1. Place Value Third and Fourth Grade

2. Third Grade Number and Operations Base Ten (Common Core) 1. Use place value understanding to round whole numbers to the nearest 10 or 100. 1.1 Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones; e.g. 3,706 = 3000 + 700 + 6 = 3 thousands, 7 hundreds, 0 tens, and 6 ones. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Third Grade Number Sense - CA State Standards 1.1 Count, read, and write whole numbers to 10,000. 1.2 Compare and order whole numbers to 10,000. 1.3 Identify the place value for each digit in numbers to 10,000. 1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand. 1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6). Fourth Grade Number and Operations Base Ten (Common Core) 1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 3. Use place value understanding to round multi-digit whole numbers to any place. Fourth Grade Number Sense – CA State Standards 1.1 Read and write whole numbers in the millions. 1.2 Order and compare whole numbers and decimals to two decimal places. 1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. 1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate. Standards

3. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Notice in the ones column the number “1” represents cube. Notice in the tens column the number “1” represents ten cubes. The “1” in the tens column represents ten times the number of cubes as the “1” in the ones column.

4. Recognize that in a multi-digit whole number, a digit in place represents ten times what it represents in the place to its right. Notice in the ones column the number “1” represents one cube. Notice in the tens column the number “1” represents one group of ten. The “1” in the tens column represents ten times the number of cubes as the “1” in the ones column.

5. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Notice in the ones column the number “1” represents one cube. Notice in the tens column the number “1” represents one group of ten. Notice in the hundreds column the number “1” represents ten group of ten. The “1” in the tens column represents ten times the number of cubes as the “1” in the ones column. The “1” in the hundreds column represents ten times the number of cubes as the “1” in the tens column.

6. Notice in the ones column the number “1” represents one cube. Notice in the tens column the number “1” represents one group of ten. Notice in the hundreds column the number “1” represents one group of a hundred. The “1” in the tens column represents ten times the number of cubes as the “1” in the ones column. The “1” in the hundreds column represents ten times the number of cubes as the “1” in the tens column. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

7. Notice in the ones column the number “2” represents two cubes. Notice in the tens column the number “2” represents two groups of ten. Notice in the hundreds column the number “2” represents two groups of a hundred. The “2” in the tens column represents ten times the number of cubes as the “2” in the ones column. The “2” in the hundreds column represents ten times the number of cubes as the “2” in the tens column.

8. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Notice in the ones column the number “2” represents two cubes. Notice in the tens column the number “2” represents two groups of ten. Notice in the hundreds column the number “2” represents two groups of a hundred. The “2” in the tens column represents ten times the number of cubes as the “2” in the ones column. The “2” in the hundreds column represents ten times the number of cubes as the “2” in the tens column.

9. This is a representation of the number “222” with the groups of a hundred stacked on top of one another. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

10. Even though the two is the “smallest digit” it represents the largest number of cubes. Why? Even though the four is the “largest digit” it represents the smallest number of cubes. Why?

11. Because the value of each place is 10 times the value of the place to the immediate right, multiplying by 10 yields a product in which each digit of the multiplicand is shifted one place to the left.

12. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Working with fractions having denominators of 10 and 100 (4 th grade Common Core) can be used as preparation to extend the base-ten system to non-whole numbers.

13. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Base-ten numerals: Number names: Expanded form: 11 eleven 10 + 1

14. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Base-ten numerals: Number names: Expanded form: 111 one hundred eleven 100 + 10 + 1

15. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Base-ten numerals: Number names: Expanded form: 222 two hundred twenty-two 200 + 20 + 2

16. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Base-ten numerals: Number names: Expanded form: 234 two hundred thirty-four 200 + 30 + 4

17. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Base-ten numerals: Number names: Expanded form: 746 seven hundred forty-six 700 + 40 + 6

18. Flexibility with Numbers Can you think of 746 written in a different way than what was in the previous slide? Could it also be 74 tens and 6 ones? Could it also be 1 hundred, 64 tens, and 6 ones? What else could it be?

19. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 234 222 > = <

20. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 234 111 > = <

21. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 745 746 > = <

22. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 746 745 > What happens if we put the 746 first and the 745 last when we compare the numbers? Will we have to change the direction of the sign? Why or why not?

23. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 746 > 745 745 < 746 Notice how the direction of the sign is based on the order in which the numbers are compared.

24. Use place value understanding to round multi- digit whole numbers to any place. There are four groups of ten filled so when you round you will keep these groups of ten. This means when you round you will not have a number less than 40. Build this number with your partner. Look at the two ones and decide if at least half of that group of ten is filled. If at least half of that group of ten is filled then you round to 50. If less than half of that group of ten is filled then you round to 40. Round to 40

25. Use place value understanding to round multi- digit whole numbers to any place. There are four groups of ten filled so when you round you will keep these groups of ten. This means when you round you will not have a number less than 40. Build this number with your partner. Look at the seven ones and decide if at least half of that group of ten is filled. If at least half of that group of ten is filled then you round to 50. If less than half of that group of ten is filled then you round to 40. Round to 50

26. Use place value understanding to round multi- digit whole numbers to any place. There are four groups of ten filled so when you round you will keep these groups of ten. This means when you round you will not have a number less than 40. Build this number with your partner. Look at the five ones and decide if at least half of that group of ten is filled. If at least half of that group of ten is filled then you round to 50. If less than half of that group of ten is filled then you round to 40. Round to 50

27. Use place value understanding to round multi- digit whole numbers to any place. Use a number line to round 42. 4045 50 4045 50 Use a number line to round 47. 42 47 42 is rounded to 40. Why? 47 is rounded to 50. Why?

28. Use place value understanding to round multi- digit whole numbers to any place. Round 145 to the nearest ten. Build this number with your partner. Round to 50 There is one group of a hundred and four groups of ten filled so when you round you will keep these groups. This means when you round you will not have a number less than 140. Look at the five ones and decide if at least half of that group of ten is filled. If at least half of that group of ten is filled then you round to 50. If less than half of that group of ten is filled then you round to 40. Final answer is 150

29. Use place value understanding to round multi- digit whole numbers to any place. Round 145 to the nearest hundred. Build this number with your partner. Round to 0 Look at the tens and decide if at least half of tens are filled. If at least half of the tens are filled then you round to 100. If less than half of the tens are filled then you round to 0. There is one group of a hundred filled so when you round you will keep this group of 100. This means when you round you will not have a number less than 100. Final answer is 100

30. Use place value understanding to round multi- digit whole numbers to any place. Round 152 to the nearest hundred. Build this number with your partner. Round to 100 Look at the tens and decide if at least half of tens are filled. If at least half of the tens are filled then you round to 100. If less than half of the tens are filled then you round to 0. There is one group of a hundred filled so when you round you will keep this group of 100. This means when you round you will not have a number less than 100. Final answer is 200

31. Use place value understanding to round multi- digit whole numbers to any place. Use a number line to round 142 to the nearest hundred. 100150 200 100150 200 Use a number line to round 152 to the nearest hundred. 142 152 142 is rounded to 100. Why? 152 is rounded to 200. Why?

32. On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. About how many miles did your family travel? Discuss with your neighbor your estimation strategies. Student 1: I first thought about 267 and 34. I noticed that their sum is about 300. Then I knew that 194 is close to 200. When I put 300 and 200 together I get 500. Student 2: I first thought about 194. It is really close to 200. I also have 2 hundreds in 267. That gives me a total of 4 hundreds. Then I have 67 and 34 together that is really close to 100. When I add that hundred to the 4 hundreds that I already had, I end up with 500. Student 3: I rounded 267 to 300. I rounded 194 to 200. I rounded 34 to 30. When I added 300, 200 and 30, I know my answer will be about 530.

33. Use place value understanding to round multi- digit whole numbers to any place. Independent practice for rounding to the nearest hundred: Work with your partner and list all the numbers between 101-200 that would round to 200. Challenge for rounding to the nearest hundred: List all the numbers greater than 200 that would round to 200. Super Challenge for rounding to the nearest thousand: List all the numbers that would round to 1,000.