ALEX Lesson Plans
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Title: Express Yourself with Patterns
Description:
During this lesson, the students will use growing patterns to develop an algebraic expression with understanding. The students will also learn mathematical vocabulary with the use of the newly created expression.
Standard(s): [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4]
Subject: Mathematics (6)
Title: Express Yourself with Patterns
Description: During this lesson, the students will use growing patterns to develop an algebraic expression with understanding. The students will also learn mathematical vocabulary with the use of the newly created expression.
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Title: Order Among Chaos
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This lesson is designed to assist students not only in using the order of operations, but also experimenting with how grouping and ordering affects answers. In groups as teams, the students will compete while finding algebraic expressions using only the numbers 1, 2, 3, and 4, as well as all operations including exponents and grouping symbols, to find a desired integer result. To gain points, the value of each formed expression must be from the set of integers 125 or 1100 depending on time constraints. They should attempt to get an expression with each of the listed integers required. Modeled examples are embedded in the directions slide show so the students are instructed in the process of the competition.
Standard(s): [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1] [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3]
Subject: Mathematics (6  7)
Title: Order Among Chaos
Description: This lesson is designed to assist students not only in using the order of operations, but also experimenting with how grouping and ordering affects answers. In groups as teams, the students will compete while finding algebraic expressions using only the numbers 1, 2, 3, and 4, as well as all operations including exponents and grouping symbols, to find a desired integer result. To gain points, the value of each formed expression must be from the set of integers 125 or 1100 depending on time constraints. They should attempt to get an expression with each of the listed integers required. Modeled examples are embedded in the directions slide show so the students are instructed in the process of the competition.
Thinkfinity Lesson Plans
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Title: Exploration of a Balance
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In this fourlesson unit from Illuminations, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. This unit includes an individual activity for four different levels from grade 1 to grade 8.
Standard(s): [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 20: Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4]
Subject: Mathematics Title: Exploration of a Balance
Description: In this fourlesson unit from Illuminations, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. This unit includes an individual activity for four different levels from grade 1 to grade 8. Thinkfinity Partner: Illuminations Grade Span: 1,2,3,4,5,6,7,8
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Title: Balancing Shapes
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In this lesson, one of a multipart unit from Illuminations, students balance shapes using an interactive pan balance applet to study equality, essential to understanding algebra. Equivalent relationships are recognized when the pans balance, demonstrating the properties of equality.
Standard(s): [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4] [MA2013] (6) 16: 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. [6EE5] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4]
Subject: Mathematics Title: Balancing Shapes
Description: In this lesson, one of a multipart unit from Illuminations, students balance shapes using an interactive pan balance applet to study equality, essential to understanding algebra. Equivalent relationships are recognized when the pans balance, demonstrating the properties of equality. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Web Resources
Lesson Plans
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Title: Talk or Text (Systems of Equations)
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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.
Standard(s): [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6EE6] [MA2013] (6) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 8: Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. [7EE2] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4]
Talk or Text (Systems of Equations)
http://illuminations...
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.
Podcasts
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Title: The Distributive Property
Description:
This webpage provides information about the distributive property, as well as a video lesson.
Standard(s): [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3]
The Distributive Property
http://www.mathplane...
This webpage provides information about the distributive property, as well as a video lesson.
Informational Materials
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Title: The Distributive Property
Description:
This webpage provides information about the distributive property, as well as a video lesson.
Standard(s): [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3]
The Distributive Property
http://www.mathplane...
This webpage provides information about the distributive property, as well as a video lesson.
Interactives/Games
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Title: Please Excuse My Dear Aunt Sally As She Makes the Number 24
Description:
The students get 4 numbers presented on a number card. With these numbers and an interactive calculator, students try to compute the number 24. Students use order of operations to solve a numerical expression that equal 24.
Standard(s): [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4]
Please Excuse My Dear Aunt Sally As She Makes the Number 24
http://www.fisme.sci...
The students get 4 numbers presented on a number card. With these numbers and an interactive calculator, students try to compute the number 24. Students use order of operations to solve a numerical expression that equal 24.
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Title: Virtual Balance Beam: Linear Equations
Description:
The National Library of Virtual Manipulatives has created a virtual manipulative that allows students to solve linear equations through the use of a balance beam. Unit blocks represent numbers and X boxes represent the unknown X. The manipulatives are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, the student can choose to perform any operation, as long as the student does the same thing to both sides, thus keeping the beam balanced.
Standard(s): [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3]
Virtual Balance Beam: Linear Equations
http://nlvm.usu.edu/...
The National Library of Virtual Manipulatives has created a virtual manipulative that allows students to solve linear equations through the use of a balance beam. Unit blocks represent numbers and X boxes represent the unknown X. The manipulatives are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, the student can choose to perform any operation, as long as the student does the same thing to both sides, thus keeping the beam balanced.
Thinkfinity Learning Activities
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Title: Pan Balance  Expressions
Description:
This interactive pan balance, from Illuminations, allows students to enter and compare numeric or algebraic expressions. They can '' weigh'' the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence.
Standard(s): [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2]
Subject: Mathematics Title: Pan Balance  Expressions
Description: This interactive pan balance, from Illuminations, allows students to enter and compare numeric or algebraic expressions. They can '' weigh'' the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

