Students may well question the importance of 2-variable equations when the function rule is presented as an abstraction, without context, from which solutions are deduced using only math rules. Leitzel of Ohio State University, in The Ideas of Algebra, NCTM, 1988 Yearbook “Establishing Fundamental Concepts through Numerical Problem Solving,” F. For the perimeter expression, students may offerĢ × īesides many other acceptable versions of varying formality and abstractness. Student responses will lead to the observation that the rule or expression for perimeter can involve different operations and different organizing and ordering symbols, such as parentheses. Now enrich the model as follows, having students work in groups to make their own pictorial models and symbolic substitutions: All choices are valid a buzz or other sound, a color or hand signal could serve as well, provided we agreed what the symbol stood for-a whole class of number possibilities. Stress that all these responses are algebraic expressions, whether they include a word, sign, letter, and that the part that stands for the changeable, or varying, amount is a variable. Accept all equivalent answers, such as:Īs well as ideas for symbols for the unknown width, such as ☐, X, w, etc. Ask for ideas on replacing the question marks with words. In the last row point out that the designer may not know what width to choose next, or may put her work aside, but that the rule remains the same. In the third row have students provide the missing values, as well as the rule by which they did so:
#LOMS MATH 6TH GRADE PLUS#
Ask: “What is the same and what different between these two rows?” (Width changes or varies length is always the width plus an unchanging or constant amount, 3). Have the class fill in the question marks for the sketches in the first two rows. “The length is always 3 inches longer than the width.” Present this table:
Say that a designer decides to keep a rule for each rectangular cut-out that she makes:
Geometry helps students visualize the role that a variable expression can play.
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