Place Value and Rounding

1. Place Value and Rounding • Objective: I can use my understanding of place value to round to the nearest 10 or 100.

2. Vocabulary • Digit: Any number between 0 and 9. Example: 234 has 3 digits • Place Value: The place in a number which represents a certain value. Example: 234 – the 2 is in the hundreds place. hundreds tens ones • Value: The actual value of a digit. Example: 234 – the value of the 2 is really 200.

3. Vocabulary • Standard Form: A number written in number form Example: 234 • Word Form: A number written out using words. Example: Two hundred thirty-four • Expanded Form: A number that is decomposed into an equation that adds each place-value together Example: 200+30+4

4. Try it. 1a. Write 347 in expanded form. 1b. Write the place value and value of each digit. Place Value Value 3 _____________ 3 ____________ 4 _____________ 4 ____________ 7 _____________ 7 ____________ 2a. Write 732 in written form. 2b. Write the place value and value of each digit. 3. Write nine hundred twenty-five in standard form.

5. Rounding Now that we are comfortable with place value, we need to review the number line song to help us with rounding. Rounding’s not that hard to do Let me teach the rules to you For the numbers 5 through 9 Round that number up the line For the numbers 4 or less Round that number down or yes!

6. How do I round whole numbers using a number line? • Step 1: First figure out what place value you are rounding to. Example: Round 53 to the nearest 10. • Step 2: Since we are concerned with the 10s place, construct a number line with 50 as the lowest number, 55 as the middle number, and 60 as the highest number. Example: 55 60 50

7. How do I round whole numbers using a number line? • Step 3: Now plot 53 on the number line. Example: • Step 4: Analyze how close 53 is to 50 and to 60. Since 53 is closer to 50, 53 rounded to the nearest 10 is 50. Example: 53 55 60 50 53 55 60 50

8. Guided Practice DIRECTIONS: Using a number line, round the following numbers to the nearest 10 and 100. • 244 rounded to the nearest 10 is ________. • 251 rounded to the nearest 100 is __________.

9. Isn’t There an Easier Way? Why yes there is an easier way… • Step 1: Look at the place value you are being asked to round. Underline that number. Example: Round to the nearest hundred. 6 4 9 • Step 2: Circle the digit to the right of the place value you are bring asked to round to. Example: 6 4 9

10. How do I round whole numbers? • Step 3: Now look at the digit that is circled. If the digit is 0, 1, 2, 3, or 4 then leave the underlined digit the same. If the circled number is 5, 6, 7, 8, or 9 then round the underlined digit up. Example: 6 4 9 Since the circled digit is a 4, we would leave the underlined digit (6) the same. • Step 4: Now turn all the digits to the right of the underlined digit into zeros. Example: 600 HINT TO REMEMBER: *5 and above give it a shove, 4 and below let it go*

11. Keep This in Mind • Even though you turn all the digits to the right of the underlined digit into zeros, leave the digits to the left the same… Example: 3,456 rounded to the nearest hundred is 3,500. The digits to the right are turned to zeros, the digits to the left remain the same.

12. Guided Practice Directions: Round each number to the nearest ten and hundred. TEN HUNDRED 535 ____________ ____________ 4, 292 ____________ ____________ 9, 472 ____________ ____________

13. Addition and Subtraction • I can add and subtract within 1000.

14. Strategies • We covered many, many, many strategies to add and subtract. • Let’s take a look at the next slide for a the list of strategies we learned this year, and I will pick one or two that I think are best for you students, and model how to use it.

15. Addition • Use place value blocks (remember to regroup) • Use a thousands chart. • Count forward on a number line. • Break apart the second number. (177 + 54 = 177 + 23 + 31) • Standard Algorithm

16. Guided Practice • Cody collected 3 rocks from his garden. The first was 235 grams, the second was 356 grams, and the last was 131 grams. What is the combined weight of all three rocks? • For lunch, 277 students selected chocolate milk, and 423 students selected regular milk. How many cartons of milk were selected in all?

17. Subtraction • Use a thousands chart. • Count backward on a number line. • Break apart the second number. (204 – 56 = 204 – 50 – 6 = 204 – 50 – 4 – 2) • Use an addition sentence. • Standard Algorithm.

18. Guided Practice • While playing his video game, Josh scored 786 points in the first round. He had a bad second round and lost 249 points. How many points did he end up with after the second round? • When Kim found out she inherited 834 dollars, she gave 372 dollars to her favorite charity. How many dollars does she have now?

19. Multiplication • I can multiply one-digit whole numbers by multiples of 10 in the range of 10-90.

20. Can You Do This? • 5 x 70 • 3 x 40 • 6 x 20

21. Strategies • Repeated addition: remember, multiplication is just repeated addition. • 5 x 70 is the same as 70 + 70 + 70 + 70 + 70 • Distributive property: we can always break down one of the numbers too. • 3 x 40 = (3 x 20) + (3 x 20) = 60 + 60 = 120

22. Strategies • Multiplication facts: 6 x 2 = 12, so 6 x 20 = 120. • Standard Algorithm (teacher will model if it was used in class).

23. Guided Practice • 7 x 90 • 6 x 40