Name __________________________
Date___________________________
Period___________________________
Student Exploration: Algebraic Expressions
Vocabulary: algebraic, object, operation, equivalent, exponent, "certain number", variable,
expression, simplify, term, order of operation, multiply, addition, subtract from, times, a number,
divided by, minus, commutative, associative
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
1. Fill in the blanks with the correct symbol or word phrase.
Minus ________________
Seven _____________
Divided by ____________
A number ___________
Times ________________
+ __________________
Subtracted from ________
Divided by ___________
z ___________________
more than ___________
2. You read an algebraic expression from ___________ to _____________ in
the same way that you are reading this sentence.
Gizmo Warm-up:
In this Gizmo, you will be asked to translate algebraic expressions into English
phrases, and translate English phrases into algebraic expressions.

At the top of the Gizmo, you will see either an algebraic expression or a
word phrase.

Beneath the expression is a set of tiles. Each tile contains a word, a
number, or an operation.

Your goal is to form a word phrase to match the algebraic expression, or
an algebraic expression to match the word phrase.

To do this, you must select the correct tiles, drag them from the middle bin
to the bottom one, and arrange them in the proper order.
Activity A:
Word Phrases
Get the Gizmo ready:
 The first expression you will see is 3 + x.
 Refresh gizmo until you see this expression.
1. This expression has a number (3), an operation (+), and a variable (x).
If numbers, variables, and operations are all considered to be objects, how many
objects are in this expression? _______________________________________
2. How many tiles will you need to write the word phrase? _________________
3. The first part of the expression 3 + x is the number 3. Which word tile should
be used to represent this number? ____________________________________
4. The second part is an operation. What should be used to represent this
operation?________________________________________________________
5. The third part of the expression is the variable x. A variable is used to
represent an unknown number. Which tile best represents an unknown number?
Your answer is correct if a check mark appears at the bottom of the screen.
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6. What is the word phrase that matches the algebraic expression 3 + x?
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7. Switch the first tile with the third tile. A check mark still indicates that the word
phrase is correct. Why was it possible to switch the tiles in this problem?
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Click NEW. The given phrase in the Gizmo is "a number divided by eight."
1. The first part of this phrase is "a number." What can represent "a number?"
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2. What symbol means "divided by"?
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3. Drag down the tiles until you have made an algebraic expression that matches
the given phrase. What expression did you make?
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Click NEW and on a separate sheet of paper, try _______ more examples. Write
down the algebraic expressions and phrases that the Gizmo gives you, and write
down your answer for each one.
Activity B:
Equivalent
Expressions
Get the Gizmo ready:
 Click NEW until the Gizmo gives you an algebraic
expression that uses addition or multiplication.
Some algebraic expressions are equivalent to more than one word phrase. For
example, the expression n + 7 is equivalent to "a number plus 7" and "7 plus a
number." In this activity, you will explore when this is true.
1. What algebraic expression were you given?
________________________________________________________________
2. Form a word phrase that means the same as the given expression. What
phrase did you make? Check to confirm gizmo is correct.
________________________________________________________________
3. In the Gizmo, move the tiles around and form another word phrase that is
equivalent to the given expression. What phrase did you form? Check to confirm
gizmo is correct.
________________________________________________________________
Click NEW and on a separate sheet of paper, try _______ more examples that
use addition or multiplication. Write down the algebraic expression the Gizmo
gives you, along with a phrase and the alternate phrase for that expression.
Challenge yourself:
If the given expression uses subtraction or division, there is only one equivalent
word phrase. For example, the expression 4 - p is equivalent to "four minus a
number," but not to "a number minus four." Explain why.
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