• lenny-learning-logoLenny Learning
  • Home
    Home
    • Lessons
    Lessons
  • Curriculum
    Curriculum
  • Surveys
    Surveys
  • Videos
    Videos
  • Support
    Support
  • Log In
lenny

Divide & Conquer!

user image

Ross Marte

Tier 1
For Schools

Lesson Plan

Divide & Conquer!

Students will be able to confidently perform long division with multi-digit numbers, including decimals, by breaking down problems into manageable steps.

Mastering long division builds a strong foundation for algebra and everyday problem-solving, like splitting costs or understanding ratios. This lesson helps students overcome common challenges and feel more confident in their math abilities.

Audience

7th Grade Students

Time

30 minutes

Approach

Interactive slides, guided practice, and independent application.

Materials

Smartboard or Projector, Divide & Conquer! Slide Deck, Warm-Up: Division Detectives, Teacher's Script: Divide & Conquer!, Long Division Practice Worksheet, Long Division Worksheet Answer Key, and Cool-Down: Exit Ticket - Long Division

Prep

Teacher Preparation

10 minutes

  • Review the Divide & Conquer! Slide Deck and ensure all technological components are working.
    - Print enough copies of the Warm-Up: Division Detectives for each student.
    - Print enough copies of the Long Division Practice Worksheet for each student.
    - Review the Teacher's Script: Divide & Conquer! and familiarize yourself with the talking points and questions.
    - Have the Long Division Worksheet Answer Key ready for quick reference.
    - Prepare copies of the Cool-Down: Exit Ticket - Long Division.
    - Gather writing materials for students.

Step 1

Warm-Up: Division Detectives

5 minutes

  1. Distribute the Warm-Up: Division Detectives to students.
    2. Instruct students to work individually to solve the warm-up problems, which will review basic division concepts.
    3. Circulate the room to offer support and gauge prior knowledge.

Step 2

Introduction to Long Division (I Do)

8 minutes

  1. Begin the lesson using the Divide & Conquer! Slide Deck and the Teacher's Script: Divide & Conquer!.
    2. Introduce the concept of long division as a step-by-step process for solving larger division problems.
    3. Explain the acronym 'Does McDonald's Sell Burgers?' (Divide, Multiply, Subtract, Bring Down, Repeat) to help students remember the steps.
    4. Work through the first example on the slide deck, clearly demonstrating each step and explaining the reasoning.

Step 3

Guided Practice (We Do)

8 minutes

  1. Move to the next example on the Divide & Conquer! Slide Deck.
    2. Guide students through the problem together, asking them to predict the next step and actively participate.
    3. Provide immediate feedback and address any misconceptions as they arise.

Step 4

Independent Practice (You Do)

7 minutes

  1. Distribute the Long Division Practice Worksheet.
    2. Instruct students to complete the problems independently, applying the 'Does McDonald's Sell Burgers?' method.
    3. Circulate and provide individualized support. Encourage students to refer to their notes or the steps on the slide deck if they get stuck.
    4. Collect the worksheets at the end of this segment.

Step 5

Cool-Down: Exit Ticket

2 minutes

  1. Distribute the Cool-Down: Exit Ticket - Long Division.
    2. Ask students to complete the single long division problem to assess their understanding of the day's lesson.
    3. Collect exit tickets as students leave to quickly gauge comprehension and inform future instruction.
lenny

Slide Deck

Divide & Conquer!

Mastering Long Division, Step-by-Step!

Greet students and prepare them for the lesson. Briefly introduce the topic of long division and its importance.

Warm-Up: Division Detectives

Solve these basic division problems:

  1. 24 ÷ 4 =
  2. 56 ÷ 7 =
  3. 81 ÷ 9 =
  4. 30 ÷ 5 =

Think: What does division mean?

Display the warm-up and give students a few minutes to work on it individually. Encourage them to recall basic division facts.

What is Long Division?

It's a way to divide larger numbers into smaller, manageable steps!

Our Secret Weapon:
Does
McDonald's
Sell
Burgers?
Repeat

Introduce the concept of long division as a method for larger numbers. Explain the acronym clearly, emphasizing each step.

Example 1: Let's Do One Together!

Divide: How many times does the divisor go into the dividend?

Multiply: Multiply the quotient digit by the divisor.

Subtract: Subtract the product from the part of the dividend.

