Lesson 17 Student Outcomes
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.
Students translate word problems to write and solve algebraic equations using tape diagrams to model the steps they record algebraically.
Lesson 17 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.
During one rainy day on the vacation, the entire family decided to go watch a matinee movie in the morning and a drive- in movie in the evening. The price for a matinee movie in the morning is different than the cost of a drive-in movie in the evening. The tickets for the matinee morning movie cost each. How much did each person spend that day on movie tickets if the ticket cost for each family member was the same? What was the cost for a ticket for the drive-in movie in the evening?
2. Another approach to solving the problem is to eliminate the coefficient first. How would one go about eliminating the coefficient?
3. How do we “undo” multiplication?
4. What is the result when “undoing” multiplication in any problem?
5. What mathematical property is being applied when “undoing” multiplication?
6. What approach must be taken when solving for a variable in an equation and “undoing” addition is required?
7. How can this approach be shown with a tape diagram?
8. What is the result when “undoing” addition in any problem?
9. What mathematical property is being applied when “undoing” addition?
10. What mathematical property allows us to perform an operation (or, “do the same thing”) on both sides of the equation?
11. How are the addition and multiplication properties of equality applied?
The cost of a babysitting service on a cruise is $10 for the first hour, and $12 for each additional hour. If the total cost of babysitting baby Aaron was $58, how many hours was Aaron at the sitter?
How can a tape diagram be used to model this problem?
How is the tape diagram for this problem similar to the tape diagrams used in the previous activity?
How is the tape diagram for this problem different than the tape diagrams used in the previous activity?