# Web Links for Algebra 1, 3rd ed.

About Links

## Web Resources

### General

- Algebra: Not ‘If’ but ‘When’—This article provides insights to when students should take Algebra I.
- Math in the Undergraduate Physical Sciences—This article explains the math that an undergraduate physical science student should expect to take.
- Texas Instruments Graphing Calculators—Compare the features of various calculators.
- TI Connect Software—Provides calculator, computer, and Internet connectivity.
- Computer-to-Calculator Connections—Programs that assist students and teachers in creating documents, solving complex problems, and constructing geometric objects.
- Math Forum High School Center—Many resources for anyone teaching or learning mathematics.
- Problems of the Week—From Math Forum.
- Project Mathematics!—Several low cost, professional videos are available here on various aspects of mathematics.
- Mathematical Quotations Server—Collection of many quotations about mathematics.

### Algebra Helps

- Mathforum.org—This Internet library contains multiple links to mathematical topics, issues in math education, teaching resources, and education levels. Search for tools, lesson plans, assessments, etc. related to a particular topic.
- The Teacher’s Corner—This site has many resources including ideas for bulletin boards, printable worksheets, and collaboration projects.
- National Library of Virtual Manipulatives—A multitude of manipulatives will enhance your teaching. Applets and ideas for class lectures or individual student enrichment activities.
- Algebra.help—Examine the lessons page to see how to use algebraic methods such as factoring, simplifying and how to solve equations. It also features an online equation calculator section.
- Ask Dr. Math—Stuck on a problem? Look here for help.
- Math Is not Linear—Prezi presentation calling for a connected teaching of mathematics.
- Hands-On Equations®—A very helpful manipulative approach to elementary algebra, including younger students.
- Algeblocks—A manipulative approach to polynomial algebra. Here you can see what actually happens when you factor a binomial.

#### Section 1.1

- Illuminations: Fractal Tool—Investigate famous fractals such as the Koch snowflake and the Sierpinski triangle.
- Design a Fractal—Interactively learn how to generate a fractal image. Make and save your own version of a Mandelbrot set.
- Hunting the Hidden Dimension—A lesson investigating fractals. Students explore the artistic characteristics of fractals and learn how they can be used to determine the length of a coastline.

#### Section 1.3

- Illuminations: Algebraic Transformations—Students determine whether an operation is commutative or associative through consecutive moves of geometric models.

#### Section 1.4

- Fractal Curves and Create Alternative Koch Snowflakes—Use these Wolfram Demonstrations to generate the Koch snowflake and other fractal curves.

#### Section 1.5

- Chaos Game—Use this Wolfram Demonstration to generate various fractals and complete Exercise 43 in Section 1.5.
- Two Dimensional Fractional Brownian Motion—Students can use this Wolfram Demonstration to generate fractal landscapes.

#### Section 1.8

- Interactivate: Order of Operations Four—A game involving the order of operations with selectable level of difficulty.
- Koch Snowflake on TI-84—Gives the code for a program that generates this fractal on the TI-84+

#### Section 2.1

- When Letters Are Numbers—This article discusses what algebra actually is, why it is important, and how we can make secure links from informal algebra at primary stages to the more formal algebra of the secondary curriculum.

#### Section 2.4

- Illuminations: Algebra Tiles—Algebra tiles used to model the solution of equations.
- Illuminations: Everything Balances Out in the End—Students use a pan balance to study equality, order of operations, numerical and variable expressions, and other key algebraic concepts.

#### Section 2.5

- Illuminations: Geology Rocks Equations—In this lesson, students explore linear equations with manipulatives and discover various steps used in solving equations.
- Interactivate: Equation Solver—This activity allows students to practice solving algebraic equations using additive and multiplicative inverses.
- Illuminations: One Step at a Time—In this lesson, students learn Polya’s four-step problem-solving heuristic and how to use metacognition, initially practicing on simple word problems and equations before applying the techniques to games and more complex problems.

#### Section 2.6

- Uluru and Kata Tjuta: A Testimony to the Flood—Creationist Articles about Ayers Rock. (p. 75)
- Uluru (Ayers Rock) in Australia—Biblical events evident in amazing study of nature.

