The learning of linear functions is pervasive in most algebra classrooms. Linear functions are vital in laying the foundation for understanding the concept of modeling. This unit gives students the opportunity to make use of linear models in order to make predictions based on real-world data, and see how engineers address incredible and important design challenges through the use of linear modeling. Student groups act as engineering teams by conducting experiments to collect data and model the relationship between the wall thickness of the latex tubes and their corresponding strength under pressure (to the point of explosion). Students learn to graph variables with linear relationships and use collected data from their designed experiment to make important decisions regarding the feasibility of hydraulic systems in hybrid vehicles and the necessary tube size to make it viable.

This Open Middle task asks students to create a table of values that represents a linear function.

This task requires students to use the fact that on the graph of the linear function h(x)=ax+b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions).

The goal of this task is to have students appreciate how the different constants (P0, K, and r) influence the shape of the graph.

This problem introduces a logistic growth model in the concrete setting of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models, studied in ``U.S. Population 1790-1860.'' This task requires students to interpret data presented.

Students will study a particular town/city of their choosing. They will create two continuous growth curves from population data roughly 80 to 100 years apart. Students will describe the location they have chosen and focus on issues that affect growth. Students will calculate population projections based on the equations created. They will also graph the data to use in their analysis of the population growth.

This task addresses the first part of standard F-BF.3: ŇIdentify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative).Ó Here, students are required to understand the effect of replacing x with x+k, but this task can also be modified to test or teach function-building skills involving f(x)+k, kf(x), and f(kx) in a similar manner.

CK-12 Foundation's Middle School Math € Grade 6 Flexbook covers the fundamentals of fractions, decimals, and geometry. Also explored are units of measurement, graphing concepts, and strategies for utilizing the book's content in practical situations.

Provides teaching tips, information on common errors, differentiated instruction, enrichment, and problem solving for teachers to use with the CK-12 Middle School Math - Grade 6, Student Edition.

A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Overview: This is a PBL project as part of an Integrated Math course with a focus on Functions and Functional Relationships related to Polynomials. The overarching objective of the project is for the student to recognize, describe, model, manipulate, use, and solve non-linear functional relationships to compare the characteristics of different function types. Through the application of these concepts, students will better understand the nature and structure of functions, especially as they pertain to polynomials, exponential functions, variation, and transformations. Note that the project was designed and delivered per the North Carolina Math 2 curriculum, but can be customized to meet your own specific curriculum needs.

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

This shows how Newton's method (also known as Newton-Raphson) is used to find a root of a function. You can show/hide various parts of the construction, and edit the particular function being considered.

This book covers the material normally presented in a two-term course on numerical analysis, starting with the basic concept and ending with topics that are more appropriate for a course in numerical analysis for differential equations: numerical solution of systems of linear and nonlinear equations, polynomial interpolation, numerical approximation of functions, numerical computation of eigenvalues, numerical derivation and integration, numerical solution of ordinary and partial differential equations.

With a focus on algorithms, it can be used as an introduction to numerical analysis for engineering and applied science students. With a focus on theory, it can be used as an introduction to numerical analysis for students in mathematics or physics. Most of the numerical methods presented in this book are accompanied by a MATLAB code.

Based on the College and Career Readiness Standards in Action- 25% of higher level math instruction should be spent on Algebra and Functions. This includes Interpreting quadratic equations, using their structure to rewrite them in equivalent forms which serve a purpose. Also creating and solving quadratic equations to solve problems, both algebraically and graphically. They are to be able to re-arrange formulas involving quadratics and highligh specific quantities. (Guide to Effectively Managing Higher-Level Content Standards in Mathematics.)The amount of OER material available to assist instruction in higher level EFL math for adults is numerous, but searching for it often gets one tangled in the pedigogical instruction, with simplistic "real-life" examples, whereas adults with REAL "real-life" experience can appreciate the topics applied to broader world examples. This curriculum guide will give suggestions  for pre-lesson activities to stimulate prior knowledge, walk you through a lesson example, and hopefully whet your appetite for using OER's in your regular instruction.