Living Math Reflections

Since I first heard about the idea of 'living math" I loved it! I loved the idea of including stories about mathematicians into our discovery of arithmetic. Reading about other people's passions often ignites passion in us and I wanted my boys to know other people in history have had a passion for numbers. I want them to wonder why and perhaps catch the passion for themselves.  I love doing math incrementally line upon line working towards mastery of a concept before moving on. I love going at their pace. I loved not having to give them a text book. Mostly I just did not want my kids to hate math. I want them to get it and master it however deep they go in it.

"Living math" is a kind of vague idea to many, and though Charlotte Mason did say a fair bit about it in her writing I found myself stabbing in the dark, adding pieces of her method here and there in our home education but never having a solid feeling I really know what I was doing. Maybe I am not alone here. So this week when I found in my inbox the weekly post from Simply Charlotte Mason announcing they were putting out a manual about living math I was on it. I have had some rich afternoons since then and now pouring over all the quotes and helpful practical tips of how to do it.

Basically as I read  through the e-book pages I have felt affirmed that my thinking about math, not to mention those little gut decisions that I made not knowing were right along with Charlotte! yeah! I also have found little things to add, tweak or wish I could redo because ahhh here is the answer I needed two years ago! If you have ever wondered about living math and wanted to know just what it is and how to do it or if you have wanted a scope a sequence to help you plan your own journey into arithmetic then you might want to read this e-book: Mathematics: an Instrument for living Teaching

One of the very first things which intrigued me was the title. How is mathematics a tool for living teaching? It comes from this quote from Charlotte's writings:

“I need not touch upon the subject of Mathematics. It is receiving ample attention, and is rapidly becoming an instrument for living teaching in our schools” (Vol. 3, p. 236).

How is mathematics a tool for living teaching? The answer is very cool. Charlotte used math to build mental and moral habits. Habits like accuracy, reasoning powers and intellectual truthfulness. Though she did not discount that it had usefulness for everyday life her focus was on the habits it established. This was a refreshing idea for me and a new way of answering to myself why do we do math?

"The practical value of arithmetic to persons in every class of life goes without remark. But the use of the study in practical life is the least of its uses. The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords to the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders” (Vol. 1, p. 254). 

So, inspired now with a new reason for doing math I began to understand better what living math is and how to go about it. I felt affirmed in my gut desire for certain ways of doing our math assignments, like my desire to have a neat math page was not picky it was important. It had a purpose to build something of value beyond that simple act. And getting the right answer was no longer just me being tough on them it was right and building in them a good habit of accuracy and intellectual truthfulness. Charlotte helped me see why I valued these things and gave me permission and a framework to continue in them.

"In my reading of Charlotte Mason’s Original Homeschooling Series, I noticed Charlotte used words I had never applied to the study of mathematics—words like joy, beauty, truth, and awe." -Richele Baburina 

To build these mental and moral habits Charlotte recommended using a curriculum which had these following characteristics: (from Mathematics: An Instrument for living teaching page 97-98)

• Provide for careful progression. We want a gradual unfolding of ideas, not
  simply a “getting through” of a course of study.
  
• Work well with a number of manipulatives in the introduction of concepts
  but not be shackled to them for the entire course of study.
  
  
• Not require expensive or complicated apparatus or work with only one type of manipulative. The child should be able to separate the facts from the objects used, so being able to utilize a variety of everyday objects is best.
  
• Not drown the subject in too much verbiage. 

• Give examples that are interesting and aimed at reality; money sums and
  those involving the familiar are best.
  
• Give examples that, while interesting, are not too difficult.
  
  
• Give examples that work well with oral work. Children’s work in Charlotte’s
  classrooms was largely oral in the earlier years, and continuous oral practice
  was still given in later years.
  
• Assist the child in arriving at the method of solving problems or making
  discoveries himself.
  
  
• Facilitate reasoning powers not just mechanical ability.
  
• Allow for short lessons, no longer than 20 minutes in the earlier years and
  30 minutes in the junior high or high school years.
  
• Allow you to adjust the pace for your child. 

• Allow for mastery of concepts. Securing your child’s understanding is a
  must before proceeding to the next concept.
  
• Allow for adequate review. Once a concept is mastered it will still need a
  sufficient review, and having examples of varying difficulty is best if your child progresses rapidly or for review the following term or year. 