Bring Down: Bring down the next digit of the dividend.

Repeat: Start the process again if there are more digits.

Problem: 65 ÷ 5

Walk through the first example slowly, explaining each part of the 'DMSBR' process. Use clear, simple language.

Example 1: Solution!

  13
5|65
 -5
 --
 15
 -15
 ---
   0

So, 65 ÷ 5 = 13

Continue with Example 1, showing the solution step by step.

Example 2: Your Turn to Help!

Let's work through this problem together!

Problem: 132 ÷ 6

Guide students through this example, prompting them to tell you the next step. Encourage participation.

Example 2: Solution!

  22
6|132
 -12
 ---
  12
 -12
 ---
    0

So, 132 ÷ 6 = 22

Reveal the solution to Example 2 after students have had a chance to work on it.

What About Remainders?

Sometimes, numbers don't divide perfectly. What do we do then?

Problem: 74 ÷ 5

Explain how to handle remainders, making it clear that sometimes numbers don't divide perfectly.

Remainders: Solution!

  14 R 4
5|74
 -5
 --
 24
 -20
 ---
   4

So, 74 ÷ 5 = 14 with a remainder of 4

Show the solution with a remainder. Emphasize how the remainder is written.

Time for Practice!

Now it's your turn to be a long division master!

Work on the Long Division Practice Worksheet independently.

Remember: Does McDonald's Sell Burgers? Repeat!

Transition to independent practice. Explain the worksheet and encourage students to use the 'DMSBR' method.

Wrap It Up!

You did a great job today!

Please complete the Cool-Down: Exit Ticket - Long Division before you leave.

This will help me see what you learned!

Conclude the lesson and explain the cool-down activity as an exit ticket.

lenny

Warm Up

Warm-Up: Division Detectives

Name: _________________________ Date: _______________

Instructions: Solve the following basic division problems. Show your work if needed!

  1. 24 ÷ 4 = ?


  2. 56 ÷ 7 = ?


  3. 81 ÷ 9 = ?


  4. 30 ÷ 5 = ?


Bonus Question: In your own words, what does division mean?




lenny
lenny

Script

Teacher's Script: Divide & Conquer!

Warm-Up: Division Detectives (5 minutes)

"Good morning, everyone! Today, we're going to become 'Division Detectives.' I have a quick warm-up for you to get our brains warmed up for some math. Please take one of these Warm-Up: Division Detectives worksheets, and work quietly to solve the problems. This will help us remember some of our division basics."

(Circulate the room, observe student work, and note any common misconceptions or students who are struggling with basic division facts. Provide quiet, individual support as needed.)

"Alright, let's quickly review the answers.

  1. 24 divided by 4 is... (pause for answer) ...6! Great.
  2. 56 divided by 7 is... (pause for answer) ...8! Excellent.
  3. 81 divided by 9 is... (pause for answer) ...9! Perfect.
  4. And 30 divided by 5 is... (pause for answer) ...6! Fantastic.

Now, for the bonus question: In your own words, what does division mean? Take a moment to think. (Pause for responses) Yes, exactly! It's about splitting a number into equal parts, or seeing how many times one number fits into another. Today, we're going to learn how to do that with bigger numbers!"

Introduction to Long Division (I Do) (8 minutes)

(Display Slide 3: What is Long Division? of the Divide & Conquer! Slide Deck.)

"So, sometimes we have numbers that are too big to divide in our heads, like the ones you just did. That's where long division comes in! Long division is a super useful tool that helps us break down big division problems into smaller, easier steps. It’s like solving a puzzle, one piece at a time.

To help us remember the steps, we're going to use a special acronym. It's a silly one, but it really works! Has anyone heard of 'Does McDonald's Sell Burgers?' before? (Pause for responses)."

(Display Slide 4: Example 1: Let's Do One Together!.)

"This stands for: Divide, Multiply, Subtract, Bring Down, and Repeat. We'll go through each of these steps as we solve a problem.

Let's look at our first example: 65 divided by 5. I'm going to walk you through this one first, so you can see how each step works. Watch closely and listen to my thinking.

First, Divide: We look at the first digit of 65, which is 6. How many times does 5 go into 6? Just one time. So, we write a 1 above the 6.

Next, Multiply: We multiply the number we just wrote (1) by our divisor (5). 1 times 5 is 5. We write this 5 right under the 6.

