Learning Math with Laura

Sometimes Ma let Laura and Mary go across the road and down the hill to see Mrs. Peterson….She was a Swede, and she let Laura and Mary look at the pretty things she had brought from Sweden….   Mrs. Peterson talked Swedish to them, and they talked English to her, and they understood each other perfectly.  She always gave them each a cookie when they left, and they nibbled the cookies very slowly while they walked home.  

Laura nibbled away exactly half of hers, and Mary nibbled exactly half of hers, and the other halves they saved for Baby Carrie.  Then when they got home, Carrie had two half-cookies, and that was a whole cookie.

This wasn’t right.  All they wanted to do was to divide the cookies fairly with Carrie….They didn’t know what do.  So each saved half, and gave it to Baby Carrie.  But they always felt that somehow that wasn’t quite fair. 
-Laura Ingalls Wilder in “Summertime” from Little House in the Big Woods

Can you believe Laura Ingalls Wilder  included a simple math lesson right there in her narrative? How convenient.  Imbedded in this brief text of a visit to a nearby neighbor, there is much more than a fraction riddle.  There is the lesson of sisterly selflessness, the lesson of developing relationships with those around us, the lesson of appreciating others and allowing them to be who they are regardless of differences.  All those will need to be explored internally or at a later time.  Now, we have to evenly divide those cookies.

G and I have just finished the first volume of Ms. Wilder’s series.  Honestly, he wasn’t thrilled about my read aloud choice until I told him there was a panther in it, and Pa cleans his rifle.  He was surprised, however, that he enjoyed listening to how Pa played the fiddle about Yankee Doodle and Ol’ Grimes, and how to make cheese and maple syrup.

After we read the above excerpt, I asked G if he could think of a way to break 2 cookies into 3 even pieces.  His immediate answer was to break it in lots of little pieces.   Hmmmm… Not a bad initial thought.  

The next day we decided to trace some circles and pretend they were Mrs. Peterson’s cookies.  G made them chocolate chip.

  
By cutting out two more circles and cutting them into halves I demonstrated how two halves is the same as one whole.  If you look carefully at Mary’s cookie in the picture you can see how G was dividing the cookie into little tiny triangular-like wedges.  Whew.  That would have been hard work for a walk home.  As he divided, he counted Mary- Laura-Carrie-Mary-Laura-Carrie-Mary-Laura-…Then he realized that was an ABC pattern.  Good for you, G.

The cookie on the right is my attempt at showing him how you could make one-third wedges out of cookies.

This all didn’t take very long, because he really needed to get back to more important things.  I mean, those pictures of Spider-Man defeating Doctor Octopus are not going to draw themselves.

Back to School

There was a great deal of complaining last year.  Math was too difficult.  We had too much work.  The dreaded ‘B’ word was bandied about.  You know, as in, This is (gasp) boring.  

After addressing each subject separately, I began to gain some clarity: the problem did not lie with the challenging subject matter, nor the words my kids – one of them in particular, let’s be honest- chose to use.  It didn’t even primarily pertain to the unwanted behaviors.  It was a deeper, yet simpler problem.  A problem of the heart.

May these words of my mouth and this meditation of my heart be pleasing in your sight,  LORD, my Rock and my Redeemer.

Psalm 19:34

I have often wondered why David mentions his words before his thoughts.  Jesus calls out his would-be followers, “Out of the overflow of the heart, the mouth speaks,” and “where your treasure is, there the heart will be also.”

My children needed to change their thinking.  Controlling my heart, my tongue, and my thoughts are not easy for me as an adult.  How much more difficult will it be for my children? They need to see me model a desire to do so, however.

Our first week of school has passed slowly, with low expectations, incrementally adding topics and subjects.  We have read, journaled, watched the news, completed some map work, and generally re-introduced the habit of sitting down to work again (as well as introduced what it will look like in our new house.  We moved in less than two weeks ago.)

Charlotte Mason’s motto has helped us in approaching this new school year with positive guidelines.

I am.. I can… I ought… I will…

I am hoping to instill in my children a proprietary sense of their education and spiritual life. You can read here for more information about Charlotte Mason’s motto and educational philosophy.

Each day we have added to our understanding of the motto with the Bible verses suggested here.

 

I am….a child of God.  I am a person of great value because God made me.

Ephesians 2:8-10  “…For we are God’s handiwork, created in Christ Jesus to do good works, which God prepared in advance for us to do.”

I can…do all things through Christ who strengthens me.  I am capable of accomplishing all I need to do.

Philippians 4:13 “I can do all this through him who gives me strength.”

I ought…. to obey God, my parents and all those who are in authority over me.

