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Fraction Constructed Response

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Fraction Constructed Response Answer Key

Dario is making a birdhouse from a board that is [math]3/4[/math] of a meter long. He cuts [math]1/2[/math] meter off the board and uses the remaining piece for the base of the birdhouse. Dario subtracts [math]1/2[/math] from [math]3/4[/math] to find the length of the base. Dario said [math]3/4 - 1/2 = 2/4[/math] and plotted [math]2/4[/math] on this number line.

Number Lines 0-2 8

[math]*[/math] Explain why Dario's answer is not reasonable.
[math]*[/math] Find the total length of the birdhouse base, in meters.
[math]*[/math] Explain how to use the number line to show your answer is correct.

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  • Student should provide a valid reason why Dario's answer is not reasonable, for example: Since Dario cut [math]1/2[/math] meter off of the board that measured less than 1 meter, his final answer should be less than [math]1/2[/math], but [math]2/4 = 1/2[/math].
    Student should correctly calculate the length as [math]3/4 - 1/2 = 3/4 - 2/4 = 1/4[/math] meter and explain how to plot on number line, for example: I start at [math]3/4[/math] and move to the left 2 [math]1/4[/math]s to subtract [math]3/4 - 2/4[/math] and plot the point at [math]1/4[/math].
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