Unit Plan Draft #1

Name: Jackson Chen

Killarney Secondary, Mathematics 9

Topic: Powers and Exponents

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Exponents expand on students’ existing knowledge on multiplication and present a simpler way to denote repeated multiplications of the same number without writing the operations out. This way, it is possible to express extremely large or small numbers using only single-digit integers. The concept of powers and exponents appears in a variety of subject areas that students will encounter later, such as physics, chemistry and economics. It also has many real-world applications like calculating growth rates (population, bank account, etc.) and in units of measurement. For example, when students grow up, they will need to know what the square feet of a house means, or why the storage of their electronic devices are labelled in gigabytes.

(2) A mathematics project connected to this unit: For this unit, students will be asked to work in pairs and complete an art project, where they must build a model for a house/building/architecture whose surface area (walls + roof) formula must include the following: ·       A base power of 2 ·       A base power of 3 ·       A base power of 5 ·       A zero exponent ·       A negative exponent ·       Two different positive exponents The dimensions of the model should be limited to centimeters (and approximated to the nearest millimeter when measured with ruler). Each group should also provide an elevation drawing/plan of their work with labelled dimensions. The final model should be visually proportional to the drawings. Students are encouraged to replicate a renowned architecture, or to design and name an original and make them as aesthetically pleasant as possible (any decorations will NOT count towards the surface area calculations). Students will also be presented a series of sample pictures/models that they can use as inspirations. This will be an opportunity to incorporate any indigenous aspects into teaching. One idea is to use the Waap Galts’ap Community House in Terrace, BC as a sample (pictured) and explaining a brief history of the first nations and how the surface area of this specific building can be calculated. (Credit: Mackin + Associates) In the end, one lesson will be dedicated to a math fair style activity in which students will see every project and try to write the formula and calculate the surface areas of each group’s creation (a worksheet will placed beside each object for ‘visitors’ to write down their answers). In the end, the projects, drawings and worksheets will be collected for grading and assessment. The projects will be evaluated on the students’ understanding of exponents (base, power, negative and zero exponents) through their applications in surface area formulas. The checklist of requirements is helpful to guide students toward their project, as well as the evaluation process. By asking students to observe and explore each other’s projects, the teacher can also get an indication of whether students have developed a deep understanding of the topic.

(3) Assessment and Evaluation:  The unit is divided into four sections: basic use of exponents to describe numbers, exponent laws, order of operations and problem solving. The formal assessment involves a quiz at the end of each section, followed by a unit test. The questions will follow closely to classroom activities and homework assignments. Students will also be assessed informally through classroom activities and the group project participation, so that their level of understanding can be gauged and used as a benchmark for formal evaluations. Students are constantly encouraged to ask questions to clear any uncertainties about the topic.

Elements of unit plan:

a) 

Lesson	Topic
1	Using exponents to describe numbers (power, base, exponent, exponential form)
2	Powers with negative exponents
3	Exponent laws (multiplication, division, raising a power, raising a product or quotient to exponent, exponent of zero)
4	Review/assessment of exponents (part 1)
5	Order of operations (introduce applications and assign project)
6	Using exponents to solve problems (geometry)
7	Using exponents to solve problems (growth rates)
8	Review/assessment of exponents (part 2)
9	Project planning/homework review
10	Project presentation day
11	Final chapter assessment

LESSON PLAN #1 – USING EXPONENTS TO DESCRIBE NUMBERS
Lesson Overview	This lesson is designed to introduce to students how to use exponents to represent repeated multiplications, and the new vocabularies that are attached with learning exponents.
Duration	60 minutes
Materials Required	Paper, pen
Introduction (10 minutes)	·       Begin with an activity: ask students to fold a piece of paper (length and width cut roughly to same length) in half, then repeat the same step three more times. Once opened up, notice how many ‘squares’ have been formed ·       Explain the concept of doubling something over and over again can be written in another way other than 2x2x2x2…
Presentation (15 minutes)	·       Introduce the terms: power, base, exponents ·       Detail the ways in which the exponent form can be read (i.e. two to the fourth) ·       Briefly discuss the history of exponents (Euclid was first to use the term “power”) ·       Go through two examples where the base and power are not 2
Activity (10 minutes)	·       Work through an exponents table that has exponents in one column and numerical values in the other
Presentation (5 minutes)	·       Show that the volume of a cube can be expressed in exponents ·       List out other formulas that have exponents (i.e. area of square)
Activity (20 minutes)	·       Using the paper they have folded, students will work in groups of 4 to figure out how many ‘squares’ there are on the four pieces of paper using only exponents ·       Can you build a cube using ALL the squares (if you cut them out)?

