Math - Guilt-Free Homeschooling

Workshop Wednesday: Money Land Game

January 15, 2013 by CarolynM Leave a Comment

I absolutely love to teach with games. Playing a game transitions a lesson concept from tedious drill to fun and… well, games. My kids might have balked at the idea of doing yet another set of math problems, but they would voluntarily play board games using money, which required the same adding and subtracting as the math problems — only they could do the money problems aloud or in their heads while handling all those tactile game parts, instead of writing them on paper. The ability to do math in your head is a distinct advantage in life, so I encouraged my kids to play money games as often as possible, but they didn’t need much encouragement at all. They loved to play board games of all types, and games with money were a distinct favorite.

I also believe in borrowing equipment from games and combining those components to create a new game or a new variation of an old game. This is how we got here today, coming up with a new variation of an old game (Candy Land) that often falls into disuse once its players begin to read and move on to more complex games. By adding the math component of money, the Candy Land game once again appeals to older students, and with several variations that increase the complexity of the money transactions, this game can help students of all ages hone their mental math skills in a very stealthy way. Every turn provides all players with opportunities to improve their math skills, whether to avoid paying fines or to catch another player in a mistake and collect a fine from him. Winning the game is highly dependent on chance, giving all players an equal playing field. (Notice that the fines are not intended as meanness, they are simply incentive to pay attention during other players’ turns and to make players aware that they are doing their own math correctly. The fines also provide another way for an alert player to make money. The fines are intended as a sporting challenge, not a way to make fun of other players. Fines may also be optional — see Fines section below.)

Instructions:

Basic Version #1 — Use the game board, cards, and pawns from a regular Candy Land game, but include the money from Monopoly, Monopoly Junior, or any other source. Begin a money “pot,” by placing $5 (in any combination of bills) on the Home Sweet Home area of the Candy Land game board, and give each player a total of $50 in bills of various denominations. Players do not all need to have the exact same denominations of bills, as long as they all start with the same total. (Suggested amounts for each player — standard denominations: 10 $1’s, 4 $5’s, 2 $10’s; Monopoly Junior denominations: 6 $1’s, 5 $2’s, 4 $3’s, 3 $4’s, 2 $5’s) Any leftover bills should be set aside and not used.

Assign the following number values to the Candy Land color cards, based on the colors of the Candy Land game board:

Purple square = $1
Blue square = $2
Green square = $3
Yellow square = $4
Orange square = $5
Red square = $6

Place the shuffled stack of cards face-down near the starting square. Play begins with the oldest player and proceeds to his left. Each player in turn draws a Candy Land card and moves his pawn to the nearest square of that color as in a normal game, but when his pawn lands on the square, he must pay the corresponding amount listed above into the Home Sweet Home pot. (The Rainbow Trail and Mountain Pass shortcuts have no significance in this game and are not used.)

Special Plays:

Doubles card — Player moves to the appropriate square and collects an amount of money from the pot that is equal to double the dollar value of his color square (Example: a double-red card = $12). The player may then take a bonus turn.

Sweet Treat card — Player moves to the appropriate square, collects all the money in the pot, and takes a bonus turn.

There is no limit to how many Doubles and/or Sweet Treat cards may be drawn in succession by a single player, as long as the pot contains sufficient funds. However, if the pot does not contain enough money when a player draws a card that would allow him to collect more, that player collects all the money available in the pot, his turn ends, and play moves to the next player. If there is no money in the pot, the player’s turn ends, and he does not move his pawn.

Sticky Spot –– A player whose pawn lands on a Sticky Spot must pay double the amount for its color, but may move on his next turn (he is not required to remain on that square until the appropriate color card is drawn). No bonus turn is awarded. In the rare event that a player draws a Doubles card that lands him on a Sticky Spot, no money is either paid or collected, and the player’s turn ends.

