Lesson Plan
Divide & Explain It!
Students will find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. They will use strategies like place value, properties of operations, and the relationship between multiplication and division, explaining their calculations with equations, arrays, or area models.
Mastering division is essential for everyday problem-solving, from sharing items fairly to budgeting money. It builds a strong foundation for future math concepts and helps you think critically about numbers.
Audience
5th Grade
Time
30 minutes
Approach
Through a warm-up, guided instruction, and an interactive activity, students will explore and practice division strategies.
Materials
Whiteboard or Projector, Markers or Pens, Slide Deck: Divide & Explain It!, Warm Up: Division Brain Teaser, Worksheet: Divide & Conquer Practice, Answer Key: Divide & Conquer Practice, and Cool Down: Reflect on Division
Prep
Teacher Preparation
10 minutes
- Review the Slide Deck: Divide & Explain It! for content and flow.
- Print copies of the Worksheet: Divide & Conquer Practice for each student.
- Have the Answer Key: Divide & Conquer Practice ready for quick checking.
- Prepare the whiteboard or projector for the lesson.
- Review the Script: Divide & Explain It! to ensure smooth delivery of instructions and explanations.
Step 1
Introduction & Warm-Up (5 minutes)
5 minutes
- Begin by presenting the Warm Up: Division Brain Teaser on the screen or whiteboard.
- Encourage students to think individually for 1-2 minutes, then share their initial thoughts with a partner.
- Facilitate a brief class discussion about their approaches and answers to the warm-up question. (Refer to Script: Divide & Explain It! for guiding questions.)
Step 2
Direct Instruction & Modeling (10 minutes)
10 minutes
- Use the Slide Deck: Divide & Explain It! to introduce the concept of whole-number division with larger dividends and two-digit divisors.
- Explain and model strategies such as place value, properties of operations, and the relationship between multiplication and division.
- Demonstrate how to illustrate calculations using equations, rectangular arrays, and/or area models. (Follow the explanations in Script: Divide & Explain It! carefully.)
- Present 1-2 example problems, working through them step-by-step with student input.
Step 3
Guided Practice & Activity (10 minutes)
10 minutes
- Distribute the Worksheet: Divide & Conquer Practice to each student.
- Instruct students to work on the problems, applying the strategies discussed.
- Circulate around the classroom, providing support and answering questions. Encourage students to explain their reasoning.
- After a few minutes, bring the class back together to discuss one or two challenging problems from the worksheet. Use the Answer Key: Divide & Conquer Practice as a reference.
Step 4
Cool Down & Wrap-Up (5 minutes)
5 minutes
- Hand out or display the Cool Down: Reflect on Division.
- Have students complete the cool-down independently to assess their understanding and reflection on the lesson.
- Collect the cool-down responses to gauge student learning and inform future instruction.
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Slide Deck
Divide & Explain It!
Mastering Big Division: Up to 4-Digit Dividends & 2-Digit Divisors!
Welcome students to the lesson. Introduce the engaging title and explain that today they will become division masters.
What is Division?
- Sharing equally (e.g., sharing 12 cookies among 3 friends)
- Grouping (e.g., how many groups of 4 can you make from 20 items?)
- Inverse of multiplication (e.g., if 3 x 4 = 12, then 12 ÷ 3 = 4)
Briefly review what division means. Ask students for examples of when they use division in real life.
Our Mission Today:
We will learn to:
1. Find whole-number answers (quotients) when dividing big numbers.
2. Use numbers up to four digits (like 1,234) and divide by numbers up to two digits (like 25).
3. Use different strategies to solve and explain our work!
Introduce the learning objective clearly. Explain why this skill is important (real-world applications, future math).
Strategy 1: Place Value Power!
We can break down larger numbers by their place value to make division easier.
Example: 480 ÷ 12
- How many '12s' are in 4 hundreds? (None)
- How many '12s' are in 48 tens? (4 tens!)
- So, 480 ÷ 12 = 40
Explain place value strategy using a simple example first, then move to a slightly more complex one. Emphasize thinking about 'how many tens, hundreds, etc.'
Strategy 2: Multiplication's Best Friend
Division and multiplication are opposites! If you know your multiplication facts, you can solve division problems!
Think: What number times the divisor equals the dividend?
Example: 75 ÷ 3 = ?
- We know 3 x 20 = 60
- And 3 x 5 = 15
- So, 3 x (20 + 5) = 75! Therefore, 75 ÷ 3 = 25
Explain how knowing multiplication facts helps directly with division. Provide an example.
Visualizing Division: Arrays & Area Models
Sometimes it helps to draw our division problems!
Rectangular Array: Think of rows and columns.
Area Model: Like a rectangle where one side is the divisor and the area is the dividend. You're trying to find the other side (the quotient!).
Example: 36 ÷ 3
Imagine 3 rows, how many in each? Or a rectangle with one side 3 and area 36.
