Teaching Resources for Algebra I
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Domain Representations- Students use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions.
- Understanding Algebraic Factoring- The lesson shows the geometric basis for algebraic factoring using algebra tiles.
- Algebra Tiles- Virtual algebra tiles to use to factor binomials and polynomials, square and multiply binomials, and use the distributive law.
- Algebra Balance Scales- A virtual manipulative to help students practice balancing linear equations in one variable.
- Algebra Tiles- NLVM- Applet introduces algebra tiles model for multiplying and factoring expressions.
- 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.
- 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.
- 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.
- 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.
- Variables Math Lesson Plan- Full lesson plan on assigning values to variables. Uses manipulatives.
- 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.
- Quadratic Transformer- demonstrate the effect on the graph of changes in the coefficients and the relationship between zeros and intercepts.
- 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.
- 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 Walk the Plank URL http://illuminations.nctm.org/LessonDetail.aspx?id=L682 Materials needed A standard bathroom scale
A thin plank of wood at least 6 feet long (a 2 by 8 works well for this activity)
Walk the Plank Activity Sheet
Solutions for Activity Sheet
Graphing calculator or computer graphing software (optional)Learning Objectives Students will:
- recognize that a real world situation is linear;
- create a graph and write an equation for various linear functions;
- determine the slope, equation, and x-intercept of a linear function.
Grade Levels Grade 7, Algebra I CA 97 Standards Grade 7 AF 3.0 Students graph and interpret linear and some nonlinear functions Algebra I 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step Algebra I 6.0 Students graph a linear equation and compute x- and y- intercepts. They also are able to sketch the region defined by linear inequality Algebra I 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula CA Common Core State Standards 8.F 3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
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 reasoningA-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. Solve equations and inequalities in one variable A-REI 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI 12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. F-IF 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
F-BF 1. Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. How could you use this resource? Students use this resource to discover linear relationships. Teacher use this resource to have students discover relationships between linear functions, graph data, and find the equation of a linear function. EL and Special Needs Uses manipulatives and involves a concrete physical activity. Lesson Plans Teacher Comments Cost Free Copyright (c)2008 NCTM
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 KeyLearning 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 reasoningAlgebra-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 Teacher Comments Cost Free Copyright (c)2008 NCTM
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Title Pan Balance - Expressions URL http://illuminations.nctm.org/ActivityDetail.aspx?ID=10 Materials needed Browser
JavaLearning Objectives Students will:
- enter and compare numeric or algebraic expressions
- practice arithmetic and algebraic skills, and investigate the important concept of equivalence.
Grade Levels Grade 6, Grade 7, Algebra I CA 97 Standards Grade 06: AF 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations and graph and interpret their results. Grade 07: AF 1.4 Use algebraic terminology correctly (e.g., variable, equation, term, coefficient, inequality, expression, constant). Algebra I: 4.0 Students simplify expressions prior to solving linear equations and inequalities in one variable such as 3(2x-5) + 4(x-2) = 12. CA Common Core State Standards Standards for Mathematical Practice:
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 reasoning6.EE 1. Write and evaluate numerical expressions involving whole-number exponents. 6.EE 2. Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).7.EE 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
8.EE 7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.A-REI 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. How could you use this resource? Students use this resource to discover similarities and differences. Teachers can use this resource to have students practice arithmetic and algebraic skills. EL and Special Needs Uses an applet to help students compare different expressions Lesson Plans Teacher Comments Cost Free Copyright (c)2000-2009 NCTM
Title Light It Up URL http://illuminations.nctm.org/LessonDetail.aspx?id=L606 Materials needed Light It Up Activity Sheet
Laser Pointer (or Flashlight)
Tape Measures
Tape
Wooden Block (at least 10 cm thick, or a thick book)
Graphing Calculator
Small, Flat Mirror
Carousel Cards
Markers
Overhead Projector
Blank Paper
Timer
ScissorsLearning Objectives Students will:
- State the domain, range and end behavior of rational functions.
- Write rational functions that model problem situations
- Use rational functions to solve problems
Grade Levels Algebra I, Mathematical Analysis CA 97 Standards Algebra I: 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques Mathematical Analysis 6.0: Students find the roots and poles of a rational function and can graph the function and locate its asymptotes. 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 reasoningAlgebra-APR 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials, and divide polynomials by monomials. Solve problems in and out of context. Functions-IF.7d; Graph rational functions, identifying zeros and asymptotes
when suitable factorizations are available, and showing end behavior.How could you use this resource? Students can use this resource in a lab to discover how rational functions are used in the real world as well as practice graphing data and drawing conclusions from data. Teachers can use this resource as a lab or a lesson as an introduction to rational functions.
