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# Multi-Step Math Problem and Teaching Methods Essay

## Description of the observation

The lesson that I observed was aimed at illustrating the distributive properties of multiplication. I can say that the teacher relied on the so-called path-smoothing model. The main peculiarity of this technique is that the educator first identified the type of problems that had to be solved and explained the method for doing such tasks. This model can be useful because, in this way, the teacher can identify possible challenges that learners can face and help them avoid these difficulties (Ernest & Greer, 2002). Later students were able to work on a set of exercises that enabled them to better understand the nature of distributive properties and apply their knowledge.

During this lesson, the teacher illustrated the use of such a method as multiplication in parts. In other words, one of the factors was broken into several summands while the second factor remained unchained. This procedure proved very useful for multiplying two and three-digit numbers. By using this algorithm, children were able to see that multiplication could be simplified.

This lesson lasted for 45 minutes; the first ten minutes were dedicated to the presentation of new information and modeling. The guided practice lasted for 20 minutes; during this part of the lesson, the learners were able to work in groups while the teacher intervened only in those cases when some students experienced difficulties. In turn, during the last fifteen minutes, the learners were doing exercises independently.

Overall, this observation has been of great value to me because I was able to learn more about the teaching methods that could be suitable for the needs of third-grade students. Furthermore, I could gain insights into the behavior of students with whom I will later interact.

## Lesson plan

### General Information

Subject(s): Mathematical Operations: Division

Topic or Unit of Study: Divisibility Rules

### Instructional Setting

This lesson took place in the third-grade classroom in which there were 16 students. Furthermore, there were four desks each of which could give room to four learners.

### Standards and Objectives

#### Your State Core Curriculum/Student Achievement Standard(s)

The students can understand the nature of such mathematical operations as addition, subtraction, multiplication, and division (Wisconsin Department of Public Instruction, 2012, p. 20). Secondly, they can perform a wide range of tasks that involve these operations. Furthermore, learners should rely on the properties of mathematical operations to calculate the products of natural numbers (Wisconsin Department of Public Instruction, 2012, p. 20).

#### Lesson Objective(s)

At the end of this lesson, students will be able to solve multi-step problems that involve such operations as division, multiplication, addition, and subtraction. Additionally, the learners will be able to recognize the numbers that are divisible by three, four, or five. They will demonstrate this skill by solving a series of multiple-step problems. They will determine whether the results of their mathematical operations can be divisible by three, four, and five.

### Materials and Resources

• Instructional Materials: Hand-outs with assignments, pens, pencils, and multiplication tables.
• Resources: Bassarear, T. (2011). Mathematics for Elementary School Teachers. New York: Cengage Learning.

### Instructional plan

The sequence of Instructional Procedures/Activities/Events (provide a description and indicate the approximate time for each):

#### Identification of Student Prerequisite Skills Needed for Lesson

In this case, the most important skills are related to the knowledge of such operations as addition, division, multiplication, and subtraction. To a great extent, the multi-step problems that will be solved will entail each of these mathematical transformations.

#### Presentation of New Information or Modeling (15 minutes)

During this part of the lesson, I will introduce the divisibility by 3, 4, and 5. I will outline the property by which one can determine whether they can be divided by 3, 4, or 5. For example, I will show that a number can be divided by three, only if the sum of its digits is divisible by three. Secondly, I will illustrate an assignment that is aimed at determining whether a certain number is divisible by 3, 4, and 5. In particular, I will solve a multi-step problem involving addition, multiplication, or subtraction, and determine whether the result of these operations can be divided into three, four, or five.

#### Guided Practice (15 minutes)

During the second part of the lesson, I will enable learners to work on a set of different tasks similar to the assignment that I explained during the presentation. They can involve addition, multiplication, subtraction, or division. However, their main purpose will be to apply divisibility rules. So, learners should determine a particular product and sum can be divided by 3, 4, and 5. During this section of the lesson, I will let learners work in groups. I will also encourage students to ask questions and come to their assistance if something is unclear.

#### Independent Student Practice (10 minutes)

During the third part of the lesson, the students will complete a short test during which learners will have to identify natural numbers that can be divisible by three, four, and five. For example, they may be asked to consider such numbers as 223, 235, or 228 and determine which of them can be divided by three.

#### Culminating or Closing Procedure/Activity/Event (5 minutes)

In the end, I will explain what kind of assignments the students should do as a part of their homework. Secondly, I will praise children for their performance during the lesson.

