Lesson and Assessments - Standard Algorithm for Division

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Progression of Skills (outline)

Before the lesson:

Prior to starting the intervention, students need to have the following:

• Fluent retrieval of multiplication and division facts through 10.
• Fluency with multi-digit addition and subtraction operations.
• Fluency multiplying by 10, 100, and 1000.

If students don’t have fluency in the listed operations, they will need support (calculator, multiplication table etc.)

During this toolkit lesson:

This intervention initially focuses on developing a conceptual understanding of division using a partitive grouping context. By the end of Step 1, students should understand that division involves taking a set of numbers and reorganizing it into smaller equal sets.

Step 2 introduces the standard algorithm using a stacking method aimed at solidifying an understanding of the place value within the standard algorithm. Students continue to use grouping language as they work through the algorithm to reinforce understanding. For example, they say, “24 divided by 4 is 4 groups of 6," to avoid the misconception that the answer is simply 6.

Step 3 focuses on dividing larger numbers while still using the grouping language. From Step 4 onward, the focus is entirely on the standard algorithm, but the grouping language is maintained by the teacher or interventionist. The goal is for students to achieve fluency in using the algorithm while also developing an innate conceptual understanding of its operations.

This intervention begins with 3rd-grade content and progresses to a 6th-grade level of rigor. It can be used at all grade levels above 3rd, but the interventionist or teacher should choose an appropriate stopping point for students below the 6th grade level.

After the lesson:

After completing this intervention, students should be able to solve real-world problems involving partitive division at the appropriate grade level. Sixth grade students should be able to solve these problems using the standard algorithm. The teacher should be able to stop the student at any time and ask them to explain their reasoning through the algorithm.

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Lesson

Read the teacher's guides for directions for each session.

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Step 1: Division - Grouping Method

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).

Time needed: 20 - 30 minutes per lesson.

Materials Needed:

• 50 counters and 5 containers (paper cups). I set per student.
• Worked examples for each lesson
• Practice set for each lesson

Directions:

It may be helpful to view the Step 1 Teacher's Guide prior to teaching this step.

Lesson 1.1

This lesson employs a grouping strategy to illustrate the concept of division. Students divide smaller numbers into groups based on specified divisors ranging from 1 to 5, aiming for whole number quotients. For a teacher demonstration watch Lesson 1.1. Lesson 1.1 Practice Set & Worked Example

Lesson script (optional)

Give each student 15 counters and 3 cups. Ask each student to count the counters to verify there are 15. Instruct them to place one counter at a time into each cup consecutively until all counters are used. Then, have them count the number of counters in each cup and state their answer. Explain that this demonstrates 15 ÷ 3, and confirm that 15 ÷ 3 = 5. Ask them to write out the equation.

Next, ask students what they notice about the total number of counters. Ideally, they will observe that the total number of counters remains the same before and after dividing. If not, prompt them with questions like, "How many total counters did you start with?" and "How many total counters do you have after dividing?" Ensure they understand that the quantity of the set remains unchanged through division.

Ask students to explain the quotient 5 using the cups. Eventually, they should conclude that 5 represents the number of counters in each cup.

Proceed to do three more problems with the students using the same method, ensuring the divisor (number of cups) remains less than five each time. (Use problems from the Lesson 1.1 practice set.) After each problem, have students write a division equation. By the final problem, students should be able to complete the activity independently and answer questions about the problem individually.

The next part of this lesson can be done on the same day but if students have been working for 30 minutes or more it would be best to give them a break before starting or continue with this the next day.

Now, put the cups away and complete similar problems using a pictorial representation (see Worked Example 1.1). Demonstrate the problem 12 ÷ 3: Have students draw 3 boxes or circles. Instruct them to place one dot at a time consecutively into each circle while counting out twelve dots. Ask them to explain what they did and write it as a division equation. Continue to emphasize that the dividend (12) is contained in the total of all groups (3 groups of 4).

Do 4 to 5 problems and conclude by asking the same questions you asked before.

