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Rounding Multi-Digit Numbers: Learn to Round to the Nearest Place Value

This lesson teaches students how to round multi-digit numbers to the nearest place value. It covers the concept of place value, rounding up and down, and provides guided practice exercises.

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Rounding Multi-Digit Numbers: Learn to Round to the Nearest Place Value

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  1. Learning Objective We will round multi-digit numbers. What are we going to do? CFU Activate Prior Knowledge Place value: The place is the position of a digit in a number. The value is the worth of the digit due to its position. 1. What is the value of the digit 9? 9 3 , 6 7 1 90,000 The value of 9 in 93,671 is _______. Students, you already know how to identify the place value of numbers. Now, we are going to use place value to round multi-digit numbers. Make Connection 2. What is the value of the digit 7? 9 7 , 5 2 6 97,000 The value of 7 in 97,526 is _______.

  2. Concept Development • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. CFU Would 4,350 rounded to the nearest thousand round up or down? How do you know? A up B down Would 5,670 rounded to the nearest thousand round up or down? How do you know? A up B down In your own words, what does it mean to round a multi-digit number? “Rounding a multi-digit number means __________.” Rounding multi-digit numbers. Round 82,273to the nearest thousand. 82,237 787,530 5,500 4,500 6,000 5,000 5,000 4,000 785,000 82,500 83,000 780,000 790,000 82,000 82,237rounded to the nearest thousand is 82,000because it is nearer in value to 82,000than 83,000. Round 787,530to the nearest ten thousand. 787,530rounded to the nearest ten thousand is 790,000because it is nearer in value to 790,000than 780,000.

  3. Skill Development/Guided Practice • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. CFU How did I/you identify the place value to round to? How did I/you label the number line? How did I/you place the given number on the number line? How did I/you round the number? Round multi-digit numbers. 1 Read the problem and identify1 the place value to round to. (circle) Label the number line with the appropriate2 numbers. Place the given number on the number line. Round the number up or down. Interpret3 your answer. (write) 1 2 3 4 2 5 3 4 36,428 45,692 36,000 37,000 45,500 36,550 45,000 46,000 45,692 36,428 36,000 46,000 1 find 2 right for a certain purpose 3 explain Vocabulary it is nearer in value to 46,000 than 45,000. it is nearer in value to 36,000 than 37,000.

  4. Skill Development/Guided Practice (continued) • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. How did I/you identify the place value to round to? How did I/you label the number line? How did I/you place the given number on the number line? How did I/you round the number? CFU Round multi-digit numbers. 1 Read the problem and identify the place value to round to. (circle) Label the number line with the appropriate numbers. Place the given number on the number line. Round the number up or down. Interpret your answer. (write) 1 2 3 4 2 5 3 4 557,065 213,462 550,000 560,000 215,000 555,000 210,000 220,000 213,462 557,065 210,000 560,000 it is nearer in value to 210,000 than 220,000. it is nearer in value to 560,000 than 550,000.

  5. Skill Development/Guided Practice (continued) • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. CFU How did I/you identify the place value to round to? How did I/you label the number line? How did I/you place the given number on the number line? How did I/you round the number? Round multi-digit numbers. 1 Read the problem and identify the place value to round to. (circle) Label the number line with the appropriate numbers. Place the given number on the number line. Round the number up or down. Interpret your answer. (write) 1 2 3 4 2 5 3 4 360,428 821,346 300,000 400,000 850,000 350,000 800,000 900,000 821,346 365,428 400,000 800,000 it is nearer in value to 800,000 than 900,000. it is nearer in value to 400,000 than 300,000.

  6. Skill Development/Guided Practice (continued) • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. How did I/you identify the place value to be rounded? How did I/you determine whether to round up or down? How did I/you round the number? CFU Round multi-digit numbers. 1 Read the problem and identify the place value to round to. (circle) Determine4 whether to round up or down. Hint: Look at the digit in the next place value lower. Round the number. Interpret your answer. (write) 1 2 3 2 4 3 3 6 9, 7 1 2 4 5 1, 6 2 3 369,712 451,623 370,000 452,000 4 figure out Vocabulary it is nearer in value to 452,000 than 451,000. it is nearer in value to 370,000 than 369,000.

  7. Skill Development/Guided Practice (continued) • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. How did I/you identify the place value to be rounded? How did I/you determine whether to round up or down? How did I/you round the number? CFU Round multi-digit numbers. 1 Read the problem and identify the place value to round to. (circle) Determine whether to round up or down. Hint: Look at the digit in the next place value lower. Round the number. Interpret your answer. (write) 1 2 3 2 4 3 3 6 5, 7 1 2 4 1 2, 6 2 3 412,623 365,712 370,000 410,000 it is nearer in value to 410,000 than 420,000. it is nearer in value to 370,000 than 360,000.

  8. Skill Development/Guided Practice (continued) • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. How did I/you identify the place value to be rounded? How did I/you determine whether to round up or down? How did I/you round the number? CFU Round multi-digit numbers. 1 Read the problem and identify the place value to round to. (circle) Determine whether to round up or down. Hint: Look at the digit in the next place value lower. Round the number. Interpret your answer. (write) 1 2 3 2 4 3 3 2 6, 7 1 2 4 5 7, 6 2 3 457,623 326,712 500,000 300,000 it is nearer in value to 500,000 than 400,000. it is nearer in value to 300,000 than 400,000.

