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Regrouping Rulz!

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Warm Up

Regrouping Warm Up: How Many?

Objective: To activate prior knowledge about place value and counting in tens and ones.

Instructions:
1. Look at the number of objects shown.
2. Count the objects and write down how many tens and how many ones you see.
3. Write the total number.

Example:
(Picture of 1 ten block and 3 unit cubes)
* Tens: 1
* Ones: 3
* Total: 13

Your Turn!

Question 1:
(Imagine a picture of 2 ten blocks and 5 unit cubes)
* Tens:


* Ones:


* Total:



Question 2:
(Imagine a picture of 1 ten block and 12 unit cubes)
* Tens:


* Ones:


* Total:



Question 3:
(Imagine a picture of 3 ten blocks and 0 unit cubes)
* Tens:


* Ones:


* Total:


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Lesson Plan

Regrouping Rulz!

Students will understand and apply the concept of regrouping (borrowing and carrying) in two-digit addition and subtraction problems, demonstrating proficiency through guided practice and independent work.

Regrouping is a fundamental skill in mathematics that builds a strong foundation for more complex arithmetic. Mastering regrouping helps students develop number sense, understand place value more deeply, and confidently solve real-world problems involving addition and subtraction.

Audience

Elementary School Students (Grades 2-4), with extended time for students with learning disabilities.

Time

40 minutes (with extended time as needed)

Approach

This lesson uses visual aids, manipulatives, and the 'I do, we do, you do' model.

Prep

Teacher Preparation

15 minutes

Step 1

Warm Up: How Many?

5 minutes

  1. Distribute the Regrouping Warm Up: How Many? to students.
    2. Instruct students to complete the warm-up activity, focusing on identifying tens and ones.
    3. Review answers as a class, reinforcing place value concepts. (Teacher Script: Regrouping Script)

Step 2

Introduction: What is Regrouping?

10 minutes

  1. Using the Regrouping Rulz! Slide Deck (Slides 1-3) and Regrouping Script, introduce the concept of regrouping.
    2. I Do: Model several examples of two-digit addition and subtraction with regrouping using Base Ten Blocks and demonstrating the written algorithm on the board.
    3. Emphasize the connection between the manipulatives and the written steps. (Teacher Script: Regrouping Script)

Step 3

Guided Practice: We Do It Together!

15 minutes

  1. We Do: Guide students through several practice problems using the Regrouping Rulz! Slide Deck (Slides 4-6) and Base Ten Blocks.
    2. Work collaboratively as a class and in small groups to solve problems, encouraging students to explain their thinking.
    3. Facilitate the Regrouping Discussion: Why Regroup? during this segment, allowing students to articulate their understanding.
    4. Provide targeted support to students with learning disabilities, ensuring they have ample time and assistance with manipulatives. (Teacher Script: Regrouping Script)

Step 4

Independent Practice: You Do It!

15 minutes (extended as needed)

  1. You Do: Distribute the Regrouping Worksheet for independent practice.
    2. Students will also engage with the Regrouping Activity: Build It, Solve It! and the Regrouping Game: Trade & Solve to solidify their understanding.
    3. Circulate the classroom, providing individual assistance and checking for understanding. Offer extended time and simplified problems or additional manipulative support for exceptional students.
    4. Encourage students to refer to the Regrouping Reading: The Power of Tens if they need a refresher. (Teacher Script: Regrouping Script)

Step 5

Assessment & Wrap-Up

10 minutes (extended as needed)

  1. Administer the Regrouping Quiz to assess immediate understanding.
    2. Conclude the lesson with the Regrouping Cool Down: One Big Idea activity.
    3. For a more comprehensive assessment, the Regrouping Test can be administered at a later time. (Teacher Script: Regrouping Script)
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Slide Deck

Regrouping Rulz!

The Power of Place Value

  • What is regrouping?
  • Why do we need it?
  • How does it make math easier?

Welcome students and introduce the exciting topic of regrouping. Explain that it's a super useful math trick!

Tens and Ones: A Quick Review

Remember your place values:

  • Ones Place: How many single units do you have?
  • Tens Place: How many groups of ten do you have?