#### Section 2.7

- The Yo-Yo Problem (Solving Linear Equations)—A lesson where students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation, and the graphing calculator.

#### Chapter 3 General

- Using Equations as a Guide to Thinking—Gives students an overall feel for the use of equations in a physics context.

#### Chapter 3 Sequences

- The Fibonacci Spiral in Nature—An interactive demonstration.
- Discovery: Numbers in Nature—A lesson demonstrating the Fibonacci Sequence and its occurrence in nature.
- Shapes, Numbers, Patterns, and the Divine Proportion in God’s Creation—An article from the Institute for Creation Research providing examples of detailed mathematical patterns found in creation.

#### Section 3.8

- Illuminations: Making Sense of Percent Concentration—These activities guide students through a rich exploration of percent concentration using both tactile experiences and real-world applications. Students predict, model, and generalize their conjectures about percent concentrations.

#### Section 4.1

- nrich: Proofs with Pictures—An article that shows how diagrams can be used to develop understanding of inequalities, especially for the visual learner.

#### Section 5.2

- Illuminations: Domain Representations—Students use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions.

#### Section 5.5

- Interactivate: Function Machine—This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs.

#### Section 5.6

- Illuminations: As People Get Older, They Get Taller—A two-lesson unit where students compare the heights of friends and classmates at different ages. Through the course of the lessons, students are exposed to algebra, measurement, and data analysis concepts. A major theme of the unit is analyzing change.
- Illuminations: Do I Have to Mow the Whole Thing?—A lesson offering examples of inverse variation. Students collect data and generate graphs before finding specific equations for inverse variation relationships and examining their graphs.

#### Section 6.2

- Illuminations: Growth Rate—Students use slope to approximate rates of change in the height of boys and girls at different ages using growth charts. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
- Illuminations: Pedal Power—Students compare the distance-time graphs for three bicyclists climbing a mountain to understand slope as a rate of change.
- Illuminations: Rise-Run Triangles—A lesson offering students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.

#### Section 6.3

- Illuminations: Walk the Plank—With one end of a wooden board placed on a bathroom scale and the other end suspended on a textbook, students can “walk the plank” and record the weight measurement as their distance from the scale changes. Surprisingly, the relationship between the weight and distance is linear, and all lines have the same
*x*-intercept. This investigation leads to a hard-to-find real world occurrence of negative slope.

#### Section 6.4

- Illuminations: Equations of Attack—Students will plot points on a coordinate grid to represent ships before playing a graphing equations game with a partner. Points along the
*y*-axis represent cannons and slopes are chosen randomly to determine the line and equation of attacks. Students will use their math skills and strategy to sink their opponent’s ships and win the game. After the game, an algebraic approach to the game is investigated.

#### Section 6.6

- Illuminations: Lines of Best Fit—An activity that allows the user to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit.

- Illuminations: Linear Regression I—An applet for investigating a
*regression line*, also known as the “line of best fit.” - Illuminations: Barbie Bungee—Cord length is a very important consideration in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and
*ouch*! In this lesson, students model a bungee jump using a Barbie^{®}doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, a linear function context. - Illuminations: Exploring Linear Data—Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of the line of best fit.
- The Futures Channel: 40 Years from Now—A lesson where students predict future sports records based on past statistics.

#### Section 6.7

- Interactivate: Inequalities—An activity for graphing linear inequalities in two variables. Users can input inequalities in algebraic form and graph them on a coordinate plane. Graph up to four inequalities as well as many ordered pairs.

#### Section 7.4

- Illuminations: Supply and Demand—Students write and solve a system of linear equations in a real-world setting. Students should be familiar with finding linear equations from 2 points or from the slope and
*y*-intercept. Graphing calculators are not necessary for this activity but could be used to extend the ideas found on the second activity sheet. - Illuminations: Exploring Equations—A lesson where students use their knowledge of weights and balance, symbolic expressions, and representations of functions to link all three concepts.
- Illuminations: Escape from the Tomb—Students balance two bowls suspended from the ceiling with springs by placing only marbles in one bowl and bingo chips in the other. How many items must be placed in each bowl so that the heights of the bowls are the same?
- Illuminations: Talk or Text—Students compare different costs associated with two cell phone plans. They write equations with 2 variables and graph to find the solution of the system of equations. They then analyze the meaning of the graph and discuss other factors involved in choosing a cell phone plan.

