Integer Algebra Word Problem Game

Integer Algebra Word Problem Quiz/Game
This game focuses on solving word problems involving Integer properties (consecutive, odd/even, sum/difference, and multiples). Scroll down the page for a more detailed explanation.

 

 

How to Play the Integer Algebra Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Integer Algebra Word Problems
Integer word problems usually describe a relationship between unknown numbers. The goal is to translate the English sentences into a mathematical equation that can be solved.

The 4-Step Framework

1. Identify the Unknowns
   Decide what you are looking for and assign a variable (usually x). If there are multiple numbers, define them in relation to x.
   Consecutive Integers: x, x+1, x+2…
   Consecutive Even/Odd Integers: x, x+2, x+4… (because they skip a number)
   
   
2. Translate to an Equation
   Look for “keywords” that signal operations. The word “is” or “results in” almost always means the equals sign (=).
   Addition (+): Sum, increased by, more than
   Subtraction (-): Difference, decreased by, less than
   Multiplication (×): Product, times, twice (2x), triple (3x)
   Division (÷): Quotient, half, divided by
   
   
3. Solve the Equation
   Combine like terms and isolate the variable.
   Example: 3x + 3 = 45
   Subtract 3: 3x = 42
   Divide by 3: x = 14
   
   
4. Answer the Specific Question
   Always check what the problem actually asked for. Did it ask for the smallest number (x), the largest (x+2), or the sum?
   Common Problem Types
   Type A: Consecutive Integer Sums
   “The sum of three consecutive integers is 45."
   Setup: x + (x+1) + (x+2) = 45
   Simplify: 3x + 3 = 45
   Solve: x = 14. The integers are 14, 15, 16.
   
   Type B: Comparison Problems
   “One number is 5 more than another. Their sum is 21."
   Setup: Small number: x
   Large number: x + 5
   Equation: x + (x + 5) = 21
   Solve: 2x = 16 → x = 8. (Numbers are 8 and 13).
   
   Type C: Operational Logic
   “Double a number increased by 7 is 31."
   Equation: 2x + 7 = 31
   Solve: 2x = 24 → x = 12.
    
   

Tips

1. “Less Than” Trap: “5 less than a number” is written as x - 5, NOT 5 - x.
   
2. Even/Odd Rule: Whether the problem asks for consecutive even or consecutive odd integers, the gap is always 2 (x, x+2, x+4).
   
3. Check your work: Plug your answer back into the original word problem to see if the logic holds up.
    
   

This video gives a clear, step-by-step approach to explain how to solve integer algebra word problems.

• Show Video

 

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