Instructional Design - Cengage



Curriculum Design

Algebra I

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By: Michelle Corron

Statement of Purpose

ALGEBRA I

A ONE-SEMESTER COURSE FOR EIGHTH/NINTH GRADERS

Learning Algebra has always been thought of as learning a new process or formula then applying it over and over to random numbers. This process would be repeated until it was memorized and then a new process would be started without any connections made back to previous ideas. There was also never a time that the mathematics being learned was related to the students’ lives outside of the classroom. This type of course normally would result in students forgetting almost everything that was learned throughout the course.

Algebra I is a course that is meant to allow students to explore many aspects of expressions, equations, and functions. Students will learn and explore the methods used to solve equations of lines and equations that equal only part of a line; they will also analyze the graphs of these types of equations. Throughout this semester students will also be exposed to several basic aspects or statistics and probability. Students will learn and explore the basic ideas such as Mean, Median, and Mode and also the use of Stem & Leaf charts and Box & Whiskers Plots.

This one-semester Algebra I course is designed to introduce eighth/ninth graders to not only the basic concepts of Algebra, but also to the real life applications of these mathematical concepts. Information that is covered in this course will provide all students with the basic background they need to be able to use the method in a real life situation. From here students will move into a hands-on replica of a real life situation in which the Algebra previously learned is being implicated. The focus of teaching this course will not only be explaining the basic skills, but also exploring the use of these skills in today’s society. Over the years mathematic students have always asked the famous question, “When are we ever going to use this?” After completing the exploration done within this course the students will be able to confidently answer this question on their own.

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Unit Outcomes

Unit 1: Tools of Algebra

✓ The students will be able to state the order of operations. (memory/ recall)

✓ The students will be able to explain the reasoning behind the use of order of operations. (comprehension)

✓ The students will be able to apply order of operations to simplifying numerical expression. (application)

✓ Given numerous numerical expressions and a solution each student will be able to determine whether or not order of operations was used correctly. (analysis)

✓ The students will be able to apply order of operations to evaluating algebraic expressions. (application)

✓ Using their knowledge on order of operations, students should be able to simplify compound expressions including real world problems. (evaluation)

Unit 2: Solving Equations

✓ The students will be able to state the addition and subtraction properties of equality. (memory/recall)

✓ The students will be able to state the multiplication and division properties of equality. (memory/recall)

✓ The students will be able to apply the addition and subtraction property of equality to solve equations. (application)

✓ The students will be able to apply the multiplication and division property of equality to solve equations. (application)

✓ The students will be able to create an equation model for a real world problem. (synthesis)

✓ The students will be able to explain the steps used in solving a two-step equation. (comprehension)

✓ Given the task to buy enough fencing to fence in a specific area, students will be able to apply what they are learning to decide on a conclusion. (application)

✓ Given numerous equations the student will be able to state whether it is an identity equation and has more than one answer. (analysis)

✓ The student will be able to analysis a collection of data by using his or her knowledge of mean, median, and mode. (application)

✓ Students will be able to develop formulas for the surface area of several different three-dimensional shapes. (application)

Unit 3: Proportions

✓ The students will be able to explain the use of ratio and rates. (comprehension)

✓ The students will be able to define ratio. (memory/ recall)

✓ The students will be able to solve proportions. (application)

✓ Given two shapes, students will be able to determine whether they are similar. (analysis)

✓ Students will be able to construct proportions that model real world situations. (synthesis)

✓ The students will be able to use their knowledge of proportions to solve percent problems. (application)

Unit 4: Graphs and Functions

✓ Students should be able to explain a situation by analyzing the graph. (analysis)

✓ Students will be able to define domain and range. (memory/recall)

✓ Students will be able to explain the difference between a relation and a function. (comprehension)

✓ Students will be able to explain what and how the vertical line test is used. (comprehension)

✓ The students will be able to model their functions by use of graphing calculator (synthesis)

