Monday, May 21, 2012

Math by the Seat of Your Pants

I often hear from people and see message board posts from others who get frustrated about how to teach young kids math, and although I understand why-- many, many people do not have happy memories of math from their own childhoods-- I have to say, math is a source of a lot of fun for my grammar stage (generally K--4) Son#2.  Why?  The concepts at this stage are so readily presented in a concrete, almost game-based form, and discussing the math in this format before getting down to the text/workbook lesson is just so much fun.  I don't have some magic resource for our games and ideas (other than a few that came from the Life of Fred Elementary series, a very fun way of approaching math during these years).  Mostly I look at the textbook-- for us that is Singapore Math, US Edition-- and let it inspire me.  I often do not have a plan before we sit down; I just let stuff happen.  It seems to work pretty well.

One new inspiration happened today.  We were reviewing factoring, and the textbook had arrays of pictures to illustrate various numbers.  We happened to have a set of several pipe cleaners on the table, so I grabbed them, and challenged DS2 to use them to illustrate different ways to factor the various arrays.  He illustrated the factors of different numbers several different ways, and despite a week's vacation from the previous lesson, he had the concept down pat in about two minutes (but kept playing with the idea for several more just for fun).

I have collected here some prior ideas that I have posted in various message boards; they're easier to locate here than buried as post#20 in thread#403,455,786,778 :).  These are all real activities that "just happened" for us at one time or another:

  • One day we were reviewing, and I opened up the fraction stacks and c-rods (Cuisinaire Rods-- in our case, unmarked wooden rods cut to different unit-lengths and each length colored a particular color; Fraction Stacks are marked and sectioned, and stack, connecting to one another) and told DS8 to just play for a bit. Then I asked him to find the sum of 1/4 and 1/2 using the stacks. He messed around, then swapped out the 1/2 block for 2 - 1/4 blocks and came up with 3/4. We got tougher and added 2/12 plus 1/3 plus 1/4 and he did the same thing eventually, swapping out all blocks for the correct number of twelfths blocks, and then figuring out how to simplify 9/12 to 3/4 by swapping them back out with the quarter blocks.
  • We did similar things with compare the fractions exercises-- what is bigger-- 2/8 or 1/6? Make a prediction, then compare. Can we simplify 2/8? Oh yeah, 2/8 = 1/4! Of course 1/4 is bigger than 1/6! It means one whole was only cut into four pieces!
  • We have used C-Rods to imitate the bar diagrams Singapore uses to solve its word problems.
  • Place a long stick (Tinker Toys work well!) across a plastic clock face to demonstrate quarters, halves, or thirds, and relate it to telling time. Cut out matching fraction shapes from paper plates to cover parts of the clock face to illustrate further if needed.
  • Measures are easier still... Grab measuring cups and rulers, and pour spill and measure and compare everything in your house. Do it before opening the book.
  • Area... Get those blocks back out (on a smaller scale, you can use the c-rods again). Use the square blocks as a unit block to figure out the area of different composite and rectangular shapes you create, and to measure their perimeter. Measure them with a ruler. Can you find a rule?
  • Adding, subtracting, multiplying, dividing-- put a giant stack of crayons or colored pencils or pennies or Legos or Playmobil guys or M&M's to great use. Take a page out of Life of Fred: Apples. If you have a pile of 7 (or any other smallish number), how many ways can you divide them up to add up to 7? How about cool numbers like 12 or 24? Can you find all the factors? Can you find common factors?
  • Collect stacks of coins or other differentiated counters, or make your own. Model Singapore's picture models-- ones, tens, hundreds, thousands, etc, and do calculations with them to understand why there is no "Borrowing," but instead "Redistributing" or as we like to call it, "Busting open" or "Tying back up." It will never be more clear why 5 ones and 5 ones make 10 ones, or one ten.

Singapore says upfront it starts with concrete. You have to provide the concrete as the flesh and blood teacher.  If you find coming up with ideas to be a challenge, there are Home Instructor Guides available to provide those ideas.  Let your child explore the idea first, then provide some guidance. Let him explore some more, the let him answer some questions and gain confidence in the idea with the manipulatives. When the lightbulb goes on, then it's time to get out the book.

You can always leave the toys out for them to explore on their own later. You may be pleasantly surprised at what creative ideas they come up with on their own. Or, your child may simply build a house out of the C-Rods, and that's okay too :)

--Thanks for Reading!


Shakespeare, on Homeschooling

Just for fun

Here in this island we arriv'd, and here
Have I, thy schoolmaster, made thee more profit
Than other princess' can, that have more time
For vainer hours, and tutors not so careful.

"Heavens thank you for't!"

(Prospero, stranded on an island with his daughter for twelve years at this point with his daughter Miranda and the monster Caliban, reflects upon the benefits of homeschooling)

--The Tempest, Act I, scene ii
Thank you to L. Nick Trefethen and the wonderful Kate for the reference!