Lesson 9

When Are They the Same?

Lesson Narrative

In this lesson students apply their knowledge of solving equations by considering two real world situations: two tanks where one is filling and the other is emptying and two elevators traveling above and below ground level. Using the given expressions for each situation, students are asked to determine when the amount of water in the tanks or the travel time of elevators will be the same. It is the work of the student to recognize that they can set the two expressions equal and solve the equation for the unknown and this work sets up the concept of substitution for the coming section on systems of linear equations.

Learning Goals

Teacher Facing

• Create an equation in one variable to represent a situation in which two conditions are equal.
• Interpret the solution of an equation in one variable in context.

Student Facing

Let’s use equations to think about situations.

Student Facing

• I can use an expression to find when two things, like height, are the same in a real-world situation.

Building Towards

Glossary Entries

• coefficient

A coefficient is a number that is multiplied by a variable.

For example, in the expression $$3x+5$$, the coefficient of $$x$$ is 3. In the expression $$y+5$$, the coefficient of $$y$$ is 1, because $$y=1 \boldcdot y$$.

• constant term

In an expression like $$5x+2$$, the number 2 is called the constant term because it doesn’t change when $$x$$ changes.

In the expression $$7x+9$$, 9 is the constant term.
In the expression $$5x+(\text-8)$$, -8 is the constant term.
In the expression $$12-4x$$, 12 is the constant term.

• term

A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression $$5x + 18$$ has two terms. The first term is $$5x$$ and the second term is 18.