Mini Abacuses

My husband uses a bead counter for gaming. He asked me to make him one to count into the 100's and this was the result. The other day, when it was out with his cards, I realized that it was a sort of mini-abacus. These little devices are great for kids, especially the ones who tend to be more visual-spatial and want to "experience" the numbers somehow. I can relate to the need to "experience numbers" but many parents and teachers have never felt this need and underestimate its impact for these kids. It certainly doesn't hurt other kinds of thinkers either.

Practical Use
We go eat a lot of potatoes in my house, so much so that I was thinking of buying larger quantities and putting them into a bin filled with sterilized sand to keep them fresh. However, I'd hate to have some getting really old at the bottom of the bin because I reloaded without realizing I still have some potatoes. A string of beads hung in the pantry nearby should be an easy way to keep track of the potatoes. But I digress....you probably want to know how to make these.

Building a Bead Counter
The only materials required are plastic pony beads (less than a penny each when bought in packs) and the cheapest polyester yarn you can find. These beads are nice because they are durable and uniform. I used double-thick yarn to string them. When the cheapest Red Heart brand yarn is doubled, it provides just the right amount of resistance for pony beads, keeping the beads in place but still easy to slide.

For a three-section bead counter, cut about 4 feet of yarn and fold it. If you have a needle that the yarn will go through, fantastic, if not glue (and allow to dry) or tape the ends to ease beading. Tie a knot an inch or so from the looped end and add ten beads to the doubled-up yarn. (The loop is great for hanging or attaching to something.) Leave about 2 inches of space before tying another knot or two. Repeat this action two more times so you have three sets of beads. Trim the end and you're done!

You can change the colors of the beads if you'd like, giving a new color for each place value. However, please do not use a mix of colors within each set of ten. Uniformity will simplify the use of these counters and lead to less confusion.

Alternatively, you can use yarn and pony beads to make something more like an abacus by making a sturdy wooden frame and threading the bead-strung yarn through it. (Just use double-thick yarn and plastic pony beads or experiment with other materials to get the right resistance.) This way you can use larger numbers or even decimals by assigning each row it's own place-value. If building a frame is not for you, try using small picture frames with the glass removed.

I'd write-up a little about using these counters but there is a lot of good information already out there. Peter Waycik's article on using the abacus in the classroom might give you some inspiration.

Alien Mutant Plants of Doom: Building the Foliage

These are the instructions for building the flower components to Alien Mutant Plants of Doom, a math puzzle. You will be building flowers and vines with stems. Since these are alien plants, the color doesn't matter. In fact, the flowers you buy can be the strangest looking ones in the store.

I considered making these with floral tape but the floral tape isn't durable enough for this kind of use. You can also substitute duct tape or masking tape. However, the electrical tape has a wonderful sort of elasticity to it that makes it just about perfect.

You need:
one bush of flowers with at least 6 stemmed blooms (I found mine at Dollar Tree)
12 bamboo skewers (I pilfered mine from my pantry)
electrical tape (again, pilfered, this time from the garage)
wire cutters
a pencil

Make the Flowers:

Remove the blooms from the stems.






Use wire cutters to blunt the ends of the skewers by cutting off about ¼.”






Place each bloom onto the narrow end of a skewer.






Wrap the length of the stem in tape. Start at the top and wind down toward the bottom.





Cut off about an inch of tape and wrap around the bloom/stem junction to secure further.





Make the Vines:

Remove and discard any leaves left on the stems.
Use wire cutters to remove individual stems from the bush.





Cover each stem with tape by wrapping down the length as with the flowers.





Wrap each tape-covered stem around a pencil to create a coil.






Attach the coiled vines to the pointed end of the skewers using tape.






Wrap the length of the bamboo skewer with electrical tape.

Activity: Alien Mutant Plants of Doom

This is an adaptation of the puzzle, the "Sword of Knowledge." In the original, a dragon starts with 3 heads and three tails. Using the Sword of Knowledge, the heads and tails must all be removed to slay the dragon. But there are, of course, certain conditions.
I adapted this puzzle to make it colorful and interesting.

Each puzzle requires:
- 6 vines (see component building or instructions with pictures)
- 6 flowers (see component building or instructions with pictures)
- 1 plastic or ceramic flower pot
- small pebbles - Often available in bags at Dollar Tree. Pea gravel and sand can also be substituted. Rough gravel or stones are harder to use.

Cost Breakdown:
$1 Bunch of silk flowers (at least 6 per game) – Wal-Mart or Dollar Tree
$0 - $1 Long bamboo skewers (at least 12) – Taken from my own pantry
$0 - $1 Electrical tape (you can substitute duct tape) – Taken from my garage
$0 - $1 Pot (plastic or ceramic) – Taken from my garage
$0 - $1 Small smooth stones, pea gravel, or sand – Wal-Mart or Dollar Tree
$0-$5 Total Cost

Assembly:
Place the pebbles into the pot. If there is a significant hole in the pot, cover with tape or cut a piece of cardboard to fill the bottom of the pot. Place three flowers and three vines in the pot. Lay three additional flowers and three additional vines beside the pot.

Display a board with the instruction sheet and the grid that shows what happens with each action. Alternately, you can provide the instructions as a large card with the grid on the reverse. To make the card, print the instructions onto cardstock and print the grid on the back. The grid is a helpful aid but it’s nice for participants to read and understand the puzzle before seeing the grid. Whether the grid is in plain sight or available after reading the directions, it’s important to have. It illustrates one way to organize information and make the connection between the written puzzle and a practical list of options.

