# Teaching Resources for Algebra I

1. Walk The Plank - When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x-intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.
2. Talk or Text- In this lesson, 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.
3. Pan Balance- Expressions -This interactive pan balance allows numeric or algebraic expressions to be entered and compared. You can "weigh" the expressions you want to compare by entering them on either side of the balance. Using this interactive tool, you can practice arithmetic and algebraic skills, and investigate the important concept of equivalence. This balance is a natural extension of Pan Balance - Shapes.
4. Light It Up- In this cooperative learning activity, students are presented with a real-world problem: Given a mirror and laser pointer, determine the position where one should stand so that a reflected light image will hit a designated target. This investigation allows students to develop several rational functions that models three specific forms of a rational function. Students explore the relationship between the graph, the equation, and problem context.
5. Egg Launch Contest- Students will represent quadratic functions as a table, with a graph, and with an equation. They will compare data and move between representations. In this activity, students encounter data that comes in different forms in the context of the description of an egg launch contest. The data for team A are shown in a table, the data for team B are expressed by an equation, and the data for team C are displayed in a graph. The data are available to students on the activity sheet.
6. Power Up- Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
7. Domain Representations- Students use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions.
8. Understanding Algebraic Factoring- The lesson shows the geometric basis for algebraic factoring using algebra tiles.
9. Algebra Tiles- Virtual algebra tiles to use to factor binomials and polynomials, square and multiply binomials, and use the distributive law.
10. Algebra A virtual manipulative to help students practice balancing linear equations in one variable.
11. Algebra Tiles- NLVM- Applet introduces algebra tiles model for multiplying and factoring expressions.
12. Fraction Game- This applet allows students to individually practice working with relationships among fractions and ways of combining fractions. For a two person version of this applet see the Fraction Track E‑Example.
13. Movement with Functions: Lesson 1- This investigation uses a motion detector to help students understand graphs and equations. Students experience constant and variable rates of change and are challenged to consider graphs where no movements are possible to create them. Multiple representations are used throughout the lesson to allow students to build their fluency with in how graphs, tables, equations, and physical modeling are connected. The lesson also allows students to investigate multiple function types, including linear, exponential, quadratic, and piecewise.
14. Movement with Functions: Lesson 2- A common problem when students learn about the slope-intercept equation y = mx + b is that they mechanically substitute for m and b without understanding their meaning. This lesson is intended to provide students with a method for understanding that m is a rate of change and b is the value when x = 0. This kinesthetic activity allows students to form a physical interpretation of slope and y-intercept by running across a football field. Students will be able to verbalize the meaning of the equation to reinforce understanding and discover that slope (or rate of movement) is the same for all sets of points given a set of data with a linear relationship.
15. Movement with Functions: Lesson 3- In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into each other.
16. Variables Math Lesson Plan- Full lesson plan on assigning values to variables. Uses manipulatives.
17. Solving Linear Equations Review Game- Solving linear equations is a cornerstone of Algebra and other higher level math classes. The skills involved are critically important to the students' confidence and success within high school mathematics. In this project, students develop a board game that help their peers review solving linear equations. This project requires internet access as the students will use various web sites to collect sample problems of varying degrees of difficulty. The entire project should use about 230 minutes of instruction time. Adjust as needed.
18. Quadratic Transformer- demonstrate the effect on the graph of changes in the coefficients and the relationship between zeros and intercepts.
19. Finding the Domain of a Function- This applet guides the user through the process of finding the domain of a function. Hints and feedback are plentiful and useful. New problems are generated at the click of a button.
20. Web Math - Students could use this as a resource for review or to clarify topics discussed in class but not fully understood. The resource is easy to use and navigate to either specific concepts or broader topics. The site also offers specific sections on the conversion of units (applicable to the sciences).