Fines — If a player either pays or collects an incorrect amount of money, or pays when he should be collecting, or collects when he should be paying, any other player who notices this mistake may point it out at the end of the player’s turn, before the next player has drawn his card. In the case of a player who has earned a bonus turn, the mistake must be pointed out before the next card is drawn. In each case, the player who made the mistake must correct the amount AND pay a $5 fine to the player who pointed it out. If a player catches himself in a mistake and corrects it before the next card is drawn, no fine is required. (Fines may be considered optional, especially when young players are just beginning to learn math facts. The fines can also be imposed by much younger players against more experienced players, and not vice versa, depending on the skill levels involved.)

Players who need to do so may make change from the pot in order to obtain the correct amount required for their turn. (Example: A player owing $8 to the pot may pay with a $10 bill and remove $2.) A player may also trade a large bill to another player in exchange for an equivalent amount of smaller bills, if the pot does not contain a sufficient amount for exchange.

If a player’s pawn lands on an occupied space, the other player’s pawn is moved backwards to the nearest empty space. The owner of the moved pawn does not pay or collect any money because his pawn was moved.

If the stack of cards runs out before the game has been won, the stack should be shuffled well and turned over to start again.

A PLAYER’S TURN ENDS WHEN —

1) he has drawn a card, moved his pawn to the appropriate square, and paid the correct amount into the pot, OR

2) he has met condition #1 as a bonus turn, following a Doubles card or Sweet Treat card, OR

3) he has collected less than what was owed to him from the pot, because it didn’t contain enough money, OR

4) he pays all of his remaining money into the pot. Any player who runs out of money during the game is out for the remainder of the game.

THE GAME ENDS WHEN —

1) one player ends up with all the money, OR

2) the game is down to the final 2 players and one is eliminated by running out of money, OR

3) one player reaches Home Sweet Home and collects any money remaining in the pot. Home Sweet Home is considered to be located anywhere after the final square of the trail (no exact count is needed). A player whose pawn lands on the final square is not considered to have reached Home Sweet Home until his next turn, provided he draws any color card and not a Sweet Treat card that would send him back to another location on the trail.

Winning — Winner is the player with the most money at the end of the game.

Basic Version #2 (Dice-Addition) — Include a regular, 6-sided game die. Players will add the number on the die to the card’s dollar value. The rest of the rules apply as above, with the only change being the amount of money paid or collected on each turn. Each player rolls the die in addition to drawing a card, and alters the dollar value of the card according to the die. If any bonus turns are awarded, the player draws a new card and rolls the die for each additional turn. The die is not rolled whenever a Sweet Treat card is turned up. The amount paid for a Sticky Spot is not affected by the die. In the case of rolling Doubles and collecting money from the pot, the number on the die is added to the doubled value of the color square (Example: double-red = $12 + 4 on the die, collect $16).

ADVANCED VERSIONS FOR PLAYERS WITH HIGHER MATH SKILLS

Advanced Version #1 — Play proceeds as in Basic Version #1, but players receive a starting total of $200 (Suggested amounts for each player: 10 $1’s, 4 $5’s, 3 $10’s, 2 $20’s, 2 $50’s). The starting pot is increased to $20, and Fines are also increased to $20 each. The dollar value of each square changes as follows:

Purple square = $1
Blue square = $4
Green square = $8
Yellow square = $12
Orange square = $16
Red square = $20

Advanced Version #2 (Dice/Addition) — Include a regular, 6-sided game die. Players will add the number on the die to the card’s dollar value. Play proceeds as Basic Version #2 (Dice-Addition), but increases the starting value of the cards to Advanced Version #1 levels before adding the number shown on the game die. Pencil and paper may be used for calculating correct values. Starting pot is increased to $100, and each player’s starting total of cash is increased to $500 (10 $1’s, 4 $5’s, 7 $10’s, 5 $20’s, 4 $50’s, and 1 $100’s). Fines are also increased to $100 each. If any bonus turns are awarded, the player draws a new card and rolls the die for each additional turn. The die is not rolled whenever a Sweet Treat card is turned up. The amount paid for a Sticky Spot is not affected by the die. In the case of rolling Doubles and collecting money from the pot, the number on the die is added to the doubled value of the color square (Example: double-red = $40 + 4 on the die, collect $44).