Introduce rectangular arrays and area models as visual tools. Explain that they help us 'see' the division. Use a simple example first.
Let's Solve Together! (Example 1)
Problem: 576 ÷ 16 = ?
Think:
1. Can we make groups of 16 from 57? How many?
2. What's left over?
3. Bring down the next digit and repeat!
(Teacher will model using the board, showing both standard algorithm and conceptual understanding.)
Walk through a more complex example. Encourage students to participate in identifying the steps and reasoning.
Another Challenge! (Example 2)
Problem: 1248 ÷ 24 = ?
Think:
1. How many groups of 24 can we make from 124?
2. What's the remainder?
3. Bring down the 8.
4. How many groups of 24 from 248?
(Teacher will model using an area model, explaining each partial quotient.)
Another example, perhaps focusing more on an area model demonstration. Ensure students understand how to set up and use the model.
Time to Practice!
Now it's your turn to apply these awesome strategies!
Work on the Worksheet: Divide & Conquer Practice independently.
Remember to show your work and try to explain your thinking using words, equations, or drawings!
Explain the activity and how the worksheet will help them practice. Emphasize using the strategies learned.
You are Division Masters!
Great job today, mathematicians!
You've learned to tackle big division problems using different strategies and explaining your work.
Keep practicing, and you'll keep getting stronger!
Conclude the lesson by reiterating the importance of division and encouraging students to keep practicing.
Script
Divide & Explain It! - Teacher Script
## Introduction & Warm-Up (5 minutes)
Teacher: "Good morning, mathematicians! Today, we're going on an exciting adventure into the world of division. We're going to become masters of tackling big division problems!"
(Display Warm Up: Division Brain Teaser)
Teacher: "Let's start our brains with a quick 'Division Brain Teaser'. Take a minute or two to think about the problem: 'Imagine you have 72 pieces of candy, and you want to share them equally among 6 friends. How many pieces of candy does each friend get?' Try to show your thinking using words, a drawing, or an equation."
(Allow students 1-2 minutes to think and work. Then, ask them to share with a partner for 1 minute.)
Teacher: "Alright, let's hear some of your brilliant ideas! Who would like to share how they approached this problem or what answer they got?"
(Call on a few students to share their strategies and answers. Guide the discussion toward the concept of equal sharing or grouping.)
Teacher: "Excellent job everyone! It looks like many of you are already thinking about division in smart ways. Today, we're going to apply these ideas to even bigger numbers!"
## Direct Instruction & Modeling (10 minutes)
(Advance to Slide Deck: Divide & Explain It! - Slide 1: Title Slide, then Slide 2: What is Division?)
Teacher: "Before we dive into bigger problems, let's quickly remind ourselves: What exactly IS division? Who can tell me in their own words?"
(Listen for student responses: sharing equally, grouping, opposite of multiplication. Reinforce these ideas using Slide 2.)
(Advance to Slide Deck: Divide & Explain It! - Slide 3: Our Mission Today:)
Teacher: "Today, our mission is to learn how to find whole-number answers, or quotients, when we divide numbers with up to four digits by numbers with up to two digits. And the best part? We'll learn different strategies to solve these problems and how to explain our thinking!"
(Advance to Slide Deck: Divide & Explain It! - Slide 4: Strategy 1: Place Value Power!)
Teacher: "Our first strategy is 'Place Value Power!' This means we think about the value of each digit. Let's look at this example together: 480 ÷ 12."
Teacher: "Can we make groups of 12 from 4 hundreds? No, not easily. What about 48 tens? How many groups of 12 can we make from 48? Yes, 4 groups! So, 48 tens divided by 12 is 4 tens, or 40. The answer is 40. See how thinking about place value can simplify things?"
(Advance to Slide Deck: Divide & Explain It! - Slide 5: Strategy 2: Multiplication's Best Friend)
Teacher: "Next, remember that division and multiplication are best friends! They're inverse operations, meaning they undo each other. If you know your multiplication facts, division becomes much easier. For example, 75 ÷ 3. What number times 3 equals 75?"
Teacher: "We can think, 3 times 20 is 60. We have 15 left. 3 times what is 15? 5! So, 3 times (20 + 5) is 75. That means 75 ÷ 3 is 25."
(Advance to Slide Deck: Divide & Explain It! - Slide 6: Visualizing Division: Arrays & Area Models)
Teacher: "Sometimes, drawing helps us understand. We can use rectangular arrays or area models. An area model is like a rectangle where the total area is our dividend, one side is our divisor, and we're looking for the other side, which is our quotient! For example, with 36 ÷ 3, you can imagine a rectangle with an area of 36 and one side of 3. What's the other side?"
(Advance to Slide Deck: Divide & Explain It! - Slide 7: Let's Solve Together! (Example 1))
Teacher: "Now let's try a bigger problem together: 576 ÷ 16. I'll use the whiteboard to show you how we can break this down."