 Title Talk or Text URL http://illuminations.nctm.org/LessonDetail.aspx?id=L780 Materials needed Computer with internet access (optional) Information about current cell phone plans (optional) Talk or Text? Activity Sheet Talk or Text? Answer Key Learning Objectives Students will: Compare two cell phone plans through examples of different usage Write equations to model allocation of money for cell phone usage Graph and solve a system of equations Analyze the solution and the meaning of the graph Grade Levels Algebra I, Algebra II CA 97 Standards Algebra I 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets Algebra II 2.0 Students solve systems of linear equations and inequalities by substitution, with graphs, or with matrices CA Common Core State Standards Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Algebra-REI 5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Algebra-REI 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations How could you use this resource? Students can use this activity in the lab to solve systems of equations or at home to find which plan would be better. Teachers can use this activity to help students discover the practicality of using systems of equations in two variables. EL and Special Needs Group discussions can be used to help EL or special needs students to understand the concepts. Other differentiation can be used by teachers based on their own class needs. Lesson Plans Share your lesson plan on MERLOT! See other teachers' lesson plans on MERLOT. Teacher Comments Share your comments on MERLOT! See other teacher comments on MERLOT. Cost Free Copyright (c)2008 NCTM
 Title Domain Representations URL http://illuminations.nctm.org/LessonDetail.aspx?id=L621 Materials needed Domain Representations Activity Sheet Graphing Calculators Learning Objectives Students will: Use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions Recognize and use connections between a function’s symbolic representation, a function’s graphical representation, and a function’s domain. Grade Levels Algebra I CA 97 Standards Algebra I: 17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression CA Common Core State Standards Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning F-IF 1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. How could you use this resource? Students can use this activity in a lab to find the domains of different functions using graphs, tables, and line graphs. Teachers can use this resource as a review for the domain of functions. EL and Special Needs Has the domain of the functions represented in multiple ways. Lesson Plans Share your lesson plan on MERLOT! See other teachers' lesson plans on MERLOT. Teacher Comments Share your comments on MERLOT! See other teacher comments on MERLOT. Cost Free Copyright (c)2000-2009 NCTM
 Title Understanding Algebraic Factoring URL http://mathforum.org/alejandre/algfac.html Materials needed Browser One set of algebra tiles that includes: 15- 1 unit by 1 unit squares 10- 1 unit by "x" unit rectangles 3- "x" unit by "x" unit rectangles Learning Objectives Students will: Be able to show the geometric basis of algebraic factoring. Grade Levels Algebra I CA 97 Standards Algebra I: 11.0 Students apply basic factoring techniques to second- and simple third degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect square binomials. CA Common Core State Standards Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning A-SSE 2.1 Apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. How could you use this resource? Students can use algebra tiles to factor second degree polynomials. The teacher can use this activity to introduce the concept of factoring for second degree polynomials and apply those basic skills to higher degree polynomials. EL and Special Needs Hands on manipulative. Lesson Plans Share your lesson plan on MERLOT! See other teachers' lesson plans on MERLOT. Teacher Comments Share your comments on MERLOT! See other teacher comments on MERLOT. Cost Free Copyright © 1994-2009
 Title Algebra Tiles URL http://nlvm.usu.edu/en/nav/frames_asid_189_g_3_t_2.html Materials needed Browser Java Learning Objectives Students will: demonstrate the distributive law using algebra tiles factor binomials and polynomials square and multiply binomials Grade Levels Algebra I CA 97 Standards Algebra I: 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x − 5) + 4(x − 2) = 12. Algebra I: 11.0 Students apply basic factoring techniques to second- and simple third degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect square binomials. CA Common Core State Standards Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning A-REI 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. A-SSE 2.1 Apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. How could you use this resource? Students can use this resource at home or in a lab to practice expanding binomials and polynomials and using the distributive law using virtual algebra tiles. Teachers can use this resource as a review for a unit involving factoring and expanding polynomials. EL and Special Needs Questions are asked on the side to help students use the virtual manipulative to discover what factoring and expanding polynomials look like geometrically as well as see their relation to each other. Lesson Plans Share your lesson on MERLOT! See other teachers' lesson plans on MERLOT. Teacher Comments Share your comments on MERLOT! See other teachers' comments on MERLOT. Cost Free Copyright © 1999-2008