Nutrition Facts – Systems of Equations Project

This project has students collect three different Nutrition Facts labels and write a system of equations in three variables using fat, carbohydrates, protein, and calories. Then they are to solve the system using a number of methods learned in class. The goal is to determine the number of calories in each gram of fat, carbohydrate, and protein of any food. At the end of the project, the student discusses which methods they preferred for solving this system and why.

CCSS Connection:
CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in three variables.
CCSS.MATH.CONTENT.HSA.REI.C.8 Represent a system of linear equations as a single matrix equation in a vector variable.
CCSS.MATH.CONTENT.HSA.REI.C.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Drawing the Conic Sections – hands on

This activity is to be used during the discussion of each conic section. Students will use wax paper and construction paper and will draw the conic sections using various folding methods. The construction paper is to keep each drawing in their binder. I liked to use this to introduce each conic, it was engaging and then the math didn’t seem so bleak.

CCSS Connection:
CCSS.MATH.CONTENT.HSG.GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
CCSS.MATH.CONTENT.HSG.GPE.A.2 Derive the equation of a parabola given a focus and directrix.
CCSS.MATH.CONTENT.HSG.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Drawing Inverse Functions – hands on

This activity uses patty paper to trace the inverse of a linear equation. It was used to introduce the concept of inverses before finding them algebraically. The attached document is my teacher notes for the lesson. The patty paper may be hard to see, but we folded the paper along the line y=x. Then we traced the line on the back of the patty paper so that the inverse showed through.

CCSS Connection:
CCSS.MATH.CONTENT.HSF.BF.B.4.A Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.