Advanced Version #3 (Dice/Multiplication) — Include a regular, 6-sided game die. Players will multiply the number on the die times the card’s dollar value. Play proceeds as Advanced Version #2 (Dice-Addition), with the only change being the amount of money paid or collected on each turn. Pencil and paper may be used for calculating correct values. Starting pot is $100, Fines are $100 each, and each player’s starting total of cash is $500. If any bonus turns are awarded, the player draws a new card and rolls the die for each additional turn. The die is not rolled whenever a Sweet Treat card is turned up. The amount paid for a Sticky Spot is not affected by the die. In the case of rolling Doubles and collecting money from the pot, the number on the die is multiplied times the doubled value of the color square (Example: double-red = $40 x 4 on the die, collect $160).

Advanced players may choose to play subsequent games, continuing with the cash accumulated from previous games (instead of re-counting to starting cash amounts). In this case, no cash is placed on Home Sweet Home as a starting pot. Each subsequent game is started by the next player to the left of the one who began the previous game. Very advanced players may choose to add more than one die to Advanced Versions #2 & 3.

© 2013 Carolyn Morrison. These rules may be printed for personal use or shared for free, but these game concepts and their rules may not be reproduced for sale. This copyright restriction must appear on any printed copies.

Filed Under: Activity Ideas, Auditory Learning, Homeschool How-To's, Kinesthetic Learning, Learning Outside the Books, Learning Styles, Math, Roadblocks to Learning, Tactile Learning, Visual Learning, Workshop Wednesday

Workshop Wednesday: Beanbags (No-Sew DIY)

January 8, 2013 by CarolynM Leave a Comment

Who has a child who can’t focus on anything while sitting in a chair? Who has a child who loves playing games and sports, but hates worksheets and written assignments? Who has a child who tries to make everything into an exhibition of physical abilities? You’re in luck! Let us help with some great ideas using beanbags that will enthuse your kinesthetic learner and keep him doing these learning activities on his own while you sneak in a coffee break!

Those energetic students are kinesthetic learners who need to move to be able to learn. Their brains don’t fully wake up and begin to learn until their arms and legs get moving, so these beanbag activities are ideal for getting them involved, holding their attention, and helping them remember what they’re learning.

Inexpensive, no-sew beanbags can be made quickly from discarded socks (no holes or thin spots) by cutting them to an appropriate size and pouring in dry beans or uncooked rice. Tie the ends shut tightly with string, yarn, or plastic zip-ties (trim the ends with scissors), leaving each beanbag about two-thirds full, so that the contents have room to slide around—if filled too full, the bag will be more likely to burst when it lands. Aquarium gravel is a suitable waterproof filler, just in case your beanbags are likely to get left outside in the rain.

What can you do with all the wonderful beanbags you’ll create from your orphan sock stash? Use them for “throwing stones” for hopscotch (and all its variations), whether playing on the sidewalk, driveway, or patio. For indoor activities, hopscotch grids can be drawn with permanent markers onto an old bed sheet or tablecloth, but please use caution when using a cloth on hard surfaces to avoid slipping.

Learning Activities with Beanbags

Matching — If your clothes dryer has given you an abundance of sock orphans, you can mark them with letters or numbers for some preschooler’s matching activities.

ABC’s — Toss a beanbag onto a jumbo ABC-grid and make the sound of the letter selected. Older students may say a word that is spelled with that letter (beginning, ending, etc. your choice). A bigger challenge is to toss two or more beanbags onto the ABC-grid and think of a word that uses all of them.

1-Sentence Stories — Lay out word cards on the floor (sticky notes will stay in place), toss beanbags onto several words, and create a one-sentence story that includes the words selected.

Hopscotch Variations — Make a parts-of-speech hopscotch grid and play the standard hopscotch game with the rules for numbers, but have players give an example of the part of speech selected, such as saying “ticklish” when picking up the beanbag from the adjective section, “skeleton” for a noun, or “angrily” for an adverb. This method can be varied for other subjects, too, such as naming the sections Nations, States, Cities, Lakes, Rivers, and so on for geography. Students would then have to name an appropriate geographical feature.