Then, Subtract: We subtract 5 from 6. 6 minus 5 is 1. We write that 1 down here.

Now, Bring Down: We bring down the next digit from our original number, which is 5. So now we have 15.

And finally, Repeat: We start the whole process again with our new number, 15. How many times does 5 go into 15? Three times. So we write a 3 next to our 1 above the 5.

Then, we Multiply again: 3 times 5 is 15. Write that under the 15.

Subtract: 15 minus 15 is 0.

Since there are no more numbers to bring down, we are done! Our answer is 13. So, 65 divided by 5 is 13."

(Display Slide 5: Example 1: Solution!.)

Guided Practice (We Do) (8 minutes)

(Display Slide 6: Example 2: Your Turn to Help!.)

"Great job following along! Now, let's try another one, but this time, I want your help. We'll work through this problem together. Our problem is 132 divided by 6.

Remember our steps: Divide, Multiply, Subtract, Bring Down, Repeat.

Who wants to tell me the first step? (Pause for response) Yes, Divide! We look at the first digit of 132. Can 6 go into 1? No. So, we look at the first two digits, 13. How many times does 6 go into 13 without going over? (Pause for response) Two times! So, where do we write the 2? Above the 3 in 13.

What's next? (Pause for response) Multiply! What do we multiply? (Pause for response) Yes, 2 times 6, which is 12. Where does that 12 go? Under the 13.

Next step? (Pause for response) Subtract! 13 minus 12 is... (pause for answer) ...1! We write the 1 down.

What comes after Subtract? (Pause for response) Bring Down! What digit do we bring down? (Pause for response) The 2! So now we have 12.

And what do we do when we bring down? (Pause for response) Repeat! We start the process again. How many times does 6 go into 12? (Pause for answer) Two times! So we write a 2 next to the other 2.

Multiply: 2 times 6 is 12. Write that under the 12.

Subtract: 12 minus 12 is 0.

Are there any more digits to bring down? No! So, we're done. What's our answer? (Pause for answer) 22! So, 132 divided by 6 is 22."

(Display Slide 7: Example 2: Solution!.)

(Display Slide 8: What About Remainders?.)

"Sometimes, when we divide, the numbers don't go in perfectly. We might have a little bit left over. That's called a remainder. Let's try one with a remainder.

Problem: 74 divided by 5.

Divide: How many times does 5 go into 7? One time. Write 1 above the 7.

Multiply: 1 times 5 is 5. Write 5 under the 7.

Subtract: 7 minus 5 is 2. Write 2 down.

Bring Down: Bring down the 4. Now we have 24.

Repeat: How many times does 5 go into 24? (Pause for response) Four times. Write 4 next to the 1.

Multiply: 4 times 5 is 20. Write 20 under the 24.

Subtract: 24 minus 20 is 4. Write 4 down.

Are there any more digits to bring down? No. Is our remainder (4) smaller than our divisor (5)? Yes. So, we're finished! We write our remainder as 'R 4' next to our answer. So, 74 divided by 5 is 14 with a remainder of 4."

(Display Slide 9: Remainders: Solution!.)

Independent Practice (You Do) (7 minutes)

(Display Slide 10: Time for Practice!.)

"You've done a fantastic job understanding the steps! Now it's time for you to become long division masters on your own. I'm going to hand out this Long Division Practice Worksheet. Your task is to complete the problems independently, using the 'Does McDonald's Sell Burgers? Repeat' method we just learned.

Remember to show your work clearly. If you get stuck, try to remember our steps, or look back at the examples on the board. I'll be walking around to help anyone who needs it. Do your best!"

(Distribute the Long Division Practice Worksheet. Circulate, offering individual support, answering questions, and providing encouragement. Ensure students are attempting to use the learned method.)

Cool-Down: Exit Ticket (2 minutes)

(Display Slide 11: Wrap It Up!.)

"Alright everyone, time is just about up for our long division practice. You've worked really hard today.

Before you leave, I have one last quick task for you. Please take one of these Cool-Down: Exit Ticket - Long Division and solve the problem on it. This will help me see what you learned and what we might need to review next time. Please turn it in as you leave.

Thank you for a great lesson, division detectives!"

lenny
lenny

Worksheet

Long Division Practice Worksheet

Name: _________________________ Date: _______________

Instructions: Solve the following long division problems. Remember to use the "Does McDonald's Sell Burgers? Repeat" method. Show all your work!

