Workshop Wednesday: Hopscotch – A Powerful Learning Game

Who knew that a patch of concrete, some chalk, and a couple of rocks could produce a fun way to learn just about anything? When I was a little girl, I played hopscotch in the traditional way, tossing my stone and jumping from square to square, just as a game for practicing my tossing and balancing skills. Hopscotch can also be used as a kinesthetic learning method, involving the big muscles of arms and legs, pumping information through the blood vessels to the brain. I can see many other uses for the basic method of hopscotch, providing a great method for teaching preschoolers, kinesthetic learners, active children, or anyone else who just needs a break from sitting at a table for one more worksheet.

Let’s start by changing the standard hopscotch pattern to a row of 10 squares, numbered from left to right, and let your little ones practice counting as they hop from box to box and back again—tossing a marker stone or beanbag can be used later as their counting skills increase. Do the same thing with a row of ABC’s, first for letter recognition and later for reciting the sounds made by each letter or for a word beginning with that letter. Mom can say a word, and the child can hop to the letter that begins the word. For more advanced students, change the ABC’s to a grid pattern, and try “Twister Spelling” by putting hands and feet in the correct squares to spell the word. Use multiple beanbags, poker chips, or plastic yogurt lids for markers, and challenge your kiddies to spell out words by placing their markers on the correct letter squares.

You can also practice addition and subtraction facts with a hopscotch grid. Draw a 1-10 grid by making two rows of five squares each: 1-5, 6-10. Make these boxes large enough for your student to stand in, sort of like a hopscotch game. Start with simple addition problems by asking: If you put down [this many] markers, starting with Box #1 and putting one marker in each box, and then you add [this many] more markers, how many boxes will have markers in them? What is the largest number box that contains a marker? Repeat this activity with as many different number combinations as possible, until your student knows addition facts from 1-10 so well that he cannot be stumped. Then draw two more rows of boxes, extending the grid to 20 (11-15, 16-20), and continue the addition practice with problems up to 20. You can also work on learning doubles in the teens: 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20. These facts will help him with problems where the answer is between 10 and 20.

Does one of your students have trouble with subtraction? Using the 1-20 grid, pick a problem that may have stumped your child, like 13-9=? In this example, cover all numbers larger than 13. Ask: If you put down 9 poker chips, with one on each box, starting with 13 and counting down, what is the largest number box that will still be showing? If he’s already experienced at using the 1-20 grid of numbered boxes, he will be able to recognize the row of 6-10 as being 5 boxes. Then he can see that there are 3 boxes for 11-13, so those two rows will use 8 of his 9 poker chips; now he can put the last chip in the largest numbered box in the top row (the 5), and he’s left with 4 as the largest number box still showing: 13-9=4

Another helpful trick is to show your student how to work up or down from 10 when the answer to a problem doesn’t come to him immediately. For example, 13-9=? Let’s see, I know that 10-9=1, and 13 is 3 more than 10, and 3+1=4, so 13-9=4! How about 17-9=? 10-9=1; 17=10+7, and 1+7=8, so 18-9=8! Did you follow that? Children can get discouraged when they don’t know or can’t remember an answer immediately. Showing them several different methods for figuring out the answer helps them to see that they are smart enough to find the answer anyway. Working toward the answer from 10 or from the nearest double is a legitimate method of solving the problem and is actually a better way to learn than just rote memorization, since it uses more creative solving methods.

Are you ready to take this up one more notch? Help your students draw a 1-100 grid (10 rows of 10 squares each, numbered 1-100) and challenge your young mathematicians to toss two beanbags onto the grid and add the resulting numbers. Add more beanbags as their skills increase, or switch to subtraction or multiplication. Use beanbags in different colors (or marked with mathematical operation symbols) for students with appropriate abilities: Color #1 means add this number, Color #2 means subtract this number, Color #3 means multiply by this number, and Color #4 means divide by this number. Use several beanbags for each mathematical operation, drawing them at random from a bucket to create an amazing running math problem. Number squares can be chosen by random tossing or through careful aim. Challenging siblings to toss the beanbags and create problems for each other to solve may result in some serious stretching of math skills! Other possibilities are to toss two beanbags to create a fraction, then simplify it as needed—and more beanbags mean more fractions, which can then be added, subtracted, multiplied, or divided, always reducing the answer to its simplest form. The hopping part of hopscotch doesn’t come into play with this method (unless your kids figure out their own creative way to use it), but the tossing and retrieving of beanbags will still give your wiggly kids plenty of action.

