Expressions and Equations / What is an Equation?

Understanding

As students begin their work with algebraic equations, they should learn to think and reason about the nature of the solutions: what values would make sense both numerically and in a given context; and how different equations representing the same situation can be related to each other.

What to look for

Students should be able to note that a variable is typically represented by a letter and takes on multiple values as replacements. An expression is a mathematical phrase involving numbers, variables, mathematical operations, and mathematical symbols such as parentheses.

Sample Assessment

If k can be replaced by any number, how many different solutions can the equation k+6=0 have?

Answer: One

The Big Idea

In an equation, a constraint is imposed such that the values of the variables involved in the expressions on each side of the equation must make the equation a true statement.

What are the students doing?

Students explore what is meant by an equation and the solution to an equation. Students also distinguish between an expression and an equation.

What is the teacher doing?

As students think about equations, help them to recall operations with fractions and mixed numbers and to apply their understanding in this new space.