EL and Special Needs Does not use vocabulary in a way that makes the lesson hard to follow. Uses manipulatives to get the students involved and to physically see what is going on and where the data is coming from.
Lesson Plans Teacher Comments Cost Free Copyright (c)2008 NCTM
Title Egg Launch Contest URL http://illuminations.nctm.org/LessonDetail.aspx?id=L738 Materials needed Egg Launch Activity Sheet
Graphing CalculatorLearning Objectives Students will:
- Move between representations of a function as a table, a graph and an equation
- Determine the maximum value of a quadratic function
- Compare quadratic functions
Grade Levels Algebra I, Algebra II
CA 97 Standards Algebra I: 21.0 Students graph quadratic functions and know that their roots are x-intercepts.
Algebra I: , 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. Algebra II: 8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. Algebra II: 10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. 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 reasoningA-SSE 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A-REI 4. Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbeHow could you use this resource? Students can use this resource in a lab to apply quadratic functions to real world problems. Teachers can use this resource as a review for a unit because it has students use equations, tables, and graphs of quadratic functions.
EL and Special Needs The activity sheet has pictures and three representations of information. The students must then fill out the information for the other two representations of the information and compare it to similar data.
Lesson Plans Teacher Comments Cost Free Copyright (c)2000-2009 NCTM
Title Power Up URL http://illuminations.nctm.org/LessonDetail.aspx?id=L699 Materials needed Voltage sensors
A collection of old batteries (all the same size)
Masking tape
Ruler (with ridge, to hold the batteries)
Graphing calculators (optional; will be needed if using the TI CBL 2TM or the Casio EA‑100 Data Analysis System, or some other calculator‑based technology)
Battery Lab Activity Sheet
Power Up Activity Sheet
Volt Meter ToolLearning Objectives Students will:
- Discover and apply the rules for addition of sign numbers.
Grade Levels Grade 6, Grade 7, Algebra I
CA 97 Standards Grade 6: NS 2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations
Grade 7: NS 1.2 Add, subtract, multiply, and divide rational numbers and take positive rational numbers to whole number powers Algebra I: 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable
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 reasoning7.NS 3. Solve real-world and mathematical problems involving the four operations with rational numbers. 7.EE 3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies How could you use this resource? Students can use this resource in a lab to discover how positive and negative integers work by using hands on manipulatives or an applet. Teachers can use this resource as an introduction to positive and negative integers.
EL and Special Needs Has students work in a group, uses hands-on manipulatives or applet.
Lesson Plans Teacher Comments Cost Free Copyright (c)2000-2009 NCTM
Title Domain Representations URL http://illuminations.nctm.org/LessonDetail.aspx?id=L621 Materials needed Domain Representations Activity Sheet
Graphing CalculatorsLearning 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 reasoningF-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 Teacher Comments 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 reasoningA-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 Teacher Comments 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
JavaLearning 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 reasoningA-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 Teacher Comments Cost Free Copyright © 1999-2008
Title Algebra Balance Scales URL http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html Materials needed Browser
JavaLearning Objectives Students will:
- practice balancing linear equations in one variable
Grade Levels Grade 6, Grade 7, Algebra I CA 97 Standards Grade 6: AF 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. Grade 7: AF 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. 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: 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 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 reasoning6.EE 1. Write and evaluate numerical expressions involving whole-number exponents. 6.EE 2. Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).7.EE 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 8.EE 7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.A-REI 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. How could you use this resource? Students can use this resource at home or in a lab to practice solving single and multi-step linear equations. Teachers can use this resource as an introduction, a demonstration, or a review on how to solve linear equations in one variable.
EL and Special Needs Provides a visual aid to show students what happens when students do not balance each side the equation correctly. Helps students practice visually how to balance a linear equation.
Lesson Plans Teacher Comments Cost Free Copyright © 1999-2008
Title Algebra Tiles- NLVM URL http://nlvm.usu.edu/en/nav/frames_asid_189_g_1_t_2.html?open=activities Materials needed Browser
JavaLearning Objectives Students will:
- use algebra tiles to multiply and factor expressions
Grade Levels Grade 7, Algebra I CA 97 Standards Grade 7: AF 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. Algebra I: 10.0 Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. 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 squares of 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 reasoning6.EE 1. Write and evaluate numerical expressions involving whole-number exponents. 6.EE 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).7.EE 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 8.EE 7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.A-REI 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. How could you use this resource? Applet introduces algebra tiles model for multiplying and factoring expressions.