For the assessment of Lesson 1.1, provide students with the equation 18 ÷ 3 = 6. Ask them to draw the problem on paper and then explain their approach. Prompt them to comment on the total number of counters. Ideally, they should recognize that the total quantity remains the same after dividing, using language appropriate for their understanding.

Lesson 1.2 (optional):

This lesson utilizes a grouping strategy to illustrate the concept of division. Students divide smaller numbers into groups based on specified divisors ranging from 1 to 5, addressing scenarios that include remainders. Only do this lesson if students are ready to start exploring the remainder. For a teacher demonstration watch Lesson 1.2. Lesson 1.2 Practice Set & Worked Examples

Repeat the same steps as in Lesson 1.1, including the evaluation.

Lesson 1.3: This lesson employs a grouping strategy to illustrate the concept of division. Students divide smaller numbers into groups based on divisors up to 10, aiming for whole number quotients. For a teacher demonstration watch Lesson 1.3. Lesson 1.3 Practice Set & Worked Example

Repeat the same process as in Lesson 1.1. This will provide the necessary repetition over consecutive days. The only difference between Lesson 1.1 and Lesson 1.3 is the difficulty of the numbers. You may want to skip using concrete manipulatives, as the larger divisors (number of cups) can get messy. The pictorial step will likely be adequate. At the end of the lesson, evaluate the students the same way as in Lesson 1.1.

Lesson 1.4 (optional):

This lesson employs a grouping strategy to demonstrate the concept of division. Students will divide smaller numbers into groups according to specified divisors up to 10, focusing on scenarios that may involve remainders. For a teacher demonstration watch Lesson 1.4. Lesson 1.4 Practice Set & Worked Examples

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Step 2: Division Using the Stacking Method Dividing 2-Digit by 1-Digit Numbers

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).
• Learning Objective 3: Students will be able to identify the value of each digit within the standard algorithm.
• Learning Objective 4: Students will independently solve division problems involving two-digit dividends and a single-digit divisor using the stacking algorithm.

Directions:

1. Study the worked example for this lesson and watch the Step 2 Teacher's Guide before attempting this lesson. The stacking method is a modified version of partial quotients, but you have not seen it before. The stacking method emphasizes place value throughout the entire algorithm.
2. Pull problems from the practice sets to select problems. These practice sets are adjusted for cognitive load. The level of the problems and the numbers selected are specifically chosen to allow for moderate steps toward mastery.
3. Have students work on graph paper.
4. Do at least one example for demonstration purposes, but make the students do the work with you. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
5. Continue the grouping focus developed in Step 1. With each step of the algorithm, have students identify how many items from the original set (dividend) have been placed in groups (top of the symbol) and how many are left to be grouped (result after subtracting). Please watch the videos for each lesson to see a clear demonstration of this.
6. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
7. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
8. By the end of each lesson, students should independently complete at least one problem.

Lesson 2.1:

This lesson introduces division using the standard method, incorporating an intermediary technique known as stacking. Stacking emphasizes place value while managing smaller quotients suitable for this method. The practice set will focus on problems yielding whole number quotients without remainders. I highly advise you watch the teacher demonstration for the stacking method. For a teacher demonstration watch Lesson 2.1. Lesson 2.1 Practice Set & Worked Example

Lesson 2.2:

This lesson progresses to division using the standard method, integrating an intermediary technique called stacking. Stacking maintains a focus on place value while handling smaller quotients appropriate for this method. The practice set will include problems yielding whole number quotients with remainders. For a teacher demonstration watch Lesson 2.2. Lesson 2.2 Practice Set & Worked Example

Lesson 2.3:

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary. Lesson 2.3 Word Problems

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Step 3: Division Using the Stacking Method Dividing 3-Digit by 1-Digit Numbers

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).
• Learning Objective 3: Students will be able to identify the value of each digit within the standard algorithm.
• Learning Objective 4: Students will independently solve division problems involving Four-digit dividends and a single-digit divisor using the standard algorithm.

