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# PARCC Math Practice

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## PARCC Math Practice Answer Key

Owen practices basketball. The time Owen spends on each skill is shown.

Dribbling: $1/3$ hour
Passing: $1/6$ hour

His coach asks Owen to compare the length of time he spends on each drill to $1/4$ hour.
1.
Owen claims he practiced dribbling for less than $1/4$ hour because the 3 in the denominator is less than 4. He also explained that he practiced passing for more than $1/4$ hour because 6 in the denominator is more than 4.

Compare $1/4$ hour to the time spent practicing each skill using the $>, <, or =$ symbol. Then explain whether Owen's reasoning is correct.

• Student should provide inequalities (or equivalent inequalities)
$1/3 >1/4$ and $1/6 < 1/4$
Student should explain that Owen is not correct and provide a valid explanation as to why he is incorrect. For example, Owen should have found common denominators before comparing
2.
Owen throws the basketball into the hoop from the distances shown.
Distance for first throw: $19 3/4$feet
Distance for second throw: $20 1/4$ feet
Owen claims that he threw the ball $1 2/4$ feet farther on his second throw than his first throw because the difference between the whole numbers is 1 and the difference between the numerators is 2.

$*$Explain why Owen's reasoning is incorrect.
$*$What is the correct distance, in feet, between the distance of Owen's first throw and the distance of Owen's second throw?

• Student should correctly calculate the difference of $2/4$ foot or equivalent fraction.
Student should reason correctly why Owen's calculation was incorrect. For example: Owen reversed the fractions and subtracted $19 1/4$ from $20 3/4$. Since addition is the opposite of subtraction, Owen could have added on by $1/4$ from $19 3/4$ to get $1/4 + 1/4 = 2/4$ foot