The Glories of a Random Number Generator

I have created four extra sheets about decimals to supplement Pamela’s math book so far. She seems to have a weak grasp of various complexities, but I hope to solidify her understanding through extra practice. Because she is a concrete-sequential learner, she does not mind rows of problems that look similar (unlike my concrete-random son). Yesterday’s spreadsheet in Excel reminded me of a high-tech tip that can make life easier when trying to think of random problems with the same structure on a sheet. When forced to do so, I fall into a rut. Pamela has an eagle eye for patterns, and I have to vary them enough for her not to guess a pattern and miss the actual concept presented. This is why I adore the concept of a random number generator, which I learned about while getting my master’s degree in operations research!

In this case, I needed to select between 1 and 99 coins. Excel has a random number generator that picks numbers between 0 and 1. If you multiply the random number by 99 and round up, you will get a random selection of numbers between 1 and 99. Once I get the formula right, I simply copy it down the column and it will generate different numbers in every cell! Here is the statement in Excel that worked:

=ROUNDUP(RAND()*99,0)

Because I wanted to make sure she had multiple chances to work with 1 to 9 coins, I copied the following formula into several of the cells to force randomly generated, single- digit numbers:

=ROUNDUP(RAND()*9,0)

In the next column, I needed to alternate between pennies and dimes from one problem to another. I set up a logical statement that puts in the word dimes when the random number is less than .5 and pennies for all other numbers. Here is what worked:

=IF(RAND()<0.5,"dimes","pennies")

Here is what these three formulas produced in ten rows of problems:

12 pennies
6 dimes
97 pennies
66 pennies
5 dimes
51 dimes
1 dimes
4 pennies
9 dimes
26 dimes

I just LOVE technology!

Navigating Questions & Answers

I am tailoring Navigating the Social World to guide activities for conversational practice. The focus is on communication and social skills (Section Two), namely basic conversational responses. At home, Pamela is adept at asking and answering questions about her enthusiasms (calendars, The Hoober-Bloob Highway, and Mario and Luigi Superstar Saga). She can ask and answer simple questions already mastered at her present level in personal description stories (see page 14) with people in the family. She needs to work on following up a statement (with either a statement or question).

I want Pamela to leave each session flush with success and joy, so I limit conversations to her interests and sentence structures she can easily do: answer and ask yes-no questions. The first time Pamela and Amy took turns asking each other what states they had visited, "Did you see Alaska?" I noticed that Pamela struggled with following up her answer by asking question. She needed prompting to continue the conversation even though it was a repetition of the same question. Clearly she had difficulties switching roles.

The second time I turned the conversation into a riddle game to simplify the conversation structure. Amy would pick a year, and Pamela would ask questions like "Is it a leap year?" or "Does it start Monday?" until she guessed the year. Then we reversed the tables: Pamela would pick a year and Amy asked her questions. Amy and I both needed a cheat sheet I made in Excel as a crutch. Pamela sees the calendar in her head and needs no crutch. When reading history books, she will often tell us the day of the week an event occurred. Pamela reveled playing a calendar game with another teen, and Amy was amazed at Pamela's savant skill.

The third time we played the riddle game, but focused on the topic of animals. Both Amy and Pamela share an interest in animals. Pamela was highly animated, and her face lit up whenever she or Amy solved the riddle. Clearly, she succeeds at Q/A/Q/A types of conversations in which one person always asks the question and one person always answers it. She has no problem being either the questioner or answerer as long as it is consistent during the conversation. At home, I plan to vary the conversations to get her used to A-Q/A-Q so that the person answering a question continues with a new question.

Nifty Science Project

My neurologically typical--the diagnosis autistic people give people like me--son is in his freshman year of high school homeschool. For junior high and high school, we plan to keep Apologia as our spine for science. David is now working his way through biology and has fallen in love with our microscope.

The junior high material is too advanced for Pamela, my autistic aphasiac teen, who functions at an upper elementary grade level. We are trying Apologia's elementary science books. Pamela chose astronomy, one of four texts. She has just completed Lesson 1, and the book has engaged her imagination.

We have thoroughly explored the bonus material for readers of the book: Pamela made a montage of her favorite photos from the Hubble Telescope, a model of planet sizes using balloons (pictured below), and a model of distances in the solar system using 392 paper clips and ten marshmallows (pictured left). She printed photos depicting the relative size of the planets and more detailed biographies of Copernicus and Galileo. She loved the online solar system animations, which stimulated her vestibular system and ignited a gigglefest. She writes her narratons on notebook pages from a PDF file: Pamela illustrates and writes a narration of every reading. Her course notebook is already quite thick after only one lesson.

We are Excel fanatics, and my husband and I both agree that no education is complete without a solid grounding in Excel. I made spreadsheets to estimate the distances between planets based upon the paper clip model and the planet sizes based upon the balloon model. When she entered the numbers, Pamela was fascinated to see the formulas calculated for her. I designed another spreadsheet in which Pamela can organize words roots. She looked up the root, language, meaning, and examples of words with the roots in a dictionary (i.e., astro-, Greek, star, astronomy, astronaut).