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Title: Factorials: Let's have a Dinner Party!
Description:
In collaborate groups of four, students will act out a dinner party where four dinner guests will attend. The students must act out the different ways to arrange four dinner guests.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [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]
Subject: Mathematics (6)
Title: Factorials: Let's have a Dinner Party!
Description: In collaborate groups of four, students will act out a dinner party where four dinner guests will attend. The students must act out the different ways to arrange four dinner guests.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Is My Vari"able" to Stand?
Description:
This crosscurricular lesson is designed to require students to apply algebra to a realworld, natural disaster situation. Students will be asked to design a tree house including a ladder. Students will set up an algebraic equation and solve for the variable. Will their treehouse be able to withstand a "jelloquake"? Students will test the strength of their treehouse and ladder in science class.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [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] [S1] (6) 2: Describe factors that cause changes to Earth's surface over time.
Subject: Mathematics (6), or Science (6)
Title: Is My Vari"able" to Stand?
Description: This crosscurricular lesson is designed to require students to apply algebra to a realworld, natural disaster situation. Students will be asked to design a tree house including a ladder. Students will set up an algebraic equation and solve for the variable. Will their treehouse be able to withstand a "jelloquake"? Students will test the strength of their treehouse and ladder in science class.
This is a College and CareerReady Standards showcase lesson plan.
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Title: What did you say? Translating from verbal to algebraic.
Description:
Students will learn about translating between verbal and algebraic expressions via game play and possibly working on an interactive web site. The four steps to explicit instruction (I do, we do, y'all do, and you do) are labeled in the procedures section.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [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]
Subject: Mathematics (6)
Title: What did you say? Translating from verbal to algebraic.
Description: Students will learn about translating between verbal and algebraic expressions via game play and possibly working on an interactive web site. The four steps to explicit instruction (I do, we do, y'all do, and you do) are labeled in the procedures section.
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Title: The Pattern of Graphing Linear Equations
Description:
The students will extend the knowledge of algebraic expressions from geometric representations and ultimately graph linear equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representations. Students may also acquire a deeper understanding of independent and dependent variables.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [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]
Subject: Mathematics (6)
Title: The Pattern of Graphing Linear Equations
Description: The students will extend the knowledge of algebraic expressions from geometric representations and ultimately graph linear equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representations. Students may also acquire a deeper understanding of independent and dependent variables.
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Title: The Pattern of Graphing Quadratic Equations
Description:
The students will develop an algebraic expression from geometric representations and ultimately graph quadratic equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representations.
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]
Subject: Mathematics (6)
Title: The Pattern of Graphing Quadratic Equations
Description: The students will develop an algebraic expression from geometric representations and ultimately graph quadratic equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representations.
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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: My Favorite Number
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The activity allows students to review many of the number theory concepts. Students will pick a composite number write verbal expressions about the number, find the factors, prime factorization, list multiples, draw a cartoon character of the number, and write a word problem. The purpose of this activity is to be a review of the number theory topics taught during middle school.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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) 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] (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]
Subject: Mathematics (4  6)
Title: My Favorite Number
Description: The activity allows students to review many of the number theory concepts. Students will pick a composite number write verbal expressions about the number, find the factors, prime factorization, list multiples, draw a cartoon character of the number, and write a word problem. The purpose of this activity is to be a review of the number theory topics taught during middle school.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Discovering Pi
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This lesson allows students to discover the number Pi. By measuring real life objects, students will get to see where the number Pi comes from as well as how the circumference formula is derived.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4]
Subject: Mathematics (6  7)
Title: Discovering Pi
Description: This lesson allows students to discover the number Pi. By measuring real life objects, students will get to see where the number Pi comes from as well as how the circumference formula is derived.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Variables and Algebraic Expressions
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Students will be actively teaching and learning vocabulary associated with algebraic expressions. They will identify each part of an algebraic expression. 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): [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
Subject: Mathematics (6), or Technology Education (6  8)
Title: Variables and Algebraic Expressions
Description: Students will be actively teaching and learning vocabulary associated with algebraic expressions. They will identify each part of an algebraic expression. 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: "Introducing Pi!"
Description:
The overriding purpose of the lesson is to actively engage students in learning activities that promote opportunities for students to discover the 'meaning' of pi. Activities will include research, handson, software applications, reading, writing, and collaborative work opportunities. The secondary purpose is to introduce and spark enthusiasm among students for our celebration of 'Pi Day'.
Standard(s): [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
Subject: Mathematics (6  7)
Title: "Introducing Pi!"
Description: The overriding purpose of the lesson is to actively engage students in learning activities that promote opportunities for students to discover the 'meaning' of pi. Activities will include research, handson, software applications, reading, writing, and collaborative work opportunities. The secondary purpose is to introduce and spark enthusiasm among students for our celebration of 'Pi Day'.