"If you don’t have a strong grasp of mathematics, please do not despair. Don’t be surprised if, as you begin applying Charlotte’s methods in mathematics, you also start seeing the reason behind the facts, discovering new relationships, and experiencing joy and delight while obtaining more mathematical understanding yourself. " -Richele author of Mathematic:A Tool for Living Teaching

Last summer I fell in love with a wonderful turn of the century math book written by Emma Serl who also authored Primary Language Lesson, a grammar study I think Charlotte would have loved. She may have loved Everyday Number Stories too for as I read through the e-book and the list above it kept occurring to me how well that this little free book fits into living math education she was writing about like a hand into a glove. By working through this math book with the boys I found real joy in math for the first time, for I saw the relationships between multiplication, division, addition, subtraction and fractions. Really fun! But more than that the real life problems and stories were easily made practical by using ordinary things around the house to explain and bring alive the abstract math. They enveloped measuring, turning problem inside out and upside down looking at an addition problem and making it into a fractions problem. Best of all it made us all think circumspectly about math in its beautiful rudiments.

I have more to read, more to implement and if this subject will be like any other Charlotte Mason methods I have implemented they will be a success.

Happy figuring!

Week Three Wrap-Up

Max

What a fast, busy, productive wild week we have had! If it were not for God in us we would be truly warped. He paced our days, gave us patience with each other and blessed us with Himself daily. What made a big difference in the week was that I spent more time in the mornings sitting with Him and singing....I love to sing especially about Him. My Favorite this week:

This week I was tempted often to add more and more things to our schedule, to go faster, to be busier. But why? I wondered. As I began to rush I often rushed the boys. I could be quick, sharp tongued and irritable. Luckily I saw the signs and slowed down. I took time to lay upon my bed and wait. I waited upon God for perspective, for help with the tasks lying undone around me and for a tangible and concrete way to remember the glorious truth that after all I am dead and He does live in me. I have a new life, a powerful one right here with me ready to orchestrate and create goodness and care in my little world. I ought to let Him. As I waited, it was easier to let go and to begin again watching instead of driving, listening instead of speaking. My sons responded with a tremendous love for me. Hugs from little boys are sooo sweet. I am addicted.

Zak with my good friend Michele's dog Kahalie

Last week we completed Bruchko and now we are reading a book from the Trailblazer series called Risking the Forbidden Game. It is about a young Muslim boy in Morocco who plays a very simple but later dangerous game of stealing items from the French soldiers or any other infidels during the Muslim celebration of Ramadan. Along the way he discovers he likes hearing stories about Jesus and those who tell about him. But he finds that his game leads to real life and death consequences for his new infidel friend. So far a great read.

We have been having so much fun draaaawwlllling to the X4 skip count song with a country western tune and Rapping with the X5 song. This little album has been such a painless way to learn these math facts. And slowly the boys are catching onto the multiplication table. So nothing new this week here just onward ho! 

But here is something new. I noticed that during the first four lessons of the day there is a lot of extra time that could be utilized. I read aloud to them for most of the morning, and I realized that they can be busy working on something that is somewhat "brainless" while I read. So, as I read a Fable from Aesop and stories from The Story of the Greeks, and  a delightful tale from The Burgess Bird Book they color and copy. This turned out to be a good way to introduce Aesop to the the boys and to my lovely copywork book. 

Knowing they just "love" doing copywork (LOL) I thought this book would work well for them because many, if not most, of the morals they copy are short. Since the copy work is short and the boys are needing a new challenge,  I upped the ante to earn a treat. This summer if they could copy the selection from their readers with no mistakes the first time: that means they don't miss any words, or forget a misspelling etc. they got a treat. If there were mistakes they had to recopy it. This year no cross outs! No Grace! First time, beautiful writing, no mistakes. They are getting it down. I am amazed at what they can do.

We are on Lesson #3 in Primary Language Lessons and should finish memorizing the poem "If I Knew" this week. We went about learning the Poem this way...

DAY ONE:  the boys read the entire poem aloud, each one taking one line at a time. Next I had them close their eyes and I read the entire poem aloud to them with emphasis and a bit of drama. Then they copied the first four lines into their composition notebooks (There are 16 lines in all) and drew a picture to go with it. Then I knew if they were understanding the meaning of the lines in the poem. 

