**Title:** Know Your Limits

**Description:**
The limit is the fundamental notion of calculus. This underlying concept is the thread that binds together virtually all of the calculus studied by the student. In this lesson, the student's knowledge of limits will be extended using some common language and illustrated ideas through simple examples. The concept of limits will be used to describe functions with specific properties. Additionally, the concept of a limit function is further developed, and theorems for limits are analyzed and applied. Students will refer to these rules as they work through exercises.
**Standard(s): **

[MA2015] PRE (9-12) 4: Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity. (Alabama)

**Subject:**Mathematics (9 - 12)

**Title:**Know Your Limits

**Description:**The limit is the fundamental notion of calculus. This underlying concept is the thread that binds together virtually all of the calculus studied by the student. In this lesson, the student's knowledge of limits will be extended using some common language and illustrated ideas through simple examples. The concept of limits will be used to describe functions with specific properties. Additionally, the concept of a limit function is further developed, and theorems for limits are analyzed and applied. Students will refer to these rules as they work through exercises.

**Title:** Whelk-Come to Mathematics

**Description:**
In this four-lesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops.
**Standard(s): **

[MA2015] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)

**Subject:**Mathematics,Science

**Title:**Whelk-Come to Mathematics

**Description:**In this four-lesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Northwestern Crows

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data.
**Standard(s): **

[MA2015] PRE (9-12) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [S-MD1]

**Subject:**Mathematics,Science

**Title:**Northwestern Crows

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Conduct an Experiment

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate whether the crows minimize their work by dropping whelks as they do. The amount of work depends upon the height of the drop and the number of times the crow has to fly to this height. To answer the question, students explore the relationship between the height of the drop and the number of drops needed.
**Standard(s): **

[MA2015] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)

**Subject:**Mathematics,Science

**Title:**Conduct an Experiment

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate whether the crows minimize their work by dropping whelks as they do. The amount of work depends upon the height of the drop and the number of times the crow has to fly to this height. To answer the question, students explore the relationship between the height of the drop and the number of drops needed.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Limits

**Description:**
This student interactive, from an Illuminations lesson, allows students to see a representation of three geometric series and the harmonic series.
**Standard(s): **

[MA2015] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)

**Subject:**Mathematics

**Title:**Limits

**Description:**This student interactive, from an Illuminations lesson, allows students to see a representation of three geometric series and the harmonic series.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12