- Introduction
- Aim
- Rationale
- Audience
- Prerequisites
- Subject Matter
- Learning Objectives
- Materials
- Instructional Plan
- Plan for Assessment
- Appendix

## Introduction

This Curriculum Web is specifically designed to support work done in Advanced Functions and Modeling offered in North Carolina. The individual projects/lessons

are sequenced, but may be used separately. The projects can also be used to support any class dealing with probability, statistics, non-linear functions, and sequences and series. Each lesson has its own form of assessment that can be used as-is or as a guide for creating a further assessment.

Activities range in form from being self-discovery to be used before a classroom lesson to being enrichment and extending for post-instruction use. Writing assignments are also included to support writing across the curriculum, research study, and mathematics appreciation.

## Aim

This curriculum web aims to teach and strengthen the skills needed for success in advanced mathematics classes to junior and senior-level high school students planning on attending a four-year university or college.

## Rationale

With the proliferation of computers in today’s modern society, many students believe that they do not need to learn higher levels of mathematics. Contrary to this belief, now is the most important time for students to continue their mathematics education. By utilizing the computer and web in the Advance Functions and Modeling course, students not only learn how math applies to everyday life in the home, work, and recreation, they will see how this knowledge can help them work more efficiently with the computers and more easily understand how they work. Additionally, by utilizing computers and the web in this course, students will be further prepared for entering college by gaining essential skills related not only to mathematics but also to computers and other similar technology.

## Audience

This curriculum web is designed for sophomore, junior, and senior high school students in the Advanced Functions and Modeling class. Text and colors will be used efficiently and effectively to add in the readability of the material and not distract from the content therein. Navigation throughout the curriculum web will primarily be non-linear. Each page will have images selected for appropriateness in order to support the content of the activity. The activities included in the curriculum web support in-class instruction and mathematics appreciation. Additionally, the activities range from general to specific, depending on the need of the activity and the goal of the instructor. Each of the activities can be used separately on its own or in order.

One secondary audience would-be educators who might find the activities useful for their students. The activities meet many of the curriculum goals set forth by the North Carolina Department of instruction and the teacher, so therefore this curriculum web will lend itself greatly towards use by other educators in North Carolina. Another secondary audience that may utilize the curriculum web would-be parents of involved students so they can know what is going on in their student’s projects.

## Prerequisites

The prerequisites for this curriculum web follow the perquisites for the course listed on the NC Standards web site:

- Describe phenomena as functions graphically, algebraically, and verbally; identify independent and dependent quantities, domain, and range, and input/output.
- Translate among graphic, algebraic, numeric, tabular, and verbal representations of relations.
- Define and use linear, quadratic, cubic, and exponential functions to model and solve problems.
- Use systems of two or more equations or inequalities to solve problems.
- Use trigonometric ratios to model and solve problems.
- Use logic and deductive reasoning to draw conclusions and solve problems.
- Minimum of basic web skills and browser function skills such as printing.
- Minimum 10th-grade reading level.

## Subject Matter

This curriculum web is based on the following topics:

- Algebra
- Trigonometry
- Statistics

## Learning Objectives

The objectives used for this curriculum web are the same as the NC Standards, seen below:

**Data Analysis and Probability**

**1.01** Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.

- Interpret the constants, coefficients, and bases in the context of the data.
- Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

**1.02** Summarize and analyze univariate data to solve problems.

- Apply and compare methods of data collection.
- Apply statistical principles and methods in sample surveys.
- Determine measures of central tendency and spread.
- Recognize, define, and use the normal distribution curve.
- Interpret graphical displays of univariate data.
- Compare distributions of univariate data.

**1.03** Use theoretical and experimental probability to model and solve problems.

- Use addition and multiplication principles.
- Calculate and apply permutations and combinations.
- Create and use simulations for probability models.
- Find expected values and determine fairness.
- Identify and use discrete random variables to solve problems.
- Apply the Binomial Theorem.

** Algebra**

**2.01** Use logarithmic (common, natural) functions to model and solve problems; justify results.

- Solve using tables, graphs, and algebraic properties.
- Interpret the constants, coefficients, and bases in the context of the problem.

**2.02** Use piecewise-defined functions to model and solve problems; justify results.

- Solve using tables, graphs, and algebraic properties.
- Interpret the constants, coefficients, and bases in the context of the problem.

**2.03** Use power functions to model and solve problems; justify results.

- Solve using tables, graphs, and algebraic properties.
- Interpret the constants, coefficients, and bases in the context of the problem.

** 2.04** Use trigonometric (sine, cosine) functions to model and solve problems; justify results.

- Solve using tables, graphs, and algebraic properties.
- Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.
- Develop and use the law of sines and the law of cosines.

** 2.05** Use recursively-defined functions to model and solve problems.

- Find the sum of a finite sequence.
- Find the sum of an infinite sequence.
- Determine whether a given series converges or diverges.
- Translate between recursive and explicit representations.

**Teacher Objectives**

- Understand some of the history of mathematics and who made it what it is today.
- Understand the application of mathematics to real-life principles both natural and man-made.

## Materials

- A Computer
- Access to the Internet
- A printer
- Paper
- Writing utensil

** Some activities are considered “open-ended” and therefore may require additional materials based on what the individual student decides to pursue for the activity.*