Key Idea: When you have 10 or more 'ones', you can regroup them into a 'ten'!

Explain the concept of place value using tens and ones. Use visual aids like Base Ten Blocks. Emphasize that ten ones make one ten.

I Do: Adding with Regrouping

Let's try an example together!

Problem: 27 + 15 = ?

  1. Start with the ones: 7 + 5 = 12
  2. Regroup: 12 ones is 1 ten and 2 ones.
  3. Write down the 2 in the ones place.
  4. Carry over the 1 ten to the tens place.
  5. Add the tens: 1 + 2 + 1 = 4

Answer: 42

I Do: Model a two-digit addition problem with regrouping. Show how to use Base Ten Blocks first, then demonstrate the written algorithm step-by-step. Talk through your thinking process.

We Do: Another Addition Problem

Your turn to help me!

Problem: 38 + 24 = ?

  1. What do we add first? (Ones place: 8 + 4 = ?)
  2. What happens when we get 12? (Regroup! 1 ten and 2 ones)
  3. Where does the 2 go? Where does the 1 go?
  4. Now add the tens! (1 + 3 + 2 = ?)

Answer: __

We Do: Lead students through a new addition problem. Have them use their manipulatives and guide them through each step. Ask questions to check for understanding.

I Do: Subtracting with Regrouping

Sometimes we need more ones!

Problem: 43 - 17 = ?

  1. Start with the ones: Can we take 7 from 3? No!
  2. Regroup: Take 1 ten from the tens place (4 becomes 3).
  3. Add 10 ones to the 3 ones (3 becomes 13).
  4. Now subtract the ones: 13 - 7 = 6
  5. Subtract the tens: 3 - 1 = 2

Answer: 26

I Do: Model a two-digit subtraction problem with regrouping. Explain why 'borrowing' is actually 'regrouping' a ten into ten ones. Use Base Ten Blocks and the written algorithm.

We Do: Another Subtraction Problem

Let's subtract together!

Problem: 52 - 28 = ?

  1. Can we take 8 from 2? (No! What do we do?)
  2. Regroup a ten! (5 tens becomes 4 tens, 2 ones becomes 12 ones)
  3. Now subtract the ones: 12 - 8 = ?
  4. Subtract the tens: 4 - 2 = ?

Answer: __

We Do: Lead students through a new subtraction problem. Emphasize that they are changing a ten into ten ones. Use manipulatives and encourage participation.

You Do: Time to Practice!

Show what you know!

Remember: You can always use your Base Ten Blocks if you need help!

Transition to independent practice. Explain the upcoming activities and encourage students to apply what they've learned. Remind them they can use manipulatives.

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Script

Regrouping Script

Introduction: Regrouping Rulz! (Corresponds to Regrouping Rulz! Slide Deck - Slide 1)

Teacher: "Good morning, mathematicians! Today, we're going to unlock a super cool math superpower called regrouping! Have you ever heard that word before? It might sound tricky, but it's actually a way to make addition and subtraction much easier, especially when numbers get a little bigger.

Regrouping is like a magic trick where we swap numbers around to help us solve problems. It helps us truly understand our numbers and how they work together. By the end of this lesson, you'll be a regrouping pro, and that's going to help you with so much more math down the road!

So, get ready to discover the power of tens and ones!"

Tens and Ones: A Quick Review (Corresponds to Regrouping Rulz! Slide Deck - Slide 2)

Teacher: "Before we jump into our superpower, let's do a quick warm-up to get our brains ready. Remember our good friends, the ones place and the tens place?"

(Distribute Regrouping Warm Up: How Many? now if not already done.)

Teacher: "On your warm-up sheet, you'll see some pictures. Your job is to count the objects and tell me how many tens and how many ones you see. Then, write the total number. For example, if you see one ten block and three single cubes, you have 1 ten and 3 ones, making a total of 13.

Take a few minutes to complete the 'How Many?' warm-up. And remember, it's okay to think out loud or use your fingers if you need to."

(Allow students to work. Circulate and assist.)

