Unit Plan and Lesson Plans

EDCP 342A Unit planning: Rationale and overview for planning a 3 to 4 week unit of work in secondary school mathematics

Your name: Ashley Tam
School, grade & course: Sir Charles Tupper Secondary School, Grade 8/9, Surface area and volume

Topic of unit: Surface area and volume

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) Surface area and volume is an important unit for students because it focuses on visualization and concrete connections to the real world. The objects students deal with are shapes they may see in their everyday life and thus they provide a relevant real world connection to mathematics. Allowing this connection can help students view mathematics as useful and interconnected, rather than isolated. It is extremely important that students are able to make these connections because research says that this can help build better understanding, which can ultimately make mathematics more meaningful for students. Additionally, visualization is also an important step in connecting mathematical understanding. Students learn to create, interpret and describe visual representations, which can help to link their mathematical understanding to something concrete and tangible. The biggest thing that I want students to learn from this unit is, how to take textual representations and turn them into visual representations. I feel a lot of true mathematical understanding comes from visualizing situations, and if a student is able to take a scenario and transcribe it into a visual, I feel they will improve their ability to understand the scenario and finally compute any numeric problems. I think this unit is beautiful because it is the first real concrete representation of mathematics, which as mentioned will allow students to take their understanding to a whole new level because of the many connections they may build.

(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) Students will work on building a traditional longhouse of the First Nation’s peoples. After having learned about the surface area and volume of a rectangular prism, students will proceed to design and construct a 3D model of a longhouse. Students will take measurements in order to provide detailed information and calculations about the surface area and volume of the longhouse. They will also be asked to write a short paragraph describing the history and uses of a longhouse in First Nation’s culture. The topic of this project is surface area and volume of a right rectangular prism, although it is possible their roof may contain other shapes and therefore students may seek more help or do further research to calculate any unknowns. The aim of this project is to help students connect mathematics to real life and develop meaning for the shapes and prisms they may see regularly. The project will also help students visualize the prism better using a physical and more kinesthetic technique to find relationships among the sides, edges and faces. The students will be first assigned this project after they learn about volume of right rectangular prisms. They will first be asked to research about longhouse and their significance in First Nations’ culture, as well as their general shape and structure. Then students will go home and bring supplies, like cardboard or other sturdy building supplies, to the next class to make their longhouses. Once the students have the required materials they will precisely measure and draw a net for the pieces of their structure. They will record these measurements and make a (not-to-scale) drawing of their net to place on their board with the detailed measurements. Then the students will construct their longhouses and secure them to their platform board, where they will also include their research paragraph about longhouses and detailed calculations for the surface area and volume. Lastly they are free to decorate and make their longhouse more visually appealing. The assignment will be due one week after it is assigned and will be given class time to work on it. The students will be graded using a rubric that assesses for the accuracy and detail of their historical research paragraph, the accuracy and work shown for their surface area and volume calculations, the precise measurement for the construction of their longhouse, the accuracy of the structure in reference to true First Nations’ longhouses and lastly, their overall visual appeal of the longhouse.

(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) For this unit I will assess the student’s understanding of each lesson by either providing a quiz on the topic for the next class or doing a marked homework check to see any errors students may be making. This will simply provide a diagnostic of how well the lesson went and how much help the students may still need. During the lessons I will do much more observational assessment in which students will work in pairs to complete example problems provided by me. Students will either work through a problem with me or they will all work on it on their own, while I circulate to ensure they are comfortable with the material and successfully performing the task. At times I will provide some more structured formative assessment using vertical non-permanent surfaces. The students will work together to solve various problems on their whiteboards and then the students can do a gallery walk of each question to take note of different problems. The summative assessment will be a unit test on all the material covered.

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	Nets
2	Making shapes from nets
3	Surface area of right rectangular prisms
4	Pythagoras
5	Surface area of right triangular prisms
6	Volume of right rectangular prisms
7	Volume of right triangular prisms
8	Surface area of a right cylinder
9	Volume of a right cylinder
10	Surface area of rectangular prism composites
(11)	Surface area of other composite objects
(12)	Volume of composite objects

b) Write a detailed lesson plan for three of the 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) social/environmental justice

c) Indigenous perspectives and cultures

d) Arts and mathematics

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’

Lesson Plan #1

Subject: Math Unit: Surface area and volume	Grade: 8/9	Duration: 60-75 minutes
Lesson Overview/Topic	Students will learn how to find the volume of a right rectangular prism. Students will begin working on a project about the First Nations’ longhouses.

Curriculum Competencies (Student’s will be able to…)	Communicate: -          Importance of rectangular prisms in everyday life -          Problem solving process to peers Visualize, Model and Construct: -          Right rectangular prisms in a variety of forms and scenarios Connect: -          Shapes and prisms to real world scenarios -          Mathematics to First Nations’ history -          Surface area to volume
Content (Student’s will know…)	-          How to calculate the volume of a right rectangular prism from a net, a 2D image of a prism or a word problem

Materials, Equipment and Resources Needed for this Lesson

-          Tablet, projector, cables -          12-18 different prism problems for students on a sticky note -          Rectangular prism volume worksheet -          Computer lab -          Lecture notes on volume of a right rectangular prism

 

