Unit Plan + 3 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:                             Jun Hwang

School, grade & course:          Mulgrave School, grade 10 & Foundations of Mathematics

and Pre-Calculus/IB Math 10

Topic of unit:                           Translating real-world problems into Linear Equations and

Systematic approach to solve them.

Preplanning questions:

Why do we teach this unit to secondary school students? (150 words) (1)  Why is this topic included in the curriculum? -       The topic is included in the curriculum because it allows us to solve not only what we consider ‘rigid’ and ‘mathematical’ problems but also many others such as in human interactions and social justice. Yet, there are limits in merely using linear equations in certain contexts hence by having included the topic in the curriculum, students obtain an opportunity to discuss the limits of linear equations in solving problems that arise in the real world. (2)  Why is it important that students learn it? -       The answer ties into (1), and that is because students only focus on solving problems especially when the problems are posed in the math classroom. Prior to assuring and understanding the need for problem solving, students may not be aware where linear equations arise in real contexts. It is the teacher’s responsibility to open up to the new realm of mathematics, that is showing them the role translation plays in problem solving in general. (3)  What learning do you hope they will take with them from this? -       To be malleable, flexible and being able to communicate with peers when solving linear equations rather than focusing on the procedural steps to solve them. (4)  What is intrinsically interesting, useful, beautiful about this topic? -       What is embedded in the topic is that having to read a literature in a different context (other than mathematics) brings students with mixture of confusion and uneasiness especially when the text is not directly translatable to mathematical equation. Hence, rather than bringing teachers’ problems onto the students’ table, let us judge collaboratively whether some texts are translatable and why some don’t in the context of linear equations.

A mathematics project connected to this unit (250 words) (1)  Plan and describe a student mathematics project that will form part of this unit. -       Math project, called ‘Drawing Birch Bark Canoes’, will display a large graph paper with numerous linear equations on the side. Each student will graph each linear equation on the side, and soon discover that the final shape of every linear equation put together forms the 3D shape of a birch bark canoe, which was the principal means of water transportation for Indigenous peoples of the Eastern Woodlands, and later voyageurs, who used it extensively in the fur trade in Canada. (2)  Describe the topic, aims, process and timing -       The topic of the math project is about the indigenous perspectives and cultures. The architectural design of the canoe was exceptional for generating a great speed and elegance. Samuel de Champlain remarked that it was ‘the only craft suitable’ for navigation in Canada. Artist and author Edwin Tappan Adney asserts that the birch bark canoe was so superior that it was adopted almost without exception in Canada. The process of the canoe drawing will take longer than 1 week because it needs architectural layout through linear graphs, coloring, and analysis of the pros and cons of the boat. (3)  What the students will be asked to produce -       The students will be asked to graph the linear equations listed on the side of the paper and will color the interior part of each 2d shape, analyze the pros and cons of the boat, create a new boat by implementing the cons and organize where such boat will be used. (4)  How you will assess the project. -       The assessment, for the most part, will be focused on whether the graph is correctly drawn. Reading the linear equation by its slope and y-intercept is the key part of understanding the unit. The supplementary assessment will be on students’ creativity to draw a new boat of one’s own and translate back into the linear equation. The discussion portion will also be used for assessment in which students are allowed to discuss different ideas to create a boat and the application of it, as a communication and participation portion.

Assessment and evaluation (100 words) How will you build a fair and well-rounded assessment and evaluation plan for this unit? 1)    formative -       Formative assessment occurs in almost any activity that the teacher assign to students. Most of the warm-up activity will have students demonstrate their communication, collaboration with peers, and math understanding. The formative assessment in the beginning will take note of the progress each student has made at the end of the class compared to the activities in the beginning. 2)    Summative -       Summative will be the progress noted in the formative assessment. Students will be notified of this fact, so that teachers can expect a minimum degree of participation in the classroom. Test materials and correctness in the reasoning will be less of a value here but will be measured at the end of each unit/lesson. 3)    informal/observational -       Take note of the formative 4)    more formal assessment modes -       Boat project, mid-term tests, mark appeal process

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	What are Linear Equations?
2	Different Forms of Linear Equations
3	Ways to Solve Linear Equations
4	Changing Word Problems into Linear Equations
5	Terminologies that Appear in Word Problems
6	How to Translate Word Problems into Math Equations
7	Linear Equation with Rational and Irrational Numbers
8	Linear Equation with Multiple Unknowns
9	Systems of Linear Equations
10
(11)
(12)