Now you think you’ve heard all of the possible ways to use hopscotch in learning, right? Not at all! Let’s go back to the original hopscotch pattern, but instead of numbering the squares, write in parts of speech: noun, pronoun, verb, adjective, adverb, conjunction, preposition,  prepositional phrase, and interjection.  Hopping through the boxes gives the student a chance to think of a correct example word to give when he stops to pick up his marker. Use more specific terms as your students’ grammar skills increase: irregular verb forms, verb tenses, plurals, reflexive pronouns, dependent clauses, and so on. I included a “sentence” space at the end, and students should make their example sentences match the level of grammar being studied.

If you have a student who is really interested in science, specifically chemistry, and if you have access to a large patch of concrete, consider helping him draw out the periodic table of elements and numbering the squares accordingly. Let him make simple flashcards for each element to fit the boxes on his diagram (cereal boxes are a great source for inexpensive flashcards; write on the back with permanent marker) and practice putting them in their proper places. Flashcards might include the atomic number, the element name and symbol, and the atomic weight. More advanced students may want to include more detailed information and use the jumbo flashcards for memory practice. Other hopscotch applications: a diagram of the solar system would provide practice at naming the planets, a simplified skeleton could be drawn for practice at naming the bones, or a map of the United States (or any geographic area) would provide practice at naming states, capital cities, or other geographic features. Coordinate planes with x- and y-axes provide a large grid for plotting specific points with poker chips. Students of advanced math can solve complex equations, plot the points from multiple solutions, and draw the curves with yarn or string.

Any of these hopscotch learning games may also be drawn with permanent markers on an old, discarded sheet or tablecloth (check local thrift stores), resulting in a reusable “game board” that can be folded up and stored between uses. Use the cloth on grass, carpeting, or other surfaces where it is less likely to slip underfoot. Beanbags aren’t required, but the “marking stone” needs to be something that won’t roll away when tossed—or blow away if used outdoors.

If the weather isn’t cooperating for outdoor activities, or if you don’t have a suitable surface for chalk, or even if your students are just not excited about going outside and jumping around where anyone in the neighborhood might see them, these activities can also be done indoors by using masking tape or sticky-notes on the floor. You can even draw the grids on a large sheet of paper and use coins or game pawns as markers.

See also:
What Is the Missing Element?
Building Blocks for Success in Math
Beanbags (No-Sew DIY)

Workshop Wednesday: Sugar Cube Math, Part 2

This topic has been explained in a previous post, but now we can supplement that with a photo. See the complete post HERE for detailed activities to make math understandable in such a fun way that it will prompt you and your kids to call it “SWEET!”

Notice that several activities are demonstrated in the picture: multiplication (upper left), showing that 2 rows of 3 cubes each is equal to 3 rows of 2 cubes each; volume (upper right), showing 3 layers of 3 rows with 3 cubes each, or 3x3x3; and the differences between area and perimeter (bottom). The four groups of sugar cubes at the bottom each contain 12 sugar cubes, so they all have an area of 12 units. However, the varying configurations show how the perimeter changes drastically. With the far right configuration, the sides in the middle hole could be counted as part of the perimeter, too, depending on the real-life application (e.g. if you were installing a fence along the sides of a trail, and the cubes represented the trail).

BONUS TIPS:
1) I wrote right on the cookie sheet with a dry erase marker and wiped it off with a tissue (but I did wash the pan well before putting it away).
2) The sugar cube activities can also be drawn on graph paper to save as a reference or worksheet.

See also:
Sugar Cube Math
What Is the Missing Element?
Building Blocks for Success in Math
Looking for the “Hard Part”
Why Does Math Class Take SO LONG?

