Divide & Conquer!

Emily Ondreas

Tier 1

Lesson Plan

Divide & Conquer!

Students will be able to solve long division problems with two-digit dividends and one-digit divisors, resulting in remainders.

Understanding long division with remainders is crucial for real-world problem-solving, like sharing items equally or understanding fractions. It builds a strong foundation for future mathematical concepts.

Audience

4th Grade Students

Time

30 minutes

Approach

Through direct instruction, guided practice, and independent application.

Materials

Smartboard or Projector, Markers/Whiteboard, Divide & Conquer Slide Deck, Warm-Up: Remainder Race, Long Division Worksheet, Long Division Answer Key, and Cool-Down: Remainder Reflection

Prep

Teacher Preparation

10 minutes

Review the Divide & Conquer Slide Deck and practice the examples.
- Print enough copies of the Long Division Worksheet for each student.
- Have the Long Division Answer Key ready for quick checking.
- Ensure the projector/smartboard is set up and working.
- Review all generated materials as needed, especially the Script: Divide & Conquer! to internalize talking points and instructions.
- Prepare materials for the Warm-Up: Remainder Race and Cool-Down: Remainder Reflection.

Step 1

Introduction & Warm-Up

5 minutes

Begin with the Warm-Up: Remainder Race to activate prior knowledge about division and introduce the concept of remainders. (2 minutes)
* Review warm-up answers as a class, guiding students to think about what a 'remainder' means. (3 minutes)

Step 2

Direct Instruction: The Division Dance

10 minutes

Introduce long division with remainders using the Divide & Conquer Slide Deck and the Script: Divide & Conquer!.
* Explain the steps of long division (Divide, Multiply, Subtract, Bring Down, Remainder) using a mnemonic like 'Dad, Mom, Sister, Brother, Rover' (D.M.S.B.R.).
* Work through 1-2 example problems together on the board, emphasizing each step and the role of the remainder.
* Encourage student participation by asking questions and checking for understanding.

Step 3

Guided Practice: Let's Do It Together!

8 minutes

Distribute the Long Division Worksheet.
* Work through the first 1-2 problems on the worksheet as a class or in small groups, providing support and clarification.
* Circulate around the room, offering individualized help and checking student progress.
* Use the Long Division Answer Key to quickly verify steps if students are struggling or to provide immediate feedback.

Step 4

Independent Practice & Wrap-Up

5 minutes

Students complete the remaining problems on the Long Division Worksheet independently.
* As students finish, have them begin the Cool-Down: Remainder Reflection as an exit ticket.
* Collect worksheets and cool-downs for assessment.

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Slide Deck

Divide & Conquer!

Long Division with Remainders

Get ready to share equally... and see what's left over!

Welcome students and introduce the lesson. Explain that today we're going to become masters of division, even when things don't divide perfectly!

What is Division?

Division is about splitting things into equal groups or sharing them fairly.

How many groups can you make?
How many are in each group?

Example: If you have 10 cookies and 2 friends, how many cookies does each friend get?

Review what division means. Ask students for examples of when they divide things in their daily lives. Emphasize that division is about fair sharing or grouping.

Leftovers, Anyone?

Sometimes, when we divide, things don't split perfectly evenly.

What happens when you have 7 cookies and 2 friends?

Each friend gets 3 cookies.
There's 1 cookie left over!

That 'left over' amount is called a remainder.

Introduce the concept of a remainder using a simple real-world example. Use visuals if possible (e.g., drawing 7 apples and 3 friends).

Long Division Steps: D-M-S-B-R

Let's learn a trick to remember the steps:

Divide (Dad)
Multiply (Mom)
Subtract (Sister)
Bring Down (Brother)
Remainder (Rover the dog!)

We repeat these steps until there's nothing left to bring down!

Introduce the DMSBR mnemonic. Explain each step clearly and slowly. This will be the foundation for their long division process.

Let's Try One! 17 ÷ 3

Dividend: 17

Divisor: 3

Divide: How many 3s go into 17?
Multiply: What is that number times 3?
Subtract: Take away what you multiplied.
Bring Down: Is there another number to bring down? (Not here yet!)
Remainder: What's left over?

Your answer will be written as: Quotient R Remainder

Walk through this example step-by-step with the students. Encourage them to say the DMSBR steps aloud with you. Show them how to write the remainder.

Another Round! 25 ÷ 4

Dividend: 25

Divisor: 4

Follow the D-M-S-B-R steps carefully!

Divide
Multiply
Subtract
Bring Down
Remainder

Remember: Your remainder must always be smaller than your divisor!

Another guided example. Emphasize checking their subtraction and ensuring the remainder is always smaller than the divisor.

Your Turn to Divide!

