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Addition & Subtraction Within 1,000
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What you will learn from this videoWhat you will learn
- 3-digit numbers can be broken down by place value: ones, tens & hundreds.
- We can add & subtract 3-digit numbers using place value or with a number line.
- When we get a number larger than 9 in any place value, we can regroup it to find the final answer.
- Discussion Questions
Before Video
Write 347 by place value. What does each place mean?ANSWER300 + 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.
After Video
How could you add 346 + 432 using base 10 blocks? ANSWERI 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.
- Vocabulary
- Friendly Number DEFINE
An adjusted number that makes an operation easier to do. For example, if we were adding 498 and 342, we could add 2 to 498 to make it 500. The 2 that was added would be taken from 342, making it 340. 500 + 340 is easier to add than 498 + 342.
- Addition DEFINE
Combining two or more numbers to find the total.
- Subtraction DEFINE
Finding the difference between two numbers, how far apart they are.
- Place Value DEFINE
The value of each digit in a number. In our number system, each place has a value 10 times more than the place value to the left. The first place is the ones, then the tens, then the hundreds. The places keep going for larger and larger numbers.
- Regroup DEFINE
Converting a place total greater than 10 to 1 of the next place, with the remainder staying in the current place. Or, converting one from a larger place to 10 of the next smaller place. Regrouping is done to keep each place less than 10 when adding, and to make it possible to subtract when the number being subtracted is larger than the other number.
- Sum DEFINE
The result when numbers are added.
- Difference DEFINE
The result when numbers are subtracted.
- Friendly Number DEFINE
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Level 1
Find the sum of 468 and 345.
Level 2
Cindy subtracted 345 from 550 and got 215. Explain what she did wrong.
Level 3
Write a short word problem where you would solve 762 - 349. Give the answer.
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