Unit 5: Linear Equations and Graphs

✓ The student will be able to state the formula for slope. (memory/recall)

✓ The student will be able to explain what slope is and what the formula means. (comprehension)

✓ Find the slope of several different linear equations. (application)

✓ Show why two lines are parallel or perpendicular by using the formula for slope. (application)

✓ When a student is asked to build a ramp given certain stipulations, they are able to apply their knowledge of slope and construct a ramp. (evaluation)

Sequencing Rationale

This one semester Algebra I course is sequenced based upon the Sophistication pattern contained under the Concept-related classification. In mathematics, concepts can be grouped together and taught in several different manners. I believe that allowing students to learn concepts that are on an easier level and then moving onto a more advanced level, is a perfect way for students to not only learn the information, but to also build the connection between the mathematical ideas.

The first unit within this course, “Tools of Algebra,” is a basic unit used as a starting point within the Algebra I course. This unit contains basic concepts that students will need to know before moving onto the more difficult concepts. The information that is taught within this first unit will be the underlying tool for students to build upon in order to receive a full understanding of the more difficult concepts to come in the future units.

The second unit, “Solving Equations,” starts out also as more of a basic unit using concepts from the first unit to solve one-step equations. The unit gradually becomes more difficult building upon the previous information. Students will be able to see relations between concepts that were taught during the first unit and also concepts that were studied at the beginning of this second unit.

“Proportions,” the third unit within the Algebra I course, expands further on the concepts that were studied during the first and second unit. Students will be using what they have learned about solving equations to know solve ratios, proportions, and percents. Students will start out slow by studying about ratio and rates, which will gradually move into solving proportions. During this unit students will also use their new knowledge of proportions to learn about percents.

Unit four, “Graphs and Functions,” steps to another level of difficulty, studying functions and the graphs that are related to them. Within this unit students are expected to use all of the information they have obtained form the first three units and apply it to equations with two variables. However, similar to the other units students will start out studying the basics of functions and move form that point into the more difficult concepts of functions.

The last unit within the course, “Linear Equations and Graphs,” will be looking at only linear equations. A linear equation is an equation of a line, which will be a new concept to all students. Students will begin the unit by looking at the individual parts of the equation until they have put together the whole equation. Form this point students will begin studying more difficult concepts using and building on their knowledge of linear equations. Throughout the unit students will use information learned during the four beginning units that construct this Algebra I course.

EVALUATION STRATEGY

In the evaluation of the one semester Algebra I course a three-step process will be used. This three step process will include a step used to collect data called Measurement, a step that is used to interpret the data collected called Assessment, and a final evaluation step that will be used to present the evidence that is collected within step one and two.

When teaching mathematics it is important to know the student’s background knowledge to be aware of what the student has previously studied. If a student does not posses the correct knowledge it may cause that student to not obtain a full understanding of the information throughout the duration of the course. This step will be done through a pre-test that will measure the knowledge each student posses. At the end of the semester the students will be asked to take a post-test to see if they have received the intended knowledge throughout the duration of the semester.

Throughout the semester the students will put together a portfolio to show the progress they have made during the course. This portfolio will be a collection of the semesters work. It will contain test, quizzes, projects, homework, class assignments, and journal entries. The portfolio will be used as an assessment tool that will show that effort that each student put forth in the course. Student’s scores from the Ohio Graduation Test (OGT) will also be used as an assessment tool to ensure that students are being properly prepared for this mandatory exam.

When writing a final evaluation and completing step three, it is important to remember to take into consideration both step one and two. Basing the final evaluation on only one of the previous steps could alter what the results appear to be. It is also important for the Measurement and Assessment step to be conducted over a three to five year period, in order to include a full array of students. Completing the three-step process over an extended period of time and comparing the results to similar curriculums, will determine whether or not the one semester Algebra I course is working as intended. Otherwise the curriculum should be altered to ensure that every student is learning the appropriate material.

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