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Title: Express Yourself
Description:
This lesson presents students with the abstract idea that letters represent unknown numbers or variables. Vocabulary pertinent to writing English phrases as algebraic expressions and sentences as equations and vice versa is introduced. A mathematics and language arts relationship is also stressed.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
Subject: Mathematics (6)
Title: Express Yourself
Description: This lesson presents students with the abstract idea that letters represent unknown numbers or variables. Vocabulary pertinent to writing English phrases as algebraic expressions and sentences as equations and vice versa is introduced. A mathematics and language arts relationship is also stressed.
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Title: It's In The Bag
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This lesson provides students with a reallife application of problem solving. Students will use color counters to model writing expressions and equations. They are given a scenario to follow where clues about the content of bags are used to determine the type of canned goods in each bag.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
Subject: Mathematics (6)
Title: It's In The Bag
Description: This lesson provides students with a reallife application of problem solving. Students will use color counters to model writing expressions and equations. They are given a scenario to follow where clues about the content of bags are used to determine the type of canned goods in each bag.
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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
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Title: Real Estate Tycoon
Description:
This yearlong project, from Illuminations, is divided into three parts and reinforces skills that lay a foundation for algebra, such as measurement, fractions, decimals, percents, and proportions. Students design, build, and sell a house and then simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, solve simple equations, and learn valuable lessons about how money really works.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [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) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [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] (8) 9: Solve linear equations in one variable. [8EE7] [SS2010] CIV (7) 7: Determine how people organize economic systems to address basic economic questions regarding which goods and services will be produced, how they will be distributed, and who will consume them. [SS2010] CIV (7) 8: Appraise the relationship between the consumer and the marketplace in the economy of the United States regarding scarcity, opportunity cost, tradeoff decision making, and the stock market. [SS2010] CIV (7) 9: Apply principles of money management to the preparation of a personal budget that addresses housing, transportation, food, clothing, medical expenses, insurance, checking and savings accounts, loans, investments, credit, and comparison shopping.
Subject: Arts,Mathematics,Social Studies Title: Real Estate Tycoon
Description: This yearlong project, from Illuminations, is divided into three parts and reinforces skills that lay a foundation for algebra, such as measurement, fractions, decimals, percents, and proportions. Students design, build, and sell a house and then simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, solve simple equations, and learn valuable lessons about how money really works. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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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: Making Your Own Product Game
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In this lesson, one of a multipart unit from Illuminations, students review strategies for playing the Product Game. In this game, players start with a set of given factors and multiply to find the product. Students then work in groups to create their own game boards.
Standard(s): [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. [3OA7] [MA2013] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4OA1] [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]
Subject: Mathematics Title: Making Your Own Product Game
Description: In this lesson, one of a multipart unit from Illuminations, students review strategies for playing the Product Game. In this game, players start with a set of given factors and multiply to find the product. Students then work in groups to create their own game boards. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Mathematics and Children's Literature
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In this fivelesson unit, from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. Five pieces of literature are applied to teaching a wide range of topics in the mathematics curriculum, from sorting and classifying to the meaning of averages.
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) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 23: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. [6G3] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [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) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9] [ELA2013] (3) 29: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories. [W.3.8] [ELA2013] (5) 1: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. [RL.5.1] [ELA2013] (5) 10: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. [RI.5.1] [ELA2013] (5) 13: Determine the meaning of general academic and domainspecific words and phrases in a text relevant to a Grade 5 topic or subject area. [RI.5.4] [ELA2013] (5) 18: Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. [RI.5.9] [ELA2013] (6) 7: Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they "see" and "hear" when reading the text to what they perceive when they listen or watch. [RL.6.7] [ELA2013] (6) 8: Differentiate among odes, ballads, epic poetry, and science fiction. (Alabama) [ELA2013] (6) 9: Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics. [RL.6.9] [ELA2013] (6) 10: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RL.6.10] [ELA2013] (7) 7: Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film). [RL.7.7] [ELA2013] (7) 8: Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history. [RL.7.9] [ELA2013] (7) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RL.7.10] [ELA2013] (8) 7: Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors. [RL.8.7] [ELA2013] (8) 8: Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. [RL.8.9] [ELA2013] (8) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of Grades 68 text complexity band independently and proficiently. [RL.8.10]
Subject: Language Arts,Mathematics Title: Mathematics and Children's Literature
Description: In this fivelesson unit, from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. Five pieces of literature are applied to teaching a wide range of topics in the mathematics curriculum, from sorting and classifying to the meaning of averages. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8
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Title: Area Formulas
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In this unit of four lessons, from Illuminations, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [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]
Subject: Mathematics Title: Area Formulas
Description: In this unit of four lessons, from Illuminations, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Finding the Area of Trapezoids
Description:
In this lesson, one of a multipart unit from Illuminations, students discover the area formula for trapezoids and explore alternative methods for calculating the area of a trapezoid.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [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]
Subject: Mathematics Title: Finding the Area of Trapezoids
Description: In this lesson, one of a multipart unit from Illuminations, students discover the area formula for trapezoids and explore alternative methods for calculating the area of a trapezoid. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Finding the Area of Irregular Figures
