Students will understand exponentiation as repeated multiplication. Then they'll use this understanding to evaluate whole numbers, decimals, or fractions, raised to whole number exponents. Ask your students to evaluate some expressions like \(6^2\) or \(3^3.\) Also ask students to evaluate expressions like \(50^2,\) \(200^3,\) etc. That is, some number for which it's easy to determine its square, plus some zeros tacked on at the end. If it's easy to determine \(2^3,\) then it's pretty easy to determine \(200^3\) as well. At some point in the lesson, show students the wheat and chessboard problem, or a variation of it. You can alter the problem as tripling, quadrupling, etc. each day, if you like. Allow students to use a calculator, as the numbers will quickly become too large for the student to multiply with. Next, give your students this challenge.

I decided to put the wheat and chessboard problem here because that's where Core Curriculum places it.

After your students are comfortable with squaring and cubing whole numbers, lead this investigation. To learn how to lead this activity, it's necessary to also watch this and this.

Watch these Khan Academy videos:

Do these Khan Academy exercises:

Next, give your students this challenge:

Make the equation below true by replacing each letter with a unique digit (0-9).

$$BA = A \times A \times A$$Here's the solution:

\(A \times A \times A = A^3.\) Thus, \(BA = A^3.\) Hence, \(BA\) is a two-digit cubed number, ending in \(A.\) By listing the first few cubes, we find \(3^3 = 27\) and \(4^3 = 64\) are the only two-digit cubed numbers, and only \(64 = 4^3\) fits \(BA = A^3.\) In conclusion, our equation is \(64 = 4 \times 4 \times 4.\)

Conclude by leading this investigation:

Square Sardine Packing (percentages, algorithm)

by MathPickle

6.EE.A.1: Write and evaluate numerical expressions involving whole-number exponents.