Math Symbols — Mark some beanbags with math operation symbols and toss them onto a jumbo 100-grid for instant math problems. Throw an unmarked beanbag onto a random square for a starting number, then draw a random operation-symbol beanbag from a sack or pillowcase and toss it onto another square, using that number for the designated operation. Repeat as long as your supply of beanbags lasts. Pencil and paper may be used to assist in calculations, but careful aim and an accurate toss may be the most help.

Target Practice — Use laundry baskets or cardboard boxes for target practice to improve eye-to-hand coordination and tossing skills (just don’t hit the lamp!).

Juggle — Learn to juggle!

These beanbags are quick to make and will add hours of fun to indoor or outdoor playtime, and they are a great way to make lessons kinesthetic for your active students!

Workshop Wednesday: Wikki Stix as Learning Tools

November 13, 2012 by CarolynM Leave a Comment

Does your hands-on learner need a new challenge? Try using Wikki Stix as manipulatives. If you’re not familiar with them, Wikki Stix are thin, wax-coated strings that resemble pipe cleaners or chenille sticks, except that they aren’t fuzzy, and they will stick to each other. The sticking-together aspect makes them wonderful learning tools, because they will also stay where you put them, and you can put them just about anywhere: table, window, cookie sheet, poster board — this list can go on forever. Stick them on the glass patio door or the refrigerator door for a kinesthetic, standing-up lesson activity. The Stix are waxy, but leave very little residue, and it is easily cleaned away. Bonus tip: If they accidentally get dropped on the floor and collect a few dust bunnies, cereal crumbs, and pet hair, holding them under running water and air-drying will restore them back to good-as-new condition.

Wikki Stix come in a variety of colors, including neons, and I have also found knock-off brands — check your favorite stores for craft or school supplies. (Wikki Stix brand have a unique bumpy texture that is both tactilely and visually interesting.) Use them full length (8″ long) or cut them into small lengths with scissors, and start creating. Let your students make letters and words, make numbers and math problems, or just have fun making all sorts of fun art projects.

Your older students can combine letters and numbers into the latest complicated formula they are trying to memorize. Yes, Wikki Stix are a fantastic tactile and visual method for color-coding the components of a mathematic or scientific formula! The tactile process of assembling a complex formula from Wikki Stix, complete with color-coding, is a very subtle way of memorizing — once your student has finished this project, he may find he has it committed to memory without even trying!

How can Wikki Stix help with lessons? First of all, let your students use the Wikki Stix as their learning aids — the kids will learn much more if they do it themselves, than if Mom just shows them what she’s made for them. The extended process of building each letter, number, or shape keeps your student’s fingers involved in the lesson, and the child’s brain has to think the process through from a different perspective than if he was just writing normally with a pencil. (By all means, do help the child who needs help getting started with this activity, but encourage his independence once he’s understood what to do.)

Color-code certain parts of words (vowels, phonics patterns, prefixes & suffixes, etc.) or math problems (use different colors for positive and negative numbers, or x-components in one color and y-components in another color).

Make Wikki Stix flashcards with spelling words, vocabulary words, or formulas on a sheet of cardstock and insert the finished cards into plastic page sleeves. Works for spelling, phonics, math, science, geography, history, foreign language, etc. Using this method to “write” troublesome spelling or vocabulary words allows the student to focus on getting each letter and each syllable in the correct order.

Make geometric shapes on flashcards, just like the idea above, and use them for identification and recall drills, or use the shapes as tactile manipulatives for math problems. For a bigger challenge, let your students try identifying the shapes by touch alone, by feeling them with their eyes closed.

Cursive writing can be tricky to practice, especially for those who are just learning it. Stick several Wikki Stix together end-to-end and shape them into cursive writing. Using Wikki Stix for cursive slows the process down considerably and allows the writer to put the lines exactly where they need to go! (and no pesky eraser crumbs!)

