Workshop Wednesday: Dot-to-Dot Skip-Counting

I bought a dot-to-dot coloring book, which was much harder to find than I had anticipated (this one is from School Zone Publishing). Their pictures only used numbers from 1-25, so I dug out some small white stickers, grabbed my scissors and a black fine-point Sharpie, and went to work. I cut the stickers into pieces small enough to cover the numbers on the picture and re-numbered the drawing using skip-counting. Sometimes the pictures are complicated enough that it’s important to only do one number at a time (cover previous number with a sticker, write new number on the sticker, then move on to next number), just so you don’t lose your place and mess up the whole thing. With more complex drawings, my stickers sometimes overlapped the lines of the picture, so I just re-connected those lines, drawing right across the sticker.

Click on photo for larger image.

I changed the directions at the bottom of the page to correspond to the new, improved numbering system: Count by 2’s; Count by 3’s; Count by 10’s; Count by 12’s; and so on. I made the skip-counting harder as the difficulty of the pictures progressed. To make things even more challenging, I changed some of the directions to say “Start at 3. Guess the rule?” so that the pictures didn’t always begin at 1 and the student would have to analyze the numbers to determine which one came next. I made some pictures start at 2, 3, 4, 5, 50, 55, 101, etc. and vary in increments. Some pages counted by 2’s on even numbers; some counted by 2’s on odd numbers. Some counted by 5’s, 10’s, or 100’s—a wide variety of skip-counting experiences.

Skip-counting is good practice for multiplication, and following the numbers of a dot-to-dot puzzle helps your students learn what interval comes next by connecting them in numerical order. The complexity of the numbering system quickly overtakes the simplicity of the picture, providing a worthy challenge to math students who might feel silly doing the simple dot-to-dot coloring page in its original version. Following the random order of the numbers on the page provides more interest and more challenge than if the student had just written out a skip-counting series, and the student can easily self-check his work by judging whether or not the picture has been completed correctly.

BONUS TIP: After you’ve gone to all the trouble of changing the numbers, wouldn’t it be nice to have this last longer than once-through-and-done by your little smarty-pants student? Cut the pages out of the book, slip a page into a plastic page protector, and let your child use a dry-erase marker on the plastic. Wet-erase markers (also called “transparency markers”) will work great, too, and they don’t rub off instantly whenever a stray sleeve crosses the page. A quick wipe with a wet tissue will clean up wet-erase markers and prepare the page for the next use. You could even use enough plastic page sleeves to hold all the pages from the entire coloring book and put them all into a 3-ring binder. Give your child the binder, some markers in assorted colors, and a couple of tissues, and you won’t hear from him for a very long time!

Workshop Wednesday: Placemat + Magnets = Educational FUN!

Find a placemat with educational information you’d like your students to learn: states & capitals, U.S. Presidents, whatever you can find. I’ve used both the laminated plastic placemats and the thicker, foam placemats. The former placemat in this photo was a laminated periodic table of elements, proving that educational manipulatives DO work for kids older than five. Notice the element in the lower right corner that is flipped over to show the magnet on its back. The placemat cost me about $3, which is an amazing price for educational gadgetry of this quality!

Periodic Table of Elements

Cut the placemat apart into its various components; scissors will usually work, but you may want to use a razor-knife or X-Acto blade for accurate cuts on thicker materials. Don’t worry about leftover pieces—you can throw them away. The thicker, foam placemat pieces are good for more projects that we’ll cover in a later post (think of them as craft foam that is not subject to static electricity), so you might choose to hang onto those for a while.

Now is a good time to rid your refrigerator door of all those freebie magnets you’ve collected from the pizza guy, hairdresser, auto mechanic, insurance agent, and every politician who marched in last summer’s parades. I always accept freebie magnets when offered (regardless of political affiliations)—they are my favorite homeschool supply! Using your scissors again, cut the magnets into pieces about ½” square or whatever size will fit easily onto the back of the placemat pieces you cut in the last step.