Problem 1:

78 ÷ 3 = ?












Problem 2:

108 ÷ 4 = ?












Problem 3:

95 ÷ 5 = ?












Problem 4:

156 ÷ 6 = ?












Problem 5 (with Remainder):

87 ÷ 4 = ?












Problem 6 (Challenge):

258 ÷ 8 = ?












lenny
lenny

Answer Key

Long Division Practice Worksheet Answer Key

Instructions: Review the step-by-step solutions for each long division problem.

Problem 1:

78 ÷ 3 = 26

Step-by-step thought process:

  1. Divide: How many times does 3 go into 7? 2 times.
  2. Multiply: 2 x 3 = 6.
  3. Subtract: 7 - 6 = 1.
  4. Bring Down: Bring down the 8, making it 18.
  5. Repeat: How many times does 3 go into 18? 6 times.
  6. Multiply: 6 x 3 = 18.
  7. Subtract: 18 - 18 = 0.
  8. No more numbers to bring down. The answer is 26.

Problem 2:

108 ÷ 4 = 27

Step-by-step thought process:

  1. Divide: How many times does 4 go into 1? 0 times. (Look at 10). How many times does 4 go into 10? 2 times.
  2. Multiply: 2 x 4 = 8.
  3. Subtract: 10 - 8 = 2.
  4. Bring Down: Bring down the 8, making it 28.
  5. Repeat: How many times does 4 go into 28? 7 times.
  6. Multiply: 7 x 4 = 28.
  7. Subtract: 28 - 28 = 0.
  8. No more numbers to bring down. The answer is 27.

Problem 3:

95 ÷ 5 = 19

Step-by-step thought process:

  1. Divide: How many times does 5 go into 9? 1 time.
  2. Multiply: 1 x 5 = 5.
  3. Subtract: 9 - 5 = 4.
  4. Bring Down: Bring down the 5, making it 45.
  5. Repeat: How many times does 5 go into 45? 9 times.
  6. Multiply: 9 x 5 = 45.
  7. Subtract: 45 - 45 = 0.
  8. No more numbers to bring down. The answer is 19.

Problem 4:

156 ÷ 6 = 26

Step-by-step thought process:

  1. Divide: How many times does 6 go into 1? 0 times. (Look at 15). How many times does 6 go into 15? 2 times.
  2. Multiply: 2 x 6 = 12.
  3. Subtract: 15 - 12 = 3.
  4. Bring Down: Bring down the 6, making it 36.
  5. Repeat: How many times does 6 go into 36? 6 times.
  6. Multiply: 6 x 6 = 36.
  7. Subtract: 36 - 36 = 0.
  8. No more numbers to bring down. The answer is 26.

Problem 5 (with Remainder):

87 ÷ 4 = 21 R 3

Step-by-step thought process:

  1. Divide: How many times does 4 go into 8? 2 times.
  2. Multiply: 2 x 4 = 8.
  3. Subtract: 8 - 8 = 0.
  4. Bring Down: Bring down the 7.
  5. Repeat: How many times does 4 go into 7? 1 time.
  6. Multiply: 1 x 4 = 4.
  7. Subtract: 7 - 4 = 3.
  8. No more numbers to bring down. The remainder (3) is less than the divisor (4). The answer is 21 R 3.

Problem 6 (Challenge):

258 ÷ 8 = 32 R 2

Step-by-step thought process:

  1. Divide: How many times does 8 go into 2? 0 times. (Look at 25). How many times does 8 go into 25? 3 times.
  2. Multiply: 3 x 8 = 24.
  3. Subtract: 25 - 24 = 1.
  4. Bring Down: Bring down the 8, making it 18.
  5. Repeat: How many times does 8 go into 18? 2 times.
  6. Multiply: 2 x 8 = 16.
  7. Subtract: 18 - 16 = 2.
  8. No more numbers to bring down. The remainder (2) is less than the divisor (8). The answer is 32 R 2.

lenny
lenny

Cool Down

Cool-Down: Exit Ticket - Long Division

Name: _________________________ Date: _______________

Instructions: Solve the following long division problem. Show all your work and remember the steps!

Problem:

115 ÷ 5 = ?













lenny
lenny