Lesson 4More Balanced Moves
Learning Goal
Let’s rewrite some more equations while keeping the same solutions.
Learning Targets
I can make sense of multiple ways to solve an equation.
Warm Up: Different Equations?
Problem 1
Equation 1
Which of these have the same solution as Equation 1? Be prepared to explain your reasoning.
Equation A
Equation B
Equation C
Equation D
Activity 1: Step by Step by Step by Step
Problem 1
Here is an equation, and then all the steps Clare wrote to solve it:
Here is the same equation, and the steps Lin wrote to solve it:
Are both of their solutions correct? Explain your reasoning.
Describe some ways the steps they took are alike and different.
Mai and Noah also solved the equation, but some of their steps have errors. Find the incorrect step in each solution and explain why it is incorrect.
Mai:
Noah:
Activity 2: Make Your Own Steps
Problem 1
Solve these equations for
Are you ready for more?
Problem 1
I have 24 pencils and 3 cups. The second cup holds one more pencil than the first. The third holds one more than the second. How many pencils does each cup contain?
Lesson Summary
How do we make sure the solution we find for an equation is correct? Accidentally adding when we meant to subtract, missing a negative when we distribute, forgetting to write an
Fortunately, each step we take solving an equation results in a new equation with the same solution as the original. This means we can check our work by substituting the value of the solution into the original equation. For example, say we solve the following equation:
Substituting 3 in place of
we get a statement that isn’t true! This tells us we must have made a mistake somewhere. Checking our original steps carefully, we made a mistake when distributing -3. Fixing it, we now have
Substituting -3 in place of
This equation is true, so