Workshop Wednesday: Patterns

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



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

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

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

See also:
What Is the Missing Element?
100-Grids and flashcard Bingo

Workshop Wednesday: Letter or Number Manipulatives (DIY)

Have you ever found yourself wishing you had a whole big bunch of fancy-schmancy letter or number manipulatives to help your struggling learner? Well, don’t move, because you’re about to learn how to make them inexpensively for yourself!

A child who has difficulty learning letters or phonics patterns, identifying syllables, spelling words, or reading will usually benefit from using letter manipulatives, something he can move around and re-position himself. The struggling student might be any age, so using letter tiles is helpful for older students who already know the letters but struggle in spelling or syllable divisions.

Number manipulatives are helpful for the student who struggles with math, as are extra tiles with math operation symbols, to use them in building and solving equations. It’s one thing to use math cubes to illustrate 3 + 2 = 5, but it’s another thing entirely to use number tiles to solve 3 + 2 = 4 + y.

It’s fairly easy to cut out letter or number shapes by enlarging a simple font to super-size status, about 3″ tall (or around 350 points) on your computer’s word processor. Experiment to find a font you like, enlarge the letters or numbers, then print them on cardstock and cut out. These shapes can also be used as templates for making cut-out letters or numbers from materials that can’t be put through a computer printer, or to get more letters or numbers from a single sheet of paper.

Squares or rectangles can be turned into cards or tiles by writing the letters or numbers on them with a Sharpie marker. I have used cardstock, sandpaper, and cereal box cardboard for these with great success. The sandpaper adds a nice tactile element for kids whose learning styles appreciate more texture. I have varied the sizes, depending on the age of the kids using them and the application they will fulfill — 6″ squares are great for matching games on the floor, but 1″ squares work great as tabletop tiles for spelling practice. We had a few hundred small letter tiles made from cardstock, which were great for building a list of spelling words.

For students who are just learning their letters, I highly recommend starting with upper case letters first, then once the student knows them without mistakes, introducing the lower case letters as the “little brothers” of the upper case. This results in less confusion and fewer possibilities for reversals.

These cut-out letter shapes are wonderful tools for teaching and learning recognition, matching, phonics, spelling, syllables, and so on, whether by themselves or in combination with cards, tiles, and a variety of sizes and font styles (especially helpful for learning to recognize all the different appearances letters can have). You could even make some in the exact same size and shape as the letter tiles from a Scrabble or Bananagrams game and combine them all for even more learning fun!

I have made letter and number shapes and cards from these materials:

  • Sandpaper (fine to medium texture works best)
  • Craft foam
  • Textured fabrics (corduroy, vinyl, fleece, denim, etc.)
  • Cardboard (including cereal boxes), poster board, etc.
  • Cardstock
  • Textured scrapbooking paper

Bonus Tips:

  • Sometimes I needed to glue an identical shape of cardstock or cardboard to the backs of some flimsy materials for stability and durability, especially with cloth or thin paper.
  • Wood or foam cut-outs can sometimes be found with craft supplies for a quicker start.
  • It can also be helpful to decorate the front side and/or bottom edge of letters and numbers to help kids learn to orient them correctly (even a line drawn with a marker can be enough to discern top from bottom or front from back).

Letter Activities:

  • Matching — sort lots of different letter shapes, tiles, and cards into separate piles for each letter. Alphabetizing — mix up one set of letters (A-Z) and put them into alphabetical order.
  • Phonics Practice — use letters to make short words (2-3 letters) and practice reading their sounds in order to read the words. Change one consonant and read again; repeat. Ditto for changing the vowel. Repeat for longer words as skills increase.
  • Spelling practice — use your supply of letter manipulatives to build spelling or vocabulary words. Add as many words as possible that use the same phonics patterns.
  • Syllables — build a vocabulary word, then scoot the letters apart to divide the word into its proper syllables. Compare to the dictionary entry to self-check.

Number Activities:

  • Matching — sort lots of different number shapes, tiles, and cards into separate piles for each number.
  • Numerical order — mix up a set of numbers (0-9 or 1-10) and put them into numerical order.
  • Number value — match the appropriate number shapes, tiles, and cards with the dots on dice or dominoes.
  • Double-digit numbers — combine digits to make teens, twenties, etc. and practice reading them. Ditto for three-digit numbers and beyond.
  • Arithmetic practice — build arithmetic problems using the number shapes, tiles, cards, and operation symbols, and put the correct numbers in place for the answers.
  • More operations — be sure to make some commas, decimal points, fraction bars, dollar & cent signs, percent signs, and anything else your student will encounter in his math lessons.