Filed Under: Activity Ideas, Homeschool How-To's, Kinesthetic Learning, Learning Outside the Books, Learning Styles, Math, Roadblocks to Learning, Spelling, Tactile Learning, Visual Learning, Workshop Wednesday

Workshop Wednesday: Pocket Charts (DIY)

October 16, 2012 by CarolynM Leave a Comment

Have you ever wished you had a pocket chart for use with your homeschool lessons? Letting kids insert flashcards into a pocket chart or rearrange them to suit the lesson concept can provide a tactile element to phonics, reading, spelling, math, geography, etc. If your cards are large enough (3×5″) or if the chart is on the wall or across the room, it can become a kinesthetic method, too. Sometimes you may have just a few uses for a pocket chart in your schooling, but not quite enough to justify investing your hard-earned funds in the fancy teacher-supply-store versions. Try these suggestions for making your own pocket charts.

Secure any of the following to a bulletin board or large sheet of poster board:

Paper envelopes (recycle some junk mail!); the front of the envelope (the side where the address would be written) will be attached to the poster board, so trim the back of the envelope (which will be the front of your pocket) to about 1″ high or enough to allow a card to rest inside but still show the information (I trimmed off the flap, too)

Photo album pages; these come in several sizes that can be carefully cut apart & taped down to poster board as needed (Consider the variety of special album pages made for film slides, baseball cards, etc.) I turned a trading card page sideways and used a razor knife to slit a side of each pocket open (to become the new top edge) and trimmed it lower (with scissors) for easy insertion of cards, then used clear tape to secure the former open/top edge (now a side).

Plastic page protectors for 8 1/2x 11″ sheets of paper; can be cut down as needed

Clear Contact paper; stick to itself (sticky sides together) to make pockets larger or longer than album pages or page protectors

Clear vinyl zippered bags from sheets, blankets, or pillows; cut them up or use “as is” for jumbo pockets to hold large cards (imagine the possibilities: label the bags with parts of speech & toss a bean bag into the correct one when Mom calls out a word — oh, but we were supposed to be talking about pocket charts here)

Vinyl upholstery fabric can be taped, sewn, or stapled together (if not transparent, cut the front of the pockets low enough that the cards’ information can be seen easily, but the cards will still stay upright in the pocket)

If you don’t have a large bulletin board, you can use brass paper fasteners to secure the pockets to poster board or cardboard, or punch holes with a large yarn needle or awl and sew the pockets to the backing cardboard with yarn or string. Clear packing tape (2″ wide) can also be strong enough to hold the charts to poster board, but is not as easy to remove.

How to use–

Letter matching: upper/lower case
Letters forming words (use game tiles!)
Reading practice with phonics patterns or rhyming words

Reading practice with words forming sentences (see photo above)
Spelling practice (game tiles again!)
Math problems: Insert some numbers and operation symbols, and let the student complete the problem, or let students try to build their own problems correctly.

Illustrate place value, borrowing, and carrying (regrouping) for understanding. The physical act of changing ten ones into a ten and moving it from the ones’ column to the tens’ column is a very powerful transformation in a young mathematician’s mind!
Chore chart
Calendar
Matching states, capitals, & postal abbreviations (see photo above)
Match vocabulary words with definitions

BONUS TIP:

Once you have made a few dozen word cards, a handy way to store them is in an index card file box. Add a set of ABC divider cards and teach your student how to sort the word cards alphabetically. Your student can even become the Official Keeper of the Word Cards, so he can pull out only the cards needed for each lesson, and then put them away again for next time. He’ll get the bonus activity of learning and practicing alphabetizing, and he’ll never realize that this fun activity is a great lesson in itself!

Filed Under: Activity Ideas, Homeschool How-To's, Kinesthetic Learning, Learning Styles, Math, Phonics, Reading, Spelling, Tactile Learning, Visual Learning, Workshop Wednesday

Workshop Wednesday: Math Measuring Tape

October 9, 2012 by CarolynM Leave a Comment

Do you have a child who needs to see things for himself in order to understand lesson concepts? Have you used math manipulative blocks but he’s still just not quite getting it? Here’s a unique idea for a powerful math tool that you can make yourself from simple graph paper. By making a special measuring tape that exactly corresponds to the size of whatever math manipulatives you use, your students will have a customized tactile and visual learning aid.

