Math 647 Unit: Early Number and Operations concepts*

Section 1b: Algebraic reasoning: Patterns and Functions*

*Patterns and functions doesn't have to go here at the beginning--we could be doing this after the other unit 1 stuff, or at the end of the course, or whatever, but we can do it here (you don't need to have done other stuff first) and you don't have to have your textbooks yet for this topic, so here it is.

computer skills needed
 help files
Answering a problem in SMART Notebook (assn 4, 5)
 Getting started with SMART Notebook
Making a superscript in Microsoft Word (Assn 6)
 Superscripts.
Scanning in a hand-written document, and embedding it in a Microsoft Word document to submit. (Assn 7)
 You will need to consult your scanner documentation to scan your page.  Once that scanned file is in your compute as a .tiff, .gif, .jpg, .bmp or .png, you can insert that picture into a Microsoft Word document like this. If you can only figure out how to get a .pdf from your scanner, you can try this (only works with single page .pdfs)

Content goals:

Introduction

Patterns and functions:
Representing patterns and functions with pictures, tables and graphs
Video 154: Representing patterns and functions
Reading: A written out summary of these examples
 D2L->Content->What is Algebra in Elementary School?
Assignment 4: Do problems 1 and 2 in this growthPatternsTiles notebook**.  Put your solutions in the Notebook file, save it, and upload it to D2L. Due May 31

Asking good questions about patterns and functions:
Video 155 A and B: questions about patterns and connections to algebra part 1; part 2.
Reading: Read this lesson plan: http://www.mathsolutions.com/documents/Solving_Problems_i33.pdf from Math Solutions
Assignment 5: Answer these questions** from page 4 of the lesson plan (the is also a SMART Notebook). Due May 31

**For reasons I have not been able to discover, some computers/web browsers/etc do not download SMART Notebooks correctly.  If you download one of these SMART Notebooks, and find that the file will not open, then you should first try downloading them from the D2L Content section, and then try e-mailing me.  So far I have not encountered any problems that attaching the files and sending them as an e-mail won't fix.

Equations for growing pattern sorts of functions.
Videos 156 A and B: Examples of figuring out functions part 1; part 2.
Reading: Written out examples of figuring out function equations
D2L->Content->Instructional Strategies for Teaching Algebra in Elementary School
Assignment 6: Go onto Wisweb, and open the Spotting Numbers Problems applet (video of navigating to the specific applet).  Find the equations for each of these patterns:
level 1: V numbers, box numbers, tower numbers, L numbers 1, L numbers 2
level 2: flip numbers
level 3: tile numbers 3
Put your answers, clearly labelled, in a Microsoft Word document, and put it in the dropbox. Due June 2

Explaining why your equation makes sense:
I expect that after the practice you had for the last assignment, that you are pretty good at finding equation forms of functions.The primary goal for this topic is for you to recognize the properties of a deductive explanation and to know how to write good deductive explanations.
Videos: 
157. Explaining a function rule with pattern blocks (the pattern blocks applet)
158. Explaining a function rule with a dot pattern.
159. Explaining a function rule with a rate.
Reading: Examples of explaining the equation for several patterns
The article "Instructional Strategies for Teaching Algebra in Elementary School" which you read for the last topic also has useful examples for this topic.
Assignment 7: Find the equation form of the function for each of these examples, and explain deductively why that function rule makes sense using the context of the problem.  Hand-write your answers so you can include labelled diagrams, scan it in, and insert the scanned image into a Microsoft Word document, which you will upload to the D2L dropbox. Due June 2