Lesson 14Evaluating Expressions with Exponents
Learning Goal
Let’s find the values of expressions with exponents.
Learning Targets
I know how to evaluate expressions that have both an exponent and addition or subtraction.
I know how to evaluate expressions that have both an exponent and multiplication or division.
Warm Up: Revisiting the Cube
Problem 1
Based on the given information, what other measurements of the square and cube could we find?
Print Version
Based on the given information, what other measurements of the square and cube could we find?
Activity 1: Calculating Surface Area
Problem 1
A cube has side length 10 inches. Jada says the surface area of the cube is 600 in², and Noah says the surface area of the cube is 3,600 in². Here is how each of them reasoned:
Jada’s Method:
Noah’s Method:
Do you agree with either of them? Explain your reasoning.
Activity 2: Expression Explosion
Problem 1
Evaluate the expressions in one of the columns. Your partner will work on the other column. Check with your partner after you finish each row. Your answers in each row should be the same. If your answers aren’t the same, work together to find the error.
column A | column B |
---|---|
Are you ready for more?
Problem 1
Consider this equation:
Can you find a different set of 3 whole numbers that make the equation true?
Problem 2
How many sets of 3 different whole numbers can you find?
Problem 3
Can you find a set of 3 different whole numbers that make this equation true?
Problem 4
How about this one?
Problem 5
Once you have worked on this a little while, you can understand a problem that is famous in the history of math. (Alas, this space is too small to contain it.) If you are interested, consider doing some further research on Fermat’s Last Theorem.
Lesson Summary
Exponents give us a new way to describe operations with numbers, so we need to understand how exponents get along with the other operations we know.
When we write
Earlier we saw situations in which
To make everyone agree about the value of expressions like
If we want to communicate that 6 and 4 should be multiplied first and then squared, then we can use parentheses to group parts together: