**Title:** There Has to Be a System for This Sweet Problem

**Description:**
In this Illuminations lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.
**Standard(s): **

[MA2015] AL1 (9-12) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [A-REI7]

**Subject:**Mathematics

**Title:**There Has to Be a System for This Sweet Problem

**Description:**In this Illuminations lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.

**Thinkfinity Partner:**Illuminations

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

**Title:** Supply and Demand

**Description:**
This Illuminations lesson focuses on having students create and solve a system of linear equations in a real-world setting. By solving the system, students find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or slope and y-intercept.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics

**Title:**Supply and Demand

**Description:**This Illuminations lesson focuses on having students create and solve a system of linear equations in a real-world setting. By solving the system, students find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or slope and y-intercept.

**Thinkfinity Partner:**Illuminations

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

**Title:** Investigating Pick's Theorem

**Description:**
In this unit of three lessons, from Illuminations, students rediscover Pick's Theorem, which they were likely introduced to in middle school, and use algebra to determine the coefficients of the equation. They explore the concept of change as a mechanism for finding the coefficients of Pick's Theorem.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics

**Title:**Investigating Pick's Theorem

**Description:**In this unit of three lessons, from Illuminations, students rediscover Pick's Theorem, which they were likely introduced to in middle school, and use algebra to determine the coefficients of the equation. They explore the concept of change as a mechanism for finding the coefficients of Pick's Theorem.

**Thinkfinity Partner:**Illuminations

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

**Title:** Pick's Theorem as a System of Equations

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem.
**Standard(s): **

[MA2015] ALT (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]

**Subject:**Mathematics

**Title:**Pick's Theorem as a System of Equations

**Description:**In this lesson, one of a multi-part unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem.

**Thinkfinity Partner:**Illuminations

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

**Title:** Escape from the Tomb

**Description:**
In this Illuminations lesson, students solve a system of equations when presented with a problem: two bowls are suspended from the ceiling by springs and one bowl is lower than the other. Placing only marbles in one bowl and bingo chips in the other, students must work out how many items should be placed in each bowl so that the heights of the bowls are the same. There are also links to online activity sheets.
**Standard(s): **

[MA2015] ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama)

**Subject:**Mathematics

**Title:**Escape from the Tomb

**Description:**In this Illuminations lesson, students solve a system of equations when presented with a problem: two bowls are suspended from the ceiling by springs and one bowl is lower than the other. Placing only marbles in one bowl and bingo chips in the other, students must work out how many items should be placed in each bowl so that the heights of the bowls are the same. There are also links to online activity sheets.

**Thinkfinity Partner:**Illuminations

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