Teaching Resources for 6-7 Algebra and Functions
- 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.
- Algebra Balance Scales- A virtual manipulative to help students practice balancing linear equations in one variable.
- 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.
- Algebra Tiles- NVLM- Applet introduces algebra tiles model for multiplying and factoring expressions.
- Growth Rate- Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
- 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 using variables to represent values. This lesson 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.
- Math 6 Spy Guys- Interactive lessons that covers multiple standards from the Mathematics Framework for California Schools. Includes a glossary, strategies, and operations.
- 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).
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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 (provided at link)
Solutions for Activity Sheet (provided at link)
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 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 reasoning8.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. 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. 8.EE 7. Solve linear equations in one variable. Algebra and Functions-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. 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 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:
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.Algebra and Functions-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 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 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 1.4 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:
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 2. Write, read, and evaluate expressions in which letters stand for numbers. 6 EE 5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Algebra and Functions-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. 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 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:
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 reasoning6EE 1. Write and evaluate numerical expressions involving whole-number exponents. Algebra and Functions-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. Algebra and Functions-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? 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 Growth Rate URL http://illuminations.nctm.org/LessonDetail.aspx?id=L668 Materials needed Browser
Java
Activity sheet
Graphing calculator
Adobe softwareLearning Objectives Students will:
- Use slope to approximate the rate of change in height for boys and girls at different ages.
- Use approximations to plot graphs of the growth rate vs. age for boys and girls
Grade Levels Grade 7 CA 97 Standards Grade 7: AF 3.4 Plot the values of quantities whose rations are always the same. Fit a line to the plot and understand that the slope of the line equals the quantities.
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 reasoning7.RP 2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 8EE 3. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. How could you use this resource? Students can use this resource in a lab to discover how slope or rate of change can be compared in real world problems. Teachers can use this resource as an introduction to slope.
EL and Special Needs Uses a hands-on chart and table of values to introduce slope.
Lesson Plans Teacher Comments Cost Free Copyright (c)2000-2010
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.
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. Functions-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. Functions-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? 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 3. Use ratio and rate reasoning to solve real-world and mathematical problems,
a. Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.7.RP 3. Use ratio and rate reasoning to solve real-world and mathematical problems,
a. 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.8.EE 3. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Algebra and Functions-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). Functions-BF 10. 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? 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
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 2. Write, read, and evaluate expressions in which letters stand for numbers. 6 EE 5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 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. 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. 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
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning6.EE 2. Write, read, and evaluate expressions in which letters stand for numbers. 6 EE 5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 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. Algebra and Functions-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. 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 Math 6 Spy Guys URL http://www.learnalberta.ca/content/mesg/html/math6web/math6shell.html#
Materials needed Computer with high speed internet
Adobe Flash Player
Learning Objectives Learning objectives vary by lesson selection and concept.
Grade Levels Grade 6 CA 97 Standards Multiple Grade 6 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
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 Grade 6 and some Grade 7 standards from the California Common Core State Standards.
How could you use this resource? Students can use this resource to clarify concepts not understood in class, interact with virtual manipulatives, and see virtual representations of concepts. This resource could be used by a teacher to show to a class as a demonstration or an introduction. This is a fairly simple site to use EL and Special Needs Visual graphics display concepts and are interactive. Lesson Plans Teacher Comments Cost Free Copyright © 2003 Alberta Education
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