Comparing Tape Diagram Solutions to Algebraic Solutions - 7.2 - Lesson 17

Student Outcomes

1. Students use tape diagrams to solve equations of the form px + q = r and p(x + q) = r, (where p, q, and r, are small positive integers), and identify the sequence of operations used to find the solution.
2. Students translate word problems to write and solve algebraic equations using tape diagrams to model the steps they record algebraically.

Lesson Questions

- How does modeling the sequence of operations with a tape diagram help to solve the same problem algebraically?
- What are the mathematical properties, and how are they used in finding the solution of a linear equation containing parenthesis?

Lesson Summary

• Tape Diagrams can be used to model and identify the sequence of operations to find a solution algebraically.
• The goal in solving equations algebraically is to isolate the variable. 
• The process of doing this requires “undoing” addition or subtraction to obtain a 0 and “undoing” multiplication or division to obtain a 1.  The additive inverse and multiplicative inverse properties are applied, to get the 0 (the additive identity) and 1 (the multiplicative identity). 
• The addition and multiplication properties of equality are applied because in an equation, A = B, when a number is added or multiplied to both sides, the resulting sum or product remains equal.