EL and Special Needs Uses an applet to help students multiply and factor different expressions Lesson Plans Teacher Comments Cost Free Copyright (c)1999-2010
Title Fraction Game URL http://illuminations.nctm.org/ActivityDetail.aspx?id=18 Materials needed Computer to view applet. Other links may vary on material, usually requires JAVA app.
Learning Objectives Students will:
Add fractions
Use equivalent fractions
Simplify fractions
Grade Levels Grade 6, Grade 7, Algebra I
CA 97 Standards Grade 06: NS 1.0 Students compare and order fractions, decimals, and mixed numbers. They solve problems involving fractions, ratios, proportions, and percentages.
Grade 07: NS 2.2 Add and subtract fractions using factoring to find common denominators. Algebra I: 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing to lowest terms.
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 reasoning5.NF 1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. 5.NF 6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 6.RP 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.A-APR 6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.How could you use this resource? This resource can be used by students to practice adding fractions, simplifying fractions, and determining sums of fractions that will add up to a given fraction. This resource can be used by teachers to have students practice adding fractions, simplifying fractions, using equivalent fractions, and using combinations of fractions.
EL and Special Needs This is a hands-on activity that allows students to practice using fractions in multiple ways. The game is fun and can be reset instantly by a click of a button.
Lesson Plans Teacher Comments Cost Free Copyright (c) 2000-2010 NCTM
Title Movement with Functions: Lesson 1 URL http://illuminations.nctm.org/LessonDetail.aspx?ID=L768 Materials needed CBR2 or other motion detector,
TI Interactive!,
TI-84 graphing calculator,
TI Nspire handheld, or other compatible graphing calculator or computer with compatible software,
How Should I Move? Overhead,
How Should I Move? Graphs Activity Sheet,
How Should I Move? Questions Activity Sheet (several copies per student),
How Should I Move? Questions Answer Key,
Comparing Graph Pairs Activity Sheet and Answer Key,
Graphing Equations Activity Sheet (optional)Learning Objectives Students will:
- Provide a conjecture on the type of motion that creates a provided graph
- Use a motion detector to re-create provided graphs
- Compare pairs of graphs by describing the similarities and differences between them in physical modeling and symbolic representations
- Create tables and equations for the graphs
- Compare the results of several graph investigations to one another
Grade Levels Grade 5, Grade 6, Grade 7, Algebra 1 CA 97 Standards Grade 5 AF 1.1 Use information taken from a graph or equation to answer questions about a problem situation. Grade 5 SDAP 1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. Grade 6 AF 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. Grade 7 AF 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. Grade 7 AF 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. Algebra 1 18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. 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 reasoning6.EE. (Cluster statement) Reason about and solve one-variable equations and inequalities.
F-IF 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 8-Cluster domain; Use functions to model relationships between quantities. 8-F.1; Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (algebraically, graphically, numerically in tables, or by verbal descriptions). 8-F.5; Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 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. How could you use this resource? This could be used by students as a lab to discover how the graphs of equations relate to the symbolic notation. Teachers can use this activity to introduce students to graphing by having students work in groups to determine the equations of multiple graphs and compare similar graphs with other groups. EL and Special Needs This is a discovery activity that can be used for all students. Students will get to work in groups to determine the equations of graphs. Lesson Plans Teacher Comments Cost Free Copyright © 2000-2010 NCTM
Title Movement with Functions: Lesson 2 URL http://illuminations.nctm.org/LessonDetail.aspx?ID=L769 Materials needed Index Cards
Stopwatch
How Did I Move? Activity Sheet
Coleman's Touchdown Activity Sheet & Answer Key
The Winning Goal Activity Sheet & Answer Key (optional)
Learning Objectives Students will:
- Collect data in an activity on a football field
- Compare movement and starting positions based on the data
- Create the slope-intercept equations relating m to their movement and speed and b to their beginning running location
- Use the equation to predict the distance at any given time
Grade Levels Grade 6, Grade 7, Algebra 1 CA 97 Standards Grade 6: AF 2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions. Grade 7 AF 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. Grade 7: AF 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the ratio of the quantities. Algebra I: 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. 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 reasoning6.RP. (Cluster statement) Understand ratio concepts and use ration reasoning to solve problems. 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6.RP.3a: Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios 6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed. 6.RP.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.RP.3d: Use ratio reasoning of a quantity to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. How could you use this resource? This resource can be used by students in a lab to build a table of values and create linear equations from data. Teachers can use this resource to develop a lesson for creating linear equations using a table of values. EL and Special Needs This is a discovery activity that can be used for all students. Students will get to work in groups to determine the equations of lines from a table of values.. Lesson Plans Teacher Comments Cost Free Copyright © 2000-2010 NCTM
