## Reflection: Perseverance Mirror Task: Understanding Equivalent Functions - Section 3: Investigation

After working through the majority of the functions unit, students are getting very good at spotting a linear pattern and naming it explicitly.  You can see, however, from the student work that they are doing so with the use of a table.  This is, of course, a completely viable method but I also wanted the students to see some structure in the situation itself.  I really forced my students to show some perseverance and stamina by asking them to find 4x+4 in another way in the picture.  I have noticed for years that students are not happy about finding "another way" to solve a problem.  Isn't one right answer good enough?  But I keep pushing them to find different ways as a way to increase their understanding.

Most groups of students (after some prodding) were able to see that the four corners of the mirror were constant and that the length and width of the mirror were the same length as the square (x).  Because of this they could see the 4x+4 reflected in the picture but most groups had trouble being able to put this observation down in words.  Some were still getting caught up with what the variable, x, represented in the picture.  Many groups wanted to say at first that the mirror sizes were 1, 4, 9, etc. rather than 1, 2, and 3, etc.  This misconception made it hard from them to generalize by looking at the picture.

Perseverance: Investigation-Reflection

# Mirror Task: Understanding Equivalent Functions

Unit 1: Functions
Lesson 8 of 18

## Big Idea: Functions that model the same situation can often be written in different ways which are all equivalent.

Print Lesson
2 teachers like this lesson
Standards:
Subject(s):
Math, Patterns (Algebra), Algebra, linear models, function, recursive, explicit
40 minutes

### James Bialasik

##### Similar Lessons

###### Graphing Radical Functions Day 2
Algebra II » Radical Functions - It's a sideways Parabola!
Big Idea: Looking back over a number of examples, students make use of the structure of equations to anticipate the graph.
Favorites(2)
Resources(7)
Fort Collins, CO
Environment: Suburban

###### The Function Game
12th Grade Math » Functioning with Functions
Big Idea: Functions are investigated using a game that is accessible and engaging.
Favorites(14)
Resources(9)
Troy, MI
Environment: Suburban

###### What is a Function?
Algebra I » Linear & Absolute Value Functions
Big Idea: Students will identify whether a relation is a function by examining its inputs and outputs or with the vertical line test.
Favorites(76)
Resources(18)
Washington, DC
Environment: Urban