Teacher: "Alright, let's go over it! For Question 1, if you had 2 ten blocks and 5 unit cubes, how many tens and ones? (Pause for answers) Right, 2 tens and 5 ones, making 25! What about Question 2? One ten block and 12 unit cubes? Uh oh! We have more than 9 ones! What can we do with those 12 ones? (Pause for answers) Exactly! We can take 10 of those ones and 'bundle' them up to make another ten! So, 1 ten and 12 ones actually becomes 2 tens and 2 ones, making 22. Great job noticing that! And Question 3, 3 ten blocks and 0 unit cubes, easy-peasy, that's 30.

This idea of bundling those 10 ones to make a ten is exactly what regrouping is all about!"

I Do: Adding with Regrouping (Corresponds to Regrouping Rulz! Slide Deck - Slide 3)

Teacher: "Now, watch me closely. This is where I show you how to use our regrouping superpower for addition. I'm going to do an example, and I'll explain every single step as I go.

Look at the problem on the slide: 27 + 15 = ?

First, I always start with the ones place. I have 7 ones and 5 ones. If I add 7 + 5, what do I get? (Pause) That's right, 12! Now, can I put '12' in the ones column? (Shake head no) Why not? Because the ones column can only hold numbers from 0 to 9! So, what do I do with that 12? I regroup it!

12 ones is the same as 1 ten and 2 ones. So, I'm going to write the '2' in the ones place, and I'm going to 'carry over' or move that '1 ten' to the tens place. I like to write a small '1' above the tens column to remind myself.

Now, I go to the tens place. I have the 1 ten I carried over, plus 2 tens, plus 1 ten. Let's add them: 1 + 2 + 1 = 4. So, I write '4' in the tens place.

My answer is 42! See how we used regrouping to make sure each place value only had one digit?"

We Do: Another Addition Problem (Corresponds to Regrouping Rulz! Slide Deck - Slide 4)

Teacher: "Fantastic! Now, it's our turn to work together. This is the 'we do' part. I need your help to solve this next problem. Get out your Base Ten Blocks, or if you don't have them, imagine them in your head. Let's look at the problem on the slide: 38 + 24 = ?

Alright, where do we always start? (Pause for answer: Ones place) Excellent! What do we add in the ones place? (Pause for answer: 8 + 4) And what's 8 + 4? (Pause for answer: 12) Perfect!

Now, what do we do with that 12? Can we put 12 in the ones column? (Pause for answer: No!) Right! So, we regroup! How do we regroup 12 ones? (Pause for answer: 1 ten and 2 ones) Awesome!

So, where does the '2' go? (Pause for answer: In the ones place!) And where does that '1 ten' go? (Pause for answer: Carry it over to the tens place!) Great job remembering to put that little '1' above the tens column.

Now for the tens place! What numbers do we add together in the tens column? (Pause for answer: 1 + 3 + 2) And what's 1 + 3 + 2? (Pause for answer: 6) You got it! So we write '6' in the tens place.

What's our final answer? (Pause for answer: 62) Wonderful! We just added with regrouping together!"

(Transition to Regrouping Discussion: Why Regroup? during this segment, asking students questions about why they needed to regroup.)

I Do: Subtracting with Regrouping (Corresponds to Regrouping Rulz! Slide Deck - Slide 5)

Teacher: "Regrouping also helps us with subtraction! Sometimes we don't have enough ones to take away, and we need to get more. This is often called 'borrowing', but remember, we're really just regrouping!

Let's look at this problem: 43 - 17 = ?

I always start in the ones place. I have 3 ones, and I need to take away 7 ones. Can I take 7 from 3? (Shake head no) No, I don't have enough! So, I need to go next door to the tens place and ask for help.

I have 4 tens in the tens place. I'm going to regroup one of those tens. So, 4 tens becomes 3 tens. I cross out the 4 and write a 3 above it. Now, that 1 ten I took is worth 10 ones. I'm going to add those 10 ones to the 3 ones I already have. So, 3 ones becomes 13 ones. I cross out the 3 and write 13 above it.

Now, I have 13 ones, and I need to take away 7 ones. 13 - 7 = 6. So, I write '6' in the ones place.

