ND Curriculum Initiative

Subject & Standards

Needs Assessment/Rational

Although not specifically listed as one of the state standards, logical reasoning is implied or is a part of North Dakota’s state standard 9-10.2.4 and West Fargo’s 12.3.1.3(Using given information, establish the validity of a conjecture using a two-column proof). While working on the North Dakota assessment test this was a standard that generally was found difficult to test. I want my students to be able to see logical reasoning including inductive and deductive reasoning in practice. I also want my students to see how congruent figures, especially congruent triangles, are valuable in real life applications.
One of West Fargo High School’s goals for NCA was to implement writing across the curriculum. Writing and technology are also included in the West Fargo standards 12.6.4.1 (Explains ideas precisely using mathematical language)and 12.6.4.2 (Presents mathematical procedure and argument using varied media; e.g. chart, graphing calculator, power points, sketchpad, etc.). Geometric and mathematical modeling are included as standards at both the state and district level. North Dakota standards 9-10.2.11 (Use geometric models to gain insights into, and to answer questions in, other areas of mathematics, other disciplines, and other areas of interest;e.g., art and architecture)and 9-10.5.14 (Draw conclusions about a situation being modeled) These are West Fargo’s standards 12.6.2.3 and 12.6.2.2, respectively. Each of these standards will be addressed in this project.
I feel we can always strive to make mathematics more real life. Some of our curriculum is still outdated and does not include many real life examples. Therefore, I saw the need to develop this advertising project. This project will carry over into two chapters in our textbook. It will be an ongoing project, just as projects are in real life. This project will allow me a chance to make geometry “real life” and also implement a variety of teaching and learning styles and strategies. As a bonus they will learn the skills of making good choices in response to the advertising slogans they see every day.

Understandings & Goals

Enduring Understanding:
Students will understand the characteristics of logical reasoning. Students will understand the difference between inductive and deductive reasoning. Students will understand how logical reasoning affects our daily lives through slogans used in advertising. Students will also understand the characteristics of congruent triangles and how the use of congruent figures can be applied to create eye-appealing logos used in advertising. Goal(s):
To become familiar with how logical reasoning is used to create slogans. To become familiar with how congruent figures are used to create appealing logos. To become familiar with how both, slogans and logos, are vital to good advertising.

Questions Answered

Essential questions:
What is logical reasoning?
How are inductive and deductive reasoning different?
How is logical reasoning used in creating slogans?
What slogans do you remember and why?
What are congruent figures?
How can congruent figures be used to create logos?
What logos appeal to you and why?
Objectives:
Students will find slogans in various forms of media. Students will study the characteristics of logical (inductive and deductive) reasoning. Students will write if-then conditional, converse, inverse, and contrapositive truth statements and will determine the validity of the truth statements. Students will study how the use of logical reasoning in slogans affects the student and his or her family. Students will use creativity to write a slogan for an imaginary product. Students will identify the characteristics of congruent triangles. Students will research logos that use congruent figures. Students will use creativity to create a logo for an imaginary product.

Assessment

 What quiz and test items (e.g. simple content-focused questions that require a single, best answer) will provide evidence of understanding?
  Quizzes using short answer responses will be used to assess the student’s progress in working with logical reasoning. Quizzes using simple content-focused questions will be used to assess progress in the student’s understanding of congruent triangles. The scope of this project covers two chapters; therefore, a test at the end of each chapter, using simple content-focused questions and a few application questions, will assess the student’s understanding of both logical reasoning and congruent triangles.

What academic prompts (e.g. open-ended questions or problems that require students to think critically and then to prepare a response / product / performance) will provide evidence of understanding?
  Investigation of the advertising project will begin by asking students to research slogans and logos. They will respond to the questions, "What makes a good slogan, and what impact does it have on you and your family?" and "How are congruent figures used in logos to create symmetric eye-catching forms?"

What performance tasks and projects (e.g. complex challenges that are authentic, mirror the real world and require a performance or product) will you include that will provide evidence of student understanding?
  Students will complete a slogan activity and a logo activity. In the Advertising Project as a whole, they will create a slogan and logo for an imaginary product.

What other evidence (e.g. observations, work samples, dialogues, student self-assessment) of understanding will you collect?
  Students will complete writing assignments to assess understanding. Their slogan and logo will be assessed using student generated rubrics. Students will write reports on the use of logic in advertising slogans and the use of congruent triangles in advertising logos. Students will also write a reaction paragraph(s) on the project as a whole.

Instructional Strategies

Students will use both inquiry-based and problem-based learning to investigate what they know about how logical reasoning and congruent figures (triangles) are used in advertising. Through the problem investigation process, students gather, record, and analyze slogans and logos to understand how logic and congruent figures (triangles)are used to create the slogans and logos used in advertising. The student will understand how logic and congruent figures can affect the uniqueness and impact of the slogan and logo. Using project-based learning, students will develop a product that uses the concepts learned to create a slogan and logo that could be used to advertise their product.