ALEX Lesson Plans
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Title: Fibonacci Poetry
Description:
Students will review the Fibonacci sequence and compose poems with the number of syllables in each line corresponding to the the numbers of that sequence.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [ELA2013] (9) 22: Write narratives to develop real or imagined experiences or events using effective technique, wellchosen details, and wellstructured event sequences. [W.910.3] [ELA2013] (9) 21: Write informative or explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. [W.910.2] [ELA] (9) 7: Write in narrative, expository, and persuasive modes using figurative language and imagery, including simile and metaphor, when effective and appropriate. [ELA2013] (9) 20: Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. [W.910.1] [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3]
Subject: English Language Arts (9), or English Language Arts (9), or Mathematics (9  12)
Title: Fibonacci Poetry
Description: Students will review the Fibonacci sequence and compose poems with the number of syllables in each line corresponding to the the numbers of that sequence.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Marathon Math
Description:
This unit on sequences and series is intended to help students make the connection from math to real life situations. Developing a marathon training program for a beginner runner is one simple way that students may use patterns in real life. The total mileage per week usually creates a pattern over time. Mathematical operations on patterns, sequences, and series enable students to do the calculations necessary for exploring the pattern. Students also explore nutrition information needed for a training program as proper nutrition is an important part of sports training.
Standard(s): [ELA2013] (9) 28: Draw evidence from literary or informational texts to support analysis, reflection, and research. [W.910.9] [ELA2013] (9) 27: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. [W.910.8] [ELA2013] (9) 26: Conduct short as well as more sustained research projects to answer a question (including a selfgenerated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. [W.910.7] [TC2] CA2 (912) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [ELA] (9) 14: Use the research process to locate, select, retrieve, evaluate, and organize information to support a thesis on a nonliterary topic. [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [MA2013] DM1 (912) 2: Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama) [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3]
Subject: English Language Arts (9), or English Language Arts (9), or Mathematics (9  12), or Technology Education (9  12)
Title: Marathon Math
Description: This unit on sequences and series is intended to help students make the connection from math to real life situations. Developing a marathon training program for a beginner runner is one simple way that students may use patterns in real life. The total mileage per week usually creates a pattern over time. Mathematical operations on patterns, sequences, and series enable students to do the calculations necessary for exploring the pattern. Students also explore nutrition information needed for a training program as proper nutrition is an important part of sports training.
Thinkfinity Lesson Plans
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Title: Golden Ratio
Description:
In this Illuminations lesson, students explore the Fibonacci sequence. They examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio and identify reallife examples of the Golden Ratio.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] DM1 (912) 2: Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama) [MA2013] MI1 (912) 5: Identify beginnings of algebraic symbolism and structure through the works of European mathematicians. (Alabama) [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics Title: Golden Ratio
Description: In this Illuminations lesson, students explore the Fibonacci sequence. They examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio and identify reallife examples of the Golden Ratio. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Counting Trains  Fibonacci
Description:
In this lesson, students use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students make algebraic connections by writing rules and representing data in tables and graphs.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3]
Subject: Mathematics Title: Counting Trains  Fibonacci
Description: In this lesson, students use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students make algebraic connections by writing rules and representing data in tables and graphs. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Vigenere Grid
Description:
This reproducible transparency, from an Illuminations lesson, depicts a Vigenere Grid, which is used for encoding a message using a polyalphabetic cipher.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Vigenere Grid
Description: This reproducible transparency, from an Illuminations lesson, depicts a Vigenere Grid, which is used for encoding a message using a polyalphabetic cipher. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Vigenere Cipher
Description:
In this lesson, one of a multipart unit from Illuminations, students learn about the polyalphabetic Vigenere cipher. They encode and decode text using inverse operations.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Vigenere Cipher
Description: In this lesson, one of a multipart unit from Illuminations, students learn about the polyalphabetic Vigenere cipher. They encode and decode text using inverse operations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Hearing Music, Seeing Waves
Description:
This reproducible preactivity sheet, from an Illuminations lesson, presents summary questions about the mathematics of music, specifically focused on sine waves and the geometric sequences of notes that are an octave apart.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] ALT (912) 38: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. [FTF2] [MA2013] ALT (912) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [FTF5] [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Arts,Mathematics Title: Hearing Music, Seeing Waves
Description: This reproducible preactivity sheet, from an Illuminations lesson, presents summary questions about the mathematics of music, specifically focused on sine waves and the geometric sequences of notes that are an octave apart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Numerical Analysis
Description:
In this lesson, one of a multipart unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. They use an interactive spreadsheet application to investigate their models.
Standard(s): [MA2013] AL1 (912) 22: 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). [AREI10] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) [MA2013] DM1 (912) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics,Science Title: Numerical Analysis
Description: In this lesson, one of a multipart unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. They use an interactive spreadsheet application to investigate their models. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Recursive and Exponential Rules
Description:
In this lesson, one of a multipart unit from Illuminations, students determine recursive and exponential rules for various sequences.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] MI1 (912) 5: Identify beginnings of algebraic symbolism and structure through the works of European mathematicians. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Recursive and Exponential Rules
Description: In this lesson, one of a multipart unit from Illuminations, students determine recursive and exponential rules for various sequences. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Symbolic Analysis
Description:
In this lesson, one of a multipart unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. They work to find additional equations and formulas to represent the data.
Standard(s): [S1] BIO (912) 5: Identify cells, tissues, organs, organ systems, organisms, populations, communities, and ecosystems as levels of organization in the biosphere. [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3]
Subject: Mathematics,Science Title: Symbolic Analysis
Description: In this lesson, one of a multipart unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. They work to find additional equations and formulas to represent the data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
ALEX Podcasts
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Title: Magic Squares
Overview:
This podcast shows what a magic square is and the varying differences between the different types. This podcast also shows how to make the simplest version of the magic square.There is an example of a sixteen cell square as well.It does not, however, show how to make a sixteen cell though.Finally, it shows how a magic square works. Standard(s):
[MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5]
Magic Squares Overview: This podcast shows what a magic square is and the varying differences between the different types. This podcast also shows how to make the simplest version of the magic square.There is an example of a sixteen cell square as well.It does not, however, show how to make a sixteen cell though.Finally, it shows how a magic square works.
Thinkfinity Learning Activities
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Title: Fractal Tool
Description:
This student interactive, from Illuminations, illustrates iteration graphically. Students can view preset iterations of various shapes and/or choose to create their own iterations.
Standard(s): [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] (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) 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] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] GEO (912) 15: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [GSRT2] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Fractal Tool
Description: This student interactive, from Illuminations, illustrates iteration graphically. Students can view preset iterations of various shapes and/or choose to create their own iterations. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