DAY TWO:  The boys read the poem aloud again each taking a turn to read one line. I read it to them, and they copied the next four lines of the poem into their composition notebook like they did on the first day and drew a picture. Same lesson with different lines and pictures to draw. 

DAY THREE: On this day the boys read the poem again line by line taking turns, and I read it to them as they sat quietly with closed eyes. Then we said the first four lines from memory each one. Then we said the first eight lines from memory. Then the boys went on to try twelve lines from memory. Then they attempted all sixteen lines. Amazing.

DAY FOUR: The boys read the poem aloud again each taking a turn to read one line. I read it to them, and they copied the next four lines of the poem into their composition notebook like they did on the first and second days and drew a picture of someone gathering frowns form the nursery, the schools and the streets and putting them into a box.

DAY FIVE: The boys read the poem aloud again each taking a turn to read one line. I read it to them, and they copied the last four lines of the poem into their composition notebook like they did on the first and second days and drew a picture. This time they got to draw a giant dropping a box of frowns into the depths of the deep deep sea. So much fun imagery.

DAY SIX: Repeat of day three. On this day the boys read the poem again for the last time line by line taking turns, and I read it to them as they sat quietly with closed eyes. Then we said the first four lines from memory each one. Then we said the first eight lines from memory. Then the boys went on to try twelve lines from memory. Then they attempted all sixteen lines. 

And they did it. They memorized their  FIRST poem. I am so proud of them!

TJ

We have begun a new dialogue in our Latin lessons called "Lepidina at the Party" We are using the Minimus Latin curriculum this year.  In our lesson we learned a lot of new vocabulary words for a birthday party. We sang happy birthday in Latin and made a birthday card for Minims the mouse.

At the end of the day we have been making Klee inspired fish paintings with black oil pastels and gauche. 

and...Klee inspired clay fish.

We used a homemade polymer clay with cornstarch, baby oil, lemon juice and white glue. The consistency of the dough was fantastic! Then we let the dough dry for a day or so and painted them.

For other art recipes I found a wonderful interest site with oodles of fun things to try. You might also find some good ideas for other Paul Klee art projects at these sites:

Art projects for kids: Mini mural
Arted-Paul Klee
Deep Space Sparkle: Modern Masters
Meet the Masters
Harmony Art Mom

Zak

And to top off our week we had a fun game/activity/scrapbook day. It all began with this video clip about the Olympics.

Max is working on a picture of Zeus the god the Ancient Greeks honored during the Olympic games. The unveiling of the scrap book pages is still to come...

We played a rousing game of Digging up Greece. This is a FREE game found online. It is another of Ellen's (creator of Prof. Pig's Magic Math) wonderful inventions. She says this about the game...

"The board is a large map of Greece (6 pages taped together!).  The die does not contain numbers, but rather modes of transportation.  The players pretend to be college students taking a semester abroad in Greece and they use boats, cars, or planes to hop around the country, visiting famous sites and collecting artifacts.   When POP QUIZ is rolled on the dice, they must answer a multiple choice question about ancient Greek history. "

We say it is a blast to play it. What a great way to learn the islands and cities why the whole map of
Greece! And a bit of Greek history to boot.

Lastly we spent time outside making an entry into our nature notebooks. This week noting something overhead.

Week Two Wrap-Up

I can't say enough about our new schedule...I just LOVE IT! We start at 11am do four lessons, break for lunch and then do four more lessons ending at 3pm or 4pm depending on the day. What I love most is having the time in the morning to get a lot done before we begin. By that time I have accomplished something or often many things and I am feeling I am ready for the boys. I am prepared to focus on them, be more patient, more relaxed and thus a better teacher and mom. I also LOVE having lunch right in the middle of the lessons to give us all a mental and emotional break. Seems to take the weight off of the day and allows us time to talk during the meal about things we have learned in the lessons. Often as they linger over the meal I read the next lesson while they are eating the last morsels of food. Ahh multi-tasking I love it too!!

This week we have been reading through Daniel. My dh does this over breakfast. We have heard the stories before many times but still I am amazed at Daniel's trust in God up to the last almost fatal moment. I would have cried "unfair!" "Enough!" when the satraps slandered him and plotted to usurp him even to kill him. But Daniel believed God would save him even though he was being thrown into a den of hungry lions. Amazing. How far would you let God seemingly ruin your life before you stopped trusting He is good enough to save you?

