The Power Roller Game gives kids the opportunity to make great choices about which number should be the base and which should be the exponent. For example, given the numbers 7 and 10, which would you make the base and which would you make the exponent to yield the largest number? They’ll definitely need good calculator skills to help them as they are computing their individual numbers and their totals. The game is well-named since students will be surprised at how quickly even a small number becomes very large when it’s taken to a power. For example, the number 5 to the 8th power yields 390,625. There’s an opportunity for students to see lots of interesting patterns as they play this game more than once.
An interesting adaptation of this game is to have students guess what numbers their expressions will yield in advance. In other words, player #1 has rolled a 7 followed later by a 5 and chooses to write his number as 7 to the 5th power. Player #2 rolls a 4 followed by an 8 and chooses to write her number as 8 to the 4th power. Have the students make a decision about which number is larger BEFORE they calculate them and then compare them. As they practice, ask them to give a more precise result for what decimal place their final number will yield before they calculate it. There will definitely be some surprises when computations and comparisons are made.
It’s a good idea to have pencil and paper handy. Ask students to write the expression out long hand and check their work. They’ll still have to use a calculator, but it’s good practice to make sure they understand that 7 to the 5th power is NOT 7 x 5 but instead the number 7 multiplied times itself 5 times or 7 x 7 x 7 x 7 x 7. The exponent shorthand is a little difficult to get used to, but this game helps kids understand the true meaning and power of exponential expressions.
Common Core Mathematical Standard
6.EE.1 Apply and extend previous understandings of arithmetic to algebraic expressions.
1. Write and evaluate numerical expressions involving whole-number exponents.