Title Movement with Functions: Lesson 3 URL http://illuminations.nctm.org/LessonDetail.aspx?ID=L770 Materials needed Stop watches
Remote-controlled cars (strongly suggested, but alternatives are described below)
Rulers
Colored Masking Tape
Collision Activity Sheet (optional pre-activity)
Road Rage Activity Sheet
What If? Activity Sheet (optional)
Road Rage Answer KeyLearning Objectives Students will:
- Collect data and graph a scatter plot to determine the speed of a remote-controlled car
- Create a line of best fit using estimation and technology
- Use tables, graphs, and algebraic calculation to determine when their cars will crash with another group's car
- Validate their calculations by crashing the cars into each other
- Analyze why their time and location estimates for the crash may not be the same as a real-life trial
Grade Levels Grade 7, Algebra I, Algebra II, Probability & Statistics, AP Probability & Statistics CA 97 Standards Grade 7: AF 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. Grade 7: SDAP 1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables. Algebra 1: 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 (in two or three variables) by substitution, with graphs, or with matrices. Probability and Statistics: 8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots. AP Probability and Statistics: 12.0 Students find the line of best fit to a given distribution of data by using least squares regression. AP Probability and Statistics 14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots. 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 reasoningGrade 6.SP.4; Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Grade 8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Grade 8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Grade 8-EE.8: Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because
points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
c. Solve real-world and mathematical problems leading to two linear
equations in two variables.Algebra-CED.3; Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Algebra-REI.7; Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Algebra-REI.10; Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Algebra-REI.12; Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. plots on a number line, including dot plots, histograms, and box plots. Statistics & Probability-ID.1; Represent data with plots on the real number line (dot plots, histograms, and box plots). Statistics & Probability-ID.5; Summarize categorical data for two categories in two-way frequency tables. Recognize possible associations and trends in the data. Statistics & Probability-ID.6; Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential model
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.Statistics & Probability-ID.7; Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Statistics & Probability-ID.8; Compute (using technology) and interpret the correlation coefficient of a linear fit. How could you use this resource? This activity can be used by students to create a systems of equations using manipulatives and data. Teachers can use this activity to create real life connections to systems of equations. EL and Special Needs This is a hands-on activity using manipulatives and group work to help students make connections for concepts and real life applications. Lesson Plans Teacher Comments Cost Free Copyright © 2000-2010 NCTM
Title Variables Math Lesson Plan URL http://www.lessonplanspage.com/MathVariablesAndSolvingFor
UnknownVars78.htmMaterials needed For each group of 3 students:
- 8 small containers
- 80 small countable objects
- code sheet prepared by teacher
Learning Objectives Students will:
- Assign values to a variable.
- Collect information about variables and be able to use the information to solve for an unknown variable.
Grade Levels Grade 6, Grade 7, Algebra 1 CA 97 Standards Grade 6 AF 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. Grade 6 AF 1.1 Write and solve one-step linear equations in one variable. Grade 6 AF 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. Grade 7 AF 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. 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 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 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 reasoning6.EE. (Cluster statement) Reason about and solve one-variable equations and inequalities. 6.EE.7: Solve real-world and mathematical problems by writing
and solving equations in the form of x + p = q and px = q for cases in
which p, q, and x are all nonnegative rational numbers.7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. 7.EE.4b: Solve word problems leading to inequalities of the form px + q > r or px + q < r where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. 8-EE.7; Solve linear equations in one variable. b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. How could you use this resource? This resource can be used by the teacher to help plan a lesson on solving equations and assigning values to variables. EL and Special Needs Provides a hands on lesson on assigning values to variables and understanding how to solve linear equations. Lesson Plans Teacher Comments Cost Free Copyright © 1996-2010
Title Solving Linear Equations Review Game URL http://www.lessonplanspage.com/MathConstructAlgebraLinearEquations
ReviewBoardGame910.htmMaterials needed
- access to the internet
- Algebra 1 textbook
- posterboard
- cardstock paper, notebook paper
- pencils, pens, markers, colored pencils
- rulers/straightedges
- dice
- game pieces
- calculator
Learning Objectives Students will:
- Solve one step linear equations using addition and subtraction.