Subject: Mathematics	Grade: 10	Date: Dec. 11, 2017	Duration: 1 week
Lesson Overview (What this lesson is about)	-       Different forms of linear equations -       How to solve it -       Extension to difficult problems
Class Profile	-       25 students, 1 IEP, 2 ELLs

Big Idea(s)

-        Operations between polynomial expressions are connected and allow us to make meaning through abstract thinking

Curriculum Competencies	-       Demonstrate fluent and flexible thinking of number -       Model mathematics in contextualized experiences
Content	-       Linear operations and the meaning of linear equations -       Where it is used and why it is important to make contextualized language into a mathematical expression -       The techniques of solving variety of forms of linear equations and how to solve it
Curriculum Objectives	-       Using the mathematical language and communicating the problem with peers and connecting it into a real world situation

Materials and Equipment Needed for this Lesson

-       5 Markers -       Big Bristol Board-like papers -       The lesson power point -       Formative assessment sheet

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up	-       Organizing with Graphic organizers and group mind-mapping for linear equation and collaborative problem solving process and fun math puzzles -       Ex) Jigsaw Puzzle	30 min
2.	Presentation	-       The different forms of linear equations. How do we solve for them? -       Introduction of the terms: Cross Multiplying, Isolating a variable: What does each do to get our x value?	20 min
3.	Practice and Production Practice, reinforcement, and extension of the new content and language.	-       Things to consider: What does it mean to isolate a variable? What does it mean to cancel out a coefficient? What kind of approach are there with variables on both left hand side and the right hand side?	20min
4.	Closure	The universe of solving systematic equations often involve more than one equations simultaneously because there are more than one unknowns to the wonders of the world. Can we still find x in such a case as well?	5 min

Assessment/Evaluation of Students’ Learning

-       Formative assessment starts from the warm-up process. In doing the jigsaw students will find the location of the jigsaw by solving linear equations shown on each puzzle piece. But, some students will solve the puzzle by trial and error. If some pieces don’t fit, the students will do it until they find the right piece. Then, they will realize the location of the puzzle is indicated in the x-value of the linear problem on the piece and find the answer to the problem that way. -       The evaluation will come up in the word problems mostly because oftentimes students get stuck to the procedure of solving linear equations. The procedure is in fact the least important thing in solving linear equations. They can isolate the variable then reduce the coefficient to 1 but they can do it in any order they want. Not to emphasize what counts as correct and what counts as not correct I will provide as many word problems as possible. The transition to get familiar with the test format this will be made first of all as a formative then to summative.

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.

-       Students often have difficulties solving linear equations for different forms of linear equations. For example, if an unknown value has a whole number coefficient, one does not know how to get cancel out the whole number greater than 1 unless teacher guides them to ‘divide’ by that whole number. If the coefficient is a rational value that is not a whole number, it becomes a whole new problem for students. -       It becomes evident when teachers observe students, they want procedural steps to find the value of x. There needs to be a transitional process and instructional guidance with teachers to explain what it means to ‘isolate’ a variable or ‘cancel’ the coefficient

Subject: Mathematics	Grade: 10	Date: Dec. 11, 2017	Duration: 1 week
Lesson Overview (What this lesson is about)	-       The Benefit of Changing Word Problems to Mathematical equations -       Terminologies that emerge in word problems -       How to translate them into math equations
Class Profile	-       25 students, 1 IEP, 2 ELLs

Big Idea(s)

-        Operations between polynomial expressions are connected and allow us to make meaning through abstract thinking

Curriculum Competencies	-       Demonstrate fluent and flexible thinking of number -       Model mathematics in contextualized experiences
Content	-       Linear operations and the meaning of linear equations -       Where it is used and why it is important to make contextualized language into a mathematical expression -       Translating variety of word problems into linear equations
Curriculum Objectives	-       Using the mathematical language and communicating the problem with peers and connecting it into a real world situation

Materials and Equipment Needed for this Lesson

-       5 Markers -       Big Bristol Board-like papers -       The lesson power point -       Formative assessment sheet

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up	-       Word Problem activities: Students will create their own problems and translate them into mathematical equations and have their ideas posted on a big Bristol board. -       Solutions to the problems that the group has come up -       Presenting it to peers and a teacher	30 min
2.	Presentation	-       Terminologies: What are the terms we are aware of in the math problems in general? What are the terms that we are not fully aware but useful for mathematical expressions? -       Translating the word problems into mathematical equations and reflecting on the systemic approach to solving the equations	20 min
3.	Practice and Production Practice, reinforcement, and extension of the new content and language.		20min
4.	Closure	The problems in the real world brings us a limitation for solving them because they are not so directly translatable. What are such problems? How can they be translated into a mathematical equation so that the problem becomes easily solvable?	5 min

Assessment/Evaluation of Students’ Learning

-       Formative assessment starts from the warm-up process where students collaborate to come up with their own word problems and making a connection to a problem that can be systematically solved by the steps we have learned in our previous lesson. The creative process inquires students to think about the new concepts and make connections to why the translation is important. -       Students will evaluate their peers and it allows teachers to evaluate where they are at in terms of what to seek and where to translate.

