Substituting Numbers for Letters

Substituting Numbers for Letters

Locomotives

Opening

Locomotives

This Burlington Northern and Santa Fe (BNSF) Railway locomotive is about 70 feet long.

  • Write an expression to describe the length of 3 locomotives in a row, where a represents the length of 1 locomotive.
  • Evaluate your expression for a = 70.

Hint:

To evaluate your expression for a = 70, you need to replace any occurrence ofa in your expression with the value 70

Math Mission

Opening

Express the lengths of the trains as algebraic expressions and then substitute to find the actual lengths.

Make a Train

Work Time

Make a Train

  • Use the Creating Trains interactive to make a train that has at least 8 cars. The table shows the types of cars that you can use to make your train.
  • Write two different expressions that represent the length of your train. Use the letters specified in the table to represent the lengths of the different types of cars.
  • Find the length of your train by replacing the letters in each of your expressions with the values given for each letter in the table. INTERACTIVE: Creating Trains

Hint:

  • Did you make a train and write an expression for the train?
  • Did you replace each variable in the expression with the appropriate car length from the table?
  • Once you complete these steps, you can calculate the length of the train.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain how you wrote your two different expressions for one of your trains.
  • Describe your methods for finding the simplest form of the expression for the train you chose to present.

Challenge Problem

  • Compare the expressions 5a + 0d and 5a. Are they equivalent? Justify your thinking.
  • Compare the expressions 5ad and 5a. Are they equivalent? Justify your thinking.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ approaches to evaluating the expressions they wrote.

Hint:

As your classmates present, ask questions such as:

  • What cars did you use in your train?
  • How do your two expressions represent your train?
  • What properties did you use to rewrite your expression to combine like terms?
  • Did you get the same answer when you evaluated each of your expressions? If not, what did you do?
  • Which expression was easier to evaluate? Why?
  • What is the length of your train? How do you know?

Evaluate Expressions Using Substitution

Work Time

Evaluate Expressions Using Substitution

Evaluate each of these expressions:

  1. 2x + 3 if x = 4
  2. 5(x – 3) if x = 6
  3. 2x + 5 + 3y if x = 2.5 and y = 5.25
  4. 23(a + b) if a = 5 and b = 4
  5. If the area of a square is s2, and a side is equal to 8 inches, what is the area?

How to Evaluate an Expression

Formative Assessment

Summary of the Math: How to Evaluate an Expression

Write a summary about how to evaluate an expression.

Hint:

Check your summary.

  • Do you explain what to do with the variables when you evaluate an algebraic expression?
  • Do you mention order of operations?
  • Did you discuss the properties of operations?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

The problems in this lesson were different from the problems in the last lesson because …