Unit 4: Decimals, Percents and algebraic reasoning.

Section 13: Algebraic reasoning: Patterns and Functions



Patterns and functions:
Representing patterns and functions with pictures, tables and graphs
Video: Representing patterns and functions
Reading: A written out summary of these examples
 D2L->Content->What is Algebra in Elementary School?
Assignment: Do problems 1 and 2 in this growthPatternsTiles notebook.

Asking good questions about patterns and functions:
Video: 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: Answer these questions from page 4 of the lesson plan.
Equations for growing pattern sorts of functions.
Videos: 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: 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
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.
Explaining a function rule with pattern blocks (the pattern blocks applet)
Explaining a function rule with a dot pattern.
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: 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.