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.

-       It is often a problem that teachers present with all the cases of word problems because otherwise students may not see the connection between where the word problems appear and why translating them to mathematical equations. Hence, it is often encouraged to guide students to come up with their own and sometimes it’s OK to have problems not necessarily be a linear problem or even unsolvable. In the end, their presentation will sum up their mistakes and observe their own why it cannot be translated to mathematical equation sometimes.

Subject: Mathematics	Grade: 10	Date: Dec. 11, 2017	Duration: 1 week
Lesson Overview (What this lesson is about)	-       Linear equation (one unknown) with rational and irrational numbers -       Linear equation with multiple unknowns
Class Profile	-       25 students, 1 IEP, 2 ELLs

Big Idea(s)

-        Operations between polynomial expressions are connected and allow us to make meaning through abstract thinking

Curriculum Competencies	-       Demonstrate fluent and flexible thinking of number -       Model mathematics in contextualized experiences
Content	-       Linear operations and the meaning of linear equations -       Where it is used and why it is important to make contextualized language into a mathematical expression -       Systematizing simultaneous linear equations to solve for multiple unknowns
Curriculum Objectives	-       Using the mathematical language and communicating the problem with peers and connecting it into a real world situation

Materials and Equipment Needed for this Lesson

-       5 Markers -       25 laminated sheets -       The lesson power point -       Formative assessment sheet

	Lesson Stages	Learning Activities	Time Allotted
1.	Warm-up	-       Organizing with Graphic organizers and group mind-mapping for linear equation and collaborative problem solving process and fun math puzzles -       Ex) Figure 1 Credit to: Bethany @ www.mathgeekmama.com -       Presentation of ‘how’ each group has solved it.	40 min
2.	Presentation	-       We are presented with linear equations that involve multiple variables. In fact, we have been using it but which one have we not seen yet? How do we solve for them? -       Introduction of the terms: Solving for equations with multiple variables: How to subtract/add/multiply/divide between equations and how to derive the unknowns	20 min
3.	Practice and Production Practice, reinforcement, and extension of the new content and language.	Practice1) Solving using graphical method: Practice2) Test: Solving using systematic approach:	10min
4.	Closure	We have been dealing with solving a equation with 1 variable with many different forms and contexts. We have seen the limits of its presentation to translating to 1 unknown oftentimes. Hence, we have seen the necessity of systematizing it by introducing multiple variables and different solutions to obtain different unknowns. The problem arises still: How can we solve for these variables which involve more wild looking unknown values such as cubed x and exponential variable?	5 min

Assessment/Evaluation of Students’ Learning

-       Students will be struck by the difficulty of the equations which they have not encountered in the previous lessons. The point is that how they collaboratively come to the agreement when solving those systems of linear equations involving more than one equations and play with variables rather than constant values existent in linear equation involving one variable. -       The presentation therefore will evaluate how they have come or not come with the solutions and how far they have gone to or close to the value of unknowns through communicating with peers -       Test papers at the practice time will be measured and extended to measure student performance in deriving the solutions to the problem (Starting from formative to summative)

Reflection

-       Linear equations with multiple equations is naturally come up in the contextualized problems that students make themselves in the previous lesson. -       The students’ own intellectual struggle to find that multiple variables is the key motivation to this lesson. The solution does not come out so easy because this time you have to apply different operations with the equations this time, not just numbers to ‘isolate’ variables or ‘reduce’ coefficients. -       Starting from students’ own brainstorming to get an idea of where and how to derive the solution to multiple variables (in our case, ice cream cost problem), they will get a brief idea what it is that we are trying to solve here. We are not only interested in just one but for many unknowns. In fact, they have been using systems of multiple linear equations themselves but somehow not so much aware of it. This time, I will introduce from how we have been afraid of this multiple equations to how familiar we were in solving different contextualized problems.