🍎Unlocking Long Division: Dividing by One-Digit Numbers

Lesson plan

Objectives

• Students will be able to identify the dividend, divisor, quotient, and remainder in a division problem.
• Students will be able to divide 2-digit and 3-digit numbers by 1-digit numbers using the long division algorithm.
• Students will be able to solve long division problems and correctly interpret any remainders.
• Students will be able to check their division answers using multiplication and addition.
• Students will be able to apply long division to solve real-world word problems.

Materials

• Whiteboard or projector
• Dry-erase markers
• Student long division worksheets
• Pencils
• Base ten blocks or other manipulatives (optional, for struggling learners)
• Index cards for exit tickets

Warm-up

Begin by writing a simple multiplication problem on the board, like 6 × 7 = ?. Ask students for the answer (42). Then, ask them how this relates to division. Write 42 ÷ 6 = ? and 42 ÷ 7 = ?. This helps connect prior knowledge of multiplication facts to the inverse operation of division, which is foundational for long division. Spend 3-5 minutes on this review.

Direct instruction

1. **Introduction to Division Terms (5 minutes):** Display the problem 15 ÷ 3 = 5. Point out and define 'dividend' (the number being divided, 15), 'divisor' (the number dividing, 3), and 'quotient' (the answer, 5). Explain that sometimes there's a 'remainder' if the numbers don't divide evenly. Emphasize that long division is just a way to solve bigger division problems systematically.
2. **Introducing the Long Division Symbol (5 minutes):** Show students how to set up a long division problem using the 'house' or 'garage' symbol. For example, for 48 ÷ 2, the 48 goes inside and the 2 goes outside. Explain that we work from left to right, starting with the largest place value.
3. **The DMSB Steps (10 minutes):** Introduce the mnemonic 'Does McDonald's Sell Burgers?' to remember the steps: **D**ivide, **M**ultiply, **S**ubtract, **B**ring Down. Model the first example: 48 ÷ 2. * **D**ivide: How many times does 2 go into 4? (2 times). Write 2 above the 4. * **M**ultiply: 2 × 2 = 4. Write 4 below the 4. * **S**ubtract: 4 - 4 = 0. Write 0. * **B**ring Down: Bring down the 8. Now we have 08 (or just 8).
4. **Repeating the DMSB Steps (5 minutes):** Repeat the DMSB steps for the new number (8): * **D**ivide: How many times does 2 go into 8? (4 times). Write 4 above the 8. * **M**ultiply: 2 × 4 = 8. Write 8 below the 8. * **S**ubtract: 8 - 8 = 0. Write 0. * No more numbers to bring down. The quotient is 24 with a remainder of 0.
5. **Modeling with a Remainder (5 minutes):** Model an example with a remainder, such as 57 ÷ 4. Walk through the DMSB steps carefully. * 4 into 5 goes 1 time. (1 × 4 = 4). 5 - 4 = 1. Bring down 7. * 4 into 17 goes 4 times. (4 × 4 = 16). 17 - 16 = 1. * The remainder is 1. Explain how to write the answer: 14 R 1.
6. **Checking Your Work (5 minutes):** Show students how to check their answer using multiplication and addition. For 57 ÷ 4 = 14 R 1, we do (Quotient × Divisor) + Remainder = Dividend. So, (14 × 4) + 1 = 56 + 1 = 57. This confirms the answer is correct.

Guided practice

Let's try one together! Write 135 ÷ 3 on the board. Guide students through each step using the DMSB mnemonic. Ask questions like: 'What's our first step?' 'How many times does 3 go into 1?' (Explain that if the first digit is smaller, we look at the first two digits, so 3 into 13). 'What do we multiply next?' 'What do we subtract?' 'What do we bring down?' Work through the problem as a class, with students telling you what to write. **Worked Example:** ``` 45 ____ 3 | 135 - 12 (3 x 4 = 12) ____ 15 - 15 (3 x 5 = 15) ____ 0 ``` * **Checking the work:** (45 × 3) + 0 = 135. The answer is 45. Ensure every student understands before moving to independent practice.

