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Comparing Tape Diagram Solutions to Algebraic Solutions

Comparing Tape Diagram Solutions to Algebraic Solutions. Vocabulary. Coefficient: The number before the variable. It is multiplying the variable -Example: 4x + 7 = 31

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Comparing Tape Diagram Solutions to Algebraic Solutions

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  1. Comparing Tape Diagram Solutions to Algebraic Solutions

  2. Vocabulary • Coefficient: The number before the variable. It is multiplying the variable -Example: 4x + 7 = 31 • Distributive Property: When multiplying a sum or difference, you can distribute the multiplication to both terms and multiply separately. coefficient

  3. Example

  4. Example

  5. On Your Own

  6. I need you to break into 7 equal groups

  7. Find the cost: • A slice of pizza, 1 plane ticket, 2 nights in the motel, and 1 evening movie • One t-shirt, 1 ticket to the baseball game, 1 day of the rental car

  8. When solving an equation with parentheses, order of operations must be followed. What property can be used to eliminate parentheses; for example, 3(𝑎 + 𝑏) = 3𝑎 + 3𝑏? • Another approach to solving the problem is to eliminate the coefficient first. How would one go about eliminating the coefficient? • How do we “undo” multiplication? • What is the result when “undoing” multiplication in any problem? • What mathematical property is being applied when “undoing” multiplication? • What approach must be taken when solving for a variable in an equation and “undoing” addition is required?

  9. What is the result when “undoing” addition in any problem? • What mathematical property is being applied when “undoing” addition? • What mathematical property allows us to perform an operation (or, “do the same thing”) on both sides of the equation? • How are the addition and multiplication properties of equality applied?

  10. 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?

  11. 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?

  12. Exit Ticket • 1. Jim’s father works two part-time jobs; one in the morning and one in the afternoon, and works a total of 48 hr. each 5-day work week. If his schedule is the same each day, and he works 4 hr. each morning, how many hours does Eric’s father work each afternoon?

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