Cut 1 or 2 sheets of graph paper into 1-inch wide strips and tape them together for the length you desire (make sure that no strips end in a partial square). Graph paper marked with five squares per inch (available in office supply stores) is compatible with the centimeter-scale Cuisenaire Rods that we used: 2 graph-squares = 1 centimeter, so marking numbers on every other line produces a centimeter measuring tape. (Yes, centimeter graph paper would have been easier to use, but I couldn’t find any in my area — so I improvised!)

To illustrate skip-counting by 2′s, accordion-fold the tape on every other number, and then say (auditory) the number for each fold-increment. Adapt and repeat for other skip-counting intervals. (The measuring tape in the photo only has numbers at intervals of 5, but feel free to write on as many numbers as your children need.)

Your students can lay Cuisenaire Rods on the tape to demonstrate addition & subtraction facts. Arranging different length rods to equal the same total (1+5, 2+4, 3+3, etc.) helps them see by yet another method that different numbers can add up to the same total. The measuring tape becomes a learning aid for memorizing facts as your kids line up blocks or rods on it and see the resulting numbers.

Repeat the same process for multiplication & division facts: 3×5, 5×3 — both measure to 15.

This method can also help students understand uneven division problems. For 15 divided by 4, start placing 4-rods at the 15 and filling in backwards toward 0, but fill in the gap with a “remainder” rod, in this case a 3-rod fits as the remainder.

We used this measuring tape by itself to illustrate multiplication and division facts by accordion-folding the paper tape into 6 sections of 8 centimeters to show 6 x 8 = 48 and other facts. My origami-loving son really enjoyed this foldable number line, and he would take a few seconds during a math problem to fold it back and forth, just to be certain of his answers.

The measuring tape can also be used as your kids run around the house, measuring everything in sight (kinesthetic) for practice at measuring and estimating how large certain objects will be, according to the scale used by your math manipulatives. For instance, my sofa may be 86″ long, but measuring it with a centimeter scale makes it 215 centimeters. My kids liked the challenge of guessing how many centimeters first, then measuring an object to confirm the answer. This is also a great way to compare inches and centimeters, and they can use a ruler, yardstick, or measuring tape in inches to confirm their answers.

If you use another form of math manipulatives other than Cuisenaire Rods, you can adapt the size of the measuring intervals on this homemade tape to coordinate with your own manipulatives. Graph paper with 4 squares per inch (1/4″ squares) can be marked for 1/2″, 3/4″, or 1-inch manipulatives. Remember the sofa we talked about above? It would be almost 115 connecting cubes long, when measured according to a scale for these 3/4″ cubes.

P.S. — We stored our measuring tape neatly by folding it up and using a large paper clip to hold it in place. ;-)

Filed Under: Activity Ideas, Auditory Learning, Homeschool How-To's, Kinesthetic Learning, Learning Outside the Books, Learning Styles, Math, Tactile Learning, Visual Learning, Workshop Wednesday

Workshop Wednesday: Patterns, Part 2 — Number Patterns

October 2, 2012 by CarolynM Leave a Comment

Are you ready for some more patterns? How about making them a little trickier? Our previous article on Patterns focused on learning to recognize patterns of colors or shapes and reproduce them accurately. This article steps that up a few notches with patterns of numbers.

We all learn a very simple number pattern when we first learn to count to 10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 — a series that increases by one with each step. Skip-counting is increasing each step by an amount larger than one, whether counting by 2’s, 3’s, 5’s, 10’s, or 87’s.

We could even select our starting point and then add by a set increment for another variation of skip-counting:

What if we varied the increments with a consistent pattern? Suppose we started at 0 and added 1, then added 2, then 3, then 4, and so on. Our number pattern would look like this: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, and on and on. If our increment added only by even numbers, the pattern would look like this: 2, 6, 12, 20, 30, 42, 56, 72, 90, 110.