Directions:

1. Study the worked examples and watch the Step 3 Teacher's Guide before attempting this lesson. The stacking method is a modified version of partial quotients, but you have not seen it before. The stacking method emphasizes place value throughout the entire algorithm.
2. Pull problems from the practice sets to select problems. These practice sets are adjusted for cognitive load. The level of the problems and the numbers selected are specifically chosen to allow for moderate steps toward mastery.
3. Have students work on graph paper.
4. Do at least one example for demonstration purposes, but make the students do the work with you. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
5. Continue the grouping focus developed in Step 1. With each step of the algorithm, have students identify how many items from the original set (dividend) have been placed in groups (top of the symbol) and how many are left to be grouped (result after subtracting). Please watch the videos for each lesson to see a clear demonstration of this.
6. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
7. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
8. By the end of each lesson, students should independently complete at least one problem.

Lesson 3.1:

This lesson progresses to division using the standard method, incorporating an intermediary technique known as stacking. Stacking emphasizes place value while handling smaller quotients suitable for this method. The practice set will focus on problems yielding whole number quotients without remainders. For a teacher demonstration watch Lesson 3.1. Lesson 3.1 Practice Set & Worked Example

Lesson 3.2:

This lesson advances to division using the standard method, integrating an intermediary technique called stacking. Stacking emphasizes place value while managing smaller quotients appropriate for this method. The practice set will include problems yielding whole number quotients with remainders. For a teacher demonstration watch Lesson 3.2. Lesson 3.2 Practice Set & Worked Examples

Lesson 3.3:

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary. Lesson 3.3 Word Problems

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Step 4: Division Using the Standard Method Dividing 4-Digit by 1-Digit Numbers

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).
• Learning Objective 3: Students will be able to identify the value of each digit within the standard algorithm.
• Learning Objective 4: Students will independently solve division problems involving four-digit dividends and a single-digit divisors using the standard algorithm.

Directions:

1. This lesson marks a complete transition to using the standard division algorithm. Although this lesson will be more familiar, please watch the Step 4 Teacher's Guide, to see how to ensure the learning goals of this step.
2. Pull problems from the practice sets to select problems. These practice sets are adjusted for cognitive load. The level of the problems and the numbers selected are specifically chosen to allow for moderate steps toward mastery.
3. Have students work on graph paper.
4. Do at least one example for demonstration purposes, but make the students do the work with you. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
5. Continue the grouping focus developed in Step 1. With each step of the algorithm, have students identify how many items from the original set (dividend) have been placed in groups (top of the symbol) and how many are left to be grouped (result after subtracting). Please watch the videos for each lesson to see a clear demonstration of this.
6. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
7. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
8. By the end of each lesson, students should independently complete at least one problem.

Lesson 4.1

In this lesson, students will utilize the standard division method. Teachers should emphasize place value reasoning and use grouping language during discussions and classroom demonstrations. The practice set will feature problems with whole number quotients and no remainders. For a teacher demonstration watch Lesson 4.1. Lesson 4.1 Practice Set & Worked Example

Lesson 4.2

In this lesson, students will continue using the standard division method. Teachers should emphasize place value reasoning and utilize grouping language during discussions and classroom demonstrations. The practice set will include problems with whole number quotients that may have remainders. For a teacher demonstration watch Lesson 4.2. Lesson 4.2 Practice Set & Worked Examples

Lesson 4.3

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary.

Common Problems:

• Lesson 4.3 Word Problems

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Step 5: Division Using the Standard Method Dividing 2-Digit by 2-Digit Numbers

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).
• Learning Objective 3: Students will be able to identify the value of each digit within the standard algorithm.
• Learning Objective 4: Students will independently solve division problems involving two-digit dividends and a two-digit divisors using the standard algorithm.

