Perimeter, Area, Volume, and All That: A Study of Measurement

Teaching strategies

In this unit, I would like to incorporate a variety of instructional strategies to meet the needs and the different learning styles of my students.

Although Eureka Math in Spanish will constitute the primary resource to guide the scope and sequence of the Math instruction, the activities suggested in this unit have the purpose of facilitating a better understanding of the differences between area and perimeter.

The activities will be taught in a sequence of mini-lessons with specific objectives.

The main teaching strategies I plan to implement are the following:

Hands-on Learning: Students will use concrete models or manipulatives (unit squares tiles). The use of manipulatives during mathematical instruction help students in the process of building their cognitive models to represent abstract mathematical concepts. Using manipulatives, students communicate with one another and with teachers. Through engaging activities with manipulatives, students can express their thinking while gaining confidence in their mathematical abilities.¹⁵

All the activities included in this unit will have a “hands-on” component. From the first activity in which students need to use tiles to determine the area of rectangles, to the final project in which they need to determine the arrangement with the best possible “walkable perimeter” to design a sensory path using sections of the school hallways as “enclosing rectangles.”

Cooperative Learning: During the completion of the activities proposed in this unit, students will have the opportunity to work with partners and in cooperative groups. They will collaborate to find solutions, sharing their methods and ideas, and promoting discussions and analysis. During this process, I will make sure to provide clear instructions and scaffolding for students to be able to successfully transition from working with a partner to small group collaboration to whole-class discussions and presentations. This strategy helps students support each other as learners because it allows productive struggle. As a result, students learn from their mistakes through explanations from their peers and the teacher. When students are in control of their learning, they have time to try out ideas, listen to one another, and gain confidence among their peers and the whole class.¹⁶All the activities proposed in this unit are designed for students to work in partners or small groups to promote collaboration and peer teaching.

Read-Draw-Write: This strategy is widely used in problem-solving situations in Eureka Math. The idea behind the plan is to approach mathematical problems by drawing pictorial representations of the given information to clarify students’ understanding of the problem. This strategy is appropriate not just for “word problems,” but it is also beneficial for approaching area and perimeter questions. This strategy consists of three specific steps:

1. READ: Students will read the problem or question. It is always a good practice to read the question at least two times and provide opportunities for students to explain their understanding of the question being asked.
2. DRAW: Students will draw a picture that represents the information given. During this step, students need to analyze what can they draw from the data presented in the problem and what could be the best model to use. For students to be able to accomplish this step, they need to be familiar with a variety of pictorial representations. It is expected that they have been exposed to a variety of graphic models in mathematics such as bar models, arrays, equal groups, groups of the same size, partitions, tiled surfaces, etc.
3. WRITE: Students will be able to draw conclusions based on the drawings in the form of a number sentence, an equation, or a statement.

With the RDW approach, students can draw a model of what they are reading, and the drawing helps lead to the understanding of the problem. Drawing a model helps students see which operation or operations are needed, what patterns might arise, and which models work and do not work. While using RDW, students have to put in practice several Standards for Mathematical Practice and in some cases, all of them. Some of these would include: make sense of problems and persevere in solving them, model with mathematics, use appropriate tools strategically, and look for and make use of structure.¹⁷ Most of the activities of this unit require pictorial representations for students to express their thinking.

Project-based learning: The unit’s culminating activity is a “real-life” application project in which students will be able to integrate their comprehension from the previous activities of the unit. In this project, students will be able to integrate hands-on and cooperative learning through the completion of the project.

Project-based learning is a pedagogical method based on the idea of John Dewey of “learning -by doing.” In this educational strategy, the teacher sets the goal and acts as a facilitator providing scaffolding and guidance when necessary. Students, working in groups, create a product to present their gained knowledge in a particular topic. The final product may include a variety of media such as writings, art, drawings, three-dimensional representations, videos, photography, or technology-based presentations. The basis of PBL lies in the authenticity or real-life application and is considered an alternative to paper-based, rote memorization, teacher-led classrooms. Some of the benefits of implementing project-based learning strategies in the classroom include gaining a greater depth of understanding of concepts, broader knowledge base, improved communication and interpersonal/social skills, enhanced leadership skills, increased creativity, and improved writing skills.¹⁸