The next step may require a trip to the scrapbooking department of whatever store is near you, unless you are already an avid scrapbooker…er, bookscrapper…uh, person who documents life events in keepsake albums with pretty papers, ribbons, and all variety of cutesy add-ons. I’m not one of them, but I do recognize the homeschooling value of all those fabulous supplies! What you need right now is a box of the adhesive squares that are used for mounting photos or other items onto scrapbook pages. Stick one of those double-stick-tape squares onto the printed side of the little magnets you just cut up, then stick the other side of the tape to the back of your placemat piece. Don’t go all perfectionist in trying to line things up, just smack it on there and move on to the next one—you’ve got a lot of these to make. When each placemat piece has a magnet on its back, stick them all to a steel cookie sheet, pizza pan, or other flat metal item that will hold magnets and is more portable than the refrigerator door.

BONUS TIP: Let your kids help you with any of these steps and they won’t be able to wait until it’s all done to play with it. Now turn them loose and pretend you really don’t care if they learn what’s printed on this new magnetic educational gadget. Your kids will think they are just playing, but you’ll know they will learn from it, even if they think they are building houses or roads or flowers with the magnetic pieces. [wink]

Workshop Wednesday: What Is the Missing Element?

Use this worksheet as an example to make simple Missing Element worksheets for your children. No one should have to stop and sing the Alphabet Song from beginning to end, just to figure out what letter comes after P. The same concept applies to numbers and counting, just without the song. My young kids viewed little worksheets like this as a fun challenge. After a little practice, they could do these orally, asking “What letter comes after V?” any time we had a few seconds to fill: while standing in line at the store, waiting for a red light, any waiting, anywhere. It kept them mentally active, which made the waiting much more bearable for them. I used the same process for numbers, asking “What number comes after 19?” and similar questions. The worksheet itself is a visual method; the oral question and answer exercise is an auditory method.

These are good mental exercises for those students who already know letters and numbers, but who don’t automatically recognize a short segment of the longer series. This is also a good skill to build into those youngsters who are just mastering the ABC’s and counting—notice that I said mastering, not initially learning.

For those students who need a more tactile application, let them match alphabet blocks or letter tiles to the challenges on the worksheet, filling in the gap with the appropriate letter on a block or tile. Number tiles can be used to create the number challenges, using multiple tiles to produce multiple-digit numbers. Borrow letter or number tiles from games, or make your own by cutting 1-inch squares from cereal box cardboard and marking with a Sharpie on the plain side.

Be sure to allow your students plenty of free-play time with the Missing Element exercise, as they will be sure to want to challenge each other (or you) with more examples. When a child continually quizzes you for the answer, give the correct answer each time, knowing that he is learning from your consistent responses. When you are confident that he really does know the correct answer, you can give the wrong answer with a questioning tone of voice or say “Is it K?” to see if he will correct you!

For a young kinesthetic learner, spread out the letter or number series on the floor using Post-It notes or flashcards and let the child hop on each one as he reads them off and shouts out the missing element as he hops into the gap. Another method for energetic children is to have flashcards for the series in one room and extra flashcards for the missing element in another room. Challenge your little Tigger to run, hop, or somersault into the other room to search for the correct card(s) to bring back and fill in the gap in the series.

Combining all of these learning style methods will give your students practice at using more than just their preferred style of learning, which helps them gain a better understanding while also broadening their experiences. As your students get older and expand their knowledge base, you can adapt this Missing Element concept for other academic pursuits as well.

Workshop Wednesday: Dominoes Make Great Tactile “Flashcards”

Wouldn’t it be wonderful to have a single set of simple math learning aids that could help your students learn everything from basic number values to fractions, decimals, and percentages? It already exists, and you may even own a set: dominoes. Ordinary flashcards appeal to the student who learns best through visual means: seeing and reading. Saying the flashcard facts aloud will work best with the student who learns well through auditory means: hearing and saying. For the student whose fingers must connect with the lesson in a tangible way for him to truly lock the facts away in the deep recesses of his mind, dominoes make ideal flashcards!

