A.3.4.2 Orange You Glad We’re Boxing Fruit?

Autor:Katie Akesson

Open the desmos link below to go along with this lesson. I suggest you split your computer screen with the desmos and this GeoGebra. desmos link: https://www.desmos.com/calculator/idcdlmuqic Watch the oranges video below and record the weight for the number of oranges in the box into your desmos table. here is the url in case the video just below won't work: oranges video: https://player.vimeo.com/video/304121358 Desmos directions: 1. Type values in the table to plot points in the plane. Make sure you have the coordinates in the right order, (x, y). 2. Click on the wrench to add labels and change the window settings, especially necessary when the x- and y-axes have different scales. 3. The green line at y = 0.5 can be changed by dragging the points at (-2, 0.5) and (2, 0.5). 4. Adjust the moveable points to fit the line to the data set as closely as possible (make the line go in the same direction as all the points and through the middle of the points).

Desmos directions: 1. Type values in the table to plot points in the plane. Make sure you have the coordinates in the right order, (x, y). 2. Click on the wrench to add labels and change the window settings, especially necessary when the x- and y-axes have different scales. 3. The green line at y = 0.5 can be changed by dragging the points at (-2, 0.5) and (2, 0.5). 4. Adjust the moveable points to fit the line to the data set as closely as possible.

Estimate a value for the slope of the line that you drew. What does the value of the slope represent?

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Estimate the weight of a box containing 11 oranges. Will this estimate be close to the actual value? Explain your reasoning.

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Estimate the weight of a box containing 50 oranges. Will this estimate be close to the actual value? Explain your reasoning.

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Estimate the coordinates for the vertical intercept of the line you drew. What might the y-coordinate for this point represent?

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Which point(s) are best fit by your linear model? How did you decide?

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Which point(s) are fit the least well by your linear model? How did you decide?

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We'll keep this data and scatter plot for a future lesson.

How would the scatter plot and linear model change if the box itself was heavier?

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Can you think of reasons why the real weight of 50 oranges might be different from the answer we get by using an estimate from the linear model?

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Since we measured 10 oranges, how does that affect your confidence in the estimate for 50 oranges?

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How would the scatter plot and linear model change if grapefruits were used instead of oranges?

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A.3.4.2 Orange You Glad We’re Boxing Fruit?

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