Students use reasoning to identify solutions to equations. They initially do this using the balance scale. They also learn that some equations may have all numbers as solutions and some equations may have no solutions.
Before beginning the formal process of solving equations, students need opportunities to use reasoning to find solutions. Students study examples where reasoning pays off. For example, in the equation 4b + 15 = 3b + 6b, students can reason that 4b + 15 = 3b + 6b, so 5b must be equal to 15, an equation which they can solve by understanding multiplication.
Students also discover that there are equations that can have every number as a solution or no number as a solution. They may recognize some equations with all numbers as solutions by recognizing that they show a property of operations, such as the commutative property of addition.
SWD: Students with disabilities may struggle to determine salient information in lessons. Preview the goals with students to support saliency determination as they move through the instruction and tasks.
Students with disabilities may struggle to self-monitor their progress through the lesson. Provide students with a copy of the lesson goals to use as a checklist as they move through the different tasks. Have students indicate when they have reached each goal for the lesson. This will also promote engagement, independence, and self-management of learning.
Goals and Learning Objectives
- Use reasoning to identify the solution to an equation.
- Recognize equations that have any number as a solution and equations that have no solutions.