 

For more activity ideas, see also (in any order):

ABC Flashcards

Building Blocks for Success in Spelling

Building Blocks for Success in Math

“Stealth Learning” Through Free Play

What Is the Missing Element?

Letter & Number Recognition

Tactile Learners

Workshop Wednesday: Untangling the Math Pages

Do your student’s math papers sometimes look more like a tangled jumble of numbers instead of neatly arranged problems? Do you have a student who gets confused over complex math problems? Our old friends, graph paper and color, can come to the rescue once again!

Graph paper was a blessing when my young students began writing math problems, but their numbers sometimes wandered aimlessly down the page, causing us to wonder which place value some digits represented. Using 1/4″ graph paper (4 squares per inch), I showed my son how to put one digit in each square and line up all of the ones’ column digits. That way, the tens’ digits ended up in the correct column, as did every other place value. It helped my student keep track of his math problems, which helped him perform the calculations correctly, which led to faster learning. It was a great benefit for the small price of a pad of graph paper.

Math function signs can be written in colors for kids who struggle with noticing which operation is required or in which order certain operations should be done. For example, parentheses in their favorite blue may catch their eyes first, and they know to do that before going on to the yellow plus signs later.

For particularly large and difficult math problems with complex fractions or higher math, I encouraged my kids to use an entire sheet of paper for each problem, if necessary. I told them they could make only as many changes per step as they were comfortable with and instructed them to leave a blank line after each step of the problem. That made it much easier for them to tell where they were and what they were doing. It also helped them to know they could use as much paper as necessary to be able to understand the steps and the transformations of tricky calculations (paper is cheap; understanding is priceless). Spread those numbers out so you can see exactly which digit belongs where, and skip a line between steps for amazing clarity in those super complicated problems.

Something my daughter Jen came up with on her own was to write each step with a different colored pencil. She is a strong visual learner, so color often played an important role in her schoolwork, and her set of colored pencils seemed like a natural tool to use for understanding the transitions in how each step changed from the one before it. The colors helped her eyes and brain differentiate one step from another, so the changes were much easier to see and understand. Using colored pencils can also work for students who get overwhelmed by trying to solve large math problems, helping them to focus on only one step at a time.

For those students who have difficulty understanding what is happening in each step, color can also be used to show the process of solving. The parent-teacher can write out everything in black pencil that remains the same for the next step, and use color only for the changing elements, to clarify what was changed in each step and exactly how it changed. Use a different color for each step to keep the transitions easier to follow.

Color can also make math more interesting for students who find math to be boring but find art to be all kinds of fun. Perhaps doing math in color is just the enticement little Billy or Sally needs! Bonus tip: Erasable colored pencils are well worth the slightly higher price!

Workshop Wednesday: Color-Coding As a Learning Tool

[This article was written by Jennifer Leonhard.]

Is your student attracted to color or motivated by markers? Does your student struggle with staying organized when studying? Color-coding is a great learning tool. Visual learners respond well to color as an organizational method, and non-visual learners can improve their visual skills by using color to organize information. As classes become more complex in high school and college, color-coding becomes an even more valuable organizational tool.

As a strong visual learner, I used assorted colors of index cards and highlighters to help me organize my thoughts and the material I was studying in my college classes. I used the order of the color spectrum as my color code whenever I needed to maintain a beginning-to-end, front-to-back sequence: red, orange, yellow, green, blue. My system always began with red (pink worked as the closest available color in note cards and highlighters) and proceeded through the spectrum to blue (violet/lavender was too hard to find in highlighters).

Here’s how I wrote the various parts of a speech or oral presentation: one pink card held the introduction, several orange cards for the information for Point 1, several yellow cards for Point 2, several green cards for Point 3, and one blue card held the conclusion. I could rehearse a presentation using these cards, and if I dropped them or they got mixed up in my backpack, I could easily put them into color spectrum order again. Any supporting quotes had their own index cards (using the appropriate color code for each point), and I would draw a squiggly outline on those cards to indicate that they contained the quotes. Each card had a topical title at the top and a number in the corner to indicate its order within each color group. I rarely ever needed to look at my note cards when giving a presentation, because I had them so well organized that I could easily see them in my head and go from there, but I did keep the cards with me in case of a blank-out moment. I could also turn them in to the teachers who asked for them as part of the assignment.

