**Title:** Penny Drop That Thang!

**Description:**
This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College- and Career-Ready Standards showcase lesson plan.
**Standard(s): **

[MA2015] AL1 (9-12) 23: Explain why the *x*-coordinates of the points where the graphs of the equations *y* = *f*(*x*) and *y* = *g*(*x*) intersect are the solutions of the equation *f*(*x*) = *g*(*x*); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where *f*(*x*) and/or *g*(*x*) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]

**Subject:**Mathematics (8 - 12)

**Title:**Penny Drop That Thang!

**Description:**This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation. This is a College- and Career-Ready Standards showcase lesson plan.

**Title:** Function Machine

**Description:**
During this lesson, eighth grade students will interpret the perimeter of a train of triangles, squares, trapezoids, or hexagons as a function (for each input, there will be exactly one output). Students will represent their data in a table, as an equation, and graphically.
**Standard(s): **

[MA2015] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2]

**Subject:**Mathematics (8)

**Title:**Function Machine

**Description:**During this lesson, eighth grade students will interpret the perimeter of a train of triangles, squares, trapezoids, or hexagons as a function (for each input, there will be exactly one output). Students will represent their data in a table, as an equation, and graphically.

**Title:** Graph Chart

**Description:**
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Graph Chart

**Description:**This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.

**Thinkfinity Partner:**Illuminations

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

**Title:** Automobile Mileage: Age vs. Mileage

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret the meaning of the slope and y-intercept of the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and y-intercept of the line and put those meanings in the context of the real-life application. This lesson incorporates an interactive regression line applet.
**Standard(s): **

**Subject:**Mathematics

**Title:**Automobile Mileage: Age vs. Mileage

**Description:**In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret the meaning of the slope and y-intercept of the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and y-intercept of the line and put those meanings in the context of the real-life application. This lesson incorporates an interactive regression line applet.

**Thinkfinity Partner:**Illuminations

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

**Title:** Exploring Linear Data

**Description:**
In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Exploring Linear Data

**Description:**In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.

**Thinkfinity Partner:**Illuminations

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

**Title:** Gallery Walk

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students view the work of other students in the class and explain their own work. Students move from graph to graph during this time and, without any talking, view the work of their classmates. While on their Gallery Walk, the students think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate. Each pair of students then stands next to their own work and explains one of the graphs.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Gallery Walk

**Description:**In this lesson, one of a multi-part unit from Illuminations, students view the work of other students in the class and explain their own work. Students move from graph to graph during this time and, without any talking, view the work of their classmates. While on their Gallery Walk, the students think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate. Each pair of students then stands next to their own work and explains one of the graphs.

**Thinkfinity Partner:**Illuminations

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

**Title:** Supreme Court Handshake

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students explore the handshake problem, a classic problem in mathematics that asks, How many handshakes occur when n people shake hands with each other? Groups work to determine how many handshakes take place among the nine Supreme Court justices, and then generalize the problem to determine the number of handshakes in any size group. Students explore the problem using a verbal description, a table, a graph, a picture and an algebraic formula.
**Standard(s): **

[MA2015] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8-F5]

**Subject:**Mathematics

**Title:**Supreme Court Handshake

**Description:**In this lesson, one of a multi-part unit from Illuminations, students explore the handshake problem, a classic problem in mathematics that asks, How many handshakes occur when n people shake hands with each other? Groups work to determine how many handshakes take place among the nine Supreme Court justices, and then generalize the problem to determine the number of handshakes in any size group. Students explore the problem using a verbal description, a table, a graph, a picture and an algebraic formula.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Beyond Handshakes

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students explore triangular numbers. This exploration enhances students ability to generalize a pattern with variables.
**Standard(s): **

[MA2015] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (*x,y*) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8-F4]

**Subject:**Mathematics

**Title:**Beyond Handshakes

**Description:**In this lesson, one of a multi-part unit from Illuminations, students explore triangular numbers. This exploration enhances students ability to generalize a pattern with variables.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Parallel Lines Exploration

**Digital Tool:**
Illuminations **Web Address URL:**
http://illuminations.nctm.org/Activity.aspx?id=4098 **Standard(s): **

[MA2015] GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]**Digital Tool Description:** The data grapher found within the Illuminations website allows students to enter data and then to graph the data in various formats. Once points have been plotted, students can analyze the data and make predictions about the linear functions.

**Title:**Parallel Lines Exploration

**Digital Tool:**Illuminations

**Digital Tool Description:**The data grapher found within the Illuminations website allows students to enter data and then to graph the data in various formats. Once points have been plotted, students can analyze the data and make predictions about the linear functions.

**Title:** What's the Function?

**Digital Tool:**
Answer Garden, an online brain-storming tool **Web Address URL:**
http://answergarden.ch/ **Standard(s): **

[MA2015] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (*x,y*) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8-F4]**Digital Tool Description:** Answer Garden is an online brainstorming tool that easily exports into other digital tools (wordle or tagxedo). It will also create a QR code which will facilitate easy access in a BYOD or 1:1 environment.

**Title:**What's the Function?

**Digital Tool:**Answer Garden, an online brain-storming tool

**Digital Tool Description:**Answer Garden is an online brainstorming tool that easily exports into other digital tools (wordle or tagxedo). It will also create a QR code which will facilitate easy access in a BYOD or 1:1 environment.

**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): **

[MA2015] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2]

**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