May 14, 2009 - Hands-on Estimating
Estimation is a very valuable skill in real life, so I tried to make the study of it somewhat real by staging a shopping experience. We used some of Sprite's Sculpey clay foods, loosely taped onto blank business cards. Then we gave each item a price. (It's not dollars but just some unknown unit, so the prices didn't have to be realistic in any specific economy.)
We used monopoly money as our currency. (Perfect! I finally didn't have to cut little slips of paper for this living math activity!) And then we just played around -- not really a game per se with a winner and loser, but just experimenting with the foods.
We each chose a meal and then compared -- who had the most expensive meal?
I planned a day's worth of meals, and gave Sprite 200 units of money. Did she have enough to pay for it? She used estimation to solve the problem. Then she gave me problems to solve.
Then we reversed the process. I have her an amount of money and had her use estimation to plan three meals for one day and stay within budget.
Why is this fun to Sprite? The math skills are identical to solving problems in a workbook, but she adores doing these kinds of role plays. Is it the toys? The play money? The silliness? Yes, it's certainly the silliness. We made some funny meals -- spaghetti, a pumpkin, and an ice cream cake, for example. We laughed about wanting pie for dinner!
It took a small amount of prep time to set up, but the pay off is so worth it. Excitement towards math is a wonderful reward for a few minutes of making tape loops!
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April 24, 2009 - Living Math with Area and Perimeter
Studying area is a great topic for comparing ways of teaching math. In the "old days" before my living math transformation, I would've breezed over the diagrams in the book as quickly as possible to get to the "real lesson" -- the formula A= l x w so we can work the problems.
But not the new improved living math Jimmie. No, I now realize that jumping too quickly to an abstract, albeit simple, formula does not foster true mathematical comprehension.
So we learned about surface area the hands-on way
with lots and lots of squares. It seems that doing living math in our house requires lots of colored squares. (It's a good thing that I have a real fetish for paper. I have all colors and thicknesses, so I'm never at a loss for something to cut up into manipulatives.)
Another great hands on tool was laminated graph paper and Vis-a-vis pens. We drew squares and irregular shapes and then counted the area and measured perimeter. We rolled a die for numbers of sides and then drew figures to see who could create the object with the longest perimeter or largest area. We marveled over shapes with identical areas but vastly different perimeters.
By the way, my favorite place for graph paper is Incompetech's PDF generaotor which you can set to whatever size you want. We chose 1 centimeter squares and 1 inch squares.
Living Math Hint --One thing I've discovered is that the "game" aspect doesn't have to be thoroughly planned out. Just spinning a spinner or dealing cards seems to make the math activity a lot more motivating.
I'm going to be honest with you. You and I know to multiply the number of rows and the number of columns to find out how many squares total. Well, I thought that would be painfully obvious to Sprite as well. But it was not immediately obvious to her. I let her count a gajillion squares until I tried to nudge her towards a simpler way than counting. It was still a bit hard to grasp. So do you know what I did? I stopped doing math that day before any frustration set in. And the NEXT day, we played a different game with the squares. She needed more experiences with the idea of area to really understand how length times width gives us the answer. And eventually she SAW the connection.
Later we used small boxes and traced all six sides onto the graph paper to determine, hands-on style, the surface area of a three -dimensional form.
Then we moved to circles a la lids. The green yarn was used to measure the circumference and diameter of each disc.
Can you see that Sprite's page has P = in front of the strand of yarn? Yes, that means perimeter. I told her to measure the distance around and to mark it on her paper. She used the word she had learned previously. And why not? Circumference is just the perimeter of a circle, isn't it? The technical word can wait.
This is living math in which we do not burden children with technical jargon unless the words are necessary or the child asks. Sprite asked me what to call the distance across the circle since she had no handy word for it. Thus she has D= on her paper for diameter.
Supposedly we could compare the ratios of the diameters and circumferences and get Pi, but I think our yarn was too stretchy and thus our figures were not accurate. So we left that for another lesson.
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April 1, 2009 - Rice Krispy Treats Math
When we were recently in another city with Western foods, I bought some marshmallows and Rice Krispy cereal to bring home. So you know where this is going, don't you? Sure! We made Krispy treats. (I think it was Sprite's first time ever!)
