This unit address components of the following Common Core learning standards:
- MATH.CONTENT.8.EE.C.7.A
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
- MATH.CONTENT.8.EE.C.7.B
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
- MATH.CONTENT.8.EE.C.8.C
Solve real-world and mathematical problems leading to two linear equations in two variables
In this unit, specific talk of linear equations and algebraic methods of problem solving are avoided so that the focus remains on the conceptual understanding of balancing equations. As such, this unit touches upon only parts of the above Massachusetts Common Core learning standards, leaving the remaining parts to be covered in future units. In all of the activities until the last day of the unit, students will actually work to balance equations in two variables to solve a variety of real-world mathematical problems. These equations all have integer coefficients, which will help students feel comfortable with the variable manipulation before they work with other rational number coefficients (i.e. fractions) in the next unit. On the last day of the unit, students will explore linear equations in one variable as they prepare to more formally solve balanced equations in the next unit. They will focus specifically on linear equations in one variable with one solution.