Mark 12:30-31 “Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.  The second is this:  Love your neighbor as yourself.  There is no commandment greater than these.”

I will…decide to keep watch over my thoughts and tongue and choose what is right even if it is not what I want.

Psalm 119:30 “I have chosen the way of faithfulness; I have set my heart on your laws.”

We have discussed the significance of each of these points and used the verses as copywork.  We are slowly incorporating them as memory work as well.  The heavy responsibilities and expectations of the school year lighten when we are reminded how loved we are, along with an encouraging reminder that we are, indeed, capable.

Who wants pi?: Book suggestions

Days away from celebrating a well-known mathematical constant, our family is eagerly planning how we will spend it.  Eagerly? Well, maybe not eagerly.   We did mention a couple of times how cool this year is.  Not only is March 14th National Pi Day, but this year is now being tauted as EPIC.  Why?  It will be 3-14-15.  Get it?  3.1415…?  And if you really want to geek out about it give a big shout out to pi at exactly 9:26:53am. Being mathematically challenged most of my life, I am certainly not a numbers or formula kind of person.  Sitting in Mrs. Lombardo’s algebra and geometry classes, I remember the unblinking digits of pi circling the room close to the ceiling, inspiring me to absolutely nothing but a slight fear of too many numbers. And why were they about to topple over onto our desks? Language, literature and history were rife with creativity and imagination.   Mathematics, however, bored me to tears of frustration.  Years later, not feeling the stress of grades and textbook problems, I can distance myself from my mathematical distaste.  Why not have fun with something anyway?  The following books certainly help.

Sir Cumference series  These clever picture books by Cindy Neuschwander and Wayne Geehan do justice to the practicality of geometry.  Set in medieval times each character’s name is a play on words, such as Sir Cumference, his wife Lady Di of Ameter, their son Radius, and a niece Per of Ameter.  Geo and Sym of Immetry, as well as Vertex are also important characters.  The stories and illustrations seem to suit the 5-7 year-old age range, however the math concepts are really geared for an older child, possibly 9-12, depending on their exposure and mastery of math.  This week we plan on calculating the areas of circles making use of pi.  There are several books in this series.

Sir Cumference and the First Round Table

Sir Cumference and the Sword in the Cone

Sir Cumference and the Dragon of Pi

Sir Cumference and the Isle of Immeter

Sir Cumference and the Great Knight of Angleland

Sir Cumference and all the King’s Tens

Navigating Early Written exquisitely by the 2010 Newberry Award winner for Moon Over Manifest, Clare Vanderpool has also penned this 2013 adventure of a boy named Jack Baker.  Navigating Early is set just after WWII and focuses on 12-year-old Jack, who is still mourning his mother’s death as his taciturn father drops him off at a Maine boarding school for boys.  While there, Jack is befriended by Early Auden, “the strangest of all boys,” who is also dealing with his great loss, the presumed death and disappearance of his brother Fisher.  With no other plans during their spring break, the two sail off down the river in search of adventure, answers and healing,  Early, although not stated as such, likely has Asperger’s, and a savant gift for memorizing numbers.  He not only knows pi to the thousands of digits and does not believe it to have an ending, but also sees the digits of pi as a distinct story, a narrative which eerily unfolds in real life as the boys continue further on into their journey.  Early’s tale of pi and the boys’ acknowledgement of what is happening to them unfolds simultaneously.  Without revealing anything further, Navigating Early is a novel of friendship, loyalty, family and endurance. Not only is this a beautiful story, but a surprisingly imaginative and heart-warming way to celebrate Pi Day.

Or any day, really.

Sharing Stone Soup – part one

 

With Chinese New Year approaching in just over a week, I have been reflecting on great children’s literature based in Chinese history and culture. Chinese New Year 2015 is February 19, the Year of the Goat. For older kids who are able to enjoy chapter books there are Grace Lin’s The Year of the Dog, I Rode a Horse of Milk White Jade by Diane Wilson, and Lloyd Alexander’s The Remarkable Journey of Prince Jen.  However, this last week G and I have thoroughly enjoyed reading and re-reading Stone Soup.  Many of you may be wondering what Stone Soup has to do with China.  Over the centuries, many countries have produced their own versions of Stone Soup or Button Soup, mostly originating in Europe.  I grew up reading a version that took place in the American colonies right around the time of the Revolution.  My favorite of them all, though, has become Jon J. Muth’s retelling set in a tiny Chinese village near the Great Wall.  Three Buddhist monks look down on a simple collection of houses as they discuss how happiness is achieved.  As is typical with Muth, his approach is very zen, yet nothing is lost with G.  From the black cat which winds its tail about the water-color characters and peeks charmingly from over a giant pot to the wise, hospitable young girl dressed in royal yellow, G has taken this version in wholeheartedly.

