Unit Plan

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

Your name: Deeya
School, grade & course: Elgin Park Secondary School, Grade 9, Mathematics

Topic of unit: Powers and Exponents

                                   

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, and beautiful about this topic? (150 words)                 Powers is a way to represent repeated multiplication. This topic is included in the curriculum as often very large or small numbers are more easily expressed in exponential form. Not only do they appear in Chemistry and Physics but in economics, social sciences, and many other disciplines. It is important for students to learn it as they can connect it with everyday connections – when calculating area of his/her room, to measure large distances (for ex distance from the moon to the earth), when counting things that grow very quickly (for ex: bacteria). Exponents are also used to represent to describe a computer’s memory, in computer games, investing and finance and population growth. I hope that from this topic, students will know how use and read a calculator, use it in other subjects, simplify their answer and use it in their everyday life. What makes it fascinating is the magical way of expressing a very large number in a shorthand expression.

(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)              It was interesting to read the history of powers and I would definitely share it with my students. The term power was used by the Greek mathematician Euclid for the square of a line and afterwards was discovered by Archimedes who proved the law of exponents, 10a 10b = 10a+b. Some mathematicians (e.g., Isaac Newton) used exponents only for powers greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as ax + bxx + cx3 + d.               To incorporate the history as part of my unit, I would talk about Euclid who is referred to as the “father of geometry” and they could even turn to Pg93 to see how he ressembled. POWER appears in English in 1570 in Sir Henry Billingsley's translation of Euclid's Elements: "The power of a line is the square of the same line." - http://mathforum.org/library/drmath/view/58247.html

(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)                  To encourage students’ active participation, I will introduce the topics with a variety of hook – (songs on powers and exponents, history) so that they find it interesting in the beginning itself.  Throughout this unit manipulatives and visual aids (posters) will be used and games as well (puzzles, kahoot, beach ball activity, spinning the wheel) will be played. This will provide multiple opportunities for students with different learning styles to gain understanding, possibly even subconsciously during the games.                I will also encourage group work as students can learn from each other. They will even get the chance to create their own game, and activities where they can mix skills they have learned in other subjects, for instance art, social studies and language, with their mathematical knowledge and discover connections for themselves.

(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) Time : 2 period / math class Title: Powers and Exponents Objective: To provide learning environment that stimulates and enhances effective learning Instructions : Students will have to submit a creative project in two days with the following requirements and they may choose a real life application of exponents from the following list ·        Light years                                                              ·        computers ·        bacterial growth ·        radioactive half-life ·        engineering ·        medicine ·        scientific notation                Requirements : a)              What is the application of exponents you researched? b)              Describe its connection to the real world. c)              What is the impact of your area of research on science and/or mathematics? d)              How would your area of research find it more difficult to work/study if exponents weren’t used? e)              Why is your area of research important/significant to your life, your community, and the world? Formats: comic strip, song, video, skit, Prezi, PowerPoint, song, brochure , or others (but need to be discussed with me first)                                    NOTE:   You may choose to work alone or with a partner.

(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)  Formative assessment Since formative assessment process provides information needed to adjust teaching and learning while they are still happening, I will often observe group interactions and individual work, do 2-3 quizzes every week, check classwork and homework, do exit- admit slip so that I can understand and quickly determine which students have it, which ones need a little help, and which ones are going to require much more instruction on the concept.  Summative assessment The tests, assignments, and projects are used to determine whether and to what degree students have learned the material they have been taught. The rubric for the project will be as shown below. Beginning Developing Accomplished Exemplary Application of Exponents in the Real World Three or more components are missing Two components are missing but the rest are fully included All components are correctly included – but briefly explained OR one component is missing and the rest are fully included All components are correctly included – detailed and thorough ·          Real world application of exponents ·          Description of it’s connection to the real world ·          Impact it has on science/math ·          Difficulty without exponents ·          Importance of this area of research to your life, community and the world Images No images are provided or they do not display a connection between exponents and the real world One image is shown and displays a connection between exponents and the real world Two images are shown but one may not display a connection between exponents and the real world Two image are shown and displays a connection between the use of exponents and the real world Clarity In sentence format and/or very disorganized Point form but somewhat  disorganized Short point form and organized Detailed but still in point form and very organized Sources Citations page included but barely filled out Website and a couple of pictures are cited Several blanks in citations Websites and most pictures cited (one or 2 blanks in citations) Websites and all pictures fully cited

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 -3.1	Using exponents to describe numbers -                    Represent repeated multiplication with exponents -                    Describe how powers represent repeated multiplication
2-3.2	Powers of tens and zero exponents
3-3.3	Exponent laws
4-3.4	Order of operations -                     Use the order of operations on expressions with powers -                    Apply the laws of exponents
5-3.5	Using exponents to solve numbers -                    Solve problems that require combining powers
6-3.6	Using exponents to solve difficult numbers (surface area) -                    Use powers to solve problems that involve repeated multiplication
7	Project
8	Project + Revision
9	Presentation
10	Chapter 3 review
11	Unit test
12

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.

