Farmer Boy Math

I cannot believe that it is almost Thanksgiving! The school year is flying by! This month went SO much better. I had a feeling that being more focused on math and less on writing would make Dallin very, very happy.

Here is a sample day in our lives:

5:30-6:30 am Mom wakes up

7:30-8:30 am kids wake up

8:30-9:00 am breakfast

(I'd really like to get going faster in the mornings, but right now I'm content to focus on all the things that are going well and not fret about the things that could go better!)

9:30-9:45 family prayer and scripture study

10:00 put Preston down for a nap while Dallin does daily math practice (a homemade worksheet with problems written especially for him by Mom)

10:20 or thereabouts weather chart--we are charting the wind direction and strength every day

Daily language: poetry recitation, riddles and tongue twisters, or spelling and short grammar work

Times Table practice--oral recitation with movement or games

Dallin takes a break and does silent reading while Sariah has her circle and story time

Math game of some type

Recall of our story-of-the-month (Farmer Boy, which we read at night) and word problems relating to it

Other projects, artistic, practical, or otherwise

By this time it's usually around 1:00 pm and time for lunch

After lunch it's time for kindergarten projects like baking, soup-making, crafts, etc.

And then starts our round of piano lessons, mom's organ lessons, Primary presidency meetings, etc. in the afternoons.

So I thought I'd divide this blog post into segments detailing some of the main components of our day (during a Math Block, things would be somewhat different during a Language Arts block).

Daily Math Practice:

Every morning I make up a handwritten worksheet with problems based on things I think Dallin needs practice with. Now, I don't literally make up the problems--I went to a math teacher's website and printed out tons of worksheets with progressively more difficult problems in addition, subtraction, multiplication, and division. I just pick and choose each day the ones to copy onto my homemade worksheet. This month we've been reviewing columnar addition and subtraction with carrying and borrowing. We also worked extensively on columnar multiplication and introduced carrying. We re-introduced division but only in horizontal form. I think he finally "gets" division! He also has 30 easy problems a day from the Making Math Meaningful book--these are problems related to basic math facts that he needs to be able to know instantly.

Daily Language:

We took our Farmer Boy block from Marsha' Johnson's files at the Waldorf Home Educators yahoo group. We learned some poems about the month of November. Both kids also had a really fun time learning this rhyme from the files:

Pretty Kitty Creighton had a cotton batten cat,

The cotten batten cat was bitten by a rat.

The kitten that was bitten had a button for an eye,

And biting off the button made the cotton batten fly!

Who knew that would be so much fun? We learned some other alliterative verses as well, but that one was the biggest hit.

The last week of the block, we returned to the spelldown using the 500 most common words in the English language. We are now almost through the 300's! We also reviewed adjectives and adverbs, which we introduced last month. Daily language takes at most about 15-20 minutes a day.

Times Table practice:

I got the book Active Arithmetic by Henning Andersen. This is a fascinating book from a theoretical perspective! In Waldorf education, math--and in this particular instance, the multiplication tables--are taught using lots of rhythm and movement, and this book is full of ideas on how to do that. Most of them were more suited for a group of children, rather than one homeschooled kid. But some we adapted. One day I put marks on the kitchen floor with tape, 12 of them in a line. We practiced the 3's times table--hopping on 1 and 2, then landing with both feet on 3... hopping on 4 and 5, then landing hard on 6, etc. I had him practice the whole entire table that way, then I did the 4's table (hop, hop, hop, jump) while he did the 3's, and we noticed the places where we jumped together. Pretty fun--and difficult to do!

I love this quote from the book:

"It has been said of music that the greatest importance is to be found less in the actual notes than in the effort our souls must make to move from one tone to another. The notes are like the milestones we find on the roadside, but it is the space in between them which moves us along...

It is the same with the tables. It is not the numbers we experience, but the space to be found between them. It is this which gives each table its own particular character, and our feet help us to understand this.

If we merely teach our pupils the numbers 3-6-9, etc., it would be the same as teaching them the mile markers between Boston and Washington, which would not be much of a geography lesson!

Our thoughts can jump over the spaces, but our feet cannot. On the contrary, our feet are a yardstick for the intervals, and it is here that the children live."

Pretty cool stuff!

Now this was fun! I taped the numbers 1-12 on the floor in a circle, like a clock. I had Dallin jump each table and see what pattern it made on the floor. (When you do this, you do it using the skip counting--so on the 3's table, you jump from 12--the starting point--to 3, 6, 9, back to 12, then keep going every three squares... even though after you've gone around the circle once, the number written on the square won't correspond with the number you're saying out loud.) Jumping the 3's table makes a square, the 4's makes a triangle, 5's makes a star, 6's makes a straight line, 12's you just keep jumping up and down on the number 12--Dallin thought this was hilarious. He also, all on his own, connected this activity to the multiplication clock we made last year using nails and string.

As one of our other math projects this month, we also made yet another multiplication clock, Robinsunne's multiplication clock. (The directions are HERE.) Even though we made lots of smaller clocks and also a big chart last year, I think it is good for Dallin to go through the process of doing it again and again. Basically, you write each table around in a circle, starting with 1's in the middle, all the way to 12's at the outer edge. I was very pleased that Dallin--all on his own--discovered that the tables also appear in the "spokes" of the clock.

Math Games:

We were very busy with math games this month! I relied heavily on the book Games for Math, by Peggy Kaye.

This was a place value game. Each glass represents a "place" (tens, hundreds, etc.) We threw little pieces of pasta in the cups, and got points depending on where they landed. So if six pieces landed in the "thousands" and four pieces in the "hundreds", then he had 6400 points. The person with the most points won. This game was hard! But he had a blast, and he reviewed place value without even knowing he was reviewing!

Another great game from the book was "Biggest and Smallest". So easy! You roll two dice and make the biggest number you can (a 6 and a 3 would give you the number 63). Then you roll the dice again and make the smallest number possible. Then you subtract the smaller number from the larger. The answer is your score. On your next turn you do the same thing, then add that answer to your score. So with each turn you are getting practice both subtracting and adding, and sometimes there is carrying or borrowing involved. The first person to reach 100 points wins. The next day we made the game harder by using three dice instead of two and going to 1000 points.

The book is full of fun and simple games like these! Those are just two of the ones we played.

This is an illustration of an activity called "Numbers Must Tell the Truth" from the book Math Lessons for the Elementary Grades by Dorothy Harrer. We talked about how numbers cannot lie, for example, 9 + 1 cannot equal 8. We did the equations on the left hand chalkboard. (I got lazy about illustrating it with red and blue dots...) Then, I put the same numbers--without symbols--on the right hand board and told Dallin that he needed to change the process signs so that the numbers still told the truth. This was a really good activity for Dallin he hadn't completely grasped the idea that, for example, addition and subtraction are opposites of one another. We did a number of written exercises with this concept that week, using all four processes.

Below is just one example of the word problems we did. We did several days of word problems each week related to Farmer Boy. I made up problems based mainly on multiplication and division, since that is what he needs the most practice with. We chose just a few each week to copy into his main lesson book. You can't really read it, but these story problems had to do with the potatoes that Almanzo and his siblings planted. If one potato has six eyes, how many eyes will there be on 8 potatoes? (In our always-perfect world, all the potatoes, naturally, have the same numbers of eyes!)