Algebra Tech Tool: Illuminations-Algebra Tiles

Algebra tiles are not a new technology to classrooms by any means, however it is not infrequent to find that tiles are missing or damaged. This tech tool can replace traditional algebra tiles in the classroom for activities related to substituting, solving, factoring and expanding algebraic expressions in the classroom. This concept is essential to progressing in mathematics and is difficult to fully and adequately expose students to in a PBL or PrBL classroom. This is a skill that requires a lot of procedural practice, which this tool provides.

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Overview

Name of Tech Tool: Illuminations - Algebra Tiles

Brief Description of Tech Tool: Four different exercises can be practiced with this technology: solving algebraic expressions, substitution, multiplication of algebraic expressions, and factoring. Manipulation of algebraic expressions are reinforced and practiced with this activity with the use of algebra tiles. This activity helps make these abstract concepts more concrete.

Link to Tech Tool or Tool homepage: http://illuminations.nctm.org/ActivityDetail.aspx?ID=216

Evaluation

Description of Learning Activity

Students have the ability to practice their algebraic skills in four areas of equations in algebra: solving, substituting, expanding and factoring. Students use manipulatives to “write” the expressions that they are given and are provided with a variety of tools to manipulate these expressions to either solve, substitute, expand or factor. This is an online version of the familiar algebra tiles that many teachers already use in their classroom, however this goes a step further by alerting students if they are or are not correct, either in their initial set-up or in their figuring on the problems.

1. Learning Activity Types

Students are able to not only practice solving, substituting, expanding and factoring algebraic equations, but they are able to do so visually, providing them with multiple representations of algebra and a more concrete understanding of why X’s and 1’s can’t be combine with one another. Teachers can use this tool with students to explore the four ideas in a conceptual manner to solidify these ideas with strong learners, and to give an alternative approach to these ideas for struggling with the concept.

2. What mathematics is being learned?

Teachers can very easily use this tool to help students represent, understand and interpret the structure of expressions. All four components of this tool have students identifying terms, factors and coefficients. Additionally, students are also rewriting equivalent expressions in various representations through the expand and factor categories.

NCTM Standards

NCTM-Alg-symbol Represent and analyze mathematical situations and structures using algebraic symbols

Proficiency Strands

• PS-conceptual understanding
• In “Adding it Up”, a key component of conceptual understanding is being able to represent mathematical situations in different ways. With this tool, students are learning how to look at a numerical expression and represent it in a visual/graphic form. This enables students to manipulate the expression and gain a deeper understanding of key ideas, such as what equality truly means in that they must continually balance their equations.
• PS-procedural fluency
• Students are also working on their basic math with arithmetic and understanding the inverse operations. Students are expanding this knowledge into a variable domain and experimenting with how those operations work with variables. In addition to practicing their arithmetic fluency on these expressions, students are also practicing their substituting and solving skills.

3. How is the mathematics represented?

This tool is a virtual manipulative that helps students to tinker with various algebraic expressions. Students are working on solving, substituting, expanding or factoring these expressions while using a technology version of algebra tiles. Students are able to check their work instantaneously with this method, as opposed to using traditional algebra tiles, which provide no feedback. This tool then, helps students and teachers alike to identify where a student is struggling: with the set up, or with the solution of a problem. It also permits them to see how well a student understands the concept conceptually, as the tool provides a secondary means of representing algebraic expressions, in addition to student’s already understood written-out way.

With this tool, students are also able to see the differences in components of algebraic expressions (terms, coefficients, etc), which can help them to gain a better understanding and appreciation of what terms can be combined with others, in that they are able to visualize the like expressions. However, students may use this tool without considering the written mathematical expression, and may think of this more visually (one red cancels out one yellow), instead of a negative number and a positive number of the same value equal zero. This is an aspect that teachers should be wary of when using this tool in the classroom.

4. What role does technology play?

• Computing & Automating -
• Representing Ideas & Thinking - This ‍tool is a nice way for teachers to let their students explore multiple representations of algebraic expressions‍, while providing them with checkpoints and immediate feedback that may not be available to students who are using a more traditional algebra tile manipulative.

• Accessing Information -
• Communicating & Collaborating -
• Capturing & Creating -

While the tool does not provide suggestions via feedback, it does indicate clearly A) that you have made a mistake (ding!) and B) where you made the mistake (turns the box orange). With these features (and the sound on, of course) teachers then can quickly scan the room to see which students are struggling on which types of problems to better address problems as they arise.

5. How does the technology fit or interact with the social context of learning?

This tool is best used as an individual tool, in my opinion, as it is practicing procedures. However, a student could benefit from having an elbow partner to work with by bouncing questions off of one another or checking one another's work, before soliciting a teacher for support. In this way, students would be practicing explaining procedures to one another, strengthening their conceptual knowledge on the subject.

4. What do teachers and learners need to know?

Teachers and learners will benefit from reading through the instructions on how to use the applet properly, as it is not necessarily intuitive from the get-go. Users do not need extensive computer knowledge, just familiarity with the applet itself.

How this Supports & Supplements PBL/PrBL

This tool is a great supplement to a PBL/PrBL classroom as it provides a means of practicing algebraic symbol manipulation conceptually and procedurally. Symbol manipulation and being able to work with equations of one variable are essential to success in later mathematics, so it is crucial to have a solid foundation. This applet helps provide additional support and practice that may be necessary for students to have, if not otherwise addressed in your classroom.