Guilt-Free Homeschooling Summer Camp: Homeschool Summer Camp FUN!

Some kids run out of ideas quickly, particularly if they’ve been used to a school schedule that has every day planned out for them. Try the articles listed below for some unique activities that your kids will love and that will also help them retain their knowledge base over the summer.

Some of these ideas were things I had intended to do with just my own kids, but their neighborhood friends begged to be included, too. Some of these ideas were things I thought would entertain my kids for an hour, but were enjoyed so immensely that they lasted all afternoon or were repeated time and time again. Some of these ideas came from trying to use old materials in new ways, such as a bucket of sidewalk chalk. Some of these ideas came from wanting my kids to practice their academic skills but needing very stealthy methods that still let them feel like they were getting a summer break. Keep some of these ideas in mind for the next time you hear “I’m bored.” If you have the supplies on hand, your kids may just come up with their own ideas, before you even have a chance to suggest anything.

Teach Your Children the Art of Amusing Themselves
“Stealth Learning” Through Free Play
Backyard Carnival
Take It Outside! 
Hopscotch—A Powerful Learning Game
It’s So HOT, You Could Fry an Egg Outside!
Jumpropes
Natural Science
Sidewalk Art

When it’s too hot to play outside or for a rainy day!
Money Land Game
Gee Whiz! Quiz
Top 10 Dress-Up Items
Beanbags (No-Sew DIY)
100-Grids and Flashcard Bingo
“Mystery Boxes” and the Scientific Method
Texture Dominoes

And many more ideas…
Topical Index: Activities

Read the entire GFHS Summer Camp series:
Homeschool Mommy Summer Camp
Homeschool Summer Camp FUN
Homeschool Summer Reading Activities
Homeschool Summer Scheduling
Encouragement Around the Campfire

Workshop Wednesday: Money Land Game

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.

Workshop Wednesday: Wikki Stix as Learning Tools

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!)

Workshop Wednesday: Grammar with Giggles, Mad Libs Style

Do grammar lessons rank among the favorite subjects at your house? Would you like to make sure they do? Would you also like to incorporate other learning style methods into a subject that typically requires only the visual skill of reading?

Mad Libs are part party game and part puzzle book. They remove key words from nursery rhymes, letters, and simple stories, and replace those words with blanks marked with the appropriate part of speech that is needed to fill in the gap. The fun comes from asking your audience for the random words first, and then reading them the completed story, using their suggested words in place of the expected ones: (adj.) Phony Miss Muffet sat on a (noun) frog, eating her (noun) henhouse and (noun) giraffe. Most kids will be begging for more at this point! Reading the sentences aloud and hearing the crazy wording are both auditory components, and the sillier these sentences come out, the more likely your students are to remember them! “Phony Miss Muffet” may even become a permanent addition to your family’s vocabulary.

I was introduced to Mad Libs back in my elementary school years, along about the time my classmates and I were learning the difference between adjectives and adverbs. Someone in my family brought home a Mad Libs book, and the next thing I remember is that we were all holding our sides, laughing until we couldn’t breathe, and the tears were running down our cheeks. We had to take turns reading the completed Mad Libs stories, because the last person to read one could no longer speak from prolonged laughter. Anything capable of producing that much hilarity is guaranteed to stick in my mind, and I very quickly learned that adjectives tell what kind and adverbs tell how or when. Years later, I used the Mad Libs process to help my own kids learn parts of speech, and they had just as much fun with it as I did.

Go grab some index cards and some colored markers, and let’s get ready to add some giggles to those grammar lessons. Take turns around the family circle choosing the words, and write one word per card, nice and large. If you already use a color code for parts of speech (great visual method), continue it in this activity, writing nouns in color #1, verbs in color #2, adjectives in color #3, adverbs in color #4, and so on. Write NOUN on the back of all the noun cards, ADVERB on the back of all the adverb cards — you get the idea. Make as many of each kind as you’d like, but keep each kind in its own stack (you’ll see why in a minute). Be sure to include articles, conjunctions, proper nouns, pronouns, and prepositions, but keep the cards and markers handy so your students can add more words whenever they want to. As your students’ grammar knowledge increases, they can add more complex parts of speech: for example, linking verbs and participles. But I’m getting ahead of myself…

To play, I mean learn, shuffle each individual stack of cards and place them upside-down, so the parts of speech (on the back) are plainly visible, and select an appropriately ordered group of cards (without peeking at the words on the face of each one) and lay them out in the order of a sentence, such as article, adjective, noun, verb, adverb. Now turn them over one at a time to watch your silly sentence take shape: The fluffy elephant danced fiercely. It will probably only take one or two rounds of this for your kids to begin thinking up more words to add! Let them make new cards to change the existing sentence, or shuffle those cards back into the stacks and start over with a new sentence combination. All the shuffling and dealing of cards are good tactile methods to keep the hands and fingers involved in the lesson. As a bonus lesson, have your students copy each silly sentence into their notebooks, underlining the words with colored pencils, if desired, to reinforce the color code for the parts of speech.

Diagramming sentences is also a valuable skill for learning grammar, and the cards can be rearranged into the proper diagram, using yarn, string, or ribbon to form the diagram lines. Spreading all the cards out into long sentences or large diagrams on the floor or table brings a kinesthetic component to normally visual-only grammar lessons. Be sure your students copy each diagram into their notebooks, too — those notes become valuable reference material for future lessons, uniting the visual skill of reading with all the other learning skills used in the same lesson.

As their grammar knowledge grows, your students can add multiple modifiers, use conjunctions to create compound subjects and verbs, expand into direct and indirect objects, plop down some prepositional phrases, and giggle their way through learning to diagram introductory adverb clauses!

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 divider cards marked for the parts of speech, and choose a student to become the Official Keeper of the Parts of Speech for the day, so he can sort them into the right categories to put them away again for next time. He’ll get the bonus activity of learning to recognize the parts of speech, and he’ll never realize that this fun activity is a great lesson in itself! (You’ll want to keep these word cards, because we’ll use them in more great grammar ideas coming soon!)

You can use the links below to find Mad Libs products or to play Mad Libs online. (No, I’m not getting a commission from this, I just love the product!)
It’s a Mad Libs World
Mad Libs
WordLibs Mad Libs Online game

See also:
Teaching Spelling (and Grammar) Through Reading and Listening
How Did You Learn to Write?

Workshop Wednesday: Pocket Charts (DIY)

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!

 

 

Workshop Wednesday: Math Measuring Tape

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. ;-)

Workshop Wednesday: Patterns, Part 2 — Number Patterns

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

See also:

Patterns