Adding Numbers with Regrouping in Ones and Tens

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The Great Regrouping Adventure!

Hey Math Explorer! Have you ever had a big pile of pennies? If you have 12 pennies, it's much easier to carry around one dime and two pennies, right? You can trade 10 of your pennies for 1 shiny dime.

Guess what? That's exactly what we do in math when we regroup! We trade a group of 10 from one place value for a '1' in the next bigger place value. It makes adding big numbers super neat and tidy!

Regrouping the Ones Place

Let's look at 28 + 5. Remember our base-ten blocks? We start with 2 tens and 8 ones. Then, we add 5 more ones.

First, add the ones: 8 + 5 = 13 ones. Uh oh! That's too many for the ones place!
We take 10 of those ones and swoosh! We trade them for 1 new ten rod.
That new ten rod moves over to the tens place. The 3 leftover ones stay put.
Now, add the tens: 1 (new ten) + 2 (old tens) = 3 tens.

So, 28 + 5 = 33!

Key Takeaway!

When any place has 10 or more, we bundle up 10 and move it to the next bigger place value on the left. (10 ones become 1 ten, and 10 tens become 1 hundred!)

Regrouping the Tens Place (and beyond!)

This amazing trick works for tens, too! Let's try 172 + 53.

Ones Place: 2 + 3 = 5. No regrouping needed here. Easy peasy!

Tens Place: 7 tens + 5 tens = 12 tens. Whoa, that's more than 9! Time to regroup. We trade 10 tens for 1 new hundred. The 2 leftover tens stay put.

Hundreds Place: 1 (new hundred) + 1 (old hundred) = 2 hundreds.

Our final answer is 225!

You are becoming a regrouping pro! It's a math superpower that lets you solve bigger and bigger problems. Keep up the fantastic work!

Sample questions

1. You have 1 ten block and 8 one blocks. If you add 5 more one blocks, how many blocks do you have in total? Remember to regroup 10 one blocks into 1 ten block.

○ 13

○ 15

○ 25

✓ 23

Answer: 23 — First, add the one blocks: 8 + 5. If you have 10 or more one blocks, trade 10 of them for 1 ten block. Then count your total tens and ones.

2. Imagine you have 2 ten blocks and 6 one blocks. If you add 7 more one blocks, what is the new total? Think about regrouping.

✓ 33

○ 23

○ 36

○ 213

Answer: 33 — Start by combining the one blocks: 6 + 7. If you can make a new ten, add it to your existing ten blocks.

3. You start with 3 ten blocks and 4 one blocks. Then you add 9 more one blocks. How many blocks do you have after regrouping?

○ 33

○ 313

✓ 43

○ 49

Answer: 43 — Add the one blocks first: 4 + 9. If you have enough, make a new ten block and add it to your other ten blocks.

Skills in this topic

Add a 2-digit number to a 1-digit number with regrouping in the ones place using base-ten blocks (Concrete)
Add two 2-digit numbers with regrouping in the ones place using place value charts (Pictorial)
Add two 2-digit numbers with regrouping in the tens place
Add a 3-digit number to a 2-digit number with regrouping in the ones and/or tens place
Explain how regrouping in addition is like exchanging smaller coins for a larger one (e.g., 10 pennies for a dime)

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