	Lesson Stages	Teacher Activities	Student Activities	Time
1	Introduction/Review	Teacher will provide each pair of students with a different surface area problem to solve together. Teacher will prompt students to recall how to find the volume of a cube, providing an example on the board if students are unclear. Then the teacher will ask them to see if they can determine the volume of their own rectangular prism in their pairs. The teacher will circulate to ensure students are correctly solving for the volume.	In pairs students will work on a review question about the surface area of a right rectangular prism. Then students will try to determine the volume of the prism and once they are finished they will share their solved problem with another group, who will also share their solved prism. Each group will check the other’s work in order to ensure each group is correctly solving their prism.	25 mins
2	Lecture and Practice	Teacher will provide a short formal lecture on how to calculate the volume of a right rectangular prism. Teacher will provide students with a worksheet of practice problems on calculating the volume of a rectangular prism from the net, the prism or a word problem.	Students will take notes on the lecture given and will work through examples in lecture. Students will complete worksheet for homework due next class.	15 mins
3	Longhouse Project	Teacher will introduce the longhouse project and rubric and bring students to a computer lab to conduct research.	Students will research history and structure of a longhouse for their project in preparation for next class when they will begin construction. They will also try and write their informative paragraph.	20 mins
4	Closure	Teacher will outline the upcoming classes and the time structure for the project. They will also allow students to work on worksheet.	Students will either continue working on their longhouse project or start their worksheet for homework.	15 mins

Lesson Plan #2

Subject: Math Unit: Surface area and volume	Grade: 8/9	Duration: 60-75 minutes
Lesson Overview/Topic	Students will learn how to find the volume of a right cylinder. Students will begin working on an informative poster about a prism of their choice.

Curriculum Competencies (Student’s will be able to…)	Communicate: -          Problem solving process to peers -          Information through poster art Visualize, Model and Construct: -          Cylinders  in a variety of forms and scenarios Connect: -          Cylinders and prisms to real world examples (deck of cards, poker chips etc.) -          Surface area to volume
Content (Student’s will know…)	-          How to find the volume of a right cylinder from nets, 2D images of the prism and word problems

Materials, Equipment and Resources Needed for this Lesson

-          Sticky notes with 12-18 different cylinder problems -          Stacks of items: cards, poker chips, coins etc. -          Lecture notes -          Tablet, projector, cords -          Poster art project rubric and instructions -          Homework questions from textbook

 

	Lesson Stages	Teacher Activities	Student Activities	Time
1	Introduction/Review	Teacher will give students a problem about surface area of a right cylinder to solve in pairs on whiteboards. Emphasizing students distinguish the area of the circular tops and bottoms of the cylinders. Teacher will hand out stacks of items such as cards, poker chips, coins etc.	Students will solve for the surface area of a cylinder given by the teacher, in pairs. They will also find the area of the circle top/bottom and note that down. Students will play with and analyze stacks of items and leave them on desks.	10-15 mins
2	Lecture and Practice	Teacher will use stacks of cards and especially poker chips and coins to explain that the volume of a cylinder is simply the area of the circular face times the height of the cylinder, using the analogy that the cylinder is made up of infinitely small slices of circles stacked up like poker chips or coins. Teacher will reveal formula and work through a few problems with the students. Teacher will challenge students to find the volume of their cylinder from the review.	The students will interact kinesthetically with the stacks of items to visualize the idea of volume. They will also take notes on the lecture and follow along with the problems. In the same pairs, students will work on finding the volume of their cylinder,.	30 mins
3	Poster Art Project	Teacher will introduce poster art project and go through expectations and rubric. Teacher will give students time to work on this project in class.	Students will choose a prism, either one covered in the course or one researched, and they will make a poster which contains how to calculate surface area and volume of the prism, a miniature net that can fold up into a prism on the page and examples of ways the world or nature uses these shapes.	20 mins
4	Closure	Teacher will assign questions from the textbook for homework and remind students of poster deadline.	Students will either work on their poster or on their homework questions.	10 mins

Lesson Plan #3

Subject: Math Unit: Surface area and volume	Grade: 8/9	Duration: 60-75 minutes
Lesson Overview/Topic	Students will learn how to find the volume of a composite object. Students will use a “thinking classroom” to analyze real life examples of composite objects.

Curriculum Competencies (Student’s will be able to…)	Communicate: -          Problem solving process to peers Visualize, Model and Construct: -          Composite objects in real life Connect: -          Composite objects to real world examples -          Surface area to volume
Content (Student’s will know…)	-          How to find the volume of a composite object from a 2D prism or word problem

Materials, Equipment and Resources Needed for this Lesson

-          Example question for composite object surface area review -          Lecture notes -          Tablet, projector, cords -          A few extra composite objects for students who may forget to bring theirs -          Unit review package for students to practice problems before test

 

	Lesson Stages	Teacher Activities	Student Activities	Time
1	Introduction/Review	Teacher will go through a guided example of a composite object surface area question.	Students will guide teacher in solving a composite object surface area problem.	10 mins
2	Lecture and Practice	Teacher will lecture on how to find the volume of composite objects, asking students to work on a few examples on their own while the teacher circulates.	Students will take notes on lecture and work through examples to ensure they understand the process.	20 mins
3	“Thinking Classroom”	Teacher will ask students to take out their composite objects they brought from home and explain instructions for the last half of class. Teacher will guide students in a gallery walk of their composite objects.	Students will get into groups of 2, grab a whiteboard, a ruler or tape measure and take out their composite objects. Each pair will draw up a sketch of their objects on their own whiteboards and label all the measurements they will take with their ruler or tape measure. Then they will be required to calculate the surface area and volume of their objects on the whiteboard. They will work together with their partner to ensure both individuals gather a accurate calculation. Once completed, students will take a gallery walk to view the other composite objects and calculations.	40 mins
4	Closure	Teacher will provide students with a review package for their unit test and tell them next class will be a review.	Students will start working on review package if time.	5 mins