Next, I go to the tens place. Remember, I only have 3 tens left. I need to take away 1 ten. 3 - 1 = 2. So, I write '2' in the tens place.

My answer is 26! We just used our regrouping superpower to subtract!"

We Do: Another Subtraction Problem (Corresponds to Regrouping Rulz! Slide Deck - Slide 6)

Teacher: "You're doing great! Let's try another subtraction problem together. Get your Base Ten Blocks ready if you're using them. The problem is: 52 - 28 = ?

Where do we start? (Pause for answer: Ones place!) Good! Can we take 8 from 2? (Pause for answer: No!) What should we do then? (Pause for answer: Regroup from the tens place!) Excellent thinking!

So, how many tens do we have in 52? (Pause for answer: 5 tens) If we regroup one of those tens, how many tens are left? (Pause for answer: 4 tens!) Yes, cross out the 5 and write 4 above it. Now, that ten we regrouped becomes 10 ones. We add those 10 ones to the 2 ones we already have. How many ones do we have now? (Pause for answer: 12 ones!) That's right! Cross out the 2 and write 12 above it.

Now, we have 12 ones and we take away 8 ones. What's 12 - 8? (Pause for answer: 4!) Super! Write 4 in the ones place.

Now for the tens place. We have 4 tens left, and we need to take away 2 tens. What's 4 - 2? (Pause for answer: 2!) Fantastic! Write 2 in the tens place.

Our final answer is 24! You are becoming regrouping masters!"

You Do: Time to Practice! (Corresponds to Regrouping Rulz! Slide Deck - Slide 7)

Teacher: "You've seen me do it, we've done it together, and now it's your turn to shine independently! You're going to use all the skills we've learned today.

First, I'm handing out the Regrouping Worksheet. You'll find some addition and subtraction problems there, just like the ones we've practiced. Use your Base Ten Blocks if you want, or try solving them on your own.

Next, we have a fun Regrouping Activity: Build It, Solve It! and a Regrouping Game: Trade & Solve to help you practice in a hands-on way. I'll be walking around to help anyone who needs it. If you get stuck, remember you can always look back at the Regrouping Reading: The Power of Tens for a quick reminder.

For my friends who sometimes need a little extra time or support, please take all the time you need. I'm here to help, and you can also use your manipulatives as much as you like. We want everyone to feel confident!

Work at your own pace, and let me know if you have any questions!"

(Circulate, provide support, and manage activities.)

Assessment & Wrap-Up (Corresponds to Regrouping Rulz! Slide Deck - No specific slide, but signals the end of direct instruction)

Teacher: "Great work everyone! To see how much you've learned, we're going to do a quick Regrouping Quiz. This will help me understand what we might need to review.

After the quiz, we'll finish up with our Regrouping Cool Down: One Big Idea. Just a quick thought about what you learned today. The Regrouping Test can be used later for a bigger assessment of your skills.

Remember, math is all about practice and understanding. You all did an amazing job today discovering the power of regrouping!"

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Worksheet

Regrouping Worksheet: Show Your Work!

Instructions: Solve the following addition and subtraction problems. Remember to show your regrouping! Use your Base Ten Blocks if you need help.

Part 1: Addition with Regrouping

  1. 45 + 27 = ?






  2. 38 + 16 = ?






  3. 59 + 23 = ?






  4. 61 + 19 = ?






  5. 24 + 37 = ?






Part 2: Subtraction with Regrouping

  1. 52 - 18 = ?






  2. 73 - 25 = ?






  3. 40 - 16 = ?






  4. 81 - 34 = ?






  5. 65 - 29 = ?






Challenge Question!

Sarah had 34 stickers. Her friend gave her 18 more. Then, she gave 12 stickers to her brother. How many stickers does Sarah have now?












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Reading

Regrouping: The Power of Tens and Ones!

Have you ever played a game where you had to trade small pieces for bigger pieces? Like trading ten pennies for a dime? Or ten single Lego bricks for one long Lego brick?

That's a lot like what we do in math when we regroup! Regrouping is a super helpful math trick we use when we add or subtract numbers.