Independent practice

Distribute the 'Long Division Practice' worksheet. Students will work independently on the problems provided. Circulate around the room, providing support to students who are struggling and checking for understanding. Encourage students to use the DMSB steps and to check their work using multiplication. Remind them to show all their work clearly in the provided space. Emphasize that it's okay to make mistakes and learn from them.

Closure

Gather students' attention. Ask a few students to share a key takeaway from today's lesson about long division. Review the DMSB steps one last time as a class. Distribute index cards for an exit ticket. **Exit Ticket Prompt:** 'Solve 78 ÷ 6 using long division. Show all your steps and write your answer with any remainder.' Collect the exit tickets to assess individual understanding and plan for future instruction.

Assessment

Mastery will be assessed through observation during guided and independent practice, completion and accuracy of the 'Long Division Practice' worksheet, and the performance on the exit ticket. The teacher will look for correct application of the DMSB algorithm, accurate calculations, and correct interpretation of remainders.

Differentiation

For struggling learners: Provide graph paper to help align digits, allow use of base ten blocks or counters for concrete representation of division, pair them with a peer tutor, provide a 'DMSB' checklist or anchor chart, start with problems that have no remainders and smaller numbers. For advanced learners: Provide multi-digit dividends (e.g., 4-digit by 1-digit divisor), include more complex word problems that require interpreting remainders (e.g., 'how many full groups can be made?'), challenge them to create their own long division word problems, or explore division with two-digit divisors as an introduction for future grades.

Long Division Practice: Divide by 1-Digit Numbers

Use the long division method to solve each problem. Remember the steps: Divide, Multiply, Subtract, Bring Down (DMSB). Show all your work in the space provided. Check your answers using multiplication and addition.

1. 1. 64 ÷ 2 =
2. 2. 93 ÷ 3 =
3. 3. 85 ÷ 5 =
4. 4. 72 ÷ 4 =
5. 5. 59 ÷ 2 =
6. 6. 75 ÷ 6 =
7. 7. 128 ÷ 4 =
8. 8. 216 ÷ 3 =
9. 9. 345 ÷ 5 =
10. 10. 408 ÷ 6 =
11. 11. 537 ÷ 4 =
12. 12. 625 ÷ 3 =

Long Division Quick Check

1. In the problem 120 ÷ 5 = 24, which number is the dividend?
   • 120
   • 5
   • 24
   • None of the above
   Answer: 120
2. What is the first step in the long division algorithm 'DMSB'?
   • Multiply
   • Subtract
   • Divide
   • Bring Down
   Answer: Divide
3. Solve: 84 ÷ 3
   • 21
   • 24
   • 28
   • 32
   Answer: 28
4. When you have a remainder in a division problem, what does it mean?
   • The answer is wrong.
   • The numbers divided evenly.
   • There is a leftover amount that cannot be divided equally.
   • You need to add it to the divisor.
   Answer: There is a leftover amount that cannot be divided equally.
5. Solve: 97 ÷ 4
   • 24
   • 24 R 1
   • 23 R 5
   • 25
   Answer: 24 R 1
6. Which operation is used to check a division problem?
   • Addition
   • Subtraction
   • Multiplication
   • Division
   Answer: Multiplication
7. If you divide 150 cookies among 6 friends, how many cookies does each friend get?
   • 20
   • 25
   • 30
   • 15
   Answer: 25
8. What is the remainder when 205 is divided by 5?
   • 0
   • 1
   • 2
   • 5
   Answer: 0

Long Division Homework Practice

Dear Families, Today in math, we started learning about long division. This is a very important skill that helps us divide larger numbers into equal groups. We learned a special set of steps: Divide, Multiply, Subtract, and Bring Down. Your child practiced dividing 2-digit and 3-digit numbers by a 1-digit number, and they also learned how to handle remainders when numbers don't divide evenly. Understanding these steps and practicing them regularly will build confidence and accuracy. Please help your child complete the problems below. Encourage them to show all their work clearly, just like we did in class. Remind them to check their answers using multiplication and addition. This practice will solidify their understanding of long division.

