Unit Plan for Pythagoras! (With one lesson plan)

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

Your name: Ian Mak
School, grade & course: King George Secondary, 8 & Mathematics

Topic of unit: Algebra

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) Without algebra, calculations and formulae from many different fields would not be possible. When Einstein theorized that E = mc^2, he was using algebra. When a business order is calculating inventory, deciding how much he needs to buy to meet expected sales for the month, he is using algebra. Moreover, this material is incredibly applicable to everyday life as well. When you calculate tips after dinner, you are using algebra! When you calculate how much time to dedicate to homework tonight and how much time to spend with friends, you’re using algebra! I hope that students not only learn the elementary operations and concepts of the unit (opposite operations, operations applied to one side must be done to the other etc), but understand the practicality of the material. I hope that they understand how pervasive these simple calculations are in our lives that are dominated by consumerism and currency exchange.

(2) What is the history of the mathematics you will be teaching, and how will you introduce this history as part of your unit? Research the history of your topic through resources like Berlinghof & Gouvea’s (2002) Math through the ages: A gentle history for teachers and others  and Joseph’s (2010) Crest of the peacock: Non-european roots of mathematics, or equivalent websites. (100 words) Algebra eliminated the necessity of approximation. Before algebra, mathematicians had to approximate many of the calculations they could now conduct WITH algebra. Algebra allowed Newton to calculate the acceleration due to gravity, and allowed Archimedes to discover the value of pi when looking at the ratios of radius to its circumference. I would use facts like these in my hooks to get students interested. I could also design worksheets in which students would, using algebra, figure out constants that have already been derived so they can understand what each philosopher had to do. For example, a worksheet centered around physics principles could have multiple questions which have the solution of -9.81, student just figured out acceleration due to gravity!

(3) The pedagogy of the unit: How to offer this unit of work in ways that encourage students’ active participation? How to offer multiple entry points to the topic? How to engage students with different kinds of backgrounds and learning preferences? How to engage students’ sense of logic and imagination? How to make connections with other school subjects and other areas of life? (150 words) It’s important to emphasize the real life applications of algebra in my examples (calculating tips, calculating tax/income percentages, cooking etc). Moreover, to emphasize the versatility of algebra as a skill to help solve almost any problem such as how much furniture you can fit in one room, how many hours you paid for in parking, or how long a pipeline needs to be to stretch from Canada to Mexico. This versatility is how I would offer multiple entry points to the topic: I can cater examples to students’ general interests so it is more personalized and directly applicable to their lives. For example, if a student loves snowboarding and is struggling, I can give them an algebra question that uses snowboarding as an illustration. For different ethnic backgrounds, I could emphasize the algebraic origins that their home country has, since algebra has history in many countries. I need to make sure, for any unit, that none of the examples are exclusionary to any person of any particular socio-economic status, religion etc.

(4) 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. (100 words) The project will be a summative assessment on lessons 1-6. Students will be placed in a heist scenario where they need to locate vaults individually by solving various one and two variable equations, both written in words and mathematically, and finally graphing the equation and answering some analysis questions about their graph. This class is a 120 minute block; they have the whole time to work on it. The process is 2 parts: first part they complete individually with the same problems, second part is individually with different problems. Students will produce a graph and two filled-out answer sheets.

(5) 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) I will have small formative assessments after lesson 2, lesson 5, and lesson 10 to make sure students are understanding these critical components of the unit. Throughout the classes though there will be informal assessment going on as homework is completed, class discussions are had, and different activities are completed. This will include written and verbal confirmation of understanding.  There will be one summative assessment toward the end of the unit that will test comprehension/communication/application of the material. Retest/corrections will be allowed for all assessments, but there will be a cap of how much higher a student’s grade can increase.

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	Introduction to Ian and Classroom Expectations Introduction to Expressions (written to variable, variable to written, what are variables?) Evaluating algebraic expressions (substitution into equations)
2	Distributive Law (feeding the chickens!) -       Dress up like a farmer and bring a chicken and a toy tractor
3	Formative Assessment on Lessons 1 and 2 Definition/terminology of polynomials Adding/Subtracting Polynomials
4	Addition and Subtraction Equations -       I’m thinking of a number… Multiplication and Division Equations
5	Combined Operations Equations containing Brackets
6	Formative Assessment on lessons 3-5 Linear Relation (Ordered Pairs) -       I’m thinking of an ordered pair… Solution to Two Variable Equations Be a wizard!
7 (Double Block)	Summative Assessment -       Heist Mission
8	Linear Models 1
9	Linear Models 2
10	Formative Assessment on Linear Models
(11)
(12)
(13)

b) Write a detailed lesson plan for one of the lessons which will not be in a traditional lecture/ exercise/ homework format.  Be sure to include your pedagogical goals, 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 for Summative Assessment Linear Relations