Why do we regroup?

Numbers are made of different places: the ones place and the tens place. The ones place holds numbers from 0 to 9. The tens place holds groups of ten.

Imagine you're adding. If you have 7 apples and then get 5 more apples, you have 12 apples, right? You can't put "12" in the ones place because it's too big! The ones place only likes single digits. So, what do you do?

You regroup! You take 10 of those 12 apples and put them in a basket. That basket is like a "group of ten"! Now you have 1 basket of ten apples and 2 single apples left over. You write the '2' in the ones place and carry the '1 basket of ten' over to the tens place.

Adding with Regrouping (Carrying Over)

When we add numbers like 27 + 15:

  1. Add the ones first: 7 ones + 5 ones = 12 ones.
  2. Regroup! Since 12 ones is 1 ten and 2 ones, we write down the '2' in the ones column.
  3. Carry the 1 ten: We move that 1 ten over to the tens column to add it with the other tens.
  4. Add the tens: Now, add all the tens together, including the one you carried over.

Subtracting with Regrouping (Borrowing)

When we subtract numbers like 43 - 17:

  1. Start with the ones: Can we take 7 ones from 3 ones? No, 3 is too small!
  2. Go to the tens place for help: We go to the number in the tens place (which is 4 tens).
  3. Regroup! We take 1 ten from the 4 tens, so it becomes 3 tens. We then turn that 1 ten into 10 ones and add it to our 3 ones, making it 13 ones.
  4. Now subtract the ones: We can now subtract 7 from 13! (13 - 7 = 6)
  5. Subtract the tens: Finally, subtract the tens, remembering that the 4 tens became 3 tens.

Regrouping is like exchanging money – you trade smaller coins for a bigger bill to make counting easier. It's a key skill for becoming a math wizard!

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Activity

Regrouping Activity: Build It, Solve It!

Objective: To physically model addition and subtraction problems with regrouping using Base Ten Blocks.

Materials: Base Ten Blocks (or other manipulatives like craft sticks, small counters, and bundles of ten)

Instructions:

Part 1: Adding with Regrouping

  1. Pick an addition problem from your Regrouping Worksheet, or choose one below:

    • 36 + 18
    • 29 + 25
  2. Build it: Use your Base Ten Blocks to build the first number (e.g., 3 tens and 6 ones for 36).

  3. Add the second number: Add the tens and ones from the second number to your blocks.

  4. Check the ones: Do you have 10 or more ones? If yes, regroup! Trade 10 ones for 1 ten block. Move the new ten block to the tens pile.

  5. Count and Solve: Count your total tens and ones. Write down your answer.

  6. Repeat with another addition problem.

Part 2: Subtracting with Regrouping

  1. Pick a subtraction problem from your Regrouping Worksheet, or choose one below:

    • 41 - 15
    • 53 - 27
  2. Build it: Use your Base Ten Blocks to build the first number (e.g., 4 tens and 1 one for 41).

  3. Look at the ones place: Do you have enough ones to take away the second number's ones? If no, you need to regroup!

  4. Regroup a ten: Take one ten block from your tens pile and trade it for 10 ones blocks. Add these 10 ones to your current ones pile.

  5. Subtract: Now, take away the correct number of ones, then take away the correct number of tens.

  6. Count and Solve: Count your remaining tens and ones. Write down your answer.

  7. Repeat with another subtraction problem.

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Discussion

Regrouping Discussion: Why Regroup?

Objective: To encourage students to articulate their understanding of why regrouping is necessary and how it works.

Instructions: Discuss the following questions with your classmates. Be ready to share your ideas with the whole class.

Discussion Questions:

  1. Imagine you have 15 single candies. Can you put all 15 candies into a box that only holds 9 candies? Why or why not?





  2. When we add 7 + 5 and get 12, why can't we just write "12" in the ones column? What do we do instead?





  3. Think about subtracting 3 from 1. Can you do it? Why not? What magic trick do we use to help us?





  4. How does using Base Ten Blocks help you understand regrouping better?





  5. Can you think of a real-life situation where you might need to regroup something? (Hint: Think about money or counting groups of things!)