Workshop Wednesday: Pipe Cleaners

A supply of pipe cleaners, also called chenille sticks, in various sizes and colors provides a great quiet-time activity that will keep almost any child busy for a good, long time. For teaching purposes, pipe cleaners can be formed into a variety of shapes as versatile manipulatives for your tactile students who need to get their hands on something to be able to learn it. The activities listed below can be used interchangeably for letters, numbers, or geometric shapes. Some students may need to try just a few of these activities, while others may want to try all of them… repeatedly.

Bonus tip: It helps to store the pipe cleaners in a shoebox or other container that is large enough to hold several of your students’ artistic creations! You can also take pictures of the more complex creations, enabling the student to dismantle the project and straighten out the pipe cleaners for their next use, while still saving proof of his hard work and imaginative designs.

• Challenge an early learner to duplicate the letters made by Mom or an older sibling.

• Use multiple pipe cleaners to make bigger letters. Using several colors can help younger students recognize the various components of each letter as the separate pencil strokes required to write it.

• Make multiples of each letter in various colors and sizes, and then play a matching game by grouping all the matching letters together. Students can also match pipe cleaner letters to other sets of letters: magnetic letters, letter tiles from games, flashcards, ABC books, etc.

• Match upper & lower case letters together as big brother/little brother pairs.

• Make letters to match those shown on letter tiles from games or on letter flashcards (even home-made). Shuffle cards and place stack face down, turning up the top card for the challenge letter, or put letter tiles in a clean sock or paper bag, then draw one tile at random for the challenge letter.

• Another version of the letter challenge game is to make the opposite case letter of the challenge card or tile. If a flashcard shows a lower case letter, challenge the student to make the upper case version of that letter; if a letter tile shows an upper case letter, make its lower case counterpart.

• Show how flipping a lower case “b” can transform it into a “d,” “p,” or “q” to help children learn to differentiate between the letters. The same principal works for turning a lower case “n” over to become a “u,” or turning an upper case “M” over to look like a “W.” Demonstrating that certain letters do have similar shapes can help children understand which is which and be certain they are using the correct one.

• Twist the ends of several pipe cleaners together to make a long line of pipe cleaners and bend it into the shape of cursive letters or entire words in cursive script.

• FEEL the letters blind-folded or with eyes closed (no peeking!) and try to identify them correctly. This can be tricky if the letter is held upside down or backwards, but turning it over and all around will help students learn to identify and distinguish between similarly-shaped letters. Some students may enjoy the challenge of trying to identify letters that are purposely positioned upside-down or backwards.

• Challenge students to “reproduce this pattern” of geometric shapes, numbers, or letters, even repeating the same colors used. This same activity works well for teaching pattern recognition when stringing beads, but mistakes can be corrected more simply in this version by moving a few pieces around, instead of un-stringing the entire project, and can therefore be less stressful for a sensitive student.

• Numbers made from pipe cleaners can be used to illustrate early math problems in a fuzzy, tactile way, providing a helpful transition between the “counting beans” stage and doing written problems.

• Lay a sheet of paper over any flat pipe cleaner creation and rub across the paper with the side of a crayon to create a “rubbing” image of the letter, number, or shape.

See also:
ABC Flashcards
Letter and Number Recognition

Workshop Wednesday: Macaroni as Manipulatives

Have you ever found yourself wishing you could afford hundreds, or maybe even thousands of letter or number manipulatives? Head for the pasta aisle in your favorite grocery store—a bag of alphabet macaroni contains both letters and numbers! The pasta is low-cost, so if you have several children who would each enjoy their own supply, you can buy several bags. Letting each student store his macaroni in a large zipper bag will help to make clean up simple and easy.

I sorted through a bag just to see if all the letters and numbers were represented, and yes, they were. My adult-sized fingers found the task a little tricky, but a set of tweezers made it simpler. Children’s small fingers are much more suited to this assignment, and tactile learners will really love digging in. Muffin pans, egg cartons, or cookie sheets are great receptacles for sorting!