• 1. Solve: 68 ÷ 2. Show all steps.
• 2. Solve: 87 ÷ 3. Show all steps.
• 3. Solve: 95 ÷ 5. Show all steps.
• 4. Solve: 79 ÷ 4. Show all steps and write any remainder.
• 5. Solve: 147 ÷ 7. Show all steps.
• 6. Solve: 258 ÷ 3. Show all steps.
• 7. Solve: 389 ÷ 6. Show all steps and write any remainder.
• 8. Explain in your own words how you know when to stop bringing down numbers in long division.

Vocabulary

Dividend · noun

The total number or amount that is being divided into smaller, equal groups.

"In the problem 24 ÷ 4 = 6, the number 24 is the dividend."

Divisor · noun

The number by which another number (the dividend) is divided; it tells you how many groups you are making or how many are in each group.

"In the problem 24 ÷ 4 = 6, the number 4 is the divisor."

Quotient · noun

The answer to a division problem; it is the number of times the divisor goes into the dividend.

"In the problem 24 ÷ 4 = 6, the number 6 is the quotient."

Remainder · noun

The amount left over when a number cannot be divided exactly by another number.

"When you divide 7 by 3, the quotient is 2 and the remainder is 1, written as 2 R 1."

Long Division · noun

A step-by-step method used to divide larger numbers, often involving multiple steps of dividing, multiplying, subtracting, and bringing down.

"We used long division to solve the problem 135 ÷ 3."

Divide · verb

To share equally into groups or to find out how many times one number fits into another.

"You need to divide the cookies equally among your friends."

Multiply · verb

To combine equal groups; the inverse operation of division.

"After we divide, the next step in long division is to multiply the quotient digit by the divisor."

Subtract · verb

To take away one number from another to find the difference.

"After multiplying, we subtract the product from the part of the dividend we are working with."

Bring Down · verb phrase

To move the next digit of the dividend down to form a new number for the next division step.

"Once you subtract, the next step in long division is to bring down the next digit from the dividend."

Estimate · verb

To make a careful guess about an amount or number that is close to the actual answer.

"Before solving, we can estimate the answer to 90 ÷ 3 by thinking 9 ÷ 3 = 3, so 90 ÷ 3 is about 30."

Inverse Operation · noun

Operations that undo each other, like addition and subtraction, or multiplication and division.

"Multiplication is the inverse operation of division, which is why we use it to check our answers."

Fact Family · noun

A set of four related multiplication and division facts using the same three numbers.

"The numbers 3, 4, and 12 form a fact family: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, and 12 ÷ 4 = 3."

Activities

• DMSB Chant and Hand Motions · 5 minutes

  Teach students a chant or song to remember the 'Divide, Multiply, Subtract, Bring Down' steps. Incorporate simple hand motions for each step (e.g., 'D' for divide, hands splitting apart; 'M' for multiply, hands coming together; 'S' for subtract, one hand wiping away; 'B' for bring down, hand sweeping down). Practice it a few times as a class to help internalize the algorithm.

• Whiteboard Division Challenge · 10 minutes

  Divide students into small groups or pairs. Give each group a mini-whiteboard and a dry-erase marker. Write a long division problem on the main board (e.g., 78 ÷ 3). Students work together to solve it on their whiteboards. The first group to correctly show all steps and the answer gets a point. Repeat with 3-4 different problems, encouraging teamwork and quick recall of DMSB steps.

• Remainder Sort · 10 minutes

  Prepare several long division problems on index cards, some with remainders and some without. Give each student or pair a problem card. Once they solve their problem, they must sort it into one of two designated bins: 'No Remainder' or 'With Remainder'. This activity reinforces the concept of remainders and provides immediate feedback on their calculations.

• Division Story Problem Creation · 10 minutes

  In pairs, students create a simple word problem that can be solved using long division with a 1-digit divisor. They should write down the problem and its solution on a separate piece of paper. Encourage them to include a scenario where a remainder might need to be interpreted (e.g., 'how many full cars can hold 5 people if there are 23 people?'). Pairs can then swap problems to solve each other's.