Visualizing Algebraic Expressions 1

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At the early stages of learning Algebra, students may get confused looking at algebraic expressions. Students may struggle to internalize the difference between x + y &amp; xy and x^2 &amp; 2x!

A geometric interpretation of algebraic expressions makes it easier for students to get a visual understanding of the difference between various algebraic expressions.

First degree expressions - Lines

An algebraic expression of first degree can be thought of as a line whose length represents the value of the variable.

Second Degree Expressions – Rectangles &amp; Squares
 * 1) &ldquo;x&rdquo; &amp; &ldquo;y&rdquo; can be thought of as lines of length x &amp; y respectively.
 * 2) &ldquo;x + y&rdquo; can be thought of as a line with length x+y.
 * 3) &ldquo;2x&rdquo; can be thought of as a line of length 2x or x+x.
 * 4) &ldquo;2x + 3y&rdquo; can be thought of as a line of length 2x + 3y

An algebraic expression of second degree can be thought of as the area represented by a rectangle (or a square as the case may be)

Understanding Bracket Operations
 * 1) &ldquo; - can be thought of as a square of side x &amp; area equal to
 * 2) &ldquo;xy&rdquo; can be thought of as a rectangle with sides x &amp; y and area xy
 * 3) &ldquo;2yz&rdquo; can be thought of as a rectangle with sides 2y and z (or 2z &amp; y) and area 2yz

Representing algebraic expressions visually also helps in understanding bracketing &amp; unbracketing operations.

It can be seen that two areas x^2 and xy can be seen together as the area of a rectangle with sides x and (x+y). This is the same as x^2 + xy = x(x + y)!

Plotting on Square Dotted Sheets

These ideas will become clearer if students draw lines and rectangles using a Square Dotted sheet. All the dots are plotted so as to form equal squares in both the horizontal &amp; vertical direction. Lines should always be drawn connecting the dots, either in the horizontal or vertical direction. (Annexure 219A gives some examples of these representations)

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