Let your students play with the uncooked macaroni at first, and see what activities they devise for themselves. If they need a little encouragement or a starting place, suggest sorting the letters, forming spelling words, making random words (like “magnetic poetry” but without the magnets), or writing sentences. If they’d like to save their work, the words can be spelled out on a line of white glue on a piece of cardstock or an index card. The glue will be invisible when dry, and the cardstock can then be cut into appropriate sizes, creating miniature word-cards (add small magnets to the backs of the cards for even more versatility; a steel cookie sheet makes a good lap desk). These cards can be arranged into sentences, poetry, or lists of rhyming words or spelling patterns, and saved in a zipper bag for another day. Be serious, get silly, have fun with nonsense words, or use the letters to form the answers to lesson worksheets, and the learning will take on a whole new dimension. Don’t stop with just phonics, spelling, and grammar, however. Use these letters to practice spelling place names for geography, complicated scientific words for science or chemistry, or important people, places, and events for history. The letters can easily be scooted apart to break words into syllables or prefixes, suffixes, and root words—a great method for word study, and it adds a memory link for better recall later.

The tiny pasta numbers can be used for sorting and matching or set up as math statements by writing operation symbols on paper, leaving blank spaces for the numbers. Select specific numbers or grab random pieces for a new twist on math problems. Younger students will enjoy the challenge of putting the numbers in order or experimenting to see how many different numbers can be formed from just a few digits. Keep the pasta dry and away from toddlers and the family dog, but rest assured that a new supply is readily available in case too many pieces get stepped on, eaten, or sucked up by the vacuum cleaner!

Workshop Wednesday: Play Money

Time to head for the game closet and dig out some play money! This stuff is a fabulous tactile learning tool that can be used for much more than just collecting $200 for passing “GO.” Use play money to practice counting by 1’s or skip-counting (by 5’s, 10’s, 100’s, etc.)with the littles,  demonstrate place value and the substitution needed for arithmetic with the middles (borrowing, carrying, trading, regrouping, swapping, bundling, or whatever you choose to call it in your lessons), practice making change, or discuss money management with the olders. You can get more creative and challenge your students to grab a handful of play money and calculate the amount, then write out the amount in both digits and words. Some of you may take up the challenge to grab several random amounts and use those for addition, subtraction, multiplication, or division problems. Here’s another challenge: let your students make up their own story problems for random amounts of play money—they’ll be getting math practice and writing practice at the same time.

If you have several games that contain play money, pull it all out and pool it together: sorting by denomination is good math practice. As seen in the picture, not all games use the same denominations, so your students can learn to adapt their math practice to the supplies that are available. I even threw in a large handful of real pennies from the coin can that serves as a doorstop here—if you have a coin can or jar, you might want to borrow some of its contents for a little more math practice. (My kids paid much closer attention to math discussions if the problems involved money or food instead of just meaningless numbers!) When the math lesson is over, let the kiddies continue sorting and counting the play money: setting up a pretend “store” is great “stealth” learning! Maybe they’d like to invent a new game that uses all this play money, plus several other random pieces from a few games. Setting up the game instructions offers writing practice, determining the rules is problem-solving practice, and playing the game will give even more practice in counting, adding, subtracting, making change, and whatever other math skills their new game includes. When the time comes, sorting all those game bits and play money back into their respective games is excellent experience for the sorting required in algebra and other higher math studies, and it gets the kids involved in putting things away, instead of leaving all the clean-up to Mom.

For more tips, see also:
Building Blocks for Success in Math
Sorting Toys Is Algebra
Gee Whiz! Quiz

Workshop Wednesday: Building Blocks for Success in Math

Math is called a foundational subject for good reason: if you don’t have a solid foundation, anything you try to build on top of it is in danger of falling apart. Math is also called a sequential subject, meaning that math skills must be mastered in sequence, each skill building on the skills before it. This picture represents my view of math skills and the order in which they should be mastered, starting at the bottom and building up, one skill upon another.

No one starts teaching math by instructing their preschoolers in differential calculus. The first math skill we teach is Sorting: Which ones match? Is this one like that one? We may start the sorting process with colors or shapes, but Sorting is still the basic skill being learned. Sorting is the #1 most important math skill, used from recognizing number value to solving the most complex equations. Counting is an extension of sorting, assigning a number name to each different quantity. We “know our numbers” when we can group the correct quantity of pieces to represent any given number. We have mastered counting when we can recite the quantities in ascending order. The ability to count backwards is preparation for further skills yet to come.