Now it's time to put your new skills to the test!

Work on your Long Division Worksheet.
Remember the D-M-S-B-R steps!
Don't forget to write your remainder!

Transition to the worksheet. Explain that they will now practice these steps on their own or with a partner. Remind them to use the DMSBR strategy.

Division Detectives!

You've cracked the code of long division with remainders!

Why are remainders important in real life?
What was one new thing you learned today?

Great job, mathematicians!

Conclude the lesson. Ask students what they learned or found challenging. Collect their worksheets and cool-downs. Reiterate the importance of remainders.

Script

Script: Divide & Conquer!

Introduction & Warm-Up (5 minutes)

"Good morning, future mathematicians! Today, we're going on an exciting adventure to become master 'Division Detectives'! We'll be solving mysteries where numbers don't always divide perfectly, and we'll learn what to do with the 'leftovers.'"

"First, let's get our brains warmed up with a quick 'Remainder Race'!"

(Distribute Warm-Up: Remainder Race)

"Look at the problems on your warm-up sheet. For each problem, I want you to quickly think about how many groups you can make and if there will be anything left over. Don't worry about solving it completely yet, just focus on identifying if there will be a remainder. You have 2 minutes!"

(After 2 minutes)

"Alright, pencils down! Let's quickly review. For number 1, 10 divided by 2, did anyone think there would be a remainder? No, because 10 divides evenly into 2 groups of 5. What about number 2, 7 divided by 2? Yes! We can make two groups of 3, but there's 1 left over. This 'leftover' is what we call a remainder!"

Direct Instruction: The Division Dance (10 minutes)

(Display Slide 3: Leftovers, Anyone? on the projector/smartboard)

"Imagine you have 7 delicious cookies, and you want to share them equally with 2 friends. How many cookies would each friend get?" (Pause for answers - likely '3' with '1 left over')

"Exactly! Each friend gets 3 cookies, and you have 1 cookie left over. That 'left over' cookie is called a remainder. It's the part that can't be divided equally into whole numbers."

(Transition to Slide 4: Long Division Steps: D-M-S-B-R)

"Now, when we do bigger division problems, we use a special method called long division. It has steps, and we have a super-fun way to remember them! Think of your family members: Dad, Mom, Sister, Brother, and Rover the dog!"

"Each letter stands for a step:

D for Divide: How many times does the divisor go into the dividend?
M for Multiply: Multiply the number you just wrote by the divisor.
S for Subtract: Subtract that product from the part of the dividend you were working with.
B for Bring Down: Bring down the next digit from the dividend.
R for Remainder: If there are no more numbers to bring down, what's left is your remainder."

"Let's try an example together using our DMSBR steps!"

(Transition to Slide 5: Let's Try One! 17 ÷ 3. Write the problem on the board as you explain.)

"Our problem is 17 divided by 3. Let's follow our steps.

Divide: How many times does 3 go into 17 without going over? We can count by 3s: 3, 6, 9, 12, 15, 18. 18 is too big, so it's 5 times! Write '5' above the 7 in 17.
Multiply: Now, multiply the 5 by our divisor, 3. What's 5 x 3? That's 15. Write '15' right below the 17.
Subtract: Next, subtract 15 from 17. What do we get? 17 - 15 = 2. Write '2' below the 15.
Bring Down: Is there another number in 17 to bring down? No, we only have the 1 and the 7. So we're done bringing down.
Remainder: What's left at the bottom is our remainder! It's 2. Notice that 2 is smaller than our divisor, 3. That's a good sign!

So, 17 divided by 3 is 5 with a remainder of 2. We write it as 5 R 2."

(Transition to Slide 6: Another Round! 25 ÷ 4. Write the problem on the board.)

"Let's try another one: 25 divided by 4. Who wants to help me with the first step, Divide? How many times does 4 go into 25?" (Call on a student. Guide them to 6.)

"Great, 6! Now for Multiply. What's 6 times 4?" (Call on a student. Guide them to 24.)

"Perfect! Next is Subtract. What's 25 minus 24?" (Call on a student. Guide them to 1.)

"One more! Bring Down. Are there any more numbers to bring down from 25? No. So, what's our Remainder?" (Call on a student. Guide them to 1.)

"Fantastic! 25 divided by 4 is 6 with a remainder of 1, or 6 R 1. Remember, your remainder must always be smaller than your divisor! If it's not, you made a mistake somewhere, probably in your division step."

Guided Practice: Let's Do It Together! (8 minutes)

(Distribute the Long Division Worksheet)

"Alright, Division Detectives! It's time to put your skills into action. I'm handing out a Long Division Worksheet. We're going to do the first two problems together on your worksheet to make sure everyone feels confident."