Directions:

1. This lesson marks a complete transition to using the standard division algorithm. Although this lesson will be more familiar, please watch the Step 5 Teacher's Guide, to see how to ensure the learning goals of this step.
2. Pull problems from the practice sets to select problems. These practice sets are adjusted for cognitive load. The level of the problems and the numbers selected are specifically chosen to allow for moderate steps toward mastery.
3. Have students work on grid paper.
4. Do at least one example for demonstration purposes, but make the students do the work with you. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
5. Continue the grouping focus developed in Step 1. With each step of the algorithm, have students identify how many items from the original set (dividend) have been placed in groups (top of the symbol) and how many are left to be grouped (result after subtracting). Please watch the videos for each lesson to see a clear demonstration of this.
6. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
7. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
8. By the end of each lesson, students should independently complete at least one problem.

Lesson 5.1:

Starting from Step 5, students will focus exclusively on achieving fluency using the standard division method. The divisors in this lesson are double-digit numbers such as 10, 11, or 12. This allows students to utilize a multiplication table as support while they continue to master the standard method. The practice set will consist of problems yielding whole number quotients without remainders. For a teacher demonstration watch Lesson 5.1. Lesson 5.1 Practice Set & Worked Examples

Lesson 5.2:

Starting from Step 5, students will exclusively work towards fluency using the standard division method. The divisors in this lesson are double-digit numbers such as 10, 11, or 12. This allows students to use a multiplication table for support as they continue mastering the standard method. The practice set will include problems yielding whole number quotients with remainders. For a teacher demonstration watch Lesson 5.2. Lesson 5.2 Practice Set & Worked Examples

Lesson 5.3:

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary. Lesson 5.3 Word Problems

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Step 6: Division Using the Standard Method Dividing 3-Digit by 2-Digit Numbers

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).
• Learning Objective 3: Students will be able to identify the value of each digit within the standard algorithm.
• Learning Objective 4: Students will independently solve division problems involving three-digit dividends and two-digit divisors using the standard algorithm.

Directions:

1. This lesson marks a complete transition to using the standard division algorithm. Although this lesson will be more familiar, please watch the Step 6 Teacher's Guide, to see how to ensure the learning goals of this step.
2. Pull problems from the practice sets to select problems. These practice sets are adjusted for cognitive load. The level of the problems and the numbers selected are specifically chosen to allow for moderate steps toward mastery.
3. Consider having students work on graph paper.
4. Do at least one example for demonstration purposes, but make the students do the work with you. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
5. Continue the grouping focus developed in Step 1. With each step of the algorithm, have students identify how many items from the original set (dividend) have been placed in groups (top of the symbol) and how many are left to be grouped (result after subtracting). Please watch the videos for each lesson to see a clear demonstration of this.
6. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
7. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
8. By the end of each lesson, students should independently complete at least one problem.

Lesson 6.1:

In this lesson, students will work with 3-digit dividends while the divisors remain double-digit numbers such as 10, 11, or 12. This setup allows students to use a multiplication table for support as they continue to master the standard division method. The practice set will consist of problems yielding whole number quotients without remainders. For a teacher demonstration watch Lesson 6.1. Lesson 6.1 Practice Set & Worked Examples

Lesson 6.2:

In this lesson, students will work with 3-digit dividends while the divisors remain double-digit numbers such as 10, 11, or 12. This setup allows students to use a multiplication table for support as they continue to master the standard division method. The practice set will include problems yielding whole number quotients with remainders. For a teacher demonstration watch Lesson 6.2. Lesson 6.2 Practice Set & Worked Examples

Lesson 6.3:

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary. Lesson 6.3 Word Problems

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Step 7: Division Using the Standard Method Dividing 4-Digit by 2-Digit Numbers

• Learning Objective 1: Students will be able to articulate an understanding that the quantity of the original set or dividend is preserved in the final answer or quotient.
• Learning Objective 2: Students will be able to explain that the solution to a division problem (quotient) represents the number of items in each group (divisor).
• Learning Objective 3: Students will be able to identify the value of each digit within the standard algorithm.
• Learning Objective 4: Students will independently solve division problems involving four-digit dividends and two-digit divisors using the standard algorithm.

