## Reflection: Staircase of Complexity Spending & Saving, and Function Notation - Section 3: Spending & Saving, Part 1b

If you've taken a look at Part 1b, you might have noticed a few problems whose formal solutions would require the use of logarithms.  But is it necessary for a student to have heard of logarithms before they can solve these problems?

A few of my students are involved in a program that pairs them with college students who volunteer as tutors.  One of my students came to class this morning to say that her tutor said she "shouldn't be learning this in 9th grade."  I find it disappointing that our educational system would lead a high school graduate to say that, because it indicates a belief that mathematics is some sort of sequentially-prescribed series of topics.

Students are often exposed to mathematical ideas before they're ready for the formal procedures of more advanced algebra.  Or at least they should be!  That's the idea behind this Atlantic article from 2014.  The sub-heading for that article says, "Why playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children to math."  Extending from that - playing with the numbers, using guess and check, or in this case, giving students a classic applications of logs before they're "in Algebra 2," builds in arithmetic drills without saying that's what we're doing.  If a student is searching for the value of x that makes 1.10^x > 20 true, they're getting a feel for the numbers, and getting more comfortable using exponents / understanding what happens to a non-integer when we raise it various powers.
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With all of that said, I do introduce logarithms to any student with the awareness to ask about the algebraic step necessary to solve for a variable exponent.  There are always at least a few such students in any 9th grade algebra class.  When asked that question, I quickly review that we know that multiplication and division are inverse operations, and that the same goes for addition and subtraction.  Then, kids are excited to learn that there's a tool called a logarithm that's the inverse of an exponent.  They've seen the "log" button on their calculators, and they're happy to know a little about it.  I'll even have them run a few calculations to see how it works, but only after they find a satisfactory solution by some informal method.  Only after all that will I say, "you'll learn a lot more about logarithms later in high school."

Teaching Logarithms in Algebra 1?
Staircase of Complexity: Teaching Logarithms in Algebra 1?

# Spending & Saving, and Function Notation

Unit 8: Linear and Exponential Functions
Lesson 11 of 19

## Big Idea: Practice with a tool like function notation is important; interpreting what that representation means in context, even more so.

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Standards:
Subject(s):
Math, Algebra, Function Operations and Inverses, Linear and Nonlinear Equations, function notation, Algebra 1, financial applications, linear function, exponential function
43 minutes

### James Dunseith

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