ALEX Lesson Plans
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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.
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.
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Title: Calendar Fun Operations
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This activity is designed to help students evaluate numerical expressions by using order of operations. The students will be provided a calendar for the current month of the year. Students will then be provided with a worksheet that contains 30 expressions and a different symbol for each expression. The students will manually calculate each expression using order of operations. Once the numerical value has been discovered for each expression, the symbol next to the expression will be drawn on the calendar for that date. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (7) 4: 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. [7NS1] [MA2013] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2] [MA2013] (7) 6: Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7NS3] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1] [MA2013] AL1 (912) 1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. [NRN1] [MA2013] AL1 (912) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [NRN2]
Subject: Mathematics (7  12)
Title: Calendar Fun Operations
Description: This activity is designed to help students evaluate numerical expressions by using order of operations. The students will be provided a calendar for the current month of the year. Students will then be provided with a worksheet that contains 30 expressions and a different symbol for each expression. The students will manually calculate each expression using order of operations. Once the numerical value has been discovered for each expression, the symbol next to the expression will be drawn on the calendar for that date. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Color this Polynomial Simplified
Description:
This lesson helps students of all levels visualize the process of polynomial simplification and replicate it with ease. Three alternate forms of assessment are given to accomodate any school's level of technology (Podcasting. Powerpoints or Poster Presentations). This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [AED] VA1 (712) 1: Create original works of art from direct observation. [TC2] CA2 (912) 6: Utilize advanced features of multimedia software, including image, video, and audio editing. [TC2] CA2 (912) 9: Practice ethical and legal use of technology systems and digital content. [TC2] CA2 (912) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [TC2] CA2 (912) 12: Use digital tools to publish curriculumrelated content. [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1] [MA2013] AL1 (912) 10: 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. [AAPR1]
Subject: Arts Education (7  12), or Mathematics (7  12), or Technology Education (9  12)
Title: Color this Polynomial Simplified
Description: This lesson helps students of all levels visualize the process of polynomial simplification and replicate it with ease. Three alternate forms of assessment are given to accomodate any school's level of technology (Podcasting. Powerpoints or Poster Presentations). This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Thinkfinity Lesson Plans
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Title: Classifying Numbers
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In this lesson, one of a multipart unit from Illuminations, students use Venn diagrams to organize information about numbers. Using the Product Game board, students look for relationships and characteristics of numbers to determine what numbers belong to a descriptor and what numbers belong to more than one descriptor.
Standard(s): [MA2013] (6) 5: Fluently divide multidigit numbers using the standard algorithm. [6NS2] [MA2013] (6) 7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. [6NS4] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1]
Subject: Mathematics Title: Classifying Numbers
Description: In this lesson, one of a multipart unit from Illuminations, students use Venn diagrams to organize information about numbers. Using the Product Game board, students look for relationships and characteristics of numbers to determine what numbers belong to a descriptor and what numbers belong to more than one descriptor. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Playing the Product Game
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In this lesson, one of a multipart unit from Illuminations, students learn the rules of and play the Product Game. In this game, players start with a set of given factors and then multiply to find the product. Students create their own game boards and develop strategies for winning the game.
Standard(s): [MA2013] (6) 5: Fluently divide multidigit numbers using the standard algorithm. [6NS2] [MA2013] (6) 7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. [6NS4] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1]
Subject: Mathematics Title: Playing the Product Game
Description: In this lesson, one of a multipart unit from Illuminations, students learn the rules of and play the Product Game. In this game, players start with a set of given factors and then multiply to find the product. Students create their own game boards and develop strategies for winning the game. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
ALEX Podcasts
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Title: Order of Operations Song
Overview:
This podcast is a song that helps middle school students to review the review of operations. Each sentence within the song is a stepbystep process in how to solve a specific order of operations problem. Standard(s):
[MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [MA2013] (7) 4: 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. [7NS1] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1]
Order of Operations Song Overview: This podcast is a song that helps middle school students to review the review of operations. Each sentence within the song is a stepbystep process in how to solve a specific order of operations problem.
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Title: Friendly Fractions Part 6
Overview:
This podcast is part of a series on operations with fractions. Designed with the middle school student in mind, it is a refresher on the basics of fractions. The lesson proportions, equivalent proportions, and solving proportions. The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves. Standard(s):
[MA2013] (6) 4: Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem. [6NS1] [MA2013] (6) 18: Solve realworld and mathematical problems by writing and solving equations of the form
x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. [6EE7] [MA2013] (7) 4: 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. [7NS1] [MA2013] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2] [MA2013] (7) 6: Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7NS3] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1] [MA2013] (7) 9: Solve multistep reallife 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. [7EE3]
Friendly Fractions Part 6 Overview: This podcast is part of a series on operations with fractions. Designed with the middle school student in mind, it is a refresher on the basics of fractions. The lesson proportions, equivalent proportions, and solving proportions. The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves.
Web Resources
Interactives/Games
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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] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1]
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.
Learning Activities
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Title: Solving Simple Sentences by Inspection
Description:
In this exercise, students practice solving sentences "by inspection".
That is, they are taught to look at the sentence, stop and think, and come up with a number that makes the sentence true.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1]
Solving Simple Sentences by Inspection
http://www.onemathem...
In this exercise, students practice solving sentences "by inspection".
That is, they are taught to look at the sentence, stop and think, and come up with a number that makes the sentence true.
Thinkfinity Learning Activities
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Title: Factor Game
Description:
This interactive game, from Illuminations, allows students to exercise their factoring ability. They can play against a friend or the computer as they take turns choosing a number and identifying all of its factors.
Standard(s): [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (6) 5: Fluently divide multidigit numbers using the standard algorithm. [6NS2] [MA2013] (6) 7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. [6NS4] [MA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7EE1]
Subject: Mathematics Title: Factor Game
Description: This interactive game, from Illuminations, allows students to exercise their factoring ability. They can play against a friend or the computer as they take turns choosing a number and identifying all of its factors. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8

