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Name: CH Date: APTER 2 Estimation and Number Theory PROBLEM SOLVING Thinking Skills 1. I am a factor of 50 and a multiple of 5. I am a 2-digit number greater than 10 but less than 40. What number am I? 2. Ms. Atkinson estimates a total cost of $90 for her grocery bill. If she rounds the cost of each item on her grocery bill to the nearest ten dollars, what is the least possible price Ms. Atkinson will pay for the fish? Items 8 Cost ($) Muffins 18 Milk 12 Meat 25 Fish ? © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. Solve. Show your work. Chapter 2 Estimation and Number Theory MS_Enrich_4A_Ch02_08-15.indd 8 1/6/09 5:34:31 PM Name: Date: © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. Solve. 3. Find the sum of all the factors of 48 and the sum of all the factors of 64. Then find the difference between the two sums. 4. Two factors of 32 are x and y. The sum of x and y is 12. The smaller of the two numbers is x. Find the value of x and y. Enrichment 4A MS_Enrich_4A_Ch02_08-15.indd 9 9 1/6/09 5:34:31 PM Name: Date: PROBLEM SOLVING Strategies 5. Ms. Duff wants to give her students some apples. If she gives each student 7 apples, there will be no apples left. If she gives each student 4 apples, there will be 18 apples left. How many students are in Ms. Duff’s class? 6. Which number does not belong in the group? Color it. Explain your answer. 72 54 24 18 49 27 10 36 15 © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. Answer the questions. Chapter 2 Estimation and Number Theory MS_Enrich_4A_Ch02_08-15.indd 10 1/10/09 4:58:26 PM Name: Date: Solve. 7. These numbers are multiples of two numbers. Rewrite them into two sets of five multiples. Some numbers will be used in both sets of multiples. 64 16 27 18 24 48 9 32 Numbers © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. 8. Multiples Ricky works part-time at a store every 2 days. Anwar also works part-time at the same store every 3 days. They first met at the store on a Monday. On which day will they meet for a. the second time? b. the third time? Enrichment 4A MS_Enrich_4A_Ch02_08-15.indd 11 11 1/6/09 5:34:32 PM Name: Date: PROBLEM SOLVING Exploration Solve. 10. 12 Make a list of the first nine multiples of 9. Then multiply 9 by consecutive whole numbers to show how to find the multiples. Lastly divide the multiples by the same consecutive whole numbers to get a quotient of 9. The first one has been done for you. Multiples of 9 Multiply Divide 9 1⫻9⫽9 9⫼1⫽9 What do you notice in the second and third columns? © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. 9. Chapter 2 Estimation and Number Theory MS_Enrich_4A_Ch02_08-15.indd 12 1/10/09 12:09:21 PM Name: Date: Answer the question. 11. Estimate the sum and the difference of 7,309 and 2,876 using two estimation methods. Which method gives you the more accurate answers? © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. Method 1 Method 2 Enrichment 4A MS_Enrich_4A_Ch02_08-15.indd 13 13 1/6/09 5:34:33 PM Name: Date: Journal Writing Solve. 12. Clark estimates the sum of two numbers using two methods. Write the steps used in each method. Name each method used. a. Method 1 4,728 ⫹ 1,095 ⫽ ? Estimated sum is 5,000. Step 1 b. Method 2 4,728 ⫹ 1,095 ⫽ ? Estimated sum is 5,800. Step 1 Step 2 14 © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. Step 2 Chapter 2 Estimation and Number Theory MS_Enrich_4A_Ch02_08-15.indd 14 1/10/09 12:09:21 PM Name: 13. Date: Jack, Keith, and Lee completed these estimation problems. Find the errors. a. Estimate the product of 247 and 3 by rounding to the nearest hundred. Jack 247 ⫻ 3 ⫽ ? 300 ⫻ 3 ⫽ 900 Error: b. Estimate the quotient of 95 and 4. Keith 95 ⫼ 4 ⫽ ? 80 ⫼ 4 ⫽ 20 © 2009 Marshall Cavendish International (Singapore) Private Limited. Copying is permitted; see page ii. Error: c. Estimate the quotient of 73 and 3. Lee 73 ⫼ 3 ⫽ ? 90 ⫼ 3 ⫽ 30 Error: Enrichment 4A MS_Enrich_4A_Ch02_08-15.indd 15 15 1/10/09 12:09:21 PM