Here is what we did:

Day One: Read the story

Drawing lesson – For those of you know me, don’t laugh.  I am honestly the last person who needs to be teaching art, unless it is simply art appreciation.  Yet, this was a simple lesson of recognizing the use of shapes.  We turned to the story’s final page and noticed how the stone bridge created a trianglular shape.  I attempted to help him draw his own two-point perspective and he included simple, waving and smiling figures.  They were happy because they had learned how to make stone soup (see my upcoming blog post).

Day Two: Read the story again (no, children do not necessarily get bored like we might from reading the same story repetitively.  As long as it is an engaging story the familiarity of the book will only serve to boost their confidence.)

Math with rocks, wood blocks and figures – The traveling Buddhist monks in Muth’s book collect three rocks for their soup.  They are stacked in the illustration from the largest on the ground to the smallest precariously perched as the head of the Buddha himself. (G thought it resembled a snowman.)  We explored our manipulative arranging them from largest to smallest, then smallest to largest, and finally creating different patterns.

Day Three – Read the story, of course.

Geography – Explore China on the map.  Some people say it is shaped like a chicken.  I can almost see it.  G did find where he imagined the beak to be.  We looked at photos of the Great Wall of China, colored a printout map which I found online, and learned a few Chinese phrases.

Ni hao ma = Hello, how are you?

Hun hao, she she = I am fine.  Thank you.

We ran out of time that day, but another fun activity could have been to build our own Great Wall out of blocks.  We like Citiblocs around here.

Day Four – Read the story

Social Studies – Create your own village of community people.  Early in the story Muth names some of the villagers who were suspiciously lurking and peering secretively through windows.  They were the doctor, scholar, tea merchant, carpenter and seamstress.  We gathered up supplies and toys from about the house and spread them throughout the living room, giving space to each community helper.  But, instead of acting stingy, we shared our talents.  G gave me a shot, served me tea and read me a book.

Day Five –  Read the story

Music and culture – Here we played with shadows, learning the farther away from our light source, the smaller the shadow.  Shadow puppetry is a Chinese traditional art form, and we had fun not only with our hands, but also S’s marionette Chinese dragon puppet.  Muth does a fabulous job with details throughout his illustrations.  Not only is the clothing seemingly accurate down to the tiny shoes, but also the prominent red lanterns and musical instruments.  The erhu and the pipa are specific instruments in Chinese folk music and play a role in the villagers’ eventual celebration feast.  You can watch a video here like we did.

There is a day six in our study of Stone Soup. Can you guess what it is?  Come back in a couple of days to see if you are right.

Finding the Motivation for Math

That is key in a variety of areas for our kids, isn’t it?  Finding the motivation.  This is particularly true with the types I am mothering.  You know, those insanely frustrating, internally driven individuals, the kind who are not to be threatened nor bribed to perform? Whatever they do, it is because they want to, not because I say it is part of the curriculum, or because they get extra time on the iPad.

It seemed easier to find ways of incorporating their interests when they were little, when so much learning was facilitated through active play, games and a good book.  It was all so natural.  Now, as they have grown a bit older, I have had to go out of my way to create meaningful methods to hold their interests on certain subjects.  Currently, that subject is math.  Several months ago I wrote here on how I tried to keep up with S’s energy level during math lessons.

Subtracting the Presidents

When A was in kindergarten he was completely focused on the U.S. Presidents. He had flashcards with their photos and would line them up in chronological order.  He knew all their pets, which political party they belonged to, and could retell at least one humorous story about each of them.  This interest in world leaders kept him going for a long while, and eventually inspired me to teach him borrowing in subtraction.  He was always asking how old Millard Filmore was when he died, or Taft, or JFK.  So, we taught him how to borrow.  He learned quickly. He needed the information.  For months afterward, we would find scrap paper, doodle pads and white boards full of subtraction problems marking the deaths and births of many of our great leaders.

Then I grew lazy.  Math simply became math.  It is definitely not A’s strongest subject, but he is certainly at grade level.  We allowed him to plod along with his worksheets and assignments.  His only frustrations have to do with some obsessive tendencies to be correct the first time.  (aaaaagh!  One of the joys of the inflexible thinking of an aspie?)

Considering Baseball Math and Statistics

However, the other night, my husband unexpectedly reminded me  yet again of the power of motivation.  I had been out for part of the evening, and as he chatted baseball with A, he brought up statistics and RBIs.  Suddenly, decimals and probability seemed of utmost interest to my sixth grader.   He wasn’t complaining that math was boring, or that he didn’t care what the answer was.  He needed this information.