LESSON PLAN #2 –EXPONENT LAWS
Lesson Overview	The objective of this lesson is to familiarize students with operations on powers
Duration	60 minutes
Materials Required	Paper, pen
Activity (10 minutes)	·       Pose the following problem: if we extend the length of a 2x1 rectangle by one unit repeatedly, what happens to the area? ·       Express the pattern in a provided table
Presentation (15 minutes)	·       Introduce the multiplication and division of powers ·       Demonstrate two methods to obtain the answers, one of which follows the law of exponents ·       Similarly, introduce what happens when you raise a power to an exponent ·       Briefly talk about Moore’s Law and how it is relevant today
Review (15 minutes)	·       Assign problems for students to review the exponent laws
Presentation (10 minutes)	·       Ask students what happens when the exponent is zero? Explain the reason using a table ·       What about when the base is zero?
Questions (10 minutes)	·       Can one side of a shape have an exponent of zero? What about negative? ·       Do negative exponents imply that the number is smaller than the base? Examples?

LESSON PLAN #3 – USING EXPONENTS TO SOLVE PROBLEMS
Lesson Overview	The aim of the lesson is to introduce problems in geometry and other applications that require exponents to solve
Duration	60 minutes
Materials Required	Paper, pen
Introduction (10 minutes)	·       Review the lesson about volumes and areas, incorporating exponents and operations ·       Use a more complex object (such as a soda cans or silo) to devise a formula
Presentation (10 minutes)	·       Explain methods to find the volume and surface areas of different objects
Activity (20 minutes)	·       Allow time for students to work on their projects, based on ideas that were just covered in class
Presentation (10 minutes)	·       Introduce problems with growth rates and how exponents can be applied ·       Demonstrate a population growth rate problem ·       Discuss with students how population growth could be an issue given the way we use resources today
Activity (10 minutes)	·       Find the population of Canada in 50 years given the current growth rate ·       What implications are there?

Reflection: Math (Un)fair

Today our class had the opportunity to attend the Math (Un)fair organized by Point Grey Academy, and I was very impressed with what I saw. The most memorable part of the experience was realizing how much effort the students had put into each project just by observing how they were designed and displayed. These took hours of planning and construction as well as support from their parents. 

For some projects, I liked their aesthetic design, while for others I was fascinated by the game mechanics. There were a variety of themes and original ideas that made each station unique. I also thought that the students' applications of probability were well executed, and many of them were able to explain to us why certain games were fair or unfair mathematically. Most of the stations used spinning wheels and dice to incorporate the element of randomization, and some of them strengthened this by adding basketball hoops or ping pong balls.

I think events such as this can definitely enrich students' learning experience, especially at an early age. Not only will they gain a deeper understanding of mathematical ideas, but they can also develop imperative skills such as teamwork and creativity. During my elementary school years, I was only involved in one science fair, so this was also a fairly new experience for me, and as a prospective teacher, it was great to learn about how children approach such projects and how this can be implemented in the classroom setting.

PS: It was also a great feeling to be rewarded with some prizes, so not all games were unfair!

Thinking About Math Textbooks

Prior to reading the paper written by David Wagner and Beth Herbel-Eisenmann, I never really thought about how the choice of words used in math textbooks (such as first person pronouns) could possibly have an effect on the outcome of students' learning.

Overall, I think the authors' model of textbook evaluation and the idea of raising "critical language awareness" provide a new perspective to math teachers, and may even influence how teachers approach their own communications with students. My school advisor during my short practicum also mentioned something similar: how students engage with your class depends on the words you use. Although this was referring to general classroom management, I still agree with the notion that what the students read or hear is extremely important to how they learn.

One thing to take into consideration is that effective usage of vocabulary and the "contextualization" of math at first glance could only work to a certain extent because for students who already have some understanding and interest in math, this kind of detail would escape them. Moreover, students' abilities to subconsciously receive and analyze diction may differ, and maybe not all will prefer the same linguistic choice used in textbooks.

Therefore, textbooks for the most part would be more helpful if they are written to recognize the students' own personal experiences and their relationship to math. Whether the learning outcome can be enhanced can only be measured by how much the students are interested in the material presented.