Subtraction within 1,000: Regrouping Ones from Tens & Multiple Regrouping
Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.
The Great Regrouping Adventure!
Have you ever tried to share your snacks, but you only have big packs and need single pieces? Imagine you have 4 packs of 10 crackers, but your friend wants 7 crackers. You can't just break a pack! Instead, you open one pack and trade it for 10 single crackers. Now you have 3 packs and 10 single crackers, and you can easily share 7!
Subtraction with regrouping is just like that! We are just trading bigger place values for smaller ones so we can subtract. Let's see how it works.
From Blocks to Numbers
We start our adventure with real tools, just like a builder! Then, we draw a map, and finally, we write the secret code (the numbers!).
- Concrete Blocks: First, we use base-ten blocks. If we need to solve 145 - 28, we see we can't take 8 ones from 5 ones. So, we trade one ten-rod for 10 one-cubes. Now we have 15 ones, and we can easily subtract 8!
- Pictorial Drawings: Next, we draw it! We draw our hundreds, tens, and ones. To regroup, we cross out a ten-stick and draw 10 little dots in the ones column. It's a picture of our trade!
- Abstract Algorithm: Finally, we use the standard algorithm. Crossing out the 4 in the tens place and writing a 3 above it is the same as taking away a ten-rod. Adding a '1' next to the 5 in the ones place to make it 15 is the same as getting those 10 new one-cubes!
Key Takeaway!
Regrouping is just trading. When you don't have enough in a column, you go next door to the left, borrow one big group, and trade it for ten smaller ones.
Challenge Mission: The Pencil Problem!
Let's solve this puzzle: A school needs 600 pencils but only has 287. How many more do they need? We need to calculate 600 - 287.
The challenge here is the zeros! How do we subtract from zero? We have to go on a double regrouping adventure! We can't borrow from the tens place, so we go all the way to the hundreds place. We trade 1 hundred for 10 tens. THEN, we can trade 1 of those new tens for 10 ones. Now we have plenty to subtract! A bar model would show a big bar for 600, with a piece for 287 and a question mark for the part we need to find.
After all that trading, 600 becomes 5 hundreds, 9 tens, and 10 ones. Now we can solve it: 10 - 7 = 3, 9 - 8 = 1, and 5 - 2 = 3. The school needs 313 more pencils! You did it!
Sample questions
Skills in this topic
- Subtract numbers involving regrouping ones from tens using concrete base-ten blocks.
- Represent subtraction with regrouping ones from tens using pictorial models.
- Subtract two 3-digit numbers with multiple regrouping (hundreds to tens, tens to ones) using the standard algorithm.
- Solve multi-step subtraction word problems within 1,000 involving multiple regrouping using bar models.
- A school needs 600 pencils and only has 287. How can you determine the exact number of pencils still needed, and what challenges might arise in the calculation?
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