPARES STUDENTS FOR ASSESSMENT IN MATHEMATICS COMPREHENSION

2 TABLE OF CONTENTS Strategy One Building Number Sense Strategy Two Using Estimation Strategy Three Applying Addition Strategies One Three REVIEW Strategy Four Applying Subtraction Strategy Five Applying Multiplication Strategy Six Applying Division Strategies Four Six REVIEW Strategy Seven Converting Time and Money Strategy Eight Converting Customary and Metric Measures Strategy Nine Using Algebra Strategies Seven Nine REVIEW Strategy Ten Using Geometry Strategy Eleven Determining Probability and Averages Strategy Twelve Interpreting Graphs and Charts Strategies Ten Twelve REVIEW Strategies One Twelve FINAL REVIEW

3 Strategy Two USING ESTIMATION PART ONE: Think About Estimation WHAT DO YOU KNOW ABOUT ESTIMATING NUMBERS? An estimate is a number that is close to another number. An estimate may be rounded to the nearest whole number, or the nearest ten, hundred, thousand, ten thousand, and so forth. Answer each question on the line provided. a. To the nearest 10: Is 38 closer to 30 or 40? b. To the nearest 100: Is 115 closer to 100 or 200? c. To the nearest 1,000: Is 2,776 closer to 2,000 or 3,000? d. To the nearest whole number: Is 29.7 closer to 29 or 30? e. To the nearest 100: Is 5,162 closer to 5,100 or 5,200? f. To the nearest 10: Is 5,162 closer to 5,160 or 5,170? Write five four-digit numbers that, when rounded to the nearest thousand, would be 4,000.,,,, and Round each decimal to the nearest whole number. Write each answer on the line provided. a would be rounded to. b. 6, would be rounded to. c would be rounded to. d. 7, would be rounded to. e would be rounded to. You just reviewed estimating and rounding numbers. 14 Using Estimation

4 WHAT DO YOU KNOW ABOUT ROUNDING NUMBERS THAT CONTAIN THE DIGIT 5? If the digit one place to the right of the place being rounded to is 5 or greater, round up. If the digit one place to the right of the place being rounded to is 4 or less, round down. Round 4,945 to the nearest 10, 100, and 1,000. a. to the nearest 10: b. to the nearest 100: c. to the nearest 1,000: Round 68,057 to the estimation indicated. a. to the nearest 10: b. to the nearest 100: c. to the nearest 1,000: d. to the nearest 10,000: Round 55,555 to the estimation indicated. a. to the nearest 10: b. to the nearest 100: c. to the nearest 1,000: d. to the nearest 10,000: You just reviewed information about rounding numbers. Together, write four five-digit numbers. Then, working alone, round each number to the nearest 10, the nearest 100, the nearest 1,000, and the nearest 10,000. Take turns sharing and discussing your results. Using Estimation 15

5 PART TWO: Learn About Estimation Estimation is used to find a number that is close to an exact number. Study the estimation chart that Sagar s teacher made. As you study, think about how to find an estimate. Nearest Nearest Nearest Nearest Number ,000 10,000 7,081 7,080 7,100 7,000 46,776 46,780 46,800 47,000 50, , , , , ,000 You use estimation to find the nearest ten, hundred, thousand, or ten thousand, and so forth, of a number. The estimate for 7,081 to the nearest thousand is 7,000. You use estimation to check if a sum of numbers makes sense. First, you round the addends. If you round the addends 1,382 and 2,716 to the nearest hundred, you get 1,400 and 2,700. If you add 1,400 2,700, you get 4,100, which is the estimated sum of 1,382 2,716. The estimated sum of 4,100 is very close to the actual sum of 4,098. You also use estimation to find the nearest whole number of a decimal. Number Nearest Whole Number , ,489 You use estimation to find a number that is close to another number. To round a number, find its nearest ten, hundred, thousand, ten thousand, and so forth. To round a decimal, find its nearest whole number. Estimate to check if a sum or a difference is reasonable. First round the numbers in the addition or subtraction problem. Then do the required operation to the rounded numbers to get the estimate. 16 Using Estimation

6 Sagar made a place-value chart for math homework. Study Sagar s chart. Think about finding the nearest ten, hundred, thousand, ten thousand, and hundred thousand of the number. Then do Numbers 1 through 4. hundred ten thousands thousands thousands hundreds tens ones tenths hundredths (100,000) (10,000) (1,000) (100) (10) (1) (.1) (.01) 3 1 2, Sagar estimated the number in the chart to the nearest thousand. Which of these numbers is the correct estimate? 313, , , , Sagar wanted to double the number in the chart. First, he rounded the number to the nearest hundred, then he doubled the number. Which of the following numbers is about twice the value of the given number? 624, , , , Sagar estimated the number in the chart to the nearest ten thousand. Which of these numbers is the correct estimate? 312, , , , Sagar estimated the number in the chart to the nearest whole number. Which of these numbers is the nearest whole number? 312, , , ,400 Talk about your answers to questions 1 4. Tell why you chose the answers you did. Using Estimation 17