First lesson of the day is reading from Buchko. I read about two chapters before the 30 minutes for the lesson is up and we are moving along to math. (I changed the order of our lesson this week to to coincide better with my planner.) We are loving to hear how Bruce is telling the stone aged indians about the gospel. How he puts it into terms and ideas the indians can understand. I simply love the idea of tying my hammock into God and getting in with both feet. This is more challenging then it seems when you realize the Motilone indians he is speaking to sleep in hammocks 25 feet off the ground. Yikes! That takes a bit of trust to tie in way up there. It is also a way they invite you to be part of them. If a girl likes a boy she ties her hammock next to his and they are then officially married. Hearing ideas we know so well put into new terms makes it more clear to us. The boys all heartily agreed tying their hammocks  into God is a wonderful idea!

We are having a lot of fun with the skip counting songs in math. We moved on to the X3 and X4 songs this week. The X4 song is a country western tune which really resonates with my bluegrass heart. Yippe i kie aaaay we skip count every day! In addition I introduced the boys to Sal from Khan Academy. (Thanks Debbie for the pointer) He has been explaining to them about what Multiplication is and what a multiplication table is. Then we made our own tables this week. Max especially liked it. We played An old style version of Multiplication Bingo that I found at the Goodwill this summer for our game-activity-fun day.

After Math we are reading from the Story of the Greeks and preparing for our Saturday Scrapbook day. The boys want to scrapbook about the Greek Olympics. So we will be working on that theme for a few weeks. We did get our books started last Saturday, see Max's inside cover and title page below.

We are using a basic wire bound sketch book for our scrapbook. The map on the cover came from Homeschool in the woods packet of old world maps. The title page is from Notebooking Pages packet of Ancient Times pages. On the other cover of the book we plan to add the old world style map for Ancient Rome. Thus the book will open left to right for Ancient Greece and right to left for Ancient Rome. Somewhere in the middle they will meet. We did more this week preparing things for the pages on the olympics but the boys wanted me to wait to show you it all when they have it done. So I will let it remain a mystery until then.

Also last week on our 6th day/fun day we did our first nature notebook entry. Using Keeping a Nature Journal by Clare Leslie Walker I introduced the boys to the scientific aspect of nature hikes/walks...recording your observations. Following Clare's advice from Chapter 2 "Beginning Your Journal" we entered our daily observations. There are eight of them noted on page 22:

1. Name
2. Date
3. Place
4. Time
5. Weather
6. First Impressions
7. Wind direction
8. Cloud Patterns

Then we drew something we loved:

Before we do an entry I read a little from her book that I think would help them form an idea about what a nature journal can be or  something that would inspire them. I love this quote form the book (Zak did too!)

"Think of a nature journal as a treasure hunt. Ask yourself, "what's out there beyond  the doorstep? What treasures will I find?" You will be amazed when you actually get outside at all the things there are to draw or write about." - Clare Walker Leslie

Following a reading from the Stories from Ancient Greece we  continue our reading through the Burgess Bird Book. We have met the fly catchers and the woodpeckers, the cow bird and many other friends of Peter Rabbit in the Old Orchard. There happens to be copious resources to go along with this book, but here are three of my favorite ones:

Audio version
Free Printables that go well with the stories
Burgess Book Companion Web site

I am however going to keep our reading simple and just read and look up birds in resources books I mentioned last week. Having said that I did decide to add one more resource, The Handbook of Nature Study. It was a DUH! moment when I realized I had the text on my shelf and the questions Max was asking could easily be answered by reading there. SO we are reading more from that book next week.

Lunch Break!!!

After eating is a Language Arts lesson or two. We have been working through a dictation lesson this week from Primary Language Lessons. The word SQUIRRELS was hard for the boys to master so we wrote the word over many times and did dictation a few days in a row on the same sentence until they got it! Boy were they proud! In the same book, PLL, we did an short lesson on when to use "is" or "are." They also wrote a short story about squirrels using "is" and "are" in their composition notebooks (which we picked up at Walmart for cheap). Take a look...