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Game

Regrouping Game: Trade & Solve

Objective: To practice regrouping in a fun, interactive way.

Players: 2-4

Materials:

  • Base Ten Blocks (or pennies/dimes, or craft sticks in bundles of ten)
  • Two dice
  • Paper and pencil for scoring

How to Play (Addition Version):

  1. Each player starts with a recording sheet.
  2. Player 1 rolls the two dice. The first die is the tens digit, and the second die is the ones digit for the first number. (e.g., if you roll a 3 and a 5, your number is 35).
  3. Player 1 rolls the two dice again to create the second number (e.g., if you roll a 2 and a 8, your number is 28).
  4. Write down the addition problem (e.g., 35 + 28 = ?).
  5. Using Base Ten Blocks, build both numbers. Combine the ones. If you have 10 or more ones, trade 10 ones for 1 ten block. Move the new ten to the tens column.
  6. Combine the tens (including any new tens from regrouping).
  7. Write down the final sum. The player explains their regrouping steps.
  8. Players take turns. The player with the highest sum at the end of 5 rounds wins!

How to Play (Subtraction Version - Advanced):

  1. Each player starts with a recording sheet.
  2. Player 1 rolls the two dice to create a two-digit number. This is the starting number (e.g., 4 and 2 makes 42).
  3. Player 1 rolls the two dice again to create the number to subtract. This number must be smaller than the starting number. If it's not, roll again (e.g., 1 and 7 makes 17).
  4. Write down the subtraction problem (e.g., 42 - 17 = ?).
  5. Using Base Ten Blocks, build the starting number (e.g., 4 tens and 2 ones).
  6. Try to subtract the ones. If you don't have enough ones (e.g., can't take 7 from 2), trade 1 ten block for 10 ones blocks. Add these 10 ones to your current ones.
  7. Now subtract the ones, then subtract the tens.
  8. Write down the final difference. The player explains their regrouping steps.
  9. Players take turns. The player with the highest difference at the end of 5 rounds wins!
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Quiz

Regrouping Quiz

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Test

Regrouping Test

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Answer Key

Regrouping Answer Key

This answer key provides solutions and step-by-step reasoning for the Regrouping Worksheet, Regrouping Quiz, and Regrouping Test.

Regrouping Warm Up: How Many? Answer Key

Question 1: (2 ten blocks, 5 unit cubes)

  • Tens: 2
  • Ones: 5
  • Total: 25

Question 2: (1 ten block, 12 unit cubes)

  • Tens: 1 (then regroup to 2)
  • Ones: 12 (then regroup to 2)
  • Total: 22
  • Reasoning: 12 ones is 1 ten and 2 ones. Add the new ten to the existing tens (1 + 1 = 2 tens). So, 2 tens and 2 ones.

Question 3: (3 ten blocks, 0 unit cubes)

  • Tens: 3
  • Ones: 0
  • Total: 30


    ## Regrouping Worksheet Answer Key

Part 1: Addition with Regrouping

  1. 45 + 27 = 72

    • Reasoning:
      • Ones: 5 + 7 = 12. Regroup 12 ones as 1 ten and 2 ones. Write 2 in the ones place, carry 1 to the tens place.
      • Tens: 1 (carried) + 4 + 2 = 7. Write 7 in the tens place.
  2. 38 + 16 = 54

    • Reasoning:
      • Ones: 8 + 6 = 14. Regroup 14 ones as 1 ten and 4 ones. Write 4 in the ones place, carry 1 to the tens place.
      • Tens: 1 (carried) + 3 + 1 = 5. Write 5 in the tens place.
  3. 59 + 23 = 82

    • Reasoning:
      • Ones: 9 + 3 = 12. Regroup 12 ones as 1 ten and 2 ones. Write 2 in the ones place, carry 1 to the tens place.
      • Tens: 1 (carried) + 5 + 2 = 8. Write 8 in the tens place.
  4. 61 + 19 = 80

    • Reasoning:
      • Ones: 1 + 9 = 10. Regroup 10 ones as 1 ten and 0 ones. Write 0 in the ones place, carry 1 to the tens place.
      • Tens: 1 (carried) + 6 + 1 = 8. Write 8 in the tens place.
  5. 24 + 37 = 61

    • Reasoning:
      • Ones: 4 + 7 = 11. Regroup 11 ones as 1 ten and 1 one. Write 1 in the ones place, carry 1 to the tens place.
      • Tens: 1 (carried) + 2 + 3 = 6. Write 6 in the tens place.