#### Pedagogical Strategy (or Strategies)

I will rely on such a method as a path-smoothing strategy that enables a teacher to identify possible challenges that learners can encounter. Furthermore, in this way, he/she can assist them in avoiding mistakes. Apart from that, I will promote the formation of cooperative learning groups so that students can work together during the guided practice. Each of the learning groups will include four learners. Such an approach is important for fostering teamwork in the classroom.

#### Differentiated Instruction

The class includes a student with a mild hearing impairment, and I will need to make certain recommendations for him. First of all, I will need to stand near this learner while explaining the new material. Secondly, I should use visual aids to explain the new material

#### Student Assessment/Rubrics

The evaluation will be based on four multiple-step problems that students had to complete during the independent practice. These assignments prompted students to carry out multiplication, division, subtraction, and addition and determine whether the result of their calculations could be divided by four, five, or three. The following rubrics were used to assess learners’ performance

 Grade Description Excellent The learner can carry out various mathematical operations and recognize the numbers that are divisible by three, four, and five. The learner does not make conceptual or computational errors. Good The student can apply divisibility rules and perform mathematical operations. However, the learner makes some minor computational errors. Needs improvement The learner cannot recognize numbers that can be divided into three, four. Furthermore, he makes both conceptual and computational errors while performing mathematical operations.

It should be noted that there are two types of errors that learners can make. In particular, computational errors occur mostly due to the lack of attention. For example, a person can overlook a certain integer in his/her calculations or forget to use the decimal mark. In contrast, computational errors arise when a learner cannot under the peculiarities of mathematical operations such as division or multiplication. More attention should be paid to the second type of mistake since they can significantly hinder a student’s progress. This is one of the issues that I considered while developing the assessment rubric.

## Responses to the guided questions

### Observation and description

This lesson was organized in the third-grade classroom. The group included 16 students who were sitting at four desks. The desks were placed in the center of the room, and I was able to monitor the activities of learners.

### Analysis, exploration, and reasoning

Overall, I did have to deviate from the plan once. During the lesson, one of the students asked whether there are any other divisibility rules apart from those that I explained. I said that there were other divisibility rules, for example, the divisibility by seven. Furthermore, I had to provide him with more complex assignments that involve this particular divisibility rule. On the whole, I did not expect this request.

### Connection to other effective teaching practices

A proponent of cooperative learning might have suggested ways of changing my lesson. For instance, learners can be encouraged to test each other’s knowledge of divisibility rules. They may ask each other to provide examples of numbers that are divisible by three, four, or five. Furthermore, learners can work together to develop mathematical tasks consisting of different operations. These are the main suggestions that should be considered.

### Evaluation

In my opinion, the teaching model that I used was quite successful, since, in this way, I was able to explain how one could apply divisibility rules while solving multi-step mathematical problems. More importantly, this approach helped me to avoid the conceptual errors that learners could make while applying the divisibility rule. Such errors are usually related to the misunderstanding of such a concept as division.

I allocated 15 minutes to the independent practice of learners. In my opinion, the learners were able to cope with a wide range of assignments that involved divisibility rules. Furthermore, students could practice various mathematical operations.

When I was thinking about practice time, I focused mostly on the need to develop various skills of students. The learners had to have enough time to solve various multi-step problems and apply divisibility rules. Moreover, I believed that during fifteen minutes, they could practice the four basic operations/ This is why I asked the students to complete four multiple-step problems and determine whether the result of their calculations can be divided by three, four, or five.

## Recommendation

The so-called challenging model could have been used during this lesson. According to this approach, learners should be able to discover mathematical properties with minimum assistance from a teacher. For instance, a teacher can provide learners with a list of numbers that are divisible by three. In turn, the students are asked to formulate the divisibility rule. The teacher encourages them to express their conjectures about these natural numbers.

The main benefit of this approach is that learners act as independent discoverers. Such an approach can be more difficult for learners, but it makes the learning process more interesting.

## Personal meaning

This teaching experience has demonstrated to me that a teacher should be able to modify his/her teaching strategies. In particular, I will be able to meet the needs of students who want more challenging tasks. This skill will be important for my professional development.

This video has demonstrated to me that a teacher should pay close attention to the conceptual errors that learners can make. The students should first understand the nature of various mathematical operations to cope with multi-step problems.

When I was thinking about personal and professional implications, I focused on two important points. In particular, I focused on such aspects as my ability to engage children and their understanding of the major mathematical concepts.

## Reference List

Bassarear, T. (2011). Mathematics for Elementary School Teachers. New York: Cengage Learning.

Ernest, P. & Greer, B. (2009). Critical Issues in Mathematics Education. New York: IAP.

Wisconsin Department of Public Instruction. (2012). Common Core State Standards for Mathematics. Web.

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