  9. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 4 Eduardo rounded the following numbers to the nearest ten thousand. Some of his answers are incorrect. Cross out any incorrect answers and write in the correct ones. 5 809,803 613,782 884,097 345, 845 610,000 340,000 880,000 810,000 350,000 669,961 125,385 695,632 731,892 670,000 690,000 120,000 730,000 130,000 700,000 Explain the mistake that Eduardo was making when he rounded the numbers above. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Eduardo rounded the numbers with 5 in the thousands place down. He should have rounded those numbers up.

  10. Relevance • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. 1 Rounding numbers will make it easier to manage money. Sarah wanted to buy a new car. The price was $19,875. She also wanted to buy a new television that cost $1,598. She knows that she needs about $22,000 to get both. Sample Test Question: 29. Which of the following numbers would be rounded down to the nearest ten thousand? 206,127 783,344 124,478 977,124 Rounding multi-digit numbers will help you do well on tests. 2 Does anyone else have another reason why it is relevant to round multi-digit numbers? (Pair-Share) Why is it relevant to round multi-digit numbers? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU Yes Yes Yes Yes No No No No

  11. To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. Skill Closure Round multi-digit numbers. Read the problem and identify the place value to round to. (circle) Determine whether to round up or down. Hint: Look at the digit in the next place value lower. Round the number. Interpret your answer. (write) 1 2 3 4 Word Bank Word Bank round value nearer greater lesser multi-digit 2 4 7, 2 6 2 7 5 8, 6 3 5 247,262 758,635 247,000 760,000 it is nearer in value to 760,000 than 750,000. it is nearer in value to 247,000 than 248,000. Access Common Core Albert thinks that 253,430 rounded to the nearest ten thousand is 260,000. Do you agree with his answer? Why or why not? Use the number line to explain. I do not agree with Albert because 253,430 is closer to 250,000. 253,430 Summary Closure 250,000 255,000 260,000 What did you learn today about rounding multi-digit numbers? (Pair-Share) Use words from the word bank.

  12. Independent Practice • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. Round multi-digit numbers. Read the problem and identify the place value to round to. (circle) Label the number line with the appropriate numbers. Place the given number on the number line. Round the number up or down. Interpret your answer. (write) 1 2 3 4 5 7 5 4, 2 0 0 8 9 5, 7 0 7 895,707 754,200 895,000 750,000 890,000 900,000 700,000 800,000 895,707 754,200 900,000 800,000 it is nearer in value to 900,000 than 890,000. it is nearer in value to 800,000 than 700,000.

  13. Independent Practice (continued) • To rounda multi-digit number is to change it to a near value. • Roundingdownchanges the number to a lesser value. • Rounding upchanges the number to a greater value. Round multi-digit numbers. Read the problem and identify the place value to round to. (circle) Determine whether to round up or down. Hint: Look at the digit in the next place value lower. Round the number. Interpret your answer. (write) 1 2 3 4 5 6 1, 1 9 0 6 5 9, 2 3 2 561,190 659,232 600,000 700,000 it is nearer in value to 700,000 than 600,000. it is nearer in value to 600,000 than 500,000. 7 3 5, 3 6 2 7 7 5, 5 4 1 735,362 775,541 740,000 776,000 it is nearer in value to 776,000 than 775,000. it is nearer in value to 740,000 than 730,000.

  14. Periodic Review 1 4 3 9, 5 7 7 4 2 3, 7 7 1 439,577 423,771 440,000 400,000 it is nearer in value to 400,000 than 500,000. it is nearer in value to 440,000 than 430,000. Access Common Core 1. When rounding to the nearest ten thousand,Dina determined that 967,583 will be rounded down. Explain why Dina is incorrect. Dina is incorrect because 7 is in the thousands place. The number is closer to 970,000 than 960,000. 2. When rounding to the nearest thousand,Joseph determined that 534,192 will be rounded up. Explain why Joseph is incorrect. Joseph is incorrect because 1 is in the hundreds place. The number is closer to 534,000 than 535,000. 3. When rounding to the nearest hundred thousand,Jody determined that 794,354 will be rounded down. Explain why Jody is correct. Dina is correct because 9 is in the ten thousands place. The number is closer to 800,000 than 700,000.

  15. Periodic Review 2 6 4 5, 1 7 9 6 2 0, 0 6 3 645,179 645,000 620,063 600,000 it is nearer in value to 645,000 than 646,000. it is nearer in value to 600,000 than 700,000. Access Common Core 1. Choose Yes or No to indicate whether each statement is true about the number 94,632. 1a. 94,632 rounded to the nearest ten is 94,630. 1b. 94,632 is nearer in value to 94,000 than 95,000. 1c. 94,632 rounded to the nearest hundred thousand is 100,000. O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No 2. Choose Yes or No to indicate whether each statement is true about the number 697,841. 1a. 697,841 rounded to the nearest ten thousand is 690,000. 1b. 697,841 is nearer in value to 700,000 than 690,000. 1c. 697,841 rounded to the nearest thousand is 697,000.

  16. Periodic Review 3 6 6 3, 7 8 5 9 4 9, 5 9 4 663,785 949,594 660,000 900,000 it is nearer in value to 660,000 than 670,000. it is nearer in value to 900,000 than 1,000,000. Access Common Core 1. Alice is rounding the number 797,908 to the nearest ten thousand. She thinks that the rounded number will be 790,000. Do you agree with her? Why or why not? No, I do not agree with her. The number is closer to 800,000 than 790,000. 2. Braden is rounding the number 989,976 to the nearest hundred thousand. He thinks that the answer will be 1,000,000. Do you agree with him? Why or why not? Yes, I do agree with him. The number is closer to 1,000,000 than 900,000.

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