Subject: Mathematics Grade:    8	Lesson Number:    8 of  10 Time: 120 minutes
Big Idea or Question for the Lesson: Can students recollect and show comprehension and understanding of Ch 5.1-5.6?
PLO foci for this lesson: All of the combined PLO from 5.1 to 5.6
Objectives: Students will be able to  (SWBATs) -        Individually recall material from Ch 5.1-5.6
Content and Language Objectives: -    Show written understanding of the material -   -		Skills/Strategies required: -  Everything from 5.1 to 5.6 -  All of the required skills from 5.1 to 5.6 lesson plans -
Materials/resources: -        “Heist” Blank Part 1 and Part 2 sheets for students -        Three 4-digit number locks for lockers -        Masking tape for grid -        Black light/ markers/ some glue -        Highlighter/yellow fluorescent paper with prewritten equations on them and names of students -        Dress up in a black outfit, black toque, black pants, black sweater, black gloves -        Alpha, Bravo, and Charlie Signs for each group of desks
Assessment Plan: -        Students must complete two summative assessment sheets with their individual solutions to problems and equations required to pull off the “Heist”
Adaptations: [ for EALs] -        Maybe need to explain what a heist is and explain some of the questions, but everything should be accessible Modifications: [for slower processers] -        No modifications Extensions: [ for the ‘quick study’ folk]
-        If student’s finish early, they can work on other class work quietly Hook and Introduction (5-7 min) (__:__ - __:__) -        Student’s desks should be oriented in three groups, with a wide open space in the middle of the class -        Students are assigned to one of the three groups: Alpha, Bravo, or Charlie. -        In the open section of the class, use the masking tape to create a 12 x 12 grid with origin in the center for a graph (x goes from -6 to 6, y goes from -6 to 6) -        Set up the two black lights at the back of the room for later -        Students! You have been recruited to break into three separate vaults that are located somewhere on this grid which is a blueprint of a bad guy’s house. The location of these vaults are located in three lockers somewhere in this school. To find the location of these lockers, you have to answer the following questions and find the clues. Development (about 100 min) (__:__ - __:__) - Teacher-led (15 min) (__:__ - __:__) Students! You must individually complete the first section before you can search for the locker. As you can see, solving the questions will help you find the floor of the locker, locker number, and the four digit combination to get into the locker. Inside you will find the clue to the location of your team’s vault. Once everyone in your group has handed in the first section to me, I will tell you the location of your team’s locker, whether your whole group got it right or not. This is not a race. You must be quiet in the hallways. There are guards that if they see you, you lose. In other words, if we catch you screaming or running, you lose marks. - Independent Work  (__:__ - __:__) Students now have to fill out Part 1 of the Summative Assessment. This has more of the equation based questions from Lessons 1-5. (30-40 mins) Once they fill out the assessment and handed in part 1 to you, you give them the instructions and each group can now go search for their locker, open it, and find their code. When they come back, with a seemingly blank piece of paper, tell them to figure out how to read it and point them to a table with a black light, some other markers to mislead them, and some glue. (10-15 mins) Say, “OH NO, it looks like we’ve been duped! There are way more than 3 vaults! Alpha Bravo and Charlie need to all split up individually to locate your own vaults!” They should find their own personalized equations to continue on with their assessment (each student has their name beside an equation). Now that they have their code (equation) they have to answer part 2 of the summative assessment. This contains a lot of graphing questions from Lesson 6. Once they have found their vault, they can tape an x where their vault is. (30 mins) - Class/Group Activity (__:__ - __:__) Finding the lockers and figuring out how to find their personal codes (use the black light!) - Independent Work  (__:__ - __:__) Part 1 and Part 2 of Summative Assessment Closing (5 min) (__:__ - __:__) -        Alpha, Bravo, and Charlie, you have all successfully found the vaults! Now we have all we need to locate the treasures inside! Perhaps next class will be entirely focusses on figuring out how to GET to the vaults (Linear Modelling lesson) -        No homework! Thanks for participating everyone!