Place Value might be considered to be an extension of Sorting by placing 1-digit numbers together in one group, 2-digit numbers as another group, yet another with 3-digit numbers, 4-digits, and so on. Children who are learning to count past 10 are learning place value, even though they are not yet adding or subtracting large enough quantities to require carrying or borrowing. Those skills work hand-in-hand with addition and subtraction, but an understanding of place value has to come first. Using a large quantity of identical small manipulatives, such as toothpicks, you can demonstrate the quantities represented by numbers in the ones column and numbers in the tens column to show how and why we write numbers the way we do. As your student gains skill with addition, you can revisit Place Value to demonstrate carrying into the tens, hundreds, thousands, and as many columns as your child wishes to add.

The next natural step after Place Value is Addition. Your child may already be using his counting skills to inform you that since he already has 1 cookie, if you would just give him 2 more cookies, then he would have 3 cookies! He may not recognize 1+2=3 on paper, but he certainly understands cookie quantities! Addition facts are best learned through using real-life objects, manipulatives, or even diagrams, rather than just expecting a young mathematician to transfer immediately to written problems. Hands-on practice makes subtraction easily evident as the un-doing process for addition, thereby taking away the stigma that subtraction is yet another new skill to learn. If a student knows addition facts to the point of quick recall, that same student will be able to perform subtraction. Therefore, a student who struggles with subtraction is a student who has not mastered addition facts.

Multiplication is often presented as one more new skill to master, but when presented as a “short-cut” to repeated addition, the student will see multiplication facts as a convenient tool, not as an obstacle to further learning. Multiplication facts can be demonstrated with a large quantity of small manipulatives that can be grouped into repeated rows (½” squares of heavy paper or cardboard work very well). Some quantities of manipulatives can be rearranged to show various factors which result in the same amount, such as 1×12, 2×6, 3×4, 4×3, 6×2, and 12×1. Grouping and regrouping the manipulatives will give your student a deeper understanding of multiplication facts as he sees the groups (visual), arranges them with his own fingers (tactile), and repeats the facts aloud (auditory). A kinesthetic learner will prefer standing or kneeling to do this activity, providing yet another sensory element.

Why isn’t Division listed in these Building Blocks? Simply because Division is un-doing Multiplication, just as Subtraction is the un-doing of Addition. The only tricky part to Division is that sometimes things don’t come out completely even, and we get “left-overs”—but every child who has tried to share 5 cookies with 3 friends understands that concept already. Division uses the quick recall skills for multiplication facts to regroup as evenly as possible, and the “left-overs” will be dealt with in more detail later on as these skills progress even further into the concepts called fractions and decimals. By the way, fractions, decimals, and percents are all “nicknames” for the same amounts—they are just different ways of looking at the same quantities, such as ½, .5, and 50%, and those all mean that you and I are sharing equal amounts of the same cookie!

The final Math Building Block to be mastered is Logic. Logic means making sense of things, so they come out right. Logic may come in the form of “If/Then” statements, such as the block in the picture shows: If all cats have 4 legs, and Fido has 4 legs, does that then mean that Fido must be a cat? Fido might be a cat, but we also know that other animals besides cats have 4 legs, so we cannot assume that Fido is a cat until we have more information. That is logic: using information to prove a point, but sometimes you realize that you don’t have enough information yet, and the point you prove could be wrong. Another use of logic is in balancing equations. A very simplified example is 7-2=5; if we add 2 to each side, we’ll see 7-2+2=5+2 or 7=7, a true statement. What we do to one side of an equation must also be done to the other side to keep it balanced, as if the equals sign was the pivot point on a balancing scale.