Part 2: Subtraction with Regrouping

  1. 52 - 18 = 34

    • Reasoning:
      • Ones: Can't subtract 8 from 2. Regroup 1 ten from 5 tens (becomes 4 tens). Add 10 ones to 2 ones (becomes 12 ones). Now, 12 - 8 = 4.
      • Tens: 4 (remaining) - 1 = 3.
  2. 73 - 25 = 48

    • Reasoning:
      • Ones: Can't subtract 5 from 3. Regroup 1 ten from 7 tens (becomes 6 tens). Add 10 ones to 3 ones (becomes 13 ones). Now, 13 - 5 = 8.
      • Tens: 6 (remaining) - 2 = 4.
  3. 40 - 16 = 24

    • Reasoning:
      • Ones: Can't subtract 6 from 0. Regroup 1 ten from 4 tens (becomes 3 tens). Add 10 ones to 0 ones (becomes 10 ones). Now, 10 - 6 = 4.
      • Tens: 3 (remaining) - 1 = 2.
  4. 81 - 34 = 47

    • Reasoning:
      • Ones: Can't subtract 4 from 1. Regroup 1 ten from 8 tens (becomes 7 tens). Add 10 ones to 1 one (becomes 11 ones). Now, 11 - 4 = 7.
      • Tens: 7 (remaining) - 3 = 4.
  5. 65 - 29 = 36

    • Reasoning:
      • Ones: Can't subtract 9 from 5. Regroup 1 ten from 6 tens (becomes 5 tens). Add 10 ones to 5 ones (becomes 15 ones). Now, 15 - 9 = 6.
      • Tens: 5 (remaining) - 2 = 3.

Challenge Question!

Sarah had 34 stickers. Her friend gave her 18 more. Then, she gave 12 stickers to her brother. How many stickers does Sarah have now?

  • Step 1: Add stickers Sarah received.
    34 + 18 = 52 stickers

    • Reasoning: 4 + 8 = 12 ones (regroup to 1 ten, 2 ones). 1 (carried) + 3 + 1 = 5 tens.
  • Step 2: Subtract stickers Sarah gave away.
    52 - 12 = 40 stickers

    • Reasoning: 2 - 2 = 0 ones. 5 - 1 = 4 tens.
  • Answer: Sarah has 40 stickers now.

Regrouping Quiz Answer Key

  1. Solve: 34 + 19 = ?

    • Answer: 53
    • Reasoning: 4 + 9 = 13 (regroup to 1 ten, 3 ones). 1 (carried) + 3 + 1 = 5 tens.
  2. Solve: 26 + 48 = ?

    • Answer: 74
    • Reasoning: 6 + 8 = 14 (regroup to 1 ten, 4 ones). 1 (carried) + 2 + 4 = 7 tens.
  3. Solve: 51 - 23 = ?

    • Answer: 28
    • Reasoning: Can't subtract 3 from 1. Regroup 1 ten from 5 tens (becomes 4 tens). 1 one becomes 11 ones. 11 - 3 = 8. 4 (remaining) - 2 = 2.
  4. Solve: 60 - 35 = ?

    • Answer: 25
    • Reasoning: Can't subtract 5 from 0. Regroup 1 ten from 6 tens (becomes 5 tens). 0 ones becomes 10 ones. 10 - 5 = 5. 5 (remaining) - 3 = 2.
  5. When you have 14 ones, what is the correct way to regroup them?

    • Correct Answer: 1 ten and 4 ones
    • Reasoning: Every group of ten ones can be exchanged for one ten. 14 ones = 10 ones + 4 ones = 1 ten + 4 ones.
  6. Explain in your own words why we need to regroup when subtracting 7 from 2 in the ones place of a problem like 32 - 17.