I recommend getting the teacher's edition to supplement the student text of PLL as it has some wonderful ideas for how to implement and further use the lessons. When it sugested writing a story or drawing a picture about squirrels I knew that would be  good switch from dictation. It also allowed them to use the word they had mastered their own way. I addition to the teacher's guide, I recommend either Living books curriculum layout workbook or Cynce's because it makes doing the lessons so much easier having places already set out to write your answers.

Here is Max's drawing from the poem "If I knew" (Where the box where the smiles were kept)

I enjoyed hearing the boys read out loud to me from Elson Reader book Three and narrate the story this week. They chose to go through this series last year and they still love it. I love it too, as the stories they read to me are good ones and though not modern they have timeless values woven into them which is refreshing. So I have them read two or three pages for me this fall. We were reading 5 to 7 this summer from Peter and Polly in Summer, but the words in these short stories are bigger, and more challenging to sound out. I don't want to tire them out, I want them to practice, so we read what they can get done in about 15-20 minutes. So far it has worked out very well. The truth be told...I don't know if I could do much more than that. Listening to three emerging readers for one hour is about my limit too!

To complete L.A. for the day we have one more lesson. Just before bed we are reading  The Wind in the Willows. Oh how I love this book! It is chocolate to the ears. To supplement my own readings I also play an audio version of the  chapters I have already read. (They just can't get enough) The audio version we have I picked up a garage sale for next to nothing. It is part of a set called The Children's Classic Library. It includes more than Wind in the Willows, it also contains  40 other classic stories like Treasure Island, Pinocchio and Heidi. I love that they are unabridged and dramatized. Gives my throat a break and they get their fill of good literature. Win win!

Onto Lain! We have made some good progress with our dialogue "meet the family" in the Minimus  Latin curriculum we are using this year. We must have listened to the dialogue about 7 times before the boys were able to read it all the way through making no mistakes and understanding the dialogue. Each time we listened to the dialogue more details became clear. Then each one was given a chance to read it out loud while the others listened. Once that was complete, we took about half of the vocab words at a time and wrote them onto 3 X 5 cards. The latin they wrote on the front and a picture of the word or the english word on the back. These flash cards that they are making for themselves was an idea from the teacher's manual. Take a look at Max's card for Feles (cat).

Once they had completed all of the vocab words we played a sort of spelling bee type of game to reinforce them. They stood up together in a line and I gave them first the latin and they gave me the english, then I gave them the english and they would give me the latin. If they failed at a word they sat down and the last one standing was the winner. We played several times and all won in the end. Today (Thursday) we translated a birthday invitation which was found at Vindolanda in an excavation.

You know a boy loves a book when he puts his legos aside just to listen. Well that is what they do when I bring out The Story of Peter Tchaikovsky by Opal Wheeler. Zak said, "I just love that horse boy."

Our look at Paul Klee this week has resulted in some fun drawings and paintings of cats.

Tj is painting a 'the cat head' based upon the coloring page we did last week called "The Head of Man."

Here is Max working on his 'cat head.' We began the drawing by tracing a bowl form the kitchen. Having the circle thus define the space made the rest of the drawing/painting a piece of cake.

We then morphed from "The Head of Man" to "The Cat head" to Klee's "Cat and Bird". There is a great site we used to guide in drawing this. You can check it out here.

Can you find their signature in the drawing? We used oil pastels to color these.

Zak said this is chocolate cat! And so it is.  I hope it is a chocolate ice cream cat!

That is all for this week. I hope you are having a good one too.

Week One Wrap-up

Yeah!!! Amongst all the messes and undone plans we had a terrific start to the year this week. Letting God take the lead in the schedule and the daily moment by moment decisions has led me to make two significant changes to our home education. They are to apply more of CM's education principles to our school and live by a new schedule.

What I have always loved about a CM education is all the good books. I like how she filled up young students with a rich banquet of ideas DAILY. I realized that I have been skimpy on the banquet of ideas putting in its place more hands on activities. And though my boys enjoy hands on activities some times, this year I have limited them and added many more living books rich with ideas for their minds to be filled with. I can see they are thriving already eating daily from a rich feast of ideas.

