Before an important playoff series, Tara and Emek studied a dashboard comparing their basketball team's first and second halves of the season. The team's three-point shooting increased from 32% to 38%, free-throw shooting rose from 75% to 81%, and average points per game climbed from 96 to 105. Tara noted that both shooting percentages had increased by 6 percentage points, but Emek explained that this did not mean their percentage changes were equal. For three-point shooting, the relative increase was 6/32 = 18.75%. For free throws, it was 6/75 = 8%. The scoring average increased by 9 points per game, corresponding to a percentage increase of 9/96 = 9.375%. Comparing the relative changes showed that three-point shooting had improved the most, even though its percentage-point gain matched the free-throw gain. Tara and Emek shared the distinction with the coach. Seeing that the team's largest relative improvement came from three-point shooting, the coach devoted the final practice to strengthening the plays that created those opportunities.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
For relative percentage increase, divide the amount of increase by the original value.
The team's three-point shooting increased from 32% to 38%. Which calculation correctly gives the relative percentage increase?
6/38 x 100% = about 15.79%38/32 x 100% = 118.75%6/32 x 100% = 18.75%38 - 32 = 6%
Correct. The 6 percentage-point increase is 18.75% of the original 32% rate.
Use the original shooting percentage, 32%, as the denominator when finding the relative increase.
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Hint
Find 9.375% of 105, add it to 105, and round the result to the nearest whole number.
Suppose the team's average points per game increases by the same 9.375% again, starting from the second-half average of 105 points per game. Rounding to the nearest whole point, what would the new average be?
Correct. Another 9.375% increase would raise the average to about 115 points per game.
Apply the 9.375% increase to the new starting value of 105, not to the original value of 96.
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Hint
Compare 6/32 with 6/75.
Three-point shooting and free-throw shooting each increased by 6 percentage points. Why was the relative improvement larger for three-point shooting?
Because 38% is less than 81%Because the same 6-point increase is a larger fraction of the original 32% than of the original 75%Because every increase in three-point shooting counts three times as muchBecause percentage-point increases and relative percentage increases are always equal
Correct. The same increase represents a larger proportion of the smaller original value.
Relative change depends on the increase compared with the original value, not just on the number of percentage points gained.
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Bir Sezondaki Gelişimi Ölçmek
TR
ARC_G12_FRD_02_STORY_01
Bir Sezondaki Gelişimi Ölçmek
Measuring a Season's Improvement
EN
ARC_G12_FRD_02_STORY_01
Measuring a Season's Improvement