If your student is struggling with any of these building block skills, back up and practice the previous block’s skills until they are mastered. Recall of these facts should come as easily as a reflex action before the student is ready to move on successfully to the next building block. Don’t worry that other students may be moving ahead already—they may not be ready either, and their “progress” will soon result in more struggles. Remember that a student who cannot do division does not know multiplication facts well enough. A student who struggles with multiplication does not know addition facts well enough, and neither does the student who struggles with subtraction. A student who has trouble with addition does not understand place value or number values well enough. Success in math is achieved by mastering skills in sequence and building a solid foundation with each skill before attempting more challenging skills.

For more tips, see also:
Looking for the “Hard Part”
Why Does Math Class Take SO LONG?

Workshop Wednesday: Sidewalk Art

What better way to incorporate drawing lessons into a beautiful homeschooling day than with chalk on the sidewalk or driveway? We often took our favorite storybooks outside with a bucket of chalk (and maybe a folded towel for under the knees) and picked some simple illustrations to duplicate.

Our favorites included the Little Miss and Mister Men characters by Roger Hargreaves and all of the fanciful creations of Dr. Seuss. Actually, we discovered that you can turn nearly any smiley-faced character into a Seuss-ian delight by adding an outcropping of tall feathers to the top of its head, a long, long, long tail, and brightly colored fur in zig-zaggy stripes. Now that’s a great lesson in cartooning! Encourage your budding artists to make a game of adding more and more features to their creatures by calling out “Heads” or “Tails” and supplementing those traits. Give each character special talents or accessories, such as juggling ice cream cones, wearing a polka-dot necktie, or holding a dozen strings tied to gigantic balloons.

Be sure to take the time to admire each other’s masterpieces and praise their unique qualities. Give each artist a turn to tell about his or her drawing, pointing out details and describing techniques used, for informal practice at oral presentations. Most of all, have fun making silly drawings and enjoying the chalk antics.

Sometimes we made several individual drawings, and sometimes we connected multiple parts into a long scene that filled our front sidewalk for the full width of our property. One summer day when lots of neighbor kids were looking for something to break up the boredom, I drew a very basic chalk outline of an old-fashioned circus train that stretched out over several blocks of our sidewalk, assigning each block (one box car) to a different child. We discussed as a group what sort of things our train should have (planning and problem-solving skills), and the children chose what they wanted to draw (delegating skills). One drew a box car with two giraffes sticking their long necks out the top. Another drew a lion in a cage, and another chose to draw the train’s steam engine with great puffs of smoke billowing out the smokestack. Our train had a few clowns, bright colored flags and pennants, and the words “Circus Train” on the side of yet another box car. The kids spent most of the afternoon drawing and coloring with the chalk and adding special touches. When anyone finished his own section, he would go help someone else, giving them all a great feeling of teamwork. The finished sidewalk “mural” received lots of admiration and compliments from neighbors and was the object of several photographs by parents. The kids all put so much work into their circus train, that we were all very glad that we had no rain for several days afterwards! However, rain was usually seen to be a magical eraser that tended to bring new inspiration for more drawings instead of disappointment that the previous masterpieces were gone.

Obviously, a variety of chalk colors makes drawing more delightful, but don’t underestimate the value of plain white chalk. Your art students will discover shading on their own, as they go over and over a section to make the color more intense, and having a limited palette of colors will make them more creative with using patterns. Be careful to use chalk marked “sidewalk chalk,” as others may not wash off as easily. I once bought a box of beautiful colored chalk at a garage sale, only to discover that the intense colors left permanent stains on the clothing we were wearing when we used it! The knees and elbows and sleeve cuffs had deep colors ground in from kneeling and leaning on the drawings, no matter how careful we had been. One more point: chalk is soft and gets used up quickly on rough surfaces, so buy in bulk! No one wants to stop in the middle of drawing an enormous stegosaurus, just because he ran out of chalk.

Whether your creations are large or small, simple or elaborate, you can enjoy a nice day outside with chalk, learning to copy drawings from books or making your own creations. Starting with simple line drawings from a favorite storybook will help beginning artists gain confidence, since they don’t have to rely on their imaginations for inspiration. After all, a large blank sidewalk can be rather intimidating! Making your drawings LARGE increases the number of details that can be added: a small face may not have room for much more than eyes and a smile, but a big face can also hold eyelashes, freckles, glasses, or a handlebar mustache!

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