I have heard that boys need time to fidget or be active before they can settle down and do seat work. SO when we were discussing how to go about our schedule I was so happy when Max came up with the idea of doing school from 11am to 4pm with a lunch break at around 1pm right in the middle of the lessons. It has worked out beautifully!!! When the boys come to lesson time after having had time to themselves to fidget and work off excess energy they do much better in school. We do more learning and less discipline. I too am benefitting from the extra time in the morning to do my own things and get ready for the day before lesson begin. My only big adjustment is to be sure to prepare lunch before lessons at 11.

Our new schedule of lessons for this year looks like this...

We begin the lessons reading a story about someone's life who walked with God. We do this to get a glimpse of who God is, how He leads those who follow Him and to see what adventures people have do follow Him. This year we have begun with Bruchko.

After reading Bruchko we do a lesson from Minimus. In this lesson we listen to a dialogue between Minimus the mouse and each member of the family. Mininmus is asking who they are. The boys just about have the dialogue down pat and can read it all by themselves for the most part. Here is Max's work sheet on the members of the household we have met so far...

We will spend most of the year on this Latin book so I am taking my time to go through it slowly. In addition to add some background to Minimus I have been reading Douglas Bond's book Hostage Lands to the boys at bedtime. It is about a young Latin student in modern day Britain who accidentally finds a set of old Roman tablets on his father farm near Hadrian's wall. The story of Hostage Lands is the story he discovers as he translates the tablets with his eccentric Latin professor. Cool thing is that both the book and Minimus take place in Britain near Hadrian's Wall.

This summer I introduced multiplication and division to the boys via Emma Serl's wonderful turn-of-the-century math primer called Everyday Number Stories. Since they did not yet know their times tables they figured out the multiplication problems and division problems using addition. WOW they sure found that cumbersome, but they are NOW ready this fall to learn the times tables, so we are doing that. I began this week with the Original Skip Count Kid Audio songs for X2 and practicing the X2 on a multiplication table. Tomorrow for our catch-up-game-activity day we will play Loot the Pirate Ship and read about a Mathematician form Mathematicians are People Too Vol. 2. I love how fun math can be.

Loot the Pirate ship!!!

History this year will involve learning about Greece and Rome. I have collected a HUGE pile of books on this over the last few years at the Goodwill etc and will have PLENTY of material to choose from as we read the fascinating stories of these ancient peoples. We begin the year with The Story of the Greeks written primarily by H. A. Gruber, and enhanced by Christine Miller from Nothing New Press. It gives a wonderful overall feel for the story of the Greek people. This week I read aloud the stories as the boys fiddled with legos or colored their pictures of the family we met in our latin study. Once this lesson is complete we eat lunch.

LUNCH

BREAK

Our nature study focuses on birds and insects, so I asked the boys which one they wanted to study first...they chose the birds. SO we read from The Burgess Bird book by Thornton Burgess each day. When we want to see the birds he is describing or hear the songs they sing, I pull out these books to learn more about the birds introduced in our story.

Bird:The Definitive Visual Guide, 100 Birds and How They Got Their Names, and Backyard Bird Songs. Tomorrow we will be outside for a nature hike and we will have our eyes open to see if we see fly catchers, sparrows, wrens and phoebes the birds we read about. I hope to find a nest or two.

Ahhh... Language Arts! Spilt into three parts we rotate them around to fit our schedule. The three parts include: Reading out loud from the Elson Reader book Three including narration of the story(s), Handwriting or copy work, and lessons from Primary Language Lessons. This week was wonderful! I heard classic tales read aloud to me with easily given narrations of them. The lessons in the PLL have copywork in them but if the lesson does not I assign a sentence or two from their reader. PLL has a new lesson for us DICTATION. Surprisingly the boys loved the challenge of it. we only did two lessons but I am at THEIR pace so it is enjoyable for us all.

Modern artists are on the docket for art history this year. So we began with Paul Klee. This week we played Go Fish for Modern Artists to see him amongst other modern artists and then a few days later the boys colored one of Mr. Klee's famous paintings "Head of Man"

 Last but certainly not least is composer study. We begin this year with Tchaikovsky! Since Opal Wheeler's books were such a great highlight to our composer study last year I chose to read her again. So we began with The Story of Peter Tchaikovsky. What a lovely little boy he was!

Each day we complete all the above lessons except for art and music which rotate out every other day. We are planning on doing a 6 day week with the 6th day being a catch-up-game-actvity day.

I am excited for another year of discovery with more rich ideas to think on and a new schedule to live by.