Equivalent Chance Practice Worksheet
Mathematics Practice • Grade 6/7
Equivalent Probability Values
TEKS 6.4G / 6.5C
Name:
Date:
Period:
Score:
Directions: Read each situation carefully. Identify the value that is equivalent to the stated chance or probability. Show your division, place-value reasoning, or equivalent fraction work in each designated workspace.
12
There is a 3 in 8 chance of a player winning a game. Which value is equivalent to the chance of the player winning a game?
F \(\frac{300}{375}\)
G \(\frac{375}{10}\)
H 3.75
J 0.375
Show Work / Reasoning
13
There is a 5 in 8 chance of drawing a winning ticket at a carnival. Which value is equivalent to the chance of drawing a winning ticket?
A \(\frac{500}{625}\)
B \(\frac{625}{10}\)
C 6.25
D 0.625
Show Work / Reasoning
14
There is a 7 in 8 chance of a meteorologist accurately forecasting rain. Which value is equivalent to the chance of accurately forecasting rain?
F \(\frac{700}{875}\)
G \(\frac{875}{10}\)
H 8.75
J 0.875
Show Work / Reasoning
15
There is a 1 in 16 chance of spinning the grand prize on a reward wheel. Which value is equivalent to the chance of spinning the grand prize?
A \(\frac{100}{625}\)
B \(\frac{625}{100}\)
C 0.625
D 0.0625
Show Work / Reasoning
Remember: "a in b" represents the fraction \(\frac{a}{b}\). Use long division or powers of 10.
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Equivalent Chance Teacher Guide
Teacher Guide & Assessment Analysis
Probability Equivalents Item Specifications
TEKS 6.4G / 6.5C CCSS 7.SP.C.5
Original Test Item 1 in 8 base
"There is a 1 in 8 chance of a player winning a game. Which value is equivalent to the chance of the player winning a game?"
F: \(\frac{100}{125}\) (0.8)
G: \(\frac{125}{10}\) (12.5)
H: 1.25
J: 0.125 ✓
New Parallel Item (Item 12) 3 in 8 base
"There is a 3 in 8 chance of a player winning a game. Which value is equivalent to the chance of the player winning a game?"
F: \(\frac{300}{375}\) (0.8)
G: \(\frac{375}{10}\) (37.5)
H: 3.75
J: 0.375 ✓
Detailed Distractor Rigor & Misconception Analysis (Item 12) Base Fraction: \(\frac{3}{8}\)
| Choice | Value | Targeted Student Misconception | Intervention Prompt |
|---|
| F | \(\frac{300}{375}\) | Ratio Inversion / Simplification Error: Student builds a fraction with the hundredths base in numerator (\(\frac{300}{375} = \frac{4}{5} = 0.8\)) rather than \(\frac{375}{1000}\). | "Does \(\frac{300}{375}\) simplify to \(\frac{3}{8}\) or \(\frac{4}{5}\)?" |
| G | \(\frac{375}{10}\) | Denominator Place Value Error: Student recognizes the digits \(375\) but assumes tenths place instead of thousandths (\(\frac{375}{10} = 37.5\)). | "Three decimal places represents tenths, hundredths, or thousandths?" |
| H | 3.75 | Decimal Shift by Power of 10: Student converts \(\frac{3}{8}\) using \(3.75\) (off by one decimal place; common when dividing without aligning place values). | "Is a chance of 3 out of 8 greater than 1 whole or less than 1 whole?" |
| J | 0.375 | Correct Answer: \(\frac{3}{8} = 3 \div 8 = 0.375\), or scaling: \(\frac{3 \times 125}{8 \times 125} = \frac{375}{1000} = 0.375 = 37.5\%\). | Benchmark Mastery ✓ |
Complete Answer Key & Step-by-Step Solutions All Items Parallel in Rigor
Item 12 Correct: J
Probability: 3 in 8 \(= \frac{3}{8}\)
Scaling: \(\frac{3 \times 125}{8 \times 125} = \frac{375}{1000} = \mathbf{0.375}\)
Division: \(3 \div 8 = 0.375\)
Item 13 Correct: D
Probability: 5 in 8 \(= \frac{5}{8}\)
Scaling: \(\frac{5 \times 125}{8 \times 125} = \frac{625}{1000} = \mathbf{0.625}\)
Distractors: A (\(\frac{500}{625}=0.8\)), B (\(62.5\)), C (\(6.25\))
Item 14 Correct: J
Probability: 7 in 8 \(= \frac{7}{8}\)
Scaling: \(\frac{7 \times 125}{8 \times 125} = \frac{875}{1000} = \mathbf{0.875}\)
Distractors: F (\(\frac{700}{875}=0.8\)), G (\(87.5\)), H (\(8.75\))
Item 15 Correct: D
Probability: 1 in 16 \(= \frac{1}{16}\)
Scaling: \(\frac{1 \times 625}{16 \times 625} = \frac{625}{10000} = \mathbf{0.0625}\)
Distractors: A (\(\frac{100}{625}=0.16\)), B (\(6.25\)), C (\(0.625\))
Instructional Strategy: Benchmark Multiplier Anchor Teach students to anchor all eighths to \(8 \times 125 = 1000\). Rather than long division which often leads to decimal placement mistakes (e.g., choices H and G), students multiply both numerator and denominator by 125. For example: \(3 \times 125 = 375 \rightarrow \frac{375}{1000} = 0.375\). This reinforces decimal place-value reasoning and immediately eliminates fractional distractors.
Equivalent Probability Values • Instructional Teacher Guide Page 1 of 1
