1. Addition and Subtraction 29 Addition and Subtraction Algorithms 2 ones plus 9 ones equal 11 ones. 11 is 1 ten and 1 one. Record the 1 one in the ones column between the equals sign. Because we have more tens, we record the 1 ten in the tens column above the equals sign. 8 tens plus 8 tens plus 1 ten equals 17 tens. 17 tens is 1 hundred and 7 tens. Record the 7 tens in the tens column between the equals sign. Because we have more hundreds, we record the 1 hundred in the hundreds column above the equals sign. 6 8 2 + 5 8 9 1 7 1 1

2. Addition and Subtraction Algorithms 2 ones plus 9 ones equal 11 ones. 11 is 1 ten and 1 one. Record the 1 one in the ones column between the equals sign. Because we have more tens, we record the 1 ten in the tens column above the equals sign. 8 tens plus 8 tens plus 1 ten equals 17 tens. 17 tens is 1 hundred and 7 tens. Record the 7 tens in the tens column between the equals sign. Because we have more hundreds, we record the 1 hundred in the hundreds column above the equals sign. 6 hundreds plus 5 hundreds plus 1 hundred is 12 hundreds. 12 hundred is 1 thousand and 2 hundreds. Because we have no more thousands, we can record the 1 thousand and 2 hundreds in the thousands and hundreds columns between the equals sign. 1 6 1 8 2 + 5 8 9 7 1 1 2 Addition and Subtraction 29

3. Addition and Subtraction Algorithms Addition and Subtraction 29 + 400 + 100 + 20 + 60 + 8 + 1 682 1082 1182 1202 1262 1270 1271 682 + 589 = 682 + 600 = 1282 1282 - 11 = 1271 682 + 589 = 1271

4. Addition and Subtraction 29 Addition and Subtraction Algorithms I don’t have enough ones to subtract 8 ones from 7 ones. So I can add ten to both numbers without changing the difference between them. I’ll add 10 ones as 10 ones to the top number. And I’ll add 10 ones as 1 ten to the bottom number. 17 ones minus 8 ones equals 9 ones. We’ll record the 9 ones in the ones column between the equals sign. 9 1 1 1 2 7 - 5 8

5. Addition and Subtraction 29 Addition and Subtraction Algorithms I don’t have enough ones to subtract 8 ones from 7 ones. So I can add ten to both numbers without changing the difference between them. I’ll add 10 ones as 10 ones to the top number. And I’ll add 10 ones as 1 ten to the bottom number. 17 ones minus 8 ones equals 9 ones. We’ll record the 9 ones in the ones column between the equals sign. I don’t have enough tens to subtract 6 tens from 2 tens. So I can add 10 tens to both numbers without changing the difference between them. I’ll add 10 tens as 10 tens to the top number. And I’ll add 10 tens as 1 hundred to the bottom number. 12 tens minus 5 tens is 7 tens. We’ll record the 7 tens in the tens column between the equals sign. 9 1 1 1 2 7 - 5 8 7 1 1

6. Addition and Subtraction 29 Addition and Subtraction Algorithms I don’t have enough ones to subtract 8 ones from 7 ones. So I can add ten to both numbers without changing the difference between them. I’ll add 10 ones as 10 ones to the top number. And I’ll add 10 ones as 1 ten to the bottom number. 17 ones minus 8 ones equals 9 ones. We’ll record the 9 ones in the ones column between the equals sign. I don’t have enough tens to subtract 6 tens from 2 tens. So I can add 10 tens to both numbers without changing the difference between them. I’ll add 10 tens as 10 tens to the top number. And I’ll add 10 tens as 1 hundred to the bottom number. 12 tens minus 6 tens is 6 tens. We’ll record the 6 tens in the tens column between the equals sign. 1 hundred plus 1 hundred equals 2 hundred. We’ll record the 2 hundred in the hundreds column between the equals sign. 9 1 1 1 2 7 - 5 8 6 1 1

7. Addition and Subtraction 29 Addition and Subtraction Algorithms I don’t have enough ones to subtract 8 ones from 7 ones. So I can change 1 ten into 10 ones. Now I have 1 ten and 17 ones. 17 ones minus 8 ones equals 9 ones. We’ll record the 9 ones in the ones column between the equals sign. 9 1 1 2 7 - 5 8 1

8. Addition and Subtraction 29 Addition and Subtraction Algorithms I don’t have enough ones to subtract 8 ones from 7 ones. So I can change 1 ten into 10 ones. Now I have 1 ten and 17 ones. 17 ones minus 8 ones equals 9 ones. We’ll record the 9 ones in the ones column between the equals sign. I don’t have enough tens to subtract 5 tens from 1 ten. So I can change 1 hundred into 10 tens. Now I have zero hundreds and 11 tens. 11 tens minus 5 tens equals 6 tens. 9 1 1 2 7 - 5 8 1 0 1 6

9. Addition and Subtraction Algorithms Addition and Subtraction 29 127 - 58 = 127 - 60 =67 67 + 2 = 69 127 - 58 = 69 - 1 - 7 - 30 - 20 69 70 77 107 127 127 - 58 =

10. What numbers did you select? How did you add / subtract your numbers? Was your strategy or an algorithm more efficient? Why? The numbers I selected are... I added / subtracted using my strategy / an algorithm by... The most efficient way was... because... Addition and Subtraction Algorithms Addition and Subtraction 29