Cube House

Getting Started

The student does not understand what it means to write a numerical expression.

The student:

• Attempts to calculate the combined areas of the floors and the volume of the house rather than represent each with an exponential expression.
• Writes an incorrect expression not involving exponents.
  
  

What were you asked to do in this problem?

Do you know what a numerical expression is? Can you write an example of a numerical expression?

What is an exponent? Can you write an example of an exponential expression?

Can you explain the equation you wrote and how it relates to the volume of the figure?

Do you know what volume means? How do you find the volume of a cube?

How do you find the area of a square?

Define the terms numerical expression, algebraic expression, and equation. Provide numerous examples of each and ask the student to classify each example as one of these three algebraic entities. Review vocabulary associated with various mathematical operations. Have the student make a chart or table that includes vocabulary that suggests operations and examples of each. Provide the student with opportunities to practice writing numerical expressions from verbal descriptions.

Review the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. Initially ask the student to evaluate a simple exponential expression such as . To reinforce the meaning of the exponent, encourage the student to write exponential expressions in expanded form before calculating (e.g., ). Then 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 as 5 x 5 x 5. Eventually, provide expressions such as 6 x 2 x 2 x 2 x 2 + 4 x 4 x 4 and ask the student to rewrite the expressions using exponents.

Provide additional opportunities to write numerical expressions involving exponents from verbal descriptions that arise in the context of problems.

Moving Forward

The student does not understand how to determine the exponent in the expression.

The student writes an exponential expression with the correct base but uses an incorrect exponent.

How did you determine the exponent in your expression? What does the exponent mean?

How many sevens are you multiplying? Can you write this out in expanded form first?

Review the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. Initially ask the student to evaluate a simple exponential expression such as . To reinforce the meaning of the exponent, encourage the student to write exponential expressions in expanded form before calculating (e.g., ). Then 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 as 5 x 5 x 5. Eventually, provide expressions such as 6 x 2 x 2 x 2 x 2 + 4 x 4 x 4 and ask the student to rewrite the expressions using exponents.

Almost There

The student writes the expression in terms of repeated factors but does not use exponents.

The student writes a numerical expression that does not involve exponents (e.g., 5 x 7 x 7x 7 or 5 x 7 x 7).

Can you use exponents to write your answer in an equivalent form?

Review the meaning of exponents. Define the terms base and exponent and explicitly describe the exponent as indicating the number of factors of the base. Guide the student to rewrite 5 x 7 x 7x 7 and 5 x 7 x 7 using exponents. Provide additional opportunities to write numerical expressions involving exponents from verbal descriptions that arise in the context of problems.

Got It

The student provides complete and correct responses to all components of the task.

The student writes:

• Total volume is  or
•  Total floor area is  or
  
  

Can you evaluate the volume and the floor area?

Can you write  as a single power of seven?

Provide additional opportunities to write and evaluate more complex numerical expressions involving whole number exponents.

Challenge the student to solve simple exponential equations such as  or .

Consider implementing MFAS task Paul’s Pennies.