SPAWN The Mother Goose Polynomial
First we read the nursery rhyme Three little kittens they lost their mittens, And they began to cry, Oh, mother dear, we sadly fear That we have lost our mittens. What! lost your mittens, you naughty kittens! Then you shall have no pie. Mee-ow, mee-ow, mee-ow. No, you shall have no pie.
The three little kittens they found their mittens, And they began to cry, Oh, mother dear, see here, see here, For we have found our mittens. Put on your mittens, you silly kittens, And you shall have some pie. Purr-r, purr-r, purr-r, Oh, let us have some pie.
The three little kittens put on their mittens, And soon ate up the pie; Oh, mother dear, we greatly fear That we have soiled our mittens. What! Soiled your mittens, you naughty kittens! Then they began to sigh, Mee-ow, mee-ow, mee-ow, They began to sigh.
The three little kittens they washed their mittens, And hung them out to dry; Oh! mother dear, do you not hear That we have washed our mittens? What! washed your mittens, then you’re good kittens, But I smell a rat close by, Mee-ow, mee-ow, mee-ow, We smell a rat close by.
S-Special Powers • The students can change an aspect of the text. • The students decided to change up the nursery rhyme. They want to decide how many pieces of pie each kitten gets depending on how many mittens they have.
P-Problem Solving • I then ask the students to find a function for the data they came up with. • First they must write their data in a table.
They then use finite differences and their graphing calculators. • Using finite differences they discover the polynomial is quadratic. • Using list plot and quadratic regression in their graphing calculator they get the function.
A-Alternative Viewpoints • Students are then asked to make up their own story with a data table, use finite differences and their graphing calculators to find a function that models their story.
W-What If? • Altering it a bit, now I ask the students to change the nursery rhyme around. This time x = the number of rats they catch and f(x) = the number of new mittens their mother dear will buy them. • I give them the data table this time:
Remember x is the dependent variable and f(x) = y = the dependent variable.
N-Next • I ask students to predict what kind of function they will have to write next? Explain why. • The prediction: • We will have to write cubic functions next, because we always learn basic examples in class and then expand our knowledge on our own.
Works Cited • Baring-Gould, W.S., & Baring-Gould, C. (1962). The annotated mother goose nursery rhymes old and new, arranged and explained. New York: Clarkson N. Potter, Inc. • Fisher, D., Brozo, W.G., Frey, N., & Ivey, G. (2011). Instructional routines to develop content literacy. Boston: Pearson.