Reflection: Intervention and Extension The Power of Exponents - Section 2: Exploration

 

I like to do this lesson because it does weave in to other strands, but primarily because I feel it is really powerful to have students creating with math. They gain so much more numeracy from "playing" with the operations and whenever their curiosity is inspired in math its a good thing! Tapping into their natural curiousity is an excellent way of promoting perseverence. If students are truly curious they will not let go of the problem, their curiosity gives the problem a certain power over them and they are less likely to give up and more likely to keep trying (MP1).

Curiosity also leads to questions, which opens up the original task to further and deeper investigation. It is really hard to predict the questions my kids will ask. I might be able to anticipate some of them and be prepared to respond and follow up, but they always come up with questions and ideas I hadn't thought of. Sometimes these open up avenues I wasn't prepared to address or follow and many times these present opportunities to differentiate learning. 

When I asked them what was the biggest number they could make I heard questions like:

  • Should I multiply with this number or use it as an exponent?
  • Should I use a bigger number for the base or for the exponent?
  • Can we use an exponent on an exponent?
  • Can we use parentheses and add two numbers together in an exponent? (an expression as an exponent)
  • What's the best way to use the 1?

All these questions helped them explore relationships between numbers and operations that gave them a deeper understanding of the meaning and magnitude of exponents and gave them more experience with expressions. After one student asked if he could use a calculator he was confused when the calculator displayed the answer in scientific notation, which lead to another lesson. By following my students questions and using them to plan further investigations they were more engaged because it was relevent to them. 
 

  Low floor, high ceiling task
  Intervention and Extension: Low floor, high ceiling task
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The Power of Exponents

Unit 1: Order of operations & Number properties
Lesson 3 of 9

Objective: SWBAT create an expression with the greatest possible number using exponents.

Big Idea: Students will learn how changes to an expression create predictable changes in the solution.

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Subject(s):
Math, exponents / powers, Expressions (Algebra), order of operations (exponents), Mental Math
  54 minutes
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