Instructions
- Find the Hidden Code: Search the grid below to find the 8 algebraic words listed in the word bank. Words can go horizontally (left-to-right) or vertically (top-to-bottom).
- Define the Language: Complete the "Language of Algebra" table. Use the provided example as your guide to define the terms you found and connect them to real life.
- Solve the Mysteries: Apply your new vocabulary to solve the real-world math puzzles in Section 3.
- Take the Balance Challenge: Complete the final puzzle to prove your algebraic balance skills!
Section 1: The Codebreaker Word Search
Find these 8 essential algebraic terms in the grid below:
- VARIABLE • EQUATION • EXPRESSION • COEFFICIENT
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CONSTANT • SOLVE • BALANCE • TERM
V A R I A B L E P Q R S T E X P R E S S I O N Y Z W Q U C O E F F I C I E N T U A B C D E F G H I J K E A K L M N S O L V E O P R T P Q R S T U V W X Y Z M I A B C O N S T A N T K X O D E F G H I J K L M N O N B A L A N C E P Q R S T
Pro-Tip: In algebra, letters aren't just letters—they are placeholders for numbers we don't know yet. Think of algebra as a detective game where you use clues to find the missing identity of the variable!
Section 2: The Language of Algebra
Use your word search terms to complete the table below. The first row has been filled out for you as a model.
| Algebraic Word | Definition (In your own words) | Math Example | Real-World Scenario |
|---|---|---|---|
| Variable (Example) | A letter that stands in for an unknown or changing value. | $x$ or $n$ | Let $h$ = the number of hours you practice guitar. |
| 1. Equation | |||
| 2. Expression | |||
| 3. Coefficient | |||
| 4. Constant | |||
| 5. Solve | |||
Section 3: Translating Real Life into Algebra
Now, let's use these tools to solve real-world problems. Read each scenario, write down the algebraic equation, and solve for the unknown variable.
Scenario 1: The StreamBox Subscription (Easy)
StreamBox video service charges a flat membership fee of $10 per month, plus $2 for every premium movie you rent.
- Write the Equation: Let $m$ be the number of movies rented, and $C$ be the total monthly cost. Equation: $10 + 2m = C$
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Solve It: If Logan's bill last month was $18, how many premium movies ($m$) did he rent?
Show your work here:
Answer: $m$ = __ movies
Scenario 2: Concert Ticket Craze (Medium)
Sarah bought 3 concert tickets online. The ticket website charged a single flat booking fee of $5 for the entire order. Her total bill came to $65.
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Write the Equation: Let $t$ represent the cost of one individual concert ticket.
Equation: _____
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Solve It: Find the cost of a single concert ticket ($t$).
Show your work here:
Answer: $t$ = $__ per ticket
Scenario 3: The Skate Park Showdown (Advanced Challenge)
Two local skate parks have different pricing structures:
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SkateTown: Charges a $15 entry fee, plus $2 per hour of skating.
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Wheelz-R-Us: Charges no entry fee, but costs $5 per hour of skating.
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Write the Equations: Let $h$ represent the number of hours spent skating.
- SkateTown Cost Equation: ___
- Wheelz-R-Us Cost Equation: _____
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Solve It: After how many hours ($h$) will both skate parks cost the exact same amount?
Show your work here:
Answer: $h$ = __ hours
Section 4: The Balance Challenge
In algebra, an equation is like a playground see-saw. Whatever you do to one side, you must do to the other side to keep it perfectly balanced.
If you have the equation:
$$2x + 7 = 15$$
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What is the first mathematical operation you should do to both sides to keep the scale balanced while isolating the variable term $2x$?
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What is the second step you must do to both sides to find the final value of $x$?
Answer Key
Section 1: Word Search Coordinates
- VARIABLE: Row 1, Col 1-8 (Horizontal)
- EQUATION: Col 1, Row 1-9 (Vertical)
- EXPRESSION: Row 2, Col 1-10 (Horizontal)
- COEFFICIENT: Row 3, Col 3-13 (Horizontal)
- SOLVE: Row 5, Col 6-10 (Horizontal)
- CONSTANT: Row 7, Col 5-12 (Horizontal)
- BALANCE: Row 9, Col 2-8 (Horizontal)
- TERM: Col 13, Row 3-6 (Vertical - T-E-R-M)
Section 2: Definitions (Accept equivalent student phrasing)
- Equation: A mathematical statement stating that two expressions are equal (contains an $=$ sign). Example: $2x + 3 = 11$.
- Expression: A mathematical phrase combining numbers, variables, and operations, but no equal sign. Example: $3x + 5$.
- Coefficient: The number multiplied by a variable. Example: In $4x$, the coefficient is $4$.
- Constant: A fixed value/number that does not change. Example: In $3x + 7$, the constant is $7$.
- Solve: To find the numerical value of the variable that makes an equation true. Example: Solving $x + 2 = 5$ gives $x = 3$.
Section 3: Word Problems
- Scenario 1: $10 + 2m = 18 \rightarrow 2m = 8 \rightarrow m = 4$ movies.
- Scenario 2: Equation: $3t + 5 = 65$. Solve: $3t = 60 \rightarrow t = \$20$ per ticket.
- Scenario 3: Equations: SkateTown $= 15 + 2h$; Wheelz-R-Us $= 5h$. Solve by setting them equal: $15 + 2h = 5h \rightarrow 15 = 3h \rightarrow h = 5$ hours.
Section 4: The Balance Challenge
- Subtract $7$ from both sides ($2x = 8$).
- Divide both sides by $2$ ($x = 4$).