"Look at problem #1. It's 34 divided by 5. Let's work through it using our DMSBR steps. Who wants to start with Divide?"

(Guide students through problem #1 and #2 on the worksheet, writing on the board or circulating to observe and assist. Provide specific feedback and address common misconceptions. Use the Long Division Answer Key as a reference.)

"Excellent work, everyone! Now that we've done a couple together, you're ready to tackle the rest on your own."

Independent Practice & Wrap-Up (5 minutes)

(Transition to Slide 7: Your Turn to Divide!)

"For the next 5 minutes, I want you to work independently on the remaining problems on your Long Division Worksheet. Remember to use our DMSBR steps for each problem, and always check that your remainder is smaller than your divisor."

"As you finish your worksheet, please grab a Cool-Down: Remainder Reflection sheet. This will be your exit ticket for today, where you can share what you've learned."

(Circulate, assist students, and collect worksheets/cool-downs as they are completed.)

(Transition to Slide 8: Division Detectives!)

"You all did an amazing job today becoming Division Detectives! Can anyone share why understanding remainders might be important in real life? Think about sharing candy or cutting a pizza!" (Allow a few student responses.)

"What was one new thing you learned or found helpful today about long division?"

"Fantastic contributions! You've learned a very important math skill today that you'll use a lot. Keep practicing those DMSBR steps! You are all awesome mathematicians!"

Worksheet

Long Division Worksheet: Divide & Conquer!

Name: _________________________ Date: _________________________

Instructions: Solve each long division problem. Remember to use the D-M-S-B-R steps (Divide, Multiply, Subtract, Bring Down, Remainder). Write your answer with a remainder (e.g., 5 R 2).

Show your work clearly in the space provided.

Problems:

1. 34 ÷ 5 =

2. 29 ÷ 3 =

3. 47 ÷ 6 =

4. 58 ÷ 7 =

5. 61 ÷ 8 =

6. 70 ÷ 9 =

7. 39 ÷ 4 =

8. 83 ÷ 9 =

Answer Key

Long Division Answer Key

Instructions: Review the step-by-step solutions for each problem on the Long Division Worksheet.

Solutions:

1. 34 ÷ 5 = 6 R 4

Divide: 5 goes into 34 six (6) times.
Multiply: 6 * 5 = 30
Subtract: 34 - 30 = 4
Bring Down: Nothing to bring down.
Remainder: 4. (4 < 5, so it's correct!)

2. 29 ÷ 3 = 9 R 2

Divide: 3 goes into 29 nine (9) times.
Multiply: 9 * 3 = 27
Subtract: 29 - 27 = 2
Bring Down: Nothing to bring down.
Remainder: 2. (2 < 3, so it's correct!)

3. 47 ÷ 6 = 7 R 5

Divide: 6 goes into 47 seven (7) times.
Multiply: 7 * 6 = 42
Subtract: 47 - 42 = 5
Bring Down: Nothing to bring down.
Remainder: 5. (5 < 6, so it's correct!)

4. 58 ÷ 7 = 8 R 2

Divide: 7 goes into 58 eight (8) times.
Multiply: 8 * 7 = 56
Subtract: 58 - 56 = 2
Bring Down: Nothing to bring down.
Remainder: 2. (2 < 7, so it's correct!)

5. 61 ÷ 8 = 7 R 5

Divide: 8 goes into 61 seven (7) times.
Multiply: 7 * 8 = 56
Subtract: 61 - 56 = 5
Bring Down: Nothing to bring down.
Remainder: 5. (5 < 8, so it's correct!)

6. 70 ÷ 9 = 7 R 7

Divide: 9 goes into 70 seven (7) times.
Multiply: 7 * 9 = 63
Subtract: 70 - 63 = 7
Bring Down: Nothing to bring down.
Remainder: 7. (7 < 9, so it's correct!)

7. 39 ÷ 4 = 9 R 3

Divide: 4 goes into 39 nine (9) times.
Multiply: 9 * 4 = 36
Subtract: 39 - 36 = 3
Bring Down: Nothing to bring down.
Remainder: 3. (3 < 4, so it's correct!)

8. 83 ÷ 9 = 9 R 2

Divide: 9 goes into 83 nine (9) times.
Multiply: 9 * 9 = 81
Subtract: 83 - 81 = 2
Bring Down: Nothing to bring down.
Remainder: 2. (2 < 9, so it's correct!)

Warm Up

Warm-Up: Remainder Race!

Name: _________________________ Date: _________________________

Instructions: For each problem, quickly decide if the answer will have a remainder or not. Circle "Yes" if you think there will be a remainder, and "No" if you think it will divide evenly.

Then, try to mentally solve for the quotient and remainder if you can! (No long division yet!)

1. 10 ÷ 2