- Solve one step linear equations using multiplication and division.
- Use two or more steps to solve linear equations.
- Solve linear equations that have variables on both sides of the equation.
- Solve linear equations involving decimals and fractions.
Grade Levels Grade 6, Grade 7, Algebra 1 CA 97 Standards Grade 6 AF 1.1 Write and solve one-step linear equations in one variable. Grade 7 AF 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Algebra I 4.0 Students simplify expressions before solving linear equations and inequalities in one variable. Algebra I 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 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 reasoning6.EE 1. Write and evaluate numerical expressions involving whole-number exponents. 6.EE 2. Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).7.EE 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 8.EE 7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.A-REI 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. How could you use this resource? This resource can be used by teachers to help develop a lesson plan that would implement a game board into the lesson. An overview of the lesson as well as objectives and directions are provided. The lesson plan is felxible enough to be used by all teachers. EL and Special Needs This resource allows students to create a board game that reviews solving linear equations. This gives students great practice in determining the answers on the game pieces as well as doing research on the interenet to help create the game. It is a hands on project that focuses students on solving linear equations in a variety of ways. Lesson Plans Teacher Comments Cost Free Copyright © 1996-2010
Title Quadratic Transformer URL http://seeingmath.concord.org/resources_files/QuadraticGeneral.html Materials needed Java-enabled web browser to run applet Learning Objectives Students understand how changes in the coefficients of a quadratic function change the graph. Students the relationship between the roots of a quadratic equation and the x-intercepts of a parabola.
Grade Levels Algebra 1 and Algebra 2 CA 97 Standards Algebra I: 21.0 Students graph quadratic functions and know that their roots are the x-intercepts. Algebra II: 9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b)^ 2+ c. Algebra II: 10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. 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 reasoningFunctions-IF 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Functions-IF 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Functions-IF 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. F-LE 6. Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. How could you use this resource? This Java applet could be shown to a class to demonstrate visually how changing the coefficients in a quadratic function changes the graph, and to show the relationship between roots and x-intercepts. Could be explored by students using a computer individually or in small groups. An included activity handout guides students to develop rules for how changes to the quadratic and constant coefficients of a quadratic function change its graph, and to briefly explore the "polynomial," "root" and "vertex" forms of a quadratic function. EL and Special Needs Primarily a visual demonstration of effects of changing coefficients; helps make the concepts accessible. Lesson Plans Teacher Comments Cost Free Copyright (c) 2005, The Concord Consortium
Title Finding the Domain of a Function URL http://www.ltcconline.net/greenl/java/IntermedCollegeAlgebra/Domain
Equations/DomainEquations.htmlMaterials needed Java-enabled web browser to run applet Learning Objectives Students will be able to find the domain of a function and graph the domain on a number line, knowing whether to include the end point or not.
Grade Levels Algebra 1 and Algebra 2 (no standard) 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
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 reasoningFunctions-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). Functions-IF 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. How could you use this resource? Students can use this resource as extra practice on finding the domain of a function and graphing the domain on a number line. Teachers can use this resource to demonstrate to students how to find the domain of a function and visually show them how to graph the domain of a function or can use the questions and other links on the page to find information to use in lesson on finding the domain of a function. EL and Special Needs There is a link on the bottom of the web page that goes to another link where a function and relation are defined using terms easily understandable with the correct math vocabulary after it. Many examples are given for students to investigate what is a function and what is not. There are examples given with solutions so students can see how the solution is derived. Lesson Plans Teacher Comments Cost Free Copyright Not available on web site
Title Web Math URL Materials needed Computer
Learning Objectives Learning objectives vary by concept.
Grade Levels K-8, Algebra 1, Geometry, Calculus, Trigonometry CA 97 Standards Multiple standards from the Mathematics Framework for California Public School. 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 reasoningCovers multiple CaCCSS across grade levels and strands. How could you use this resource? 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).
EL and Special Needs Visual graphics display concepts and are interactive. Lesson Plans Teacher Comments Cost Free Copyright (c) 2009 WebMath.com