**Thinking Algebraically**

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The 3 Aspects of Algebraic Reasoning:

**Chapter 16**

**By: Lindsey Sokana**

Algebra

Algebra is more than solving for x; it is a study of patterns, functions, and relationships. Algebra allows students to generalize from arithmetic to discern relationships, to make predictions from observed patterns, and to develop a powerful problem solving process. In short, algebra is a way for students to "recognize order and organize their world" (National Council of Teachers of Mathematics, 2000, p.91).

Main Ideas:

The value of patterns and patterning activities for young children.

Activities to introduce the concept of variable.

Importance of equality in equations.

Concept of functions in developing algebraic reasoning

Patterns, Equations and Variables, Functions

Equations and Variables

Equations: An important aspect about equations is that it shows the equality of two quantities in a relationship.

Variables: There are many different uses of variables. It is important to provide students with enough experience in working with variables so students clearly understand the role of variables in representing numbers.

http://nlvm.usu.edu/en/nav/frames_asid_324_g_4_t_2.html?open=instructions&from=grade_g_4.html

Patterns

Patterns are a repeated sequence of objects, actions, sounds or symbols. Starting simple, children recognize, represent, extend, and create patterns with different arrangements of elements.

Functions

A function is the pairing of members of two sets so that given the value of a member of one set; the related member of the second set can be predicted or determined.

The role of a function is to reveal the general relationship or to produce a result based on the general relationship.

Check this out!

Let's Try It!

http://illuminations.nctm.org/Activity.aspx?id=3482

Algebra Song- "Repeat It"

Hands-On Equations

x – 3 = 1 = ________ check: _____

2x = x + 5 = ________ check: _____

x + 6 = 2x – 3 = ________ check: _____

http://nlvm.usu.edu/en/nav/frames_asid_191_g_4_t_1.html?from=grade_g_4.html

Research Study

"Developing Algebraic Reasoning in the Elementary School"

Elementary school students can learn to adapt their thinking about arithmetic so that it is more algebraic in nature.

They can learn that the equal sign represents a relation, not a sign to carry out a calculation.

They can learn to generalize and to express their generalizations accurately using natural language and symbols.

All students benefit by engaging in the kinds of interactions that are required to make generalizations explicit, represent them accurately with natural language and symbols, and demonstrate that they are valid for all numbers.

Learning to use precise language and communicate about mathematical ideas addresses not only an important goal of the mathematics curriculum, but also important issues of equity.

The best students have always figured out how to derive generalizations and thereby make mathematics easier to learn and apply.

In My Classroom!

Beacon Tree Elementary

Mrs. Buczak

5th Grade Classroom

We have just started a unit on graphing ordered pairs. This is a form of functions. We have gone over the basics of graphing and are now ready to start graphing. I have also spoken with my teacher about what is to come next, and in January we will start by interpreting numerical expressions like: 5 x (5+2)=. We will then discuss order of operations and my favorite PEMDAS.

Resources:

Carpenter, T. (2009). Developing algebraic reasoning in the elementary school. Retrieved from http://www.wcer.wisc.edu/news/coverStories/developing_algebraic.php

Kennedy; Tipps (2013-02-01). Guiding Children's Learning of Mathematics (Page 384). Wadsworth Publishing. Kindle Edition.

Hands on equations: Student worksheet. (n.d.). Retrieved from http://fcit.usf.edu/fcat8m/resource/activity/handsos.pdf

http://illuminations.nctm.org/Default.aspx

http://nlvm.usu.edu/en/nav/frames_asid_324_g_4_t_2.html?open=instructions&from=grade_g_4.html

Legos!

Lindsey, Julie, and Chris are building a model out of Legos. The top level is a 1 by 2 rectangle. The level directly underneath is a 2 by 3 rectangle. The level underneath is a 3 by 4 rectangle. How many Legos will they need if their building is to be 12 levels high?

What's the rule?

Ann made the pattern of numbers.

18, 14, 10, 6

What is the rule she used? Will 2 be apart of the pattern? Why or why not?

Using the calendar, add any three dates that appear next to each other (consecutively). Can you find the pattern?

iTunes Needs Help!

iTunes wants to increase the sale of iBooks in. They decide to offer an incentive by reducing the price of iBooks by $1 for each additional iBook purchased. What advice would you give them about this plan?

It's Your Turn

Create a pattern, then switch with a partner and solve their pattern.

Let's Read and Learn about Algebra!