Unit and Lesson Plan

 

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

Your name: Megan Fan
School, grade & course: Cambie Secondary, Richmond
Course: Math

Grade: 8
Topic of this Unit: Surface Area and Volume for Regular Prisms and Cylinders 

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)   This topic is included in the curriculum because geometric knowledge is the key to understanding some other topics or subjects. This topic is the foundation for the 3D object learning for measuring the surface area and volume, closely connected to the real world, we are three-dimensional living. We need measurement and calculation skills to design and build objects to meet our needs.  Calculating the surface area and volume of prisms and cylinders are the extensions of measuring objects for the earlier grades. After learning this unit, I hope my students can draw and construct nets and draw the top and side views of 3D objects. They will understand the concept of surface area and volume and develop the formulas to solve the problem involving surface area and volume of prisms and cylinders. I think this topic is interesting and useful since it is visual and related to the real world. It is easy to connect to many fields like city planning, interior designing, or other mathematical arts to apply project-based learning on this topic.

(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) The mathematical project connects to this unit. I would like my students to ask them to pretend to be interior designers to design their bedroom. The bedroom dimension is 5m x 4m x 2.5m (L x W x H). 1.  What kind of furniture and objects they want in this bedroom, and what are the dimensions of those objects will be to fit in the bedroom?  There will be at least 5 items but no more than 15 items. 2.      If they need to paint their bedroom walls and ceiling, how many cans of paint they need assuming each can of paint cover 10m2/L?  How much will it cost roughly? 3.      If they are allowed to build a pet home for their pet in your bedroom, what shape it should be to maximize the volume and what is it? They need to make drawings of their designed bedroom. The list of the rough dimensions of the furniture and objects in your bedroom. The budget of your painting and the detailed reasoning for this project. I will ask students to demonstrate their designed bedroom in the classroom and explain this project's process. What did we learn from this project, and what are the topics they want to learn more about? I want to evaluate the student by assigning this project with the two weeks timing limit.   This project assesses students' understanding of the shapes and understanding of the surface area and volume and calculates the surface area and volumes for 3D objects. This project helps students develop creative thinking, critical thinking skills, research skills, measuring skills, and the connection with the real world.

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	3D object Net
2	3D Objects and views
3	Surface Area for rectangular prism
4	Surface Area for the right triangular prism
5	Volumes of the rectangular and other right prisms
6	Surface Area and Volume of Cylinder
7	Project-based learning- Design and decorate your bedroom
8	Chapter reviews
9	Unit Test
10	Project presentation
(11)
(12)

b) Write a detailed lesson plan for three lessons, which will not be in a traditional lecture/ exercise/ homework format.  These three lessons should include at least three of the following six elements related to your mathematical topic. (And of course, you could include more than three!)

These elements should be thoroughly integrated into the lessons (i.e., not an add-on that the teacher just tells!)

a) History of this mathematics
b) Arts and mathematics
c) Indigenous perspectives and cultures
d) Social/environmental justice
e) Open-ended problem-solving in groups at vertical erasable surfaces (“thinking classroom”)
f) Telling only what is arbitrary, and having students work on what is logically ‘necessary..’

Be sure to include your pedagogical goals, the topic of the lesson, preparation and materials, approximate timings, an account of what the students and teacher will be doing throughout the lesson, and ways that you will assess students’ background knowledge, student learning, and the overall effectiveness of the lesson. Please use a template that you find helpful and that includes all these elements.

Lesson Plan 1: Net

Subject: Math	Grade: 8	Date: Dec 6th,2020	Duration: 60 minutes
Lesson Overview	Students will begin their unit on Three-Dimensional Object with a lesson on the prism and nets concept. Through this lesson, students will be able to draw or construct nets from prisms and can predict and create 3D objects from the nets of prisms.
Class Profile	Total: 23 students One student has a hearing issue and requires teachers to wear a device to help students' learning challenges.

 

Big Idea(s) (Select one or two big ideas from the new BC curriculum): https://curriculum.gov.bc.ca/curriculum

The relationship between 3D objects and the nets. Nets of the 3D objects can be used to describe, measure, and compare spatial relationships.