Dominoes make great tactile “flashcards”!

Dominoes are wonderfully tactile, whether they are the smooth, heavy plastic ones that look like imitation ivory or the pressed wood versions with a decorative design embossed on the back side. The dots are usually carved out, and the depressions are filled with bright colors of paint. There is also usually some physical attribute serving as a divider between the two halves of the domino, either a carved or embossed line. All of these features work together to provide textural interest to the fingers that get to hold them – much more interesting than flat, boring, cardstock flashcards. Flipping through a stack of thin cards is one thing; stacking up dominoes, as one masters the facts they represent, is quite another thing. Dominoes appeal to many senses and learning styles with their bright colors, heavy thickness, and the wonderful sound they make as they clink together.

Let’s look at the wide variety of math exercises, from beginner level to more advanced skills, that can be performed with a set of dominoes.

Number Value

Count the spots. Say the number, or write the number. Repeat as needed for practice until the student knows how many seven is and can identify a group of dots with the appropriate number. Substitute a matching number of candies, blocks, or toy cars for the dots and repeat the counting exercise until the student understands that numbers can apply to more than just small colored dots in orderly patterns. Once the student has mastered the number relating to each distinct pattern of dots, arrange the same number of objects in different patterns to show that each number can occur in various types of groupings (e.g. four objects in a straight line is still four, even though they do not form a square, as on the domino).

Smaller v. Larger

When the student understands the principle of assigning values to digits, that same student can begin to differentiate smaller groups from larger groups. Since each domino conveniently displays two number groupings, use them to practice smaller v. larger numbers: help the student decide which group of dots represents the smaller number and turn that side to be on the left, leaving the larger number group on the right side. Repeat as needed for practice until the student can tell at a glance which number is smaller and which number is larger. Practice saying the numbers and deciding which is smaller and which is larger, and then count the dots, if necessary, for confirmation.

Two-Digit Numbers

Once again, each domino represents two digits. Help the student learn to read and write the two-digit numbers shown on each domino’s face. For example, if a domino shows a two and a six, that domino may be read as 26 or as 62. Dominoes that have no dots on one side can be read as a one-digit number and a two-digit number (e.g. 3 and 30). The smaller v. larger exercise can then be repeated with these two-digit numbers.

Addition

Students can begin simple addition problems by adding the two numbers represented on a domino and then counting the total of all dots for confirmation.

Subtraction

By holding a domino vertically with the larger number on top and the smaller number on the bottom, the student can begin learning to write and perform subtraction problems. More advanced students, who have learned the concepts of positive and negative numbers, can reverse the domino, placing the smaller number on top, and proceed with the subtraction exercise.

Multiplication

Dominoes can be used as multiplication flashcards by attempting to multiply the two numbers represented. If the student is unsure of an answer, it is advisable to consult a reference chart for the correct answer, rather than merely guess. Seeing the correct answer time after time will help the student memorize it by sight, and the student will eventually trust his memory instead of taking the time to look at the chart for the answer. (A calculator may also be used to check answers, but pressing a wrong button can deceive the student into believing a wrong answer.)

Division

Holding the dominoes horizontally can represent the numbers in a division problem. The student can write those numbers down on paper to practice dividing. The beginning student should only divide small numbers into larger numbers, until his knowledge of decimals allows him to practice dividing larger numbers into smaller numbers.

Manipulatives

Turn the dominoes face-down, so the dots are not visible. Practice counting, adding, and subtracting. Subtraction is merely undoing the addition process, and this can be easily illustrated by grouping and re-grouping the dominoes. Arrange groups of dominoes into rows to illustrate multiplication facts, and discuss how dividing is just undoing multiplication, but sometimes with leftovers called “the remainder.”

