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Game Studio: Balance Checks worksheet preview

Worksheet

Game Studio: Balance Checks

Check equations and inequalities by substitution while testing video game scores, level limits, and reward settings.

Grade 6MathInteractive · Printable

Aligned to6.EE.B.5

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What’s included

  • Single worksheet
  • Auto-graded online
  • 1 Common Core standard
  • Printable answer key
  • 14 questions
  • Classroom-ready

Details

Format
Interactive · Printable
Grade
Grade 6
Subject
Math
Question types
Fill in the blank, Multiple choice, Circle the answer, Sorting, Short answer

About this worksheet

What students practice

  • Students substitute given values to determine whether equations and inequalities are true.
  • Students identify values from a specified set that satisfy a game design rule.
  • Students explain why a boundary value satisfies an equation but not a strict inequality.

How to use

Have students substitute each candidate value before making a decision. Discuss how equality and strict inequality treat boundary values differently.

Curriculum

Common Core standard covered

6.EE.B.5

Understand solving an equation or inequality as finding values that make it true, and check values by substituting.

Preview

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Name Date

Game Studio: Balance Checks

Substitute test values to check level rules and scoring targets.

Test the Settings

A game studio checks proposed settings before releasing a level. Substitute each value into the stated rule. A solution makes the rule true.

1.
A level's target score follows x + 18 = 25. Test x = 7.

After substitution, the left side equals  . The right side equals  .

2.
Each token is worth x points. A tester collects 6 tokens for exactly 42 points, so 6x = 42. Which substitution makes the equation true?
  • A. With x = 8, 6 × 8 = 42.
  • B. With x = 7, 6 × 7 = 42.
  • C. With x = 6, 6 × 6 = 42.
  • D. With x = 36, 6 × 36 = 42.
3.
A bonus remains active when x + 9 < 16. Select every listed value of x that makes this inequality true.

5678

4.
A reward rule is x ÷ 4 ≥ 3. Sort each proposed value of x by whether it makes the rule true.
x = 8x = 12x = 14x = 16
Makes the rule trueMakes the rule false
5.
An animation lasts x seconds, followed by a 1.25-second pause. Test x = 1.5, 2, and 2.5 in x + 1.25 = 3.75.

Which tested value makes the equation true? x =  

Decide Which Tests Pass

Use each level's equation or inequality to check the proposed settings. Select all values only when the question asks for every value.

6.
A level starts with 11 points and awards 4 points per gem. To meet its score target, the rule is 4x + 11 ≥ 35, where x is the number of gems. A tester collects 6 gems. Which check is correct?
  • A. The test fails because 4 × 6 + 11 = 21, and 21 < 35.
  • B. The test passes because 4 × 6 + 11 = 39, and 39 > 35.
  • C. The test fails because 4 × 6 + 11 = 35, and 35 = 35.
  • D. The test passes because 4 × 6 + 11 = 35, and 35 ≥ 35.
7.
A challenge awards a badge only if its timer setting satisfies x + 2.5 < 9. Select every proposed setting that qualifies.
Proposed Timer Settings
Settingx (seconds)
A5.5
B6.5
C7
D6

Setting ASetting BSetting CSetting D

8.
A power-up uses 3/4 of an energy bar each second. Its duration x must satisfy (3/4) × x ≤ 3. Test the proposed durations 2, 3, 4, and 5 seconds.

How many of the four proposed durations make the inequality true?   durations

9.
A level designer needs exactly 32 points from a starting bonus of 5 points and x gates worth 3 points each. The rule is 3x + 5 = 32. Which proposed number of gates passes the check?
  • A. A setting of x = 9 gates passes the check.
  • B. A setting of x = 7 gates passes the check.
  • C. A setting of x = 11 gates passes the check.
  • D. A setting of x = 27 gates passes the check.
10.
A checkpoint must satisfy both rules: 2x ≥ 10 and x + 4 < 12. Select every listed value of x that makes both rules true.

4578

Audit the Balance Report

Check the report by substituting values into the original rules. Use calculations, not just the size of a proposed value.

11.
Jalen claims that x = 8 satisfies 5x = 45 because 8 is less than 45. Which response correctly checks his claim?
  • A. The claim is true because 5 × 8 = 40, and 40 < 45.
  • B. The claim is true because 5 + 8 = 13, and 13 < 45.
  • C. The claim is false because 5 × 8 = 40, and 40 ≠ 45.
  • D. The claim is false because 45 − 8 = 37, and 37 ≠ 5.
12.
A level awards a speed badge when 1.5x + 2 ≤ 11. Complete the check for x = 6.

Substituting gives 1.5 × 6 + 2 =  . Write true or false: x = 6 makes the badge rule  .

13.
Two proposed level rules use the same expression: Rule A is 2x + 1 = 13. Rule B is 2x + 1 > 13. Sort each test value by which rule it satisfies.
x = 5x = 6x = 6.5x = 8
Rule A onlyRule B onlyNeither rule
14.
Mina tests x = 4 in the score equation 3x + 2 = 14 and the bonus rule 3x + 2 > 14. She says, “The equation is true, so the bonus rule must be true too.” Explain her mistake. Use substitution to check both statements.

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