The Problem
The total number of participants who went on the seventh-grade field trip to the Natural Science Museum consisted of all of the seventh-grade students and 7 adult chaperones. Two-thirds of the total participants rode a large bus, and the rest rode a smaller bus. If 54 students rode the large bus, how many students went on the field trip?
Students were asking questions like: "What represents the total number of participants?" "What can take the place of the word of?" Using notes from class, coaching from the teacher, and ideas from the group, students were engaged in some excellent mathematical conversations.
Eureka Math lessons encourage students to focus on the process of solving problems and to explore the concepts of math rather than memorize specific problem-solving steps. Below is the summary of the key concepts being addressed in this lesson:
Lesson Summary
- Algebraic Approach: To solve an equation algebraically means to use the properties of operations and if-then moves to simplify the equation into a form where the solution is easily recognizable. For the equations we are studying this year (called linear equations), that form is an equation that looks like 𝑥𝑥 = a number, where the number is the solution.
- If-Then Moves: If 𝑥𝑥 is a solution to an equation, it will continue to be a solution to the new equation formed by adding or subtracting a number from both sides of the equation. It will also continue to be a solution when both sides of the equation are multiplied by or divided by a nonzero number. We use these if-then moves to make zeros and ones in ways that simplify the original equation.
- Useful First Step: If one is faced with the task of finding a solution to an equation, a useful first step is to collect like terms on each side of the equation.