Next school year we may be creating word problems which include pitchers and first basemen.  Algebra equations and geometry proofs. Or he might have moved on to something totally different.  It’s hard to foresee.  Regardless, I don’t want to forget the power of motivation.  I always want to know my guys so well that I can readily pull a math lesson out of a hat – or batting helmet.

 

Who Said Math Was Fun?!

Math, in any of its forms, has never been my favorite subject.  Once I had mastered rote memorization, I quickly lost interest, and quite frankly, easily became confused.  For this reason I was somewhat surprised when one of the motivating factors in beginning our homeschool journey was teaching math to my own children.  Now I want to pause and insert a disclaimer here.  In no way do I have a bad taste in my mouth regarding public education, or the new methods of teaching mathematics.  However, what do you moms really think of front end estimation or the lattice method for multiplication?  It is very likely that since mathematics has first been taught, parents have complained , “Well, that is not how we did it back in the day.”  I remember my father and uncle patiently attempting to teach me algebra while I cried out of frustration.  They attempted while I lamented, “That is not how Mrs. L—— showed us.”  Once my children reach pre-calculus, we may learn the “newfangled” methods.  In the meantime, I will show them the tried and true ways which have got me thus far.

Anyway.  While allowing my kiddos to get those mathematical bits of rote information down pat, we could make it a bit fun every once in awhile.  This is easily achieved with my three-year old.  Math is everywhere around us.  Once the older boys are on to me that we are actually reviewing lessons learned, and not just playing, it had better be fun.

My nine-year old, S,  is learning division this year, but still struggles to have his multiplication facts as firmly in his head as I would like them.  He also has that nine-year-old boy energy that would just prefer to jump up and down repeatedly like a pogo stick than, say, write out his multiplication table over and over.  The world is his trampoline.  So, the kind-hearted and understanding mother that I am, I came up with what he calls, “run-around-the-house math.”

Run-around-the-house math – This is a fun activity we use at the beginning or end of a week after the hard work (I didn’t say boring) has already been done.  We use it as a refresher.  I collect about ten 3×5 index cards.  On one side I write a math sentence.  For example, 9 x 7 = 63 or   63 / 9= 7.  If I want him to have a greater challenge, I write it down without the product or quotient.  On the flip side I write the location of where he will find his next note card.  I place them all around the house, upstairs and down, some even in the backyard, then instruct him to place his spiral notebook and pencil in one particular location.  It is usually on his desk in his bedroom.  His job is to read the first card, e.g. 24 / 6 = 4.  Then, he reads  the opposite side, which may read, “under the kitchen table.”  He places the card back down, races upstairs to his room, records it in his notebook, runs to the kitchen table and gets the next card.  This is repeated until all ten cards are completed.  By this time, he has tripped once or twice, and is out of breath, and laughing.  My hope is that the slight delay in having to remember a couple of things simultaneously, going through the motion of writing it down, combined with a little bit of moving around will all work together to help something stick in his head.  In any case, it is his favorite day of math.

Odd One Out– This is another activity we do with index cards, but is stationary.  After cutting several cards in half to save paper, I group them in fours.  Three numbers will belong together to form a true math sentence.  The fourth will be the “odd one out.”  His job is to recognize as quickly as possible which one that is.  The first group of number cards might reveal 6, 42, 8, 7.  Obviously, the 8 is the odd one out, because 7 x 6 = 42.  This is a fun exercise to strengthen his knowledge of patterns and relationships in math, or what today’s elementary children call “fact families.”

With G, my three-year-old, math practice is easier and naturally more fun.  There is not much to plan ahead, because at this age counting with numbers just happens organically through play and conversation.  I do, however, have a couple of activities for G that we like to get out when he wants to join his brothers and “do math.”

Sensory math – With toddlers and preschoolers the more senses they are able to use, the better.  This is even true for certain learning styles as we get older.  Last year I made G a simple (I am not at all a craftsy person) flannel board with a tree, apples, basic geometric shapes and numbers.  We like to play with these in different ways.

G lining up numbers and shapes

One-to-one counting with apples

Threading Beads – I have been proud of how G has grown in his hand-eye coordination.  Scissors are still a challenge for him. I frequently need to remind him that his thumb goes on top while he is cutting.  He has, however,  truly mastered threading his wooden beads  through the laces even with the tiny holes.  He also uses index cards or colored card stock with a number.  He, then, counts his beads as he strings them on the laces.

This seems to be meaningful for him as he often initiates counting throughout his day.  “Let me see how many apple slices I have on my plate.”  Or,  “One, two, three, four, five, six ducks in that pond.”

It’s not pre-caluculus yet, but we are getting there.