Fractions: Proper & Improper, Simplifying

Holding a domino vertically, the two numbers can represent the numerator (top) and denominator (bottom) of a fraction. Proper fractions always have the larger number in the denominator, while improper fractions always have the larger number in the numerator and can be simplified into a mixed number fraction. When reading the domino as a fraction, the student can decide if the fraction can be simplified and what that new fraction should be. Advanced students may select two dominoes and attempt to add them together as fractions, converting them to common denominators as needed. Subtraction, multiplying, and dividing fractions may also be practiced by selecting random dominoes to use as the fractions in each problem. Students should always be encouraged to write math problems in a notebook — when needed for reference, the student can easily look back at his previous work to see how he solved similar problems.

Fraction, Decimal, & Percentage Equivalents

Students with a working knowledge of fractions may move on to the decimal equivalents of fractions. Percentages are another form of fractions. Fraction, decimal, percentage, and ratio can all be thought of as “nicknames” for equivalent amounts. Arranging face-down dominoes to illustrate the problem, writing out the problems, and drawing diagrams will all help the students understand how the amounts are equivalent. Then the student may wish to use face-up dominoes as flashcards again, using the two numbers shown as a fraction and determining the decimal and percentage equivalents.

Perimeter, Area, & Volume

Using the dominoes face-up, a student can build “fences” to illustrate perimeter, or the distance around the outside of a specific shape. Count only the edges of each domino, and count each half of the long sides as a separate unit: a domino at a corner would count as 3 units: one for the short end on one side of the corner, and two along the long side of the domino on the other side of the corner. Filling in that shape solidly with “floor tiles” relates to the concept of area. Again, count each half of a domino (each separate section of dots) as one “floor tile.” Stacking multiple layers of dominoes can illustrate the 3-dimensional concept of volume. For example, an area represented by two rows of three dominoes each will contain six dominoes. Stack up several identical layers to show that each layer contains six dominoes. Multiply the area of six times the number of layers to determine the total number of dominoes used.

Play Domino Games

What better way to show that math is valuable in everyday life than to play a game of dominoes? Advanced players might enjoy the competitive element of keeping score, but those playing just for the fun of the game can proceed more quickly by simply playing their dominoes on the matching numbers and moving on to the next turn. There are a variety of domino games, so expand your knowledge base and learn several.

Line Dominoes Up on Edge for Physical Science Domino Effect

No one should go through life without lining up dominoes in curvy lines or intricate patterns and then gently pushing over the first one in line to watch all the others tumble in turn. Setting up the dominoes on end is good for honing the fine motor skills of small hand muscles — great care must be used to ensure that the dominoes don’t fall too early! Repeat as often as possible and search You-Tube for massive domino displays to enjoy!

How to Adapt Lessons to Fit Your Student’s Interests and Make Learning Come Alive

A GFHS reader wrote to me, concerned about her student’s lack of interest in doing homeschool lessons, although he showed a wide capacity for learning and retaining facts about sports. The mom was frustrated as to how to get any actual lessons accomplished, since their days were an endless series of disagreements and strife. This is when out-of-the-box thinking can really pay off. Taking the lessons out of the box and away from the textbooks can make a huge difference and ignite the spark of learning in a “reluctant” learner such as this student. The examples given here will relate to football (this particular child’s passion), but you can easily adapt these ideas to wherever your students’ interests lie.

When a child is keenly interested in football or other sports, that can be used as an “in” for other subjects. For instance, put a map of the USA on a bulletin board and have him stick a pin in the approximate places where his favorite NFL players were born. Then have him place another pin in the city where each player went to college and connect the two pins for each player with a piece of yarn. Suddenly he’ll be up to his elbows in a fascinating research project and geography lesson that doesn’t feel like schoolwork to him at all!

Take this in a slightly different direction by challenging him to do some research on the NFL teams, making a chart showing when each team was founded, where it began, and if or where it has moved. Have some of the teams’ names or colors or mascots changed throughout the years? Now he’s found a history lesson that he can really enjoy! Give him more pins for the map (and a different color of yarn) to show the movements of the teams. A little more research can reveal what important world events coincided with significant team events or crucial games for more history, this time linking football to other events. Find inventions or products that were introduced during the years that match up to his favorite events regarding games, teams, or players, and that can bring in some science lessons. Look at how football uniforms, pads, helmets, and other equipment have changed over the years and why for some more science and history.