I also used this system for writing extensive research papers to create an outline in this format. I could put anything supporting Point 1 on orange cards and just go through all the orange cards later to put them in order for writing my paper.  When doing research papers and printing out a stack of articles for a 50+ page paper, I would use highlighters in the same colors as my note cards to circle significant points in the article. I could then grab all articles with orange outlines and work just on my first point without being distracted by all the other sections.  If an article had information for several points I would do a thicker outline in the color that it discussed the most and a thinner outline in the color of the point it discussed less, and then highlight or circle the section of text that pertained to each part in the appropriate color.  I could flip through my notes very quickly and efficiently in this way and find exactly what I was looking for at any particular moment.  I rarely had a “blanking” moment when writing, because I had a system that provided me with a place to start.  I didn’t have to write the individual sections of the paper in any particular order, and if I found myself overwhelmed by the sheer amount of research information I had printed, I could simply start color-coding instead of freaking out.  If I found myself unsure of where to stand on an issue or how to phrase my findings, I could simply grab all of the items outlined in orange and start highlighting, circling, or underlining the important sections that I wanted to use.  Stuck on what to write for orange? No problem! Just work on the yellow items for a while, and then come back to orange later.  I had no fear of getting confused or forgetting what I was doing next, because everything was very plainly color-coded for picking up where I left off.

Similarly, I would use this method to study complex material. I used the same color-code for highlighters, note cards, in my lecture notes, and in the text books, so that I could start the process while reading and know what to put on the index cards later. I used yellow as my color-code for keywords from the text. Pink was for any important dates to remember, green signified important people, and orange was for formulas and diagrams. Blue was for any other information I needed to make sure to remember. By categorizing things like this, I could pull out just my orange cards right before a test and review the formulas and diagrams, if I thought I was suddenly blanking on something. I’m bad at remembering specific dates, so I could grab the pink cards to quiz myself on those. This made it easier to categorize the test elements in my head, and instead of all the information being a blur of grey pencil notes on white lined paper, I could focus my memory on just the orange parts, or just the pink parts. The colors became just as important as the facts themselves, especially when trying to sort through all the facts in my head to find the one correct answer I needed on a test.

Whatever color-coding system you choose to use, the color significance can vary from subject to subject, but consistency within each subject is the key to making your system work. Yes, I bought a lot of index cards and highlighters, but they became valuable assets to my study habits, and the positive results proved their worth. Other colored items could also be added to a colorized system, such as colored pencils, file folders, pocket folders, notebooks, divider tabs, sticky-flag bookmarks, and whatever else your favorite office supply store has crammed into its aisles. Using color-coding is a great organizational and memory tool, and it strengthens your visual learning skills, even if visual skills are not your strongest learning style. And who doesn’t like playing with a whole rainbow of highlighters?

Workshop Wednesday: Tactile Card Holders, Version 2

Based on last week’s Tactile Card Holders, Version 1, this week’s version uses a few different supplies to create a similar product.

Equipment:
Cereal box cardboard
Photo corners for index cards
Glue (optional)

Yes, we are breaking out our old friends, the cereal boxes, to make yet another great learning tool. I cut the cardboard into pieces larger than my index cards and attached self-stick photo-corners in the middle for the index cards. You can use 3×5″ or 4×6″ index cards, depending on what you have available and how much information will be put onto the cards. Then I decorated the surrounding “border” with whatever was available (1 “theme” per card), using glue to attach the things that weren’t already self-stick.

Edges decorated with:
Ribbon
Sequins
Craft foam/felt stickers & shapes
Sandpaper
Acrylic rhinestones/gems
Textured papers

The examples in the picture show photo corners without an index card inserted, along with a few examples of spelling rules. As in last week’s article, these card holders can be especially helpful for older students who are trying to memorize more complicated information and formulas. Once learned, the note cards can be easily switched with new cards for studying new facts. The border textures work by appealing to tactile fingers and giving them something to focus on while the eyes are busy reading the facts on the cards. Later on, when the mind tries to remember the facts, the textures, patterns, and colors from the borders of each card holder will serve as markers on a virtual road map to help the brain find those facts and pull them up into view. Students who have had trouble memorizing dull, dry facts in the past will find these note card holders add some pizazz to the process and actually help stimulate their memories.

The borders of these card holders will offer even more tactile interest than the ones from last week that simply had their edges trimmed with special scissors. My favorites among these have to be the cards with sandpaper borders — I made several of those, each with a different level of coarseness. Satin ribbons offer a smoother texture, but grosgrain ribbon is different yet. I also found some wonderful textured papers at a scrapbooking supplies store to expand the variety of textures and visual appeal. Other cards had their borders adorned with thick felt stickers, craft foam shapes, acrylic “gems,” and other crafty materials to add texture and color. Let these examples spark your imagination and see what you can come up with!

Workshop Wednesday: Tactile Card Holders, Version 1

Sometimes certain facts work well for studying from homemade flashcards. However, some students just don’t do well with trying to learn from ordinary index cards. Today, we’re going to make those cards extraordinary! These card holders will work especially well for teens who are trying to learn complicated facts and formulas, but who need some extra learning methods thrown in.