7 PART THREE: Check Your Understanding Remember: You use estimation to find a number that is close to another number. To round a number, find its nearest ten, hundred, thousand, ten thousand, and so forth. To round a decimal, find its nearest whole number. Estimate to determine if an actual answer is reasonable. First round the numbers in the problem. Then do the required operation to the rounded numbers to get the estimate. Solve this problem. As you work, ask yourself, What is the rounded number of each addend? 5. Sagar estimated the sum of to the nearest whole number. What is the correct estimate? Solve another problem. As you work, ask yourself, How do I round this number to the nearest ten, hundred, thousand, or ten thousand, and so forth? 6. Sagar determined that his heart beats about 705,600 times per week. What number is 705,600 rounded to the nearest thousand? 700, , , , Using Estimation

8 Look at the answer choices for each question. Read why each answer choice is correct or not correct. 5. Sagar estimated the sum of to the nearest whole number. What is the correct estimate? 721 This answer is not correct because , when rounded, is , which has a sum of 722, not This answer is not correct because , when rounded, is , which has a sum of 722, not This answer is correct because , when rounded, is , which has a sum of This answer is not correct because , when rounded, is , which has a sum of 722, not Sagar determined that his heart beats about 705,600 times per week. What number is 705,600 rounded to the nearest thousand? 700,000 This answer is not correct because 705,600, rounded to the nearest thousand, is 706,000, not 700, ,000 This answer is not correct because 705,600, rounded to the nearest thousand, is 706,000, not 704, ,000 This answer is not correct because 705,600, rounded to the nearest thousand, is 706,000, not 705, ,000 This answer is correct because 705,600, rounded to the nearest thousand, is 706,000. Using Estimation 19

9 PART FOUR: Learn More About Estimation You estimate when you round a number. Numbers can be rounded to different places, such as hundredths, tenths, ones, tens, hundreds, thousands, and so forth. To round a number to a particular place, look at the digit to the right of that place. For example, to round 5,763 to the nearest hundred, look at the 6. The digit 5 is the midpoint for rounding. Numbers that fall below that midpoint are rounded down. Numbers that fall on or above that midpoint are rounded up. The 6 in 5,763 falls above the midpoint. Therefore, 5,763 to the nearest hundred is 5,800. Sagar wrote some problems for a math contest. Do Numbers 7 through There are 1,760 yards in a mile. What is this number rounded to the nearest hundred yards? 1,700 1,800 1,750 2, What is 125,880 rounded to the nearest ten thousand? 120, , , , Shawna worked for 7.28 hours, Marlene worked for 8.53 hours. To the nearest whole number, about how many hours did both girls work? 14 hours 15 hours 16 hours 17 hours 10. Estimate, to the nearest thousand, the sum of 21,384 74, ,000 96,400 96,000 90, Using Estimation

10 Read this part of a report that Sagar wrote about populations. Then do Numbers 11 through 14. Last year, 31,748 people lived in Ashton Falls. This year, the population is 32,336. So, our town population has grown by 588 people. There are reasons why the population has changed. The town had 150 deaths and 300 births, and 438 people moved to town from other areas. Here are the populations of four other cities. Dakari: 992,038 Sampson: 734,676 Mouton: 614,289 Bickford: 547, What is the population of Mouton rounded to the nearest hundred people? 614, , , , What is the population of Bickford rounded to the nearest hundred people? 547, , , , Round Dakari s population to the nearest thousand people. 990, , , , To the nearest ten thousand people, what is the population of Sampson? 740, , , ,000 Using Estimation 21

11 PART FIVE: Prepare for a Test A test question about estimation may ask you to round a number to its nearest ten, hundred, thousand, ten thousand, and so forth. A test question about estimation may ask you to round a decimal to its nearest whole number. A test question about estimation may ask you to estimate to determine if an actual answer is reasonable. Read the article that Sagar read about Alaska. Then do Numbers 15 and 16. Large but Small Alaska is the largest state in the U.S. It covers a land area of 570,374 square miles. However, Alaska ranks forty-eighth among the states in population. The population of Alaska in 2000 was 626,932. Nearly half of Alaska s population live in Anchorage. Anchorage is the most populated city in Alaska, with an estimated population of 260,000. ALASKA Anchorage Using Estimation Using Estimation 15. To the nearest hundred thousand square miles, what is the estimate of Alaska s land area? 500,000 square miles 600,000 square miles 570,000 square miles 570,400 square miles 16. Anchorage s estimated population is about 260,000. Which of these numbers could be the actual population of Anchorage? 245, , , , Using Estimation

12 Sagar read an article about Nevada. Read what he learned. Then do Numbers 17 and 18. The Silver State Nevada is called the Silver State, a reference to its earlier days as a place where silver was mined. The state of Nevada covers 110,567 square miles, or 286, square kilometers. The capital of Nevada is Carson City. Las Vegas and Reno are two other cities in Nevada. In 2003, Las Vegas had a population of 517,017 and Reno had a population of 193,882. NEVADA Using Estimation 17. Sagar correctly determined, to the nearest hundred people, the combined population of Las Vegas and Reno. What was his correct estimate? 710, , , ,100 Using Estimation 18. Sagar determined that Nevada has an area of 286, square kilometers. What is the number 286, rounded to the nearest whole number? 287, , , ,360 Using Estimation 23