Exponent challenge question

At OAME I learned several new problems which I have been sharing with my classes, colleagues, and friends. One that’s been particularly fun with grade 9s has been an exponent question.

The question is: how many digits are in the answer to this question.

We quickly notice that calculators can’t handle this problem (phones can, so I’ll need to change it for the future). It’s fun to tackle problems that are too big for calculators, but our brains can figure them out.

This question illustrated so many misconceptions my students have about exponents. It was good to see them exposed so we could tackle them together and build more number sense.

The first misconception was that the base and the exponent would both be changed when raised to a new power. This makes me think we’ve done too much practice with algebraic bases where we’ve ignored the base because it’s a letter. They knew that the power of a power multiplies the exponents together, but they missed the idea that it’s that many 2s or 5s being multiplied together.

The next misconception is that when multiplying, we add the exponents and multiply the different bases. They are used to adding exponents together when the bases are the same, and maybe thought that you do that all the time. They are working on remembering rules, and not understanding the concepts.

We brought it down to a smaller scale to see if that would help. We tried 2 squared x 5 squared etc,

Students were making connections more quickly now, seeing that all the answers were powers of 10. We’d just done scientific notation so this was a nice connection to see.

Some spent a lot of time exploring various powers of 2 and 5 and seeing how they grew. We practiced how to calculate this (where the exponent buttons are) and how to interpret scientific notation on our calculators.

While consolidating the lesson we had time to talk about many aspects of the math that we’ve learned. We reviewed what exponents mean, and what the power of a power does, and why the base stays the same.

We reviewed 2 different ways to multiply 16×625, using area model or by doubling 4 times.

We looked at powers of 10 as well and made the connection to the scientific notation that we’ve practiced.

We looked at how a power of a product is the product of the power as well.

All in all we have enjoyed working with this problem in several classes now. It helps to show what skills are solid, and where we need some more practice.