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In this lesson, one of a multipart unit from Illuminations, students estimate the areas of highly irregular shapes and use a process of decomposition to calculate the areas of irregular polygons.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [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]
Subject: Mathematics Title: Finding the Area of Irregular Figures
Description: In this lesson, one of a multipart unit from Illuminations, students estimate the areas of highly irregular shapes and use a process of decomposition to calculate the areas of irregular polygons. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Surface Area
Description:
This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for computing the surface area of cylinders and rectangular prisms.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics Title: Surface Area
Description: This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for computing the surface area of cylinders and rectangular prisms. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Discovering the Area Formula for Circles
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In this lesson, one of a multipart unit from Illuminations, students use a circle that has been divided into congruent sectors to discover the area formula by using their knowledge of parallelograms. They then calculate the area of various flat circular objects that they have brought to school. Finally, students investigate various strategies for estimating the area of circles.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4]
Subject: Mathematics Title: Discovering the Area Formula for Circles
Description: In this lesson, one of a multipart unit from Illuminations, students use a circle that has been divided into congruent sectors to discover the area formula by using their knowledge of parallelograms. They then calculate the area of various flat circular objects that they have brought to school. Finally, students investigate various strategies for estimating the area of circles. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Finding the Area of Parallelograms
Description:
In this lesson, one of a multipart unit from Illuminations, students use their knowledge of rectangles to discover the area formula for parallelograms.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [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]
Subject: Mathematics Title: Finding the Area of Parallelograms
Description: In this lesson, one of a multipart unit from Illuminations, students use their knowledge of rectangles to discover the area formula for parallelograms. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Archimedes' Puzzle
Description:
In this lesson, students learn about the history of the Stomachion, an ancient tangramtype puzzle. Students use the puzzle pieces to create other figures, learn about symmetry and transformations and investigate the areas of the pieces.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8G1] [MA2013] (8) 17: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8G2] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4]
Subject: Mathematics Title: Archimedes' Puzzle
Description: In this lesson, students learn about the history of the Stomachion, an ancient tangramtype puzzle. Students use the puzzle pieces to create other figures, learn about symmetry and transformations and investigate the areas of the pieces. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Patterns and Function
Description:
In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two and threedimensional shapes.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [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) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [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) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics Title: Patterns and Function
Description: In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two and threedimensional shapes. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: On Fire
Description:
This unit of five lessons, from Illuminations, introduces the components of a firesafe and firewise environment. Students create a firewise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a firewise property and testing their firewise IQ.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [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) 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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [MA2013] (8) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical 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. [8EE6] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3]
Subject: Mathematics Title: On Fire
Description: This unit of five lessons, from Illuminations, introduces the components of a firesafe and firewise environment. Students create a firewise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a firewise property and testing their firewise IQ. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Web Resources
Podcasts
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Title: Order of Operations TV
Description:
This video gives multiple solution videos for solving problems using the order of operations.
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] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
Order of Operations TV
http://www.mathtv.co...
This video gives multiple solution videos for solving problems using the order of operations.
Interactives/Games
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Title: The Order of Operations Millionaire Game
Description:
The Order of Operations Millionaire Game can be played alone or in two teams. If you are using this game in the classroom as a contest between two teams, the teacher can modify the scores at any point by clicking the score box of a team and editing the numbers.
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] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
The Order of Operations Millionaire Game
http://www.mathplay...
The Order of Operations Millionaire Game can be played alone or in two teams. If you are using this game in the classroom as a contest between two teams, the teacher can modify the scores at any point by clicking the score box of a team and editing the numbers.
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.
Teacher Tools
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Title: Order of Operations TV
Description:
This video gives multiple solution videos for solving problems using the order of operations.
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] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
Order of Operations TV
http://www.mathtv.co...
This video gives multiple solution videos for solving problems using the order of operations.
Thinkfinity Learning Activities
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Title: Learning about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures: Side Length, Volume, and Surface Area of Similar Solids
Description:
This is part two of a twopart eexample from Illuminations that illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In this part, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two threedimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath Investigations.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [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]
Subject: Mathematics Title: Learning about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures: Side Length, Volume, and Surface Area of Similar Solids
Description: This is part two of a twopart eexample from Illuminations that illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In this part, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two threedimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath Investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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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