(Model long division on the board, explaining each step. Ask guiding questions: "How many groups of 16 can we make from 57?" "What's left over?" "What do we do next?")
(Advance to Slide Deck: Divide & Explain It! - Slide 8: Another Challenge! (Example 2))
Teacher: "Let's try one more example, and this time, I'll show you how an area model can work for 1248 ÷ 24."
(Model the area model for division on the board, showing how to find partial quotients and add them up to get the final quotient. Emphasize the connection between the model and the standard algorithm.)
## Guided Practice & Activity (10 minutes)
(Advance to Slide Deck: Divide & Explain It! - Slide 9: Time to Practice!)
Teacher: "You've seen different strategies, and now it's your turn to practice! I'm handing out a Worksheet: Divide & Conquer Practice. Your task is to solve these problems using any of the strategies we discussed: place value, multiplication, or even drawing an array or area model. Make sure to show your work and try to explain your thinking!"
(Distribute the worksheets. Circulate around the room, offering support and prompting students to explain their methods. After about 7-8 minutes, call the class back together.)
Teacher: "Let's pause there. Did anyone find a problem particularly tricky or interesting? Would someone like to share their solution to a problem and explain their steps?"
(Choose one or two problems from the worksheet for students to share and discuss. Refer to the Answer Key: Divide & Conquer Practice as needed.)
## Cool Down & Wrap-Up (5 minutes)
(Advance to Slide Deck: Divide & Explain It! - Slide 10: You are Division Masters!)
Teacher: "Fantastic work today, everyone! You've tackled some challenging division problems and used a variety of strategies. To wrap up, I'd like you to complete this quick 'Cool Down: Reflect on Division'. This will help me see what stuck with you today."
(Distribute Cool Down: Reflect on Division. Collect responses upon completion.)
Teacher: "Keep practicing your division skills; they're super important for all sorts of real-life situations. You are all becoming amazing division masters!"
Worksheet
Divide & Conquer Practice
Instructions: Solve the following division problems. Show your work using any strategy you like (place value, multiplication, equations, rectangular arrays, or area models). Explain your thinking clearly.
---
### Problem 1
450 ÷ 18 = ?
---
### Problem 2
960 ÷ 15 = ?
---
### Problem 3
1,344 ÷ 21 = ?
---
### Problem 4
2,175 ÷ 25 = ?
---
### Problem 5
A baker made 1,512 cookies. She wants to pack them into boxes, with 12 cookies in each box. How many boxes will she need?
Answer Key
Divide & Conquer Practice - Answer Key
---
### Problem 1
450 ÷ 18 = 25
Thought Process:
- I know 18 x 10 = 180.
- 180 x 2 = 360 (so 18 x 20 = 360).
- I have 450 - 360 = 90 left.
- I know 18 x 5 = 90.
- So, 18 x (20 + 5) = 18 x 25 = 450.
---
### Problem 2
960 ÷ 15 = 64
Thought Process (Area Model Example):
- Create a rectangle with one side 15 and area 960.
- Think: 15 x 60 = 900 (This is our first partial quotient).
- Remaining area: 960 - 900 = 60.
- Think: 15 x 4 = 60 (This is our second partial quotient).
- Add partial quotients: 60 + 4 = 64.
---
### Problem 3
1,344 ÷ 21 = 64
Thought Process:
- How many 21s are in 134? Estimate: 130 ÷ 20 = 6.5, so try 6.
- 21 x 6 = 126.
- Subtract 126 from 134, which leaves 8.
- Bring down the 4, making it 84.
- How many 21s are in 84? Estimate: 80 ÷ 20 = 4. So try 4.
- 21 x 4 = 84.
- Subtract 84 from 84, which leaves 0.
- The quotient is 64.
---
### Problem 4
2,175 ÷ 25 = 87
Thought Process:
- I know 25 x 4 = 100.
- So, 25 x 40 = 1000.
- 25 x 80 = 2000.
- I have 2175 - 2000 = 175 left.
- I know 25 x 7 = 175.
- So, 25 x (80 + 7) = 25 x 87 = 2175.
---
### Problem 5
A baker made 1,512 cookies. She wants to pack them into boxes, with 12 cookies in each box. How many boxes will she need?
Answer: 126 boxes
Thought Process:
- This is a division problem: 1,512 ÷ 12.
- How many 12s in 15? One group (12 x 1 = 12). 15 - 12 = 3. Bring down the 1, making 31.
- How many 12s in 31? Two groups (12 x 2 = 24). 31 - 24 = 7. Bring down the 2, making 72.
- How many 12s in 72? Six groups (12 x 6 = 72). 72 - 72 = 0.
- So, 1,512 ÷ 12 = 126. The baker will need 126 boxes.
Cool Down
Reflect on Division
## Cool Down Activity
1. What was one new strategy or idea you learned about division today?
2. Explain in your own words how you would solve 840 ÷ 14. You don't have to solve it, just describe the steps or strategy you would use.