The Puzzle:
Evil mutant plants of doom have landed on Earth. The plants are very destructive to the planet and mankind. Unless they are destroyed, they will grow until they fill the entire surface of the planet! Each plant has three flowers and three vines. You must destroy the plants by removing all of the flowers and vines. You can remove flowers and vines but you can only remove one or two at a time. When you remove a vine, two vines grow in its place. When you remove a flower, a new flower grows in its place. When two vines are taken off, one flower grows. Taking off two flowers results in no extra growths.


Encouraging Problem-Solving:
This puzzle is a great opportunity to use the strategies “Trial and Error” and “Look for a Pattern.” It’s important that participants are encouraged to dig in and try it rather than standing around thinking too much about it. In this puzzle, making mistakes is a very good way to discover the strategy that works to solve the problem.

Solution:
The key to the puzzle is to realize that you can’t leave one flower behind, or the plant will never be destroyed. Also, it’s important to see that nothing grows back when you remove two flowers at a time.

One possible solution is:
Remove two vines. (a flower grows)
Remove one vine (two vines grow)
Remove one vine (two vines grow)
Remove one vine (two vines grow)
Remove two vines (a flower grows)
Remove two flowers.
Remove two flowers.
Remove two flowers.

Component Building
Supplies:
Bunch of silk flowers (with at least 6 blooms)
Long bamboo skewers (12)
Electrical tape
Wire cutters
Pencil

Flowers:
- Remove the blooms from the stems.
- Use wire cutters to blunt the ends of the skewers by cutting off about ¼.”
- Place each bloom onto the narrow end of a skewer.
- Wrap the length of the stem in tape. Start at the top and wind down toward the bottom. Cut off about an inch of tape and wrap around the bloom/stem junction to secure further.

Vines:
- Remove and discard any leaves left on the stems.
- Use wire cutters to remove individual stems from the bush.
- Cover each stem with tape by wrapping down the length as with the flowers.
- Wrap each tape-covered stem around a pencil to create a coil.
- Attach the coiled vines to the pointed end of the skewers using tape.
- Wrap the length of the bamboo skewer with electrical tape.


I have a PDF available of all instructions as well as the instructions sheet and grid shown here:

Preparation

I've got some projects lined up for this site but most aren't ready for posting. I'm digging through my Family Math Night computer files for games that I've made. Unfortunately, I don't have the games anymore as they were given to the school that used them. I also don't have pictures of them.

It's just as well. I can rebuild them with some pictures and instructions so other people can reproduce them. It will be math and craft combined. Don't worry, it's not hard and it's not expensive.

All teachers and schools are on budgets and Math activities are restricted in the same way. It is a challenge to make a full color activity set-up for under $5 but it can be done! Creativity is the key. There is no reason you should have to go out and buy specialty manipulatives for math activities.

My Math Rant

When I was a kid learning math seemed weird and officious. Half of the time I thought the teachers were nuts when they explained how numbers could be used, as though they were trying to convince us to buy something. When I was excited to "discover" something about math, something which we would be later taught in some methodical fashion, the teachers would often wonder what I was talking about. Most seemed unable to relate to math outside the context of a lesson. This sounds very computationally elite and snobby of me but sometimes I think I understood the nature of numbers better than they did because I didn't have the good sense to be terrified of math.

I thought I would probably stop taking math after high school. It seemed to be more of memorization than anything. It was boring and nobody ever bothered to explain the connections. When I was older, the larger concepts began to unfold more sensibly. I finally saw the grander picture--or pieces of it. Why don't more high school teachers encourage kids to think about math conceptually? Probably the better question is, why does math have to be such a terrifying experience in grade school?

Many elementary-level teachers aren't enthusiastic about math. I took a lot of math in college with the goal of teaching it. While on this path, I also took various courses on elementary math instruction because I thought it could be helpful. My adviser told me he could waive the elementary math methods classes because of the amount of upper-division math I had already taken. However, understanding how educators embraced the development of math concepts in younger kids was of interest to me.

What I discovered shocked me. Future educators were being taught some truly dynamic math development concepts. Why didn't they teach it like this to kids? A big problem was that the university professors were excited about their subject and the students, future elementary-level educators, were not. A good percentage of my fellow students were on their 2nd time in the classes (after receiving failing grades initially.) This was not the case universally but it was true far too much of the time.

Many of these future teachers admitted being terrified of taking these classes because they "always hated math." It only takes one teacher's clear dislike of the subject to alter a child's perception irrevocably. Clearly, "hating math" is a case of the chicken and the egg.

We've somehow raised generations of math phobics. However, the previous generations are just as queasy about math and so on and so on. As a result, subsequent generations of teachers are often very single-minded in their approach to mathematics education, relying on memorization of formulas and even confusing the use of manipulatives. Too many kids are learning rote methods of computation without any clue that there are conceptual equivalents. If a kid has a question that is not directly dealt with in the teacher's manual, it may not be addressed and a curious child will become a hardened one. They don't get the play with the numbers and see what they can do. No monkey bars with 4, no tag with 7, nothing.

Kids need to learn that it's ok to take their numbers out to play, that there is more than one way to divide or multiply. Dividing by a fraction isn't about "flipping over" the divisor and multiplying. What if you can't remember the rote method for dividing by fractions? What do you do then? If you are comfortable rooting through the mathematics toolbox, there are numerous tools to help you reinvent the wheel so you don't have to memorize strict methods of computation.