My kids loved to watch an old PBS television show called Square One TV that had a segment called Mathnet, where math “detectives” solved mysteries dealing with numbers. One episode of Mathnet (The Case of the Unnatural) involved a couple of friends who regularly challenged each other with a game they called “Guess My Rule,” where a player had to figure out what rule had been used to create a series of numbers and respond with the next four numbers in the series. The strings of numbers they gave were more complicated than simple skip-counting. For example, the series of 1, 3, 7, 15 is achieved by doubling a number and adding 1: starting at zero, double it (still zero), then add 1, gives 1 as the first number in the series; double it to 2 and add 1, equals 3; and so on. This rule is “double plus 1,” and the next number after 15 would be 31. To play it yourselves, have one player create a series of at least four numbers, and the second player has to determine the “rule” and give the next four number in the series. What number rules can you create to make interesting number patterns? Remember that the rule must be consistent throughout your series.

Another fascinating number pattern is called the Fibonacci series, in which the next number is created by adding the previous two numbers together, for as long as you’d like to keep adding.

Fibonacci numbers are found throughout nature in very intriguing places. You may already know that if you slice a banana and then break that slice apart, the banana will naturally separate into 3 segments. But notice the banana skin: there are 5 segments or sides to an unpeeled banana — 3 and 5 are adjacent Fibonacci numbers. Some very interesting Fibonacci numbers have been observed in nature — petals on some flowers, leaves and branches on some plants, scales on pineapples, bracts on pine cones, and seeds in sunflowers all occur in arrangements that use Fibonacci numbers. Just like the banana segments and the sides of an unpeeled banana, the numbers often show up as adjacent Fibonacci numbers. The Creator of the universe is not just an artist, He’s a mathematician, too!

Check out these websites for more fascinating info on number patterns:

Square One TV/Mathnet, The Case of the Unnatural

Fibonacci in Nature

Fibonacci Numbers, the Golden Section and Plants — detailed site including do-it-yourself activity ideas

Who Was Fibonacci? Leonardo of Pisa

Workshop Wednesday: Patterns

September 25, 2012 by CarolynM 2 Comments

Patterns are everywhere! Patterns can be small, large, or in-between. Patterns can be simple or complex. Recognizing patterns is a fundamental math skill that we use everyday, from sunrise and sunset to left and right shoes. Patterns are not just what keeps the peanut butter on the inside of our sandwiches, they are also what makes life fun and interesting. Let’s explore some designs, just to see if we can spot the patterns (hold your cursor over each picture for a hint). Looking for patterns sharpens your visual skills!

Create a simple pattern of colors or shapes using game pieces, beads, coins, buttons, or anything suitable you have on hand, and challenge your students to repeat it. Beginners may need a little help with recognizing what makes the pattern, analyzing when and how it repeats, and the logic of what comes next, but they will catch on quickly. Some students may repeat a pattern accurately the first time, but may not catch a mistake if they are repeating it multiple times. Help them learn to check their own work for errors.

Anne Sullivan taught Helen Keller using this method and stringing beads.

Beads can be strung in patterns on yarn, ribbon, shoestrings, leather boot laces, fishing line, pipe cleaners, toothpicks, etc. Use large wooden beads, plastic pony beads, Hama beads, tiny glass beads, etc. Slice pool noodles into jumbo beads to string onto heavy wire, garden hose, or a yardstick. Start a pattern, and let your kids finish it — or let them challenge themselves or each other in making patterns.
We make patterns when we set the table with plates and silverware. We make patterns when we match up socks in the laundry. We make patterns with our footprints when we walk through sand or snow. Pattern recognition can be applied to all phases of life, from lining up toy trucks to analyzing when a machine can be expected to break down from wear. Yes, that’s another application of patterns! And now, just for fun, watch this crazy video from Weird Al, all about PATTERNS! Want to grab some graph paper and colored pencils and make more patterns?