So after we let them set in the refrigerator for a while, we cut them up to enjoy our "hard work." Trying to emphasize math as much as possible, I asked Sprite how many pieces we'd have since I was cutting the four rows into four pieces. She answered correctly, and we each ate one. Yum.
Then I realized our dilemma and decided to use it to my advantage to have some math fun! There were 14 left, and we're a family of three. So I asked Sprite how we should divide them evenly. She proposed some solutions, but none of them worked to divide 14 Rice Krispy bars evenly three ways.
I gave her a hint, "What if we ate some more? How many would we need to eat to have a number that's easy to divide by three?"
I could see by the glint in her eye that she understood my devious plan. We each ate one more rice krispy treat.
Then the next day we divulged to my husband what we'd done, all in the name of fairness. I mean, this was the only way we could each have the same number -- four each.
Funny, he didn't see it that way.
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March 12, 2009 - Graphing and Tangrams with Living Math
More adventures into living math!
I took a look at what topics in our Singapore Math we had not yet finished. Then I went through my Family Math book to find or think of hands-on activities and puzzles that would teach those concepts.
Graphs were easy enough. For data, we went to the sidewalk and recorded the types of vehicles that passed during a four minute period. We had quite a discussion when a woman pushing a wheelbarrow passed by. Is a wheelbarrow a vehicle? Sprite decided it did qualify as a vehicle, so it got added to the data sheet.
First, I have Sprite number blocks and asked her to create a graph of her data with them. I got this idea from Westward's blog post of making 3D graphs.
Then she input this data at this site to make a fancy circle graph.
Another topic was angles, so I chose tangrams. We read our brand new book The Warlord's Puzzle, made homemade tangrams with craft foam, and of course solved tangram puzzles. (All of the tangram resources are linked at Tangrams.)
Sprite created some tangram inspired art and ATCs (artist trading cards) as well.
Jockeys on horses.
These ATCs are a work in progress that we will finish later.
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March 5, 2009 - My Living Math Book List
I had a couple of requests for my Amazon living math book list. So here it is.
I actually went so far as to make a list at Amazon to keep it organized as I was deciding what to buy. That listmania list is called Living Math Assortment. I kept adding and deleting things and once it was exactly what I wanted, I simply hit "add all to cart." Voila! Here are the titles with prices.
1 "Brown Paper School book: Math for Smarty Pants"
Marilyn Burns; Paperback; $10.19
2 "Brown Paper School book: I Hate Mathematics! (Brown Paper School Books)"
Linda Allison; Paperback; $10.19
3 "The Librarian Who Measured the Earth"
Kathryn Lasky; Hardcover; $12.23
4 "The 5,000-Year-Old Puzzle: Solving a Mystery of Ancient Egypt"
Claudia Logan; Hardcover; $13.60
5 "Seeker of Knowledge: The Man Who Deciphered Egyptian Hieroglyphs"
James Rumford; Paperback; $6.95
6 "The Wonder Clock (Starscape)"
Howard Pyle; Paperback; $5.99
7 "Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians"
Luetta Reimer; Paperback; $17.95
8 "The Joy of Mathematics: Discovering Mathematics All Around You"
Theoni Pappas; Paperback; $8.76
9 "Math Talk: Mathematical Ideas in Poems for Two Voices"
Theoni Pappas; Paperback; $8.95
10 "The Great Number Rumble: A Story of Math in Surprising Places"
Cora Lee; Paperback; $10.17
11 "The Warlord's Puzzle"
Virginia Walton Pilegard; Hardcover; $10.85
12 "The Warlord's Beads"
Virginia Walton Pilegard; Hardcover; $12.44
13 "What's Your Angle, Pythagoras? A Math Adventure"
Julie Ellis; Paperback; $7.95
14 "The Warlord's Puppeteers"
Virginia Walton Pilegard; Hardcover; $15.95
15 "The Adventures of Penrose the Mathematical Cat"
Theoni Pappas; Paperback; $8.76
16 "Further Adventures of Penrose the Mathematical Cat"
Theoni Pappas; Paperback; $8.76
I got most of these titles from recommendations by Julie at Livingmath.net. I purchased her lesson plans for Cycle 1, Unit 1 Intermediate level. On the right side, there is a book list. I pored over that list and her lesson plans and sought input from moms at the Living Math Yahoo group. I read Amazon reviews and finally compiled the list above.
And in addition to those math books, I ordered the Draw Squad book, two books on the Periodic Table, and Hitty.
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