In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission comes from my former student Kelsie Teague. Her topic, from Pre-Algebra: powers and exponents.
What interesting word problem using this topic can your students do now?
For the topic of powers and exponents I want to bring in the idea of money, and doubling a salary. The word problem I would give them to start with and to get them thinking would be this:
Two companies were offering you a job. Company A is offering you a salary of $1,000 a day for 30 days and Company B is offering you a salary of $2 the first day and it doubles each day after that for 30 days. Which job is the better offer?
Since this is just my engage problem I’m not expecting them to be able to tell me that the answer is Company B because the answer is 
How can this topic be used in your students’ future courses in Mathematics or Science?
I believe powers and exponents are important knowledge because students will be using them for the rest of their math career. This comes up when teaching functions, learning the graphs of functions, trig, pre-calculus, Calculus and etc. Powers and exponents are used extensively in algebra and it is important that students have a strong understand of how and why they work before continuing onto those higher classes. For example, when you have 
What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?
The earliest exponents came from the Babylonians. The number system was extremely different from modern mathematics. The earliest known mention of Babylon was mentioned on a tablet found around 23rd century BC. Even then they were messing with the concept of exponents.
I would show my students this picture and explain to them what the symbols mean and ask them if they feel any better about doing math in modern times rather than working with these symbols to add, subtract, divide, exponents, power and doing equations. This also shows that this concept has been around for many thousands of years and something that is obviously very important if we still use it in modern math. I might also bring up the website least below that talks about modern exponents and works backwards and talks about where they came from to give the students more depth in this knowledge.
Mean Green Math 