 

Curricular Competencies (What the students will do)   (Select appropriate curricular competencies from the new BC curriculum):   https://curriculum.gov.bc.ca/curriculum	Students will: ●       Explore, analyze, and apply mathematical ideas using modeling, technology, and other tools ●       Visualize to explore and illustrate mathematical concepts and relationships ●       Use mathematical vocabulary and language to contribute to discussions in the classroom
Content Objectives	Draw nets of prisms            From nets can predict 3D object prisms
Core Competencies	Communications:            Small group discussions and group project Thinking:            Draw relations between 3D prisms and nets Personal and social:           Real world applications and examples
Language Objectives	Prisms and Nets            Prism            Net            polyhedron            regular prism            right prism

 

Materials and Equipment Needed for this Lesson

Computer, slides, blackboard, colored markers, ruler, pencil, sheet paper, clear tape, 3D prisms

 

 

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up and Get students’ attention, connect to previous knowledge and explain why the topic is important to learn.	Ask leading questions:  Show some 3D object models, I got from the law class project and ask them what other shapes of 3D objects they see in life? Discuss and share with the class.	5 minutes
	Pre-teach	Activity: Make 3D objects and decorate them as the ornament for their classroom’s decoration   Show 3D object models from the preprinted net of the models and ask students to think what it will look like, and ask them to make the 3D object using the net. Decorate with mathematical patterns, shapes, symbols, signs they know.	10minutes
2.	Presentation   Teach new content and language.	Present slides: Prism and Net       Introduce prism and net       How to draw the net from  3D prisms       From the net to 3D prism object	15 minutes
3.	Practice and Production   Practice, reinforcement, and extension of the new content and language.	I will preprint worksheets for nets of prisms. Ask students to find  relations between 3D prisms and the nets            Prism            Net Compare answers to your group and discuss with your group members. I will walk around in the class to make sure ALL students get help if needed.	20 minutes
4.	Closure	Ask what they learned from this lesson? Why are they important to learn?           Prisms           Nets Assign homework for this topic. Next class topic: The surface area for the rectangular prisms.	10 minutes

 

 

 

 

Assessment/Evaluation of Students’ Learning

Diagnostic Assessment            Pre-teach,, I ask the related question to assess            During the presentation, I ask students for help to work along with me in the example problems            Closure stage, I ask what they take away from this lesson            Ask students in groups to solve problems and discuss answers.            Walking around to check if someone needs help.

 

 

Reflection   Reflect on your process of developing this lesson plan. Explain how your lesson plan relates to some of the theoretical concepts acquired in this course so far.   https://www.math-salamanders.com/3d-geometric-shapes.html

I tried to make this lesson plan engaging and straightforward. Students will be engaged from beginning to end with demonstrations, hands-on activities, and discussions. This reflective teaching method created an active learning environment and can stimulate students with critical thinking and help students understand the hard mathematical concepts and terminologies through this lesson.   I offer students opportunities to work individually and in groups. I can assess students at pre-teach, during presentation and practice and production, and at closure stages. Evaluating students in the class can help me learn students’ understanding of the topic and adjust my teaching plan accordingly.

Lesson Plan 2: Surface Area of Rectangular Prism

Subject: Math	Grade: 8	Date: Dec 6, 2020	Duration: 60 minutes
Lesson Overview (What this lesson is about)	Students will begin their unit on surface area and with a lesson on the concept of surface area for the right prism. Through this lesson, students will be able to find the surface area for the right prisms.
Class Profile Construct a hypothetical class profile, in which you specify how many students are in your class, their learning challenges, and their levels of English proficiency	Total: 23 students One student has a hearing issue and requires teachers to wear a device to help students' learning challenges.

Big Idea(s) (Select one or two big ideas from the new BC curriculum): https://curriculum.gov.bc.ca/curriculum

The relationship between the area of 2D shapes and the surface area of 3D objects can describe, measure, and compare spatial relationships.

.

Curricular Competencies (What the students will do)   (Select appropriate curricular competencies from the new BC curriculum):   https://curriculum.gov.bc.ca/curriculum	Students will: ●       Explore, analyze, and apply mathematical ideas using modeling, technology, and other tools ●       Visualize to explore and illustrate mathematical concepts and relationships ●       Use mathematical vocabulary and language to contribute to discussions in the classroom
Content Objectives (What the students will know)	exploring strategies to determine the surface area of a regular solid object            calculate surface area of regular solid, right prisms            surface area = sum of the areas of each side
Core Competencies	Communications:            Small group discussions and group project Thinking:            Solving for surface area Personal and social:            Real world applications and examples
Language Objectives   (What new language the students will learn)	Surface area            polyhedron            regular prism            right prism       rectangular prism

Materials and Equipment Needed for this Lesson

Computer, slides, blackboard, colored markers, ruler, pencil, sheet paper, clear tape, 3D rectangular prism

