Unit Plan ........

 EDCP 342A Unit planning: Rationale and overview for planning a unit of work in secondary school mathematics

Your name: Elvie Wu
School, grade & course: Seaquam Secondary School, Foundations of Mathematics and Pre-calculus 10

Topic of unit: Trigonometry Ratios

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic? (150 words) First of all, this unit is an essential unit because it prepares students for future study in mathematics, it helps students to get ready for pre-calculus and applied math streams. Most real-life measurement problems involve heights, distance, angles, and slopes, and this unit introduces the foundational tools needed to solve these situations when direct measurement is not possible.These skills are not only central to the mathematical field, but also deeply connected to other fields such as science, physics, engineering, computer science, and architecture. Even if students don’t plan to major in math, the thinking and problem-solving skills they learn through trigonometry are still useful in many other fields. As a practical topic, trigonometry bridges classroom learning with the real world and provides an early opportunity for students to develop their abstract thinking. Through this process, it can develop students’ core competency and build students’ logical reasoning skills, analytical thought and creative problem-solving skills. For instance, students learn to visualize shapes, interpret diagrams, and reason about angles and distances. Moreover, students also learn to connect numeric and geometric representation and practice their communication skills during the hands-on measurement activities and collaborative projects.

(2) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce, and how you will assess the project. (250 words) Topic: This project focuses on applying right triangle trigonometry (sine, cosine, and tangent) to measure the height of a tree. Students will take on the role of the owner of a Christmas tree shop, where accurate tree height measurement is essential for determining pricing.  Aim: The aim of this project is to help students apply right triangle trigonometry in real-world situations through a realistic business scenario. Students will learn how to use trigonometric ratios to estimate the heights of trees and understand how accurate measurements inform pricing decisions. This project also develops students’ problem-solving abilities, enhances their mathematical modelling skills, and strengthens their capacity to justify their calculations. In addition, it encourages students to communicate their reasoning clearly within a meaningful context. Process and Timing: This project will be separated into 2 classes. In the first class: Students will be working on this project as a group of 2-3.  In the first 20 minutes, they need to plan how to measure distance from the tree and the angle of elevation with the given tools. After the discussion, they need to collect tools including measuring tape, protractor, a straw, a string, and a weight. Students go outside and start measuring. They need to choose three different heights of the trees and measure each of them. Record data clearly for later calculation. This process will take around 35-40min. In the last 10 minutes, students will go back to the classroom and reflect on the measuring process about the difficulties and what they found interesting. In the second class: Students need to work on the project in groups. They need to choose the appropriate trigonometric ratio and calculate the height of the tree step-by-step.  In the project, students need to show the angle, distance with a right triangle diagram. Justify why they chose their specific trigonometric ratio based on the data they collect. With a pricing guideline for Christmas trees, students need to determine a reasonable market price for their trees. They also need to justify their pricing in relation to the tree’s height and quality. Furthermore, they need to write a reflection not the accuracy, limitations, and what are the real-world implications. This project will assess both their mathematical accuracy and their ability to communicate their reasoning with a real-world context.

(3) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words) To build a fair and well-rounded assessment plan for this unit, I will use different approaches. Each lesson will include formative assessments such as homework check, exit tickets, group discussion, and whiteboard practices. I will also observe students  during group work and problem-solving tasks to assess their understanding and adjust my teaching strategies accordingly. During the second class of the project assignment, I will check in with each group, monitor their process, and provide support based on their questions. In this process, by knowing their difficulties, I can assess them formatively. In addition, quizzes, unit tests, and group project will function as summative assessments to evaluate their core concepts.

Elements of your unit plan:

a)  Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them. 

Lesson	Topic
1	history
2	tangent
3	sine and cosine
4	review
5	quiz
6	solving right triangles
7	project 1
8	project 2
9	review
10	unit test
(11)
(12)

Reflection on "textbook"

 I believe the existence of textbooks helps to standardize teaching content and maintain consistency across classrooms. They serve as an important reference point for both teachers and students, ensuring that key mathematical ideas are taught systematically. Many textbooks also include well-designed tasks and real-world connections, which can help students see the relevance of mathematics beyond abstract symbols. Additionally, textbooks provide a rich problem bank that supports practice and reflection, allowing students to consolidate and deepen their understanding.

As both a teacher candidate and a former student, I see mathematics textbooks as valuable tools that have shaped much of how we learn and teach mathematics. When I think back to my own experience as a student, I used textbook as a tool that can provide a sense of what to learn and step-by-step examples. However, from a teacher's perspective, i realize that textbook can offer structure and guidance, at the same time, it should not dominate the learning experience. As Herbel-Eisenmann and Wagner suggest, how textbooks use language and images can shape how students view themselves in relation to mathematics, however, it sometimes also limiting creativity for students. Therefore, teachers have the responsibility to use textbooks critically and flexibly.

