ALEX Lesson Plans
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
Subject: Mathematics Title: Counting Embedded Figures
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Description: In this Illuminations lesson, students look for patterns in an embeddedsquare problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Exact Ratio
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Description: This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Health,Mathematics Title: Make a Conjecture
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Description: In this lesson, one of a multipart unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Recursive and Exponential Rules
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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
Subject: Mathematics,Science Title: Numerical Analysis
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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
Subject: Arts,Mathematics Title: Hearing Music, Seeing Waves
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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
Subject: Arts,Mathematics Title: Seeing Music
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Description: In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: Seeing Music, Hearing Waves: Selected Answers and Solutions
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Description: This reproducible teacher sheet, from an Illuminations lesson, provides selected solutions to an activity in which students calculate the frequencies of two octaves of a chromatic musical scale in standard pitch. Students then experiment with different combinations of notes and related sine waves to observe why some combinations of musical notes sound harmonious and others have a dissonance. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Vigenere Cipher
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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
Subject: Arts,Mathematics Title: Seeing Music, Hearing Waves
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Description: Using this reproducible activity sheet, from an Illuminations lesson, students calculate the frequencies of two octaves of a chromatic musical scale in standard pitch. They then experiment with different combinations of notes and related sine waves to observe why some combinations of musical notes sound harmonious and others have a dissonance. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: Fretting
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Description: In this lesson, one of a multipart unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then compare geometric sequences with exponential functions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: To Fret or Not to Fret
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Description: This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students compare geometric sequences with exponential functions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: Not to Fret
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Description: This reproducible activity sheet, from an Illuminations lesson, presents a line drawing of a guitar's neck showing the location of the nut and the 12th fret. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Vigenere Grid
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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
Subject: Mathematics Title: Fractal Tool
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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
Subject: Mathematics Title: To Fret or...
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Description: This reproducible activity, from an Illuminations lesson, features questions dealing with measuring distances on fretted stringed instruments. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: Exploring Measurement, Sequences, and Curves with Stringed Instruments
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Description: In this lesson, one of a multipart unit from Illuminations, students measure lengths on stringed musical instruments. They discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics,Science Title: Smokey Bear Takes Algebra
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Description: In this lesson, from Illuminations, students learn about the many factors that play a role in creating a forestfire danger rating index. They work with the Angstrom and Nesterov Indexes, explain the relationship between relative humidity and fire danger, and use graphing calculators to model the relationship between the slope of the land versus the rate of fire spread. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: To Fret or Not to Fret
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Description: In this unit of two lessons, from Illuminations, students explore geometric sequences and exponential functions by considering the placement of frets on stringed instruments. They study the placement of frets on a fretted instrument then use their discoveries to place frets on a fretless instrument. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