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up Get students’ attention, connect to previous knowledge and explain why the topic is important to learn.	Ask leading questions: How much paper will you use to wrap your gift box?	5minutes
	Pre-teach	Activity 1. Teacher: show the gift box and give each student one rolls of string; ask students to roughly estimate the surface area of the gift box indigenous way. Then ask students to draw nets for the model, then hand out the preprinted net of the models, and ask students to measure the area of the net and determine the surface area.      Estimate the total area of the box and describe the strategy for estimating	10minutes
2.	Presentation   Teach new content and language.	Present slides: Surface Area         Introduce the right prism      What is surface area      What is the relation net area and surface area?         Example 1 shows how to solve       Extended Example	15minutes
3.	Practice and Production   Practice, reinforcement, and extension of the new content and language.	Activity 2 I will ask students to play “face it” card game in groups, each student get three number cards and ask students to solve the surface area for           rectangular prism          right triangle prism compare answers to the group and discuss with your own group members what will the surface area change if the cards are used in a different order? I will walk around in the class to make sure ALL student get help if needed	20minutes
4.	Closure	Ask what they learned from this lesson What other times you use surface area in your life? Why are they important?              Surface area = Sum of all face area            Surface area of prisms Assign homework for this topic Next class topic: The surface area for cylinders	10minutes

Assessment/Evaluation of Students’ Learning

Diagnostic Assessment            Pre-teach,, I ask a related question to assess            During the presentation, I ask students for help to work along with me in the example problems            Closure stage, I ask what they take away from this lesson Practice and Production            Ask  students in groups to solve problems and discuss their answers            Walking around to check if someone need help

Reflection   Reflect on your process of developing this lesson plan. Explain how your lesson plan relates to some of the theoretical concepts acquired in this course so far.   https://www.math-salamanders.com/3d-geometric-shapes.html

I tried to make this lesson plan engaging and straightforward. Students will be engaged from beginning to end with demonstrations, hands-on activities, and discussions. This reflective teaching method created an active learning environment and can stimulate students with critical thinking and help students understand the hard mathematical concepts and terminologies used in this lesson.   I offer students opportunities to work individually and in groups. I can assess students at pre-teach, during presentation and practice, and at closure stages. Evaluating students in the class can help me assess students’ understanding of the topic and adjust my teaching plan accordingly.

Lesson Plan 3: Surface area and Volume of Cylinder

Subject: Math	Grade: 8            Date: Dec                                       6, 2020	Duration: 60 min
Lesson Overview	Surface Area and Volume of cylinders.
Lesson profile	23 students One student has a hearing issue and requires teachers to wear a device to help students' learning challenges.
Big Idea(s)	The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships. Taken from the BC Math Curriculum guide, found at (https://curriculum.gov.bc.ca/curriculum/mathematics/8)          Relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships          Computational fluency and flexibility extend to operations with fractions
Curricular Competencies	Taken from the BC Math Curriculum guide, found at (https://curriculum.gov.bc.ca/curriculum/mathematics/8)         Reasoning and analyzing     o   Use reasoning and logic to explore, analyze, and apply mathematical ideas   o   Use tools or technology to explore and create patterns and relationships, and test conjectures     Understanding and solving     o   Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving     o   Visualize to explore mathematical concepts    Communicating and representing         o   Represent mathematical ideas in concrete, pictorial, and symbolic forms o   Explain and justify mathematical ideas and decisions
Content Objectives	Exploring strategies to determine the surface area and volume of regular solids using objects, proper use of units, calculations with Surface area: 2πr2 + 2πr * h volume: πr2 * h

Materials and Equipment Needed for this Lesson ●       Piece of paper 8.5in x 11in ●       Laptop ●       Tablet with stylus

Learning Activities	Time Allotted
Introduction review: ●     What is the area of a circle? ●     What is the circumference? ●     How do you get radius if you know circumference? ●     What is surface area? ●     What is the volume?   ●     Activity 1: Which Cylinder has greater surface area and volume? (5 min)  Prepare a sheet of 8.5inx 11in a paper (pre-class)  Step 1, roll it along the longer side to a cylinder  Step 2, roll it along the short side to a cylinder   Question: do they have the same surface area and volume? If not, what is the ratio? - poll   Presentation: ·        How to calculate the surface area and volume of a cylinder                                     Surface area: 2πr2 + 2πr * h Volume: πr2 * h	15 min
After 15min presentation, ask students to solve the surface area and volume for the two paper cylinders to compare with their prediction   Hand out the worksheet: surface area and volume of a cylinder   Activity 2: Designing a garbage bin for the city, what the shape they want to use to maximize the volume, and calculating surface area and volume, and what do you want to paint on the surface?   ○     Students will be asked to create their own garbage bin using their knowledge of composite shapes with a cylinder. They will create their own measurements to determine the total surface area and volume of their shape and thus how many liters of garbage their shape can hold ○     The teacher will facilitate discussion and encourage students to share their drawings and ideas	15 min