1. Boxes, Chains, & Extras by Denise Carroll

2. Digits We can use the digits 0 – 9 to make any number. Each number is called a digit. Counting the zero, we have ten digits. Where we place the digits will give the digits there value.

3. Extras Each paper clip represents one. We call these ones, extras. = 5 ones or 5 extras = 1 one or 1 extra

4. Chain We can group the paper clips. When we link ten extras together, this makes a chain. 10 ones = 1 ten or 1 chain 1 ten + 0 ones = 10 1 chain + 0 extras = 10

5. Is there one digit that represents twelve? Remember, 0 – 9 are our digits. How do we represent twelve with digits?

6. There is not one digit to represent twelve. We need two digits. Twelve = 12 What does the one represent? What does the two represent?

7. 12 tens + ones The one represents 1 ten or one chain. The two represents 2 ones or two extras. one ten + two ones = 12 one chain + two extras = 12 10 + 2 = 12

8. Let’s try... 16 How can we group sixteen extras?

9. 16 The one represents 1 ten or one chain. The six represents 6 ones or six extras. 1 ten + 6 ones = 16 1 chain + 6 extras = 16 10 + 6 = 16

10. Base Ten Blocks We can also use base ten blocks to represent tens and ones. = 1 one or 1 extra = 1 ten or 1 chain

11. = 2 tens or 2 chains = 7 ones or 7 extras 2 tens + 7 ones = 27 2 chains + 7 extras = 27 20 + 7 = 27 27

12. Let’s try... 54 How many chains do we need? How many extras do we need? We have _____ tens. We have _____ ones.

13. 5 tens + 4 ones = 54 5 chains + 4 extras = 54 50 + 4 = 54 54 tens + ones The five represents 5 tens or five chains. The four represents 4 ones or four extras.

14. Boxes One box holds one hundred paper clips. When we group 10 tens together, this makes 100 or a box. = 100 or 1 box = 10 tens or 100 = 100 or 1 box

15. 253 hundreds + tens + ones 2 hundreds + 5 tens + 3 ones = 253 2 boxes + 5 chains + 3 extras = 253 200 + 50 + 3 = 253 The two represents 2 hundred or two boxes. The five represents 5 tens or five chains. The three represents 3 ones or three extras.

16. Let’s try... How can we group 412? How many boxes do we need? How many chains do we need? How many extras do we need? We have _____ hundreds. We have _____ tens. We have _____ ones.

17. 412 hundreds + tens + ones The four represents 4 hundreds or 4 boxes. The one represents 1 ten or one chain. The two represents 2 ones or two extras. 4 hundreds + 1 ten + 2 ones = 412 4 boxes + 1 chain + 2 extras = 412 400 + 10 + 2 = 412

18. Congratulations! You’re a Math Whiz! You have learned that we use the digits 0 – 9 to make any number. You have also learned that where we place a digit determines the value of each digit.

19. Resources http://images.search.yahoo.com http://office.microsoft.com/clipart