#### Section 8.5

- Illuminations: Shedding Light on the Subject—This activity explores the development of a mathematical model for the decay of light passing through water. The goal of this investigation is a rich exploration of exponential models in context. Movie clips provide visualization of the activity.
- Rhinos and M&M’s (Exponential Models)—The objectives of this lesson are for students to explore the patterns of exponential models in tables, graphs, and symbolic forms and to apply what they have learned to make predictions in a real situation.
- Getting Out of Line (Patterns and Functions)—Students explore basic connections between graphs, tables, and symbolic representations for lines, parabolas, inverse models, and exponential models. One of the primary goals of this lesson is to help students begin to recognize patterns that are different from lines.

#### Section 8.6

- Exponential Growth Applet—Interesting visualization of growth rate. Note: The birth rate dialog box actually describes the growth factor, not the growth rate.
- Illuminations: To Fret or Not to Fret—Students explore geometric sequences and exponential functions by considering the placement of frets on stringed instruments.
- Illuminations: Drug Filtering—A lesson where students observe a model of exponential decay, and how kidneys filter their blood. They will calculate the amount of a drug in the body over a period of time. Then, they will make and analyze the graphical representation of this exponential function.

#### Section 9.1

- Polynomials—Polynomial video presents real-life examples with animated graphs of polynomial curves.

#### Section 9.3

- Illuminations: Algebra Tiles—Algebra tiles used to model polynomial multiplication and factoring.
- Area Algebra—Interactive algebra tiles.

#### Section 9.4

- Multiplying Binomials— Downloadable activity for use with Cabri Jr. on the TI-84.

#### Section 10.4

- Factoring Special Cases—Students can use this downloadable activity to explore geometric proofs of factoring rules.

#### Section 11.1

- Illuminations: Golden Ratio—Students explore the Fibonacci sequence, examine how it is used to determine the Golden Ratio, and identify real-life examples of the Golden Ratio.
- Illuminations: Allow Me 2 Reiterate—A lesson where students use a computer software program to assist in determining the square root of 2 to a given number of decimal places. They will study the repeating-decimal phenomenon of rational numbers and explore the system property of irrationality of numbers such as 2.
- Illuminations: Stacking Squares—A lesson that prompts students to explore ways of arranging squares to represent equivalences involving square- and cube-roots. Students’ explanations and representations (with their various ways of finding these roots) form the basis for further work with radicals.

#### Section 11.6

- Illuminations: Proof Without Words: Pythagorean Theorem—Why is
*c*2 =*a*2 +*b*2? Watch a dynamic, geometric, wordless proof of the Pythagorean Theorem. Can you explain the proof?

#### Section 12.3

- Illuminations: Proof Without Words: Completing the Square—Completing the square involves taking half the coefficient of
*x*in the expression*x*2 +*ax*and adding its square. This interactive geometric proof illustrates that*x*2 +*ax*= (*x*+*a*/2)2 – (*a*/2)2.

#### Section 12.7

- Illuminations: Function Matching—See how well you understand function expressions by trying to match your function graph to a generated graph. Choose from several function types or select “random” and let the computer choose.
- The Futures Channel: The Kitchen Paraboloids—Downloadable lesson on making measurements to determine which of several bowls is closest to paraboloid in shape.

#### Section 12.8

- Illuminations: Egg Launch Contest—Students represent quadratic functions with a table, a graph, and an equation. They compare data and move between representations.
- Running the Bases: Graphing Calculator Activity—Students use their graphing calculator to curve fit information about baseball. Simultaneous and quadratic equations are used.
- Toothpicks and Transformations—Students investigate quadratic functions using geometric toothpick designs.

- QUIA: Graphing Quadratic Functions—A Jeopardy-style game reviewing three forms of quadratic equations––standard, vertex, and intercepts. Students will find the vertex and intercepts, describe the function’s graph, and solve applications.

#### Section 13.6

- The Futures Channel: The Body Mechanic—Students see the use of rational equations in physical therapy problems.

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