Challenge him to research the backgrounds of a few favorite players and write “color commentary” that could be used by a sportscaster, and you’ll have a writing assignment he’ll be eager to do! Challenge him to write his own sports “column” or read and critique the sports columns or blogs by professional sports writers, and he’ll have reading material, comprehension studies, and analytical writing assignments that hold his interest. To round out the language arts lessons, focus on his content first, then work on helping him correct spelling, punctuation, and grammar — always examining the rules for each change, not just criticizing his writing without reasons. He may even learn to spot spelling and grammar errors in the professionals’ columns for an important lesson in why accuracy matters!

Players’ statistics can be analyzed for some practical, real-life applications in math. Calculate the total yards of passing or rushing, the percentage of completed passes, or how a player’s averages have improved or declined over his career. Math practice is math practice, regardless of whether it uses random problems on a worksheet or real-life statistics. When the real-life applications mean something to the student, he will have motivation to complete the work. Learning one fact will spur curiosity to learn more facts, and before long, the student will be knee-deep in new information and hungry for more.

The homeschooling mom mentioned earlier took this advice and began adapting lessons to her son’s interest in football. When his curriculum focused on poetry, they searched the internet for poems about football—and were delighted with their results. One poem prompted a discussion, which led to further studies and more topics. This simple substitution transformed a struggle over a single, uninteresting lesson into a day filled with curiosity, researching, exploring, and learning.

Lessons that are based on real-life interests will combine several academic subjects all at once, rather than following the institutional school model of working on each individual subject for forty minutes before switching to the next unrelated subject for the next forty-minute period. Your student can research a given topic, study and analyze the reading material, pursue more research as to the geography, science, or history related to the topic, perform some math calculations to gain better understanding of the data, create a timeline of events, and express his conclusions and personal opinions in a variety of formats. The analysis of the information is conveyed, whether it takes on the form of a formal essay, a news story, editorial column, a poem, song, or rap, or even a personal journal entry. My own student who was reluctant to read assigned stories outside his field of interest became a voracious reader when the subject matter fed his curiosity. (How many adults would waste valuable time reading things in which they have no interest?) Adapting lessons to your students’ interests teaches those students how to learn from every facet of life and sets them firmly on the path to life-long learning.

See also:
The Value of Supplemental Activities
10 Ways to Improve a Lesson
How Can I Teach Out-of-the-Box Thinking?
Is Learning Limited to Books?
Every Day Is a Learning Day, and Life Is Our Classroom

Outdated Excuses for Why You Could Never Homeschool

The following article was written by Jennifer Morrison Leonhard, a light-hearted homeschool graduate who believes life is what you make it. What she usually makes it is funny!

“I’m not smart enough to homeschool my kids.” A typical answer from me is that you do not need to have the encyclopedia memorized, and you do not have to be a former valedictorian — you can simply learn right along with your kids. You start with colors and shapes and letters and from there you grow one day at a time. Lessons are usually fully explained in their textbooks, so you can read along and learn it all just ten seconds before your student does! It is now 2011, and I could argue that yo’ momma and her smartphone could homeschool your kids. (Bet you weren’t expecting a good momma joke, were you?) You do not have to buy a single book or even own a library card anymore. Like the popular commercial says “There’s an app for that” — whatever it is that you want to know or do. Science? My phone can take my pulse through the camera! Or try Google Sky Map to learn the stars. Music? I have a drum kit on my touch phone, and I’ve never had so much fun with an instrument! Not to mention that Pandora allows me to experience a wide variety of music styles. Learning directions is no longer something you have to do with a laminated “placemat” map and crayon (yep, that’s how I learned when I was still in public school) — now you can use Google Maps on your phone. For teaching math there are applications to teach formulas, offer practice math problems, flash cards, and math games. You can get an application for reading ebooks, search random questions with your browser, and document your findings with a “notepad” application and your camera feature. My mom always told us that as long as we knew how and where to find information, there are very few situations in life that require you have everything memorized.

