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The Spache Readability Formula is designed to categorize reading materials for grades 1 through 3. For a passage of text, the variables are S, the number of sentences, W, the number of words, and U, the number of unfamiliar words (words not on a specific list). The formula (as revised) for the grade level is
Grade level = 0.121(w/s)+ 0.082U + 0.659
In this exercise we consider passages having 270 words and using 8 unfamiliar words.
(b) What is the maximum possible number of sentences?

Sep 24th, 2015

Thank you for the opportunity to help you with your question!

First, let G represent Grade level and calculate G: G = 0.121 * (270/S) + 0.082 *8 + 0.659. Simplifying, we get

G = 8.47 / S + 0.656 + 0.659 = 8.47 / S + 1.315, so

G = 8.47 / S + 1.315. Now rewrite the equation so that S is by itself.

First, subtract 1.315 from both sides of the equation, gettinng G - 1.315 = 8.47 /S.

Then, multiply both sides of the last equation by S, getting S(G - 1.315) = 8.47.

To get S by itself, divide both sides of the last equation by (G - 1.315) to get S = 8.47 / (G - 1.315) which is valie provide G isn't equal to 1.315 (which it can't be since G can only be 1, 2 or 3).

Now consider the equation S = 8.47 / (G - 1.315). If G were 1, then S would be negative, which makes no sense.

So, G could be 2 or 3. Try both.

S(2) = 8.47/(2-1.315) = 8.47 / (0.685)

S(3) = 8.47/(3-1.315) = 8.47 / (1.685)

which is bigger, S(2) or S(3)?

S(2) ~  12.37 ~ 12

S(3) ~ 5.02 ~ 5

So, the maximum number of sentences would be 12 (for grade 2)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 25th, 2015

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Sep 24th, 2015
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Sep 24th, 2015
Oct 19th, 2017
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