Lesson 6 ProblemStory Of Units1. Break Apart 54 To Solve $54 \div 6$. ${ \begin{aligned} 54 \div 6 & = (30 \div 6) + (24 \div 6) \ & = 5 + 4 \ & = 9 \end{aligned} }$2. Break Apart 49 To Solve $49 \div

Lesson 6: Problem-Solving with Units

Understanding the Concept of Breaking Apart Numbers

In mathematics, breaking apart numbers is a fundamental concept that helps students develop problem-solving skills and understand various mathematical operations. This technique involves dividing a number into smaller parts, making it easier to perform calculations and arrive at the correct solution. In this lesson, we will explore how to break apart numbers to solve division problems, specifically focusing on the concept of units.

Breaking Apart Numbers: A Step-by-Step Guide

Breaking apart numbers is a simple yet effective technique that can be applied to various mathematical operations, including addition, subtraction, multiplication, and division. To break apart a number, we need to identify the units or the smallest parts of the number. For example, if we have the number 54, we can break it apart into 30 and 24, which are both multiples of 6.

Applying the Concept to Division Problems

Let's consider the problem $54 \div 6$. To solve this problem, we can break apart the number 54 into two smaller parts: 30 and 24. We can then rewrite the problem as $30 \div 6 + 24 \div 6$. This allows us to perform the division operation more easily, as we can now divide each part separately.

Using the Concept of Units to Solve Division Problems

When breaking apart numbers, it's essential to understand the concept of units. A unit is the smallest part of a number, and it's the building block of all mathematical operations. In the case of division, the unit is the divisor, which is the number by which we are dividing. For example, if we are dividing 54 by 6, the unit is 6.

Applying the Concept of Units to the Problem $54 \div 6$

To solve the problem $54 \div 6$, we can break apart the number 54 into two smaller parts: 30 and 24. We can then rewrite the problem as $30 \div 6 + 24 \div 6$. This allows us to perform the division operation more easily, as we can now divide each part separately.

Solving the Problem $54 \div 6$

Using the concept of breaking apart numbers, we can solve the problem $54 \div 6$ as follows:

$$54 \div 6 = (30 \div 6) + (24 \div 6)$$

$$= 5 + 4$$

$$= 9$$

Breaking Apart Numbers: A Real-World Example

Breaking apart numbers is not only a mathematical concept but also a real-world skill that can be applied to various situations. For example, imagine you have 54 cookies that you want to package in boxes of 6. To determine how many boxes you can fill, you need to divide 54 by 6. Using the concept of breaking apart numbers, you can break 54 into 30 and 24, and then divide each part separately.

Conclusion

Breaking apart numbers is a fundamental concept in mathematics that helps students develop problem-solving skills and understand various mathematical operations. By applying the concept of units and breaking apart numbers, students can solve division problems more easily and arrive at the correct solution. In this lesson, we explored how to break apart numbers to solve division problems, specifically focusing on the concept of units.

Discussion Questions

1. What is the concept of breaking apart numbers, and how is it applied to division problems?
2. How can breaking apart numbers help students solve division problems more easily?
3. What is the concept of units, and how is it related to breaking apart numbers?
4. Can you think of a real-world example where breaking apart numbers is useful?

Practice Problems

1. Break apart 49 to solve $49 \div 7$.
2. Break apart 36 to solve $36 \div 4$.
3. Break apart 72 to solve $72 \div 9$.
4. Break apart 90 to solve $90 \div 10$.

Answer Key

1. $$49 \div 7 = (40 \div 7) + (9 \div 7)$$

$$= 5 + 1$$

$$= 6$$

2. $$36 \div 4 = (30 \div 4) + (6 \div 4)$$

$$= 7 + 1$$

$$= 8$$

3. $$72 \div 9 = (60 \div 9) + (12 \div 9)$$

$$= 6 + 1$$

$$= 7$$

4. $$90 \div 10 = (80 \div 10) + (10 \div 10)$$

$$= 8 + 1$$

= 9$<br/> **Lesson 6: Problem-Solving with Units - Q&A**

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions related to breaking apart numbers and solving division problems.

Q: What is the concept of breaking apart numbers?

A: Breaking apart numbers is a mathematical technique that involves dividing a number into smaller parts, making it easier to perform calculations and arrive at the correct solution.

Q: How is breaking apart numbers applied to division problems?

A: Breaking apart numbers is applied to division problems by dividing the number into smaller parts, each of which can be divided separately. For example, to solve the problem $54 \div 6$, we can break apart 54 into 30 and 24, and then divide each part separately.

Q: What is the concept of units, and how is it related to breaking apart numbers?

A: A unit is the smallest part of a number, and it's the building block of all mathematical operations. In the case of division, the unit is the divisor, which is the number by which we are dividing. Breaking apart numbers involves identifying the units and dividing each part separately.

Q: Can you think of a real-world example where breaking apart numbers is useful?

A: Yes, breaking apart numbers is useful in many real-world situations. For example, imagine you have 54 cookies that you want to package in boxes of 6. To determine how many boxes you can fill, you need to divide 54 by 6. Using the concept of breaking apart numbers, you can break 54 into 30 and 24, and then divide each part separately.

Q: How can breaking apart numbers help students solve division problems more easily?

A: Breaking apart numbers can help students solve division problems more easily by making the calculations more manageable. By dividing the number into smaller parts, students can perform the division operation more easily and arrive at the correct solution.

Q: What are some common mistakes students make when breaking apart numbers?

A: Some common mistakes students make when breaking apart numbers include:

• Not identifying the units correctly
• Not dividing each part separately
• Not checking the solution for accuracy

Q: How can teachers help students understand the concept of breaking apart numbers?

A: Teachers can help students understand the concept of breaking apart numbers by:

• Providing examples and practice problems
• Encouraging students to identify the units and divide each part separately
• Checking the solution for accuracy and providing feedback

Q: What are some real-world applications of breaking apart numbers?

A: Breaking apart numbers has many real-world applications, including:

• Packaging and shipping
• Cooking and recipe scaling
• Budgeting and financial planning

Q: Can breaking apart numbers be applied to other mathematical operations, such as addition and subtraction?

A: Yes, breaking apart numbers can be applied to other mathematical operations, such as addition and subtraction. However, the technique is most commonly used for division problems.

Q: How can students apply the concept of breaking apart numbers to more complex mathematical operations?

A: Students can apply the concept of breaking apart numbers to more complex mathematical operations by:

• Identifying the units and dividing each part separately
• Using the concept of breaking apart numbers to simplify the problem
• Checking the solution for accuracy and providing feedback

Conclusion

Breaking apart numbers is a fundamental concept in mathematics that helps students develop problem-solving skills and understand various mathematical operations. By applying the concept of units and breaking apart numbers, students can solve division problems more easily and arrive at the correct solution. In this article, we addressed some of the most frequently asked questions related to breaking apart numbers and solving division problems.