Getting Started |
| Misconception/Error The student does not understand the meaning of exponents. |
| Examples of Student Work at this Level The student is unable to correctly expand any of the exponential expressions. |
| Questions Eliciting Thinking How do you read  out loud? Which number is the base? Which number is the exponent? What does the exponent mean?
What does it mean to square a number? What does it mean to cube a number? |
| Instructional Implications Provide instruction on the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. To reinforce the meaning of the exponent, initially encourage the student to write exponential expressions in expanded form before calculating (e.g., = 2 x 2 x 2 x 2).
Ask the student to write simple numerical expressions with exponents (using single-digit whole number bases), describe them with mathematical vocabulary, and rewrite them in expanded form. For example, the student might write  , describe this expression as “five to the third power,” “five to the power of three,” or “five cubed,” identify the base as five and the exponent as three, and rewrite it as 5 x 5 x 5.
Ask the student to create a repeated multiplication expression. Then, ask the student to explain, using mathematical vocabulary, how to rewrite the expression in exponential form. For example, a student might write 8 x 8 x 8 x 8 x 8 and explain that 8 x 8 x 8 x 8 x 8 is equal to  because eight is the base since it is the factor in the multiplication, and five is the exponent because there are five factors of eight. |
Making Progress |
| Misconception/Error The student can expand exponential expressions but is unable to correctly evaluate them. |
| Examples of Student Work at this Level The student may correctly expand and evaluate as 2 x 2 x 2 x 2 = 16. However, the student is unable to correctly evaluate (2/5)(2/5)(2/5) or (0.8)(0.8).
|
| Questions Eliciting Thinking How did you multiply 0.8 x 0.8?
How would you calculate (2/5) x (2/5)? How do you multiply two fractions? |
| Instructional Implications Explain that in an expression such as  , the number 0.8 is the base, so this expression represents two factors of 0.8. As needed, provide a review of multiplying decimals (see MFAS tasks for MAFS.5.NBT.2.7).
Explain that in an expression such as  , the fraction  is the base, so this expression represents three factors of  . As needed, provide a review of multiplying fractions (see MFAS tasks for MAFS.5.NF.2.4). |
Got It |
| Misconception/Error The student provides complete and correct responses to all components of the task. |
| Examples of Student Work at this Level The student correctly expands and evaluates each expression:
- 2 x 2 x 2 x 2 = 16
- x x =
- 0.8 x 0.8 = 0.64
|
| Questions Eliciting Thinking How are exponents related to multiplication?
What are the terms that describe the parts of an exponential expression? |
| Instructional Implications Provide more opportunities to work with exponential expressions. For example, ask the student to find the unknown in equations such as  = 2401 or  = 32.
Ask the student to explain (in oral or written form) the process of evaluating exponential expressions. Guide the student to use correct mathematical terminology such as base, exponent, and factor. Have the student consider possible misconceptions about exponential expressions that his or her peers might hold. Provide more opportunities for other students to evaluate exponential expressions and ask the Got It student to assist peers. |
