Student Exploration Sheet: Growing Plants



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: |Get the Gizmo ready: | |

| |The first expression you will see is 3 + x. | |

|Word Phrases |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: |Get the Gizmo ready: | |

| |Click NEW until the Gizmo gives you an algebraic expression that uses addition or | |

|Equivalent Expressions |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?

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2. Form a word phrase that means the same as the given expression. What phrase did you make? Check to confirm gizmo is correct.

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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.

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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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