Addition & Subtraction Within 1,000

300 + 40 + 7. The 3 is 3 hundreds or 300. The 4 is 4 tens or 40. The 7 is 7 ones, or 7.

When we add or subtract we need to work with the same place value from each number. We can only add tens to tens and ones to ones. If there are more than 10, then we can make one group of the next place.

First we can break down the numbers by place value: 37 = 30 + 7 and 28 = 20 + 8. Then we can add by place value. First the tens: 30 + 20 = 50, then the ones: 7 + 8 = 15. Now we have 50 + 15, but we need to regroup 15 as 1 ten and 5 ones: 50 + 10 + 5 = 65. So, 37 + 28 = 65.

First write the numbers by place value: 74 = 70 + 4 and 56 = 50 + 6. Next we would like to subtract by place value, but 6 is greater than 4. So, we can rewrite 70 + 4 as 60 + 14, taking one ten and regrouping it as 10 ones. Now we can subtract the tens: 60 - 50 = 10, and then the ones: 14 - 6 = 8. 10 + 8 = 18, so 74 - 56 = 18.

If 37 + 49 is 86, then that means that 86 is 49 away from 37. If I start at 37 on the number line, I would go 49 to get to 86. This also means that 86 - 37 is 49 for the same reason. The difference between 86 and 37 is 49. The numbers are 49 away from each other.

I could use base-10 blocks, or a number line. I could start with 3 hundreds, 4 tens and 6 ones to represent 346, and 4 hundreds, 3 tens, and 2 ones to represent 432. Putting the blocks together I would have 7 hundreds, 7 tens, and 8 ones, for a total of 778 blocks.

297 is very close to 300, which would be easier to add to 528 because only the hundreds would change. 297 is 3 away from 300, so I can take 3 from 528, making it 525, and give the 3 to 497, making it 500. Since the 3 is still included, the total won’t change. Now we have 525 + 300. 500 + 300 = 800, with 25 more, or 825.

503 is close to 500, which would be easier to subtract from 737. I can take 3 from 503 to make it 500, but I also need to take 3 from 737 so the numbers stay the same amount apart, so 737 becomes 734. Now we have 734 - 500. 700 - 500 = 200, 34 more, or 234.

Since 800 has no tens or ones to subtract we can regroup 1 hundred as 10 tens, and one of the tens as 10 ones. So 800 becomes 700 + 90 + 10. Now we can write 347 as 300 + 40 + 7 and subtract by place value: 700 - 300 = 400, 90 - 40 = 50, and 10 - 7 = 3. So we have 400 + 50 + 3 = 453. We could also count up from 347 to 800 on the number line. First hop 3 from 347 to 350. Then hop 50 to 400, and then hop 400 to 800. Altogether we hopped 3, then 50, then 400, or 453.

She is not correct. If Wendy was correct then 211 + 438 should be 647. If we add the ones: 1 + 8 = 9, but there is a 7 in the ones place of 647. When Wendy subtracted the ones, she did not see that 8 is greater than 7. She should have regrouped a ten as 10 ones, but looked at the difference between 7 and 8 and got 1.