Directions:

1. This lesson signifies a shift from relying on multiplication tables for support. Additional time may be required to develop strategies for estimating components of the divisor.
2. This lesson marks a complete transition to using the standard division algorithm. Pull problems from the practice sets to select problems. These practice sets are adjusted for cognitive load. The level of the problems and the numbers selected are specifically chosen to allow for moderate steps toward mastery.
3. Consider having students work on graph paper.
4. Do at least one example for demonstration purposes, but make the students do the work with you. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
5. Continue the grouping focus developed in Step 1. With each step of the algorithm, have students identify how many items from the original set (dividend) have been placed in groups (top of the symbol) and how many are left to be grouped (result after subtracting). Please watch the videos for each lesson to see a clear demonstration of this.
6. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
7. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
8. By the end of each lesson, students should independently complete at least one problem.

Lesson 7.1:

In this lesson, students advance to working with 4-digit dividends, while the divisors remain double-digit numbers such as 10, 11, or 12. This approach allows students to utilize a multiplication table for support as they continue to master the standard division method. The practice set will consist of problems yielding whole number quotients without remainders. For a teacher demonstration watch Lesson 7.1. Lesson 7.1 Practice Set & Worked Examples

Lesson 7.2:

In this lesson, students progress to working with 4-digit dividends, while the divisors remain double-digit numbers such as 10, 11, or 12. This approach allows students to utilize a multiplication table for support as they continue to master the standard division method. The practice set will include problems yielding whole number quotients with remainders. For a teacher demonstration watch Lesson 7.2. Lesson 7.2 Practice Set & Worked Examples

Lesson 7.3:

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary. Lesson 7.3 Word Problems

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Step 8: Division Using the Standard Method Dividing all Digits, Divisors above 12

Directions:

1. The teacher should begin each lesson by demonstrating one problem using concrete manipulatives. Students should then be tasked with solving 3 to 4 additional problems using manipulatives, guided by the teacher. The remainder of the lesson should involve a pictorial approach (refer to worked examples).
2. For each teacher-led example, provide simple context that is accessible to all learners, including those with learning disabilities and limited language access. For example, when dividing 8 by 2, the teacher could say, "Grandma has 8 cookies and wants to give each of her 2 grandchildren an equal number of cookies. How many cookies will each child get?"
3. Each lesson includes a worked example, which serves as an excellent resource for novice learners. As part of the gradual release of learning responsibility, students can study the worked example to assist them in solving new problems.
4. Teacher explanations should be concise, primarily introducing mathematical language to be used throughout the lesson. Learning should quickly transition to student-led exploration. If students are in groups, they should initially collaborate under the teacher's guidance to resolve misconceptions and ensure proper use of terminology.
5. By the end of each lesson, students should independently complete at least one problem.

Lesson 8.1:

In this lesson, students are expected to be fluent in using the standard method for division. The practice set includes 2-digit dividends and 2-digit divisors, with divisors now exceeding 12. Students may require multiple practice sessions as they learn to determine the initial multiplier. For a teacher demonstration watch Lesson 8.1. Lesson 8.1 Practice Set & Worked Examples

Lesson 8.2:

In this lesson, students are expected to be fluent in using the standard method for division. The practice set includes 3-digit dividends and 2-digit divisors, with divisors now exceeding 12. Students may need multiple practice sessions to master how to find the initial multiplier. For a teacher demonstration watch Lesson 8.2. Lesson 8.2 Practice Set & Worked Examples

Lesson 8.3:

In this lesson, students are expected to be fluent in using the standard method for division. The practice set includes 4-digit dividends and 2-digit divisors, with divisors now exceeding 12. Students may require several practice sessions to understand and apply how to determine the initial multiplier. For a teacher demonstration watch Lesson 8.3. Lesson 8.3 Practice Set & Worked Examples

Lesson 8.4:

By the time students reach this lesson, they should have received ample context through prior instruction. At this stage, you can present them with problems and allow them to work independently. Encourage them to navigate through the challenges, providing scaffolded support as necessary. Lesson 8.4 Word Problems

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