Equivalent Expressions
In this activity you will investigate algebraic expressions that are equivalent.
Equivalent expressions look different but always have the same value.
EXPRESSIONS AND ALGEBARS
Algebars are bars that
r
epresent algebraic
quantities. Red bars
•epresent variables;
green bars represent
expressions.
1. Open Equivalent Expressions.gsp and press the Show Variables button. Two red
algebars appear representing the variables a and b.
2. Press the Show Algebars 1 button. Two green algebars appear, labeled with their
algebraic expressions: a+band b+a.
fo a+b
t<° b+a
: Dars are always
length, they ent
equivalent sions.
Try many • of the
variables s you
decide that :
eoressions are =
ent.
Q1 Predict what will happen if you change a and b by dragging the tips of the red
algebars. Will the green algebars remain equal in length? Drag a and b to find
out. Were you right? Are the two algebraic expressions equivalent? If so, write
the result as an equation.
3. Press the Show Algebars 2 button. Two more green algebars appear, representing
two different algebraic expressions.
re indicator lines
ate the values
; -: o.
Q2 Drag a and b again. Are the new algebars always equal in length? Are there any
positions for a and b that make these bars equal? Describe them. Are the two
algebraic expressions equivalent?
4. Press the Show Algebars 3 button. Two more green algebars appear, representing
two different algebraic expressions.
Q3 Drag a and b again. Are the new algebars always equal in length? Are the two
algebraic expressions equivalent? If so, write your result as an equation.
5. Press the ShowAigebars 4 button. Two more green algebars appear without
their labels.
Q4 Drag a and b again. Are these bars always equal in length? If not, when are they
equal? Do you think the algebraic expressions for these two bars are equivalent?
Q5 Press the Show Expressions 4 button to see the labels for the last two bars. On
your paper summarize your conclusions by filling in the blanks in a sentence
like this:____________ = _____________ when ____________ .
ng Algebra 1 with The Geometer's Sketchpad
: Key Curriculum Press
3: Algebraic Expressions
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