**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): **

**Subject:**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.

**Title:** Recursive and Exponential Rules

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students determine recursive and exponential rules for various sequences.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**Recursive and Exponential Rules

**Description:**In this lesson, one of a multi-part unit from Illuminations, students determine recursive and exponential rules for various sequences.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8,9,10,11,12

**Title:** Numerical Analysis

**Description:**
In this lesson, one of a multi-part 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): **

[MA2015] DM1 (9-12) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama)

**Subject:**Mathematics,Science

**Title:**Numerical Analysis

**Description:**In this lesson, one of a multi-part 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

**Title:** Hearing Music, Seeing Waves

**Description:**
This reproducible pre-activity 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): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Hearing Music, Seeing Waves

**Description:**This reproducible pre-activity 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

**Title:** Exact Ratio

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**Exact Ratio

**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

**Title:** Make a Conjecture

**Description:**
In this lesson, one of a multi-part 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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Health,Mathematics

**Title:**Make a Conjecture

**Description:**In this lesson, one of a multi-part 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

**Title:** Counting Embedded Figures

**Description:**
In this Illuminations lesson, students look for patterns in an embedded-square problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**Counting Embedded Figures

**Description:**In this Illuminations lesson, students look for patterns in an embedded-square 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

**Title:** Seeing Music

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Seeing Music

**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

**Title:** Seeing Music, Hearing Waves

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Seeing Music, Hearing Waves

**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

**Title:** Seeing Music, Hearing Waves: Selected Answers and Solutions

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Seeing Music, Hearing Waves: Selected Answers and Solutions

**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

**Title:** To Fret or Not to Fret

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**To Fret or Not to Fret

**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

**Title:** To Fret or...

**Description:**
This reproducible activity, from an Illuminations lesson, features questions dealing with measuring distances on fretted stringed instruments.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**To Fret or...

**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

**Title:** Not to Fret

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Not to Fret

**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

**Title:** To Fret or Not to Fret

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**To Fret or Not to Fret

**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

**Title:** Exploring Measurement, Sequences, and Curves with Stringed Instruments

**Description:**
In this lesson, one of a multi-part 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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Exploring Measurement, Sequences, and Curves with Stringed Instruments

**Description:**In this lesson, one of a multi-part 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

**Title:** Fretting

**Description:**
In this lesson, one of a multi-part 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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Fretting

**Description:**In this lesson, one of a multi-part 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

**Title:** Smokey Bear Takes Algebra

**Description:**
In this lesson, from Illuminations, students learn about the many factors that play a role in creating a forest-fire 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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics,Science

**Title:**Smokey Bear Takes Algebra

**Description:**In this lesson, from Illuminations, students learn about the many factors that play a role in creating a forest-fire 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

**Title:** Vigenere Cipher

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students learn about the polyalphabetic Vigenere cipher. They encode and decode text using inverse operations.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**Vigenere Cipher

**Description:**In this lesson, one of a multi-part 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

**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): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**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

**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): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**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