Title: Powers and Exponents
Duration: 1h15mins
Grade Level: Grade 9
Rationale: Students will be familiar with the laws of exponents and able to apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols.
SWBAT: -                    solve a given problem by applying the order of operations without the use of technology -                    solve a given problem by applying the order of operations with the use of technology -                    identify the error in applying the order of operations in a given incorrect solution
Objective	Time	Activity	Materials
Attendance Review	10 minute	Welcome the students and review a bit what we did in the previous classes. Students will play the jeopardy game for a quick revision. http://www.math-play.com/Exponents-Jeopardy/Exponents-Jeopardy.html	Laptop, smart board, buzzer for the jeopardy game
Introduction/ hook	5 minutes	Imagine you are about to get your L license. How ugly would that be if everybody decided to drive on any side of the road they wanted to? Crash, collision!! So for Math too there are rules that we need to obey – Recap : BEDMAS	Laptop, L sign
Lesson notes & practice	20	Will explain, using examples, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents: I will solve some examples on the board and afterwards the students will be encouraged to come and solve it on the board	Worksheet, laptop, smart board
CW	20	Students will be given some CW Pg 111 no 5-13	Book, smart board
Activity	15	Spinning the wheel The students will be sitting in group of 4. Each color represents a number. The group who gets the correct answer will get the chance to spin the wheel	Spinning wheel, paper, pen
Closure	5	Recap on the rules of powers

John Mason's Questioning In Math class

The author’s ideas are connected with inquiry-based learning in secondary school mathematics. He values the questions and thoughts of the students. He believes that “students whose teacher challenges them appropriately but significantly are likely to develop flexibility and creativity in their thinking.” Another method of inquiry I learnt from this reading is asking the student “how do you know?’. Thus the student will reflect on his thoughts and push the student to think beyond the answer and find the “why”.

Moreover, I was surprised the way they teach in Japan, “in how many ways can you find the answer?”. This is a good method as the student will learn different ways and adapt to the one he/she prefers. During my long practicum, I would definitely try this method and ask the students to come to the board if ever they came up with a different way of solving.

Also, I would try to make some puzzle where answers will be in small envelopes and the student will have to figure out what kind of questions fit this solution. Students will be more engaged working in a group rather than just learning the traditional way and solving equations, or learning formulas.

Group Micro-Teaching Reflection

I really enjoyed doing this micro-teaching with Etienne and Ying-Ting. The overall response from our colleagues was very constructive.

·         Time: I found it hard to manage the time and since I was teaching the zero solution I was done quite fast, with the activity and handouts. I wished I had plan something more to engage my peers.

·         Activity: The activity was quite interesting but that’s true sticks being colorful would have attracted the kids more and maybe more clear. Wrong perception, I thought I was teaching grade 11 and colorful stick won’t make a difference, but they did actually prefer colors. J

·         Topic : Only sine law was written on the board when we started doing a little revision(prior knowledge) of the previous class, but when we eventually started on today’s (Monday ) topic we forgot to write that we are doing The Ambiguous Case of Sine Law. I love writing the day, date and topic before starting the class. Strange that we forgot to write the one we are teaching – might be we were too rushed, or stressed.

Micro-Teaching Lesson Plan

Title: Learning the different cases of the Sine Law
Date: November 30, 2015
Grade Level: Pre-Calculus 11
Prescribed Learning Outcomes: Solve problems, using the sine law, including the ambiguous case.
General Purpose: This class will look at how the Sine Law can be used to find the unknown length of a side of a triangle given one angle and the lengths of the other two sides. We will look at three cases: 1) where there is no solution, 2) where there is one solution, 2) where there are two solutions.
SWBAT: 3.5 Sketch a diagram and solve a problem, using the sine law. 3.6 Describe and explain situations in which a problem may have no solution, one solution or two solutions.
Probing of previous knowledge: We are assuming that in the class previous to the one we are teaching, students had learned about the Sine Law and about how to derive it. They also know basic properties of triangles, like how all the interior angles of a triangle add up to 180 degrees.
Objective	Time	Activity	Materials
Introduction/ hook	1 minute	Give students a little background information about the use of trigonometry - how it had been used early on as a way of measuring long distances, by calculating angles and smaller distances, and using perspective to approximate the longer distances.
Summary	2 minutes	Review the concept of the Sine Law (presented from a previous class). Ask the students whether they think they can find an unknown side length of a triangle given an angle of that triangle and the lengths of the other two sides.  Is this always possible?	·
Inquiry project	3x3 = 9 minutes	Illustrate the three different cases for Sine Law (whether one, two or no solutions) by dividing the class into three groups, and having one instructor (Ying Ting, Deeya or Etienne) assigned to each group. Each instructor will present a different case. They will give students sets of three sticks, with which the students have to make as many different triangles as they can. Once they have come up with an answer as to what the max number of triangles they can make is, they have to explain why their solution is correct. The instructor will help guide the students, writing the problem on the board and explain why there is indeed only one, two, or no solution. The instructors will spend 3 minutes with each group, and then rotate, for a total of 9 minutes.	Measured sticks with which to make triangles. Multiple sets for each case (one solution, two solutions, or no solution).
Handout+ summary	3 minute	Give students the handout on the Sine Law cases. Go over the handout briefly. Use it to show students that the three different cases necessarily have one, two or no solutions. Illustrate this on the board, clearly. Show the implications of this for when solving the Sine Law.
Summative Evaluation: By having students use the sticks to make up different triangles, students will illustrate their knowledge of the different number of triangles that can be made given certain lengths of the sides.