During my short practicum, I noticed that my SAs did not strictly follow the textbook. Instead, they used it as a reference, adjusting the order of chapters and integrating other materials to better fit students’ needs. With digital tools, inquiry-based teaching was often delivered through exploration, discussion, and personalization, which allowing students to take more initiative in their learning.

Reflection to "Flow"

When I first learned about the concept of flow, I immediately connected it with my own experiences as both a teacher candidate and a student. There were many moments when I felt completely immersed in an activity, and time seemed to pass unnoticed. These moments often occurred when the task was fascinating and slightly challenging, but still within my ability to understand or solve. For example, while working on mathematical problems, I often experienced flow when a topic initially seemed difficult, yet I felt confident that I could figure it out through effort and reasoning. 

As a teacher, I believe it is essential to create similar experiences for my students. When activities are engaging, appropriately challenging, and suitable for their age, students are more likely to enter this state of focused enjoyment. For instance, using a math bingo game can combine fun with learning: students compete to solve problems, stay motivated by the game’s structure, and practice important concepts in an active way. During my short practicum, I also learned from my SA, who designed a scavenger hunt for her Grade 8 class, posting fraction problems around the classroom. Her students were highly engaged, running around, collaborating, and solving as many problems as possible. Such activities not only make learning enjoyable but also help students experience the kind of deep engagement and satisfaction that Csikszentmihalyi describes as flow.

Learning becomes most meaningful when students are both challenged and supported. Being a teachers, my role is not only to deliver content but also to design opportunities that stimulate enthusiasm, curiosity, focus, and joy. By intentionally creating moments where students can lose themselves in learning—just as Csikszentmihalyi’s concept of flow suggests—we help them experience the true satisfaction of growth and discovery. Ultimately, when students find themselves deeply engaged, learning becomes more than a task; it becomes a source of happiness and fulfillment.

Reflection to The Giant Soup Can of Hornby Island

As i saw this puzzle, I found that i need to search the dimension of the Real Campbell’s Soup Can, A “medium-sized hybrid bike” size and the amount of water required to put out an average house fire.

Real Campbell’s Soup Can Dimension:

Height: h = 10.5 cm

Diameter: d = 7 cm

Radius = 3.5 cm

Ratio: h/r=10.5/3.5=3/1

A medium-sized hybrid bike's wheelbase is about 170cm (1.7m). As I noticed from the picture, water tank length is about 3 times of bike length. So we get the tank length is around 510cm (5.1m). Because the tank has the same proportions as the can, knowing h/r=3/1, we can get the radius and dimension of the tank.

Tank Dimension:

Height: h = 510 cm (5.1m)

Diameter: d = 340 cm (3.4m)

Radius = 170 cm (1.7m)

Knowing that the volume of cylinder is V=πr^2h, the water tank volume is about 46.3m^3, which is 46300L.

I searched that an average house fire may require 38000-110000 L of water. So this tank have enough water to put out an average house fire.

The picture above is the Red Cedar Stump in Surrey, which is an example of old growth forest that once covered all of Surrey. The stump is of a tree estimated at 500 to 1000 years old, 30 feet in circumference. 

Please use the height of the white fence as a reference to estimate the height of the stump.

Assume that the original tree had a similar base-to-height ratio to modern red cedars, and calculate:

• The approximate height of the stump based on your fence estimate.
• The approximate height of the original full tree, using the modern red cedar base-to-height ratio.
• The approximate volume of wood in the original tree.

Reflection to Arbitrary and necessary

After reading Dave Hewitt’s “Arbitrary and Necessary: A Way of Viewing the Mathematics Curriculum,” I started to think more deeply about how students actually learn mathematics and how I should design my lessons. In Hewitt’s framework, arbitrary knowledge refers to things that students can only know by being told, such as names, symbols, and conventions that are decided by people. In contrast, necessary knowledge refers to ideas and relationships that students can figure out through reasoning and awareness.

This distinction makes me reflect on how I want to teach mathematics in my classroom. Usually, math teaching focuses on memorizing formulas or following fixed procedures, which can make students see mathematics as a subject of rules to remember rather than ideas to understand. Hewitt’s argument reminds me that real mathematics begins when students start to reason, question, and discover why something must be true. If I only tell them what to do, I might take away their chances to think mathematically.

In my future lessons, I want to be more intentional about separating what is arbitrary from what is necessary. For the arbitrary parts, such as notation or vocabulary, I will make sure to give clear explanations and support their memory. But for the necessary parts, I want to create meaningful activities that allow students to explore and make sense of patterns on their own. For example, instead of directly telling them that the angles in a triangle add up to 180°, I can guide them to discover it through cutting, folding, or measuring. I believe this approach will help students build a deeper connection with mathematics, where they are not just remembering facts but truly understanding them. As Hewitt says, “If I’m having to remember, then I’m not working on mathematics.”