    • Sample Answer: You can't take away 7 from only 2 because 2 is a smaller number than 7. So, you have to go to the tens place and "borrow" or regroup one of the tens. That ten becomes 10 ones, and you add it to the 2 ones you already have, making 12 ones. Then you can subtract 7 from 12.

Regrouping Test Answer Key

Addition with Regrouping

  1. 28 + 35 = 63

    • Reasoning: 8 + 5 = 13 (regroup to 1 ten, 3 ones). 1 (carried) + 2 + 3 = 6 tens.
  2. 46 + 17 = 63

    • Reasoning: 6 + 7 = 13 (regroup to 1 ten, 3 ones). 1 (carried) + 4 + 1 = 6 tens.
  3. 59 + 23 = 82

    • Reasoning: 9 + 3 = 12 (regroup to 1 ten, 2 ones). 1 (carried) + 5 + 2 = 8 tens.
  4. 77 + 14 = 91

    • Reasoning: 7 + 4 = 11 (regroup to 1 ten, 1 one). 1 (carried) + 7 + 1 = 9 tens.
  5. 32 + 58 = 90

    • Reasoning: 2 + 8 = 10 (regroup to 1 ten, 0 ones). 1 (carried) + 3 + 5 = 9 tens.

Subtraction with Regrouping

  1. 90 - 45 = 45

    • Reasoning: Can't subtract 5 from 0. Regroup 1 ten from 9 tens (becomes 8 tens). 0 ones becomes 10 ones. 10 - 5 = 5. 8 (remaining) - 4 = 4.
  2. 64 - 27 = 37

    • Reasoning: Can't subtract 7 from 4. Regroup 1 ten from 6 tens (becomes 5 tens). 4 ones becomes 14 ones. 14 - 7 = 7. 5 (remaining) - 2 = 3.
  3. 83 - 19 = 64

    • Reasoning: Can't subtract 9 from 3. Regroup 1 ten from 8 tens (becomes 7 tens). 3 ones becomes 13 ones. 13 - 9 = 4. 7 (remaining) - 1 = 6.
  4. 50 - 26 = 24

    • Reasoning: Can't subtract 6 from 0. Regroup 1 ten from 5 tens (becomes 4 tens). 0 ones becomes 10 ones. 10 - 6 = 4. 4 (remaining) - 2 = 2.
  5. 41 - 18 = 23

    • Reasoning: Can't subtract 8 from 1. Regroup 1 ten from 4 tens (becomes 3 tens). 1 one becomes 11 ones. 11 - 8 = 3. 3 (remaining) - 1 = 2.

Word Problems

  1. Maria had 25 balloons. Her friend gave her 17 more. How many balloons does Maria have now?

    • Answer: 42 balloons
    • Reasoning: 25 + 17 = ?
      • Ones: 5 + 7 = 12 (regroup to 1 ten, 2 ones).
      • Tens: 1 (carried) + 2 + 1 = 4 tens.
  2. There were 43 birds in a tree. 16 birds flew away. How many birds are left in the tree?

    • Answer: 27 birds
    • Reasoning: 43 - 16 = ?
      • Ones: Can't subtract 6 from 3. Regroup 1 ten from 4 tens (becomes 3 tens). 3 ones becomes 13 ones. 13 - 6 = 7.
      • Tens: 3 (remaining) - 1 = 2.

Challenge Question

  1. If you have 3 tens and 14 ones, and you regroup, what number do you have? Explain how you regrouped.
    • Answer: 44
    • Explanation: 14 ones can be regrouped into 1 ten and 4 ones. You already have 3 tens. So, add the new 1 ten to the existing 3 tens (3 + 1 = 4 tens). This leaves you with 4 tens and 4 ones, which is the number 44.
lenny
lenny

Cool Down

Regrouping Cool Down: One Big Idea

Instructions: In your own words, write down one big idea or one important thing you learned about regrouping today.













Bonus Question: What is one question you still have about regrouping?







lenny
lenny