Equations and Their Solutions

5 min

Narrative

This Warm-up prompts students to recall what they know about the solution to an equation in one variable. Students interpret a given equation in the context of a situation, explain why certain values are not solutions to the equation, and then find the value that is the solution.

Launch

Give students continued access to calculators.

Student Task

Cement is made by mixing water and concrete mix. The amount of water, ww, added to the concrete mix can affect the strength of the material. One liter of water weighs 2.2 pounds.

The equation 2.2w+80=86.052.2w + 80 = 86.05 represents the relationship between these quantities.

  1. What could the 80 represent in this situation?
  2. Priya said that neither 2 nor 3 could be the solution to the equation. Explain why she is correct.
  3. Find the solution to the equation.

Sample Response

  1. Sample response: It could represent the weight of the concrete mix in pounds that will go into the cement mixture.
  2. Sample explanation: 2.2(2)+802.2(2)+80 is 84.4, not 86.05, and 2.2(3)+802.2(3)+80 is 86.6, not 86.05.
  3. w=2.75w = 2.75
Activity Synthesis (Teacher Notes)

Focus the discussion on how students knew that 2 and 3 are not solutions to the equation and how they found the solution. Highlight strategies that are based on reasoning about what values make the equation true.

Ask students: "In general, what does a solution to an equation mean?" Make sure students recall that the solution to an equation in one variable is a value for the variable that makes the equation a true statement.

Standards
Addressing
  • A-REI.3·Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A-REI.3·Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A-REI.3·Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A-REI.A·Understand solving equations as a process of reasoning and explain the reasoning
  • HSA-REI.A·Understand solving equations as a process of reasoning and explain the reasoning.
  • HSA-REI.B.3·Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

15 min

15 min