“I do not have the time to homeschool my kids.”
Yeah, you’re probably too busy telling them to stop texting, get off that computer, and put away that video game. Again, in an electronic age, if your biggest hurdle is getting them away from electronics, you can probably find ways to substitute actual learning into those same gadgets — gadgets that frequently fit into a pocket and go everywhere anyway. It really doesn’t require a lot of time to homeschool. Once you cut out standing in line for this and that, waiting for the other students to catch up, or waiting for everyone to be quiet, you can see that only a few hours of real learning time are necessary. Unschooling is currently popular, so if electronics aren’t something your family indulges in, you can simply learn from Life. You can’t exactly avoid Life, and there are plenty of lessons to be learned each day, with or without 21st century electronic assistance.

“I could not stand to spend that much time with my kids.” Fine, send them to their rooms, and then Facebook friend-request them, and message their lessons to them. No face to face contact needed. They can chat with you when they need individual help, and message back or post photos and videos of their work. You, in turn, can post back their grades using the “Comment” feature, or for pass/fail there is a “Like” button included. The “Like” button would also give you feedback from their peers and other parents if you felt that you needed an outside opinion on a subject in which you are not an expert. Your children can also use the privacy features offered on Facebook to prevent certain friends and family from seeing their schooling, if that option is preferred. The Facebook photo albums are also a handy way to maintain homeschooling records if your state requires a portfolio for legal reasons. There it is: photographic documentation, all neatly packaged, and no fear of fire, flood, or other natural disaster wiping it all out, such as you would have had in the age of paper records only. And it all stores much more neatly, too. For added security, you can back up your files on flash-drives or with Carbonite.

“Socialization.” Did I mention electronic devices? Smartphones? Facebook? I think I did. Oh, and if you prefer actual human contact, go outside. There are still a few people left out there who aren’t busy on Facebook or their smartphones. There may also be some out there that are probably still on their smartphones and Facebook, so please drive defensively.

Family Planning (No, Not That Kind)

Planning is vital — but I don’t mean planning every moment of every day, deciding what lessons you will do when or to which organized activities you will deliver your children every day. The most important thing to schedule is your time together as a family. Set aside an evening for a light supper, then watch a family movie together, with plenty of popcorn and apple slices. Plan a family game night and try your hands at Jabberwocky Scrabble (anything goes, but players must pronounce and define each “word” — be prepared for side-splitting laughs) or a similarly fun twist on any other game that’s been gathering too much dust on the shelf. Reserve an entire day for a family outing: take sandwiches, fruit, and a large jug of ice water and head for a park with a lake or nature trails or playground equipment and spend the day disconnecting from everything and everyone else. Block out a weekend on the calendar for a family get-away and then get away from your normal schedule and routine.

Do only what your budget will allow, and trust me when I say that fun doesn’t have to cost anything. We tramped through the woods, stopped to look at the wildflowers, marveled at the tiny fish or tadpoles at the lake’s edge, or dipped our fingers and toes in the chilly water. We watched the clouds for drago-saurs and ele-raffes, skipped rocks on the lakes, and let the ripples on the water mesmerize us until we had forgotten everything else. Take turns playing follow-the-leader around, over, and through all of the swings and slides, take giant steps or silly, head-bobbing, arm-flapping walks round and round the trees, and let yourselves laugh freely and enjoy the company of the people who matter most in this world. Wander through a free museum or turn a lingering trip through an antique store into a spontaneous walk through history.

Why do these things need to be scheduled? Because if you don’t schedule time for your family first, your time will be scheduled for you by other people, other groups, or by other activities, and your family’s time together will be vaporized into the mist of a busy life. Family must come first, and it doesn’t count if you are all attending a group activity but participating as individuals instead of as a family unit. If this is a foreign concept to you, dare to try a brand new activity where you and your spouse and your children interact together for the entire time. It may take a while for this new bond to develop to fullness, but there is a unique and lasting experience ahead of you, and family is well worth cultivating.

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