Equipment:
Index cards to hold the facts or information
Bright colored card stock
Razor knife for cutting slits
Scrapbooking scissors for trimming edges

How To:
I started with 8 1/2″ x 11″ sheets of brightly colored card stock and cut them in half to make two pieces 5″ x 8 1/2″. Lay an index card in the middle of each of these sheets and mark about 1/2″ from each corner. Use the razor knife to cut angled slits (connecting the marks you just made) for the corners of the index cards. You don’t need to get the cards exactly centered or the slits angled perfectly; if you have a student who is fanatical about precision, give this job to him. Either 3×5″ or 4×6″ index cards will work, depending on what size you have on hand or how much info will be put on each card. The bright colors add visual interest to the boring facts (did I just say boring? oops), and colored index cards can do the same thing (the ones in the photo are light blue, but white cards work just fine). Just be careful that the colors don’t clash or create such a visual disturbance that no one can stand to look at them!

I had a variety of scrapbooking scissors available, so I trimmed the edges of the card holders, using a different pattern on each card. If you only have one or two fancy scissors (or even just a pair of pinking shears), that will still work. You could even use regular scissors and just cut some wavy or zig-zaggy edges. The idea here is to create a little bit of tactile interest for the fingers that will be holding the cards.

As your student studies the facts on each card, the bright color of the card holder will become a visual cue to those facts, and the tactile edge will do the same for his fingers. Reading the card information aloud lets the student say and hear the info, important methods for auditory learning — and when he stops reading aloud, he’ll catch himself wandering off-topic. The large size of these card holders makes them more of a kinesthetic learning tool than just small index cards are. The colors, edge textures, size, and reading aloud will all provide memory keys that his brain can rely on when trying to remember the facts on each card. Hmm… that card was in a red holder… I was holding it with both hands… the edges were pointy… I remember hearing myself say these points over and over… I know — it said THIS!

By inserting the index card’s corners into slits, the holder becomes reusable. When this set of facts has been learned and the student is ready to move on to learning different information, the index card can easily be slipped out and another inserted in its place. Make as many card holders as needed, but if possible, trim the edges of like colors with different patterns to make them different (notice that the 2 blue card holders in the photo have different edge patterns).

The cards shown here are for fallacies of reasoning, but you can use this method for learning vocabulary words, their spelling, and meanings; math or science formulas; historical events or people; or anything else that needs to be memorized.

Also see Tactile Card Holders, Version 2 for more ideas!

Workshop Wednesday: The Moving Answer Worksheet

Addition facts are not tricky; they are merely a short-cut to counting from one number to a higher number. Subtraction is not a difficult procedure; subtraction is just un-doing addition. When taught together, addition and subtraction become different ways of looking at the same problem. Children often get the impression that addition is one skill, and subtraction is a completely different skill. They are not different skills, they are just different methods of looking at the same facts. It’s the same principle as if you and I were holding several pencils, but I give you a pencil, and then you give me a pencil. We can trade pencils back and forth for as long as we want, but we are still holding the same total number of pencils.

When my kids got stumped on variations of the same math fact (is 2+3 different from 3+2?), I created a simple worksheet to show them how to see those variations as always being the same statement, no matter what form it took. I rearranged the numbers in every way possible, and I moved the answer blank around to different locations, too. By completing this short worksheet, my kids learned to see the statement as a whole, instead of seeing each variation of it as a completely different problem. By combining the addition and subtraction variations of the same math fact, my kids caught on quickly to the idea that those particular numbers always went together, whether adding or subtracting.

Some math teachers and some math programs only place the answer blank at the extreme right end of each problem at this stage. Some students who experience this consistency can become incredibly confused when they are eventually presented with a problem that has the answer blank in a different location. Learning to relate to each set of facts as a completed puzzle helps students identify which piece of the puzzle is missing, and the many variations possible in this worksheet will prepare students for later math (such as algebra) when the answer blanks shift around to different positions within the problems.

Notice how this method was extended in a few examples to include the arithmetic symbols, as well as the numbers, such as in 2 ___ 3 = 5. Obviously, a plus sign belongs in that space, since 2 and 3 must be added to equal 5. It’s obvious to you and me, because we’ve been doing this for so many years, but to a youngster just learning arithmetic, it’s not quite as apparent, and a little discovery is good for the brain cells.

This principle can also be applied to multiplication and division facts, as division is simply the un-doing of multiplication. The stage of learning the facts is a good time to combine these skills, since there are no remainders yet.

The worksheets don’t have to be fancy at all — a handwritten version is just as valid as a computer printed one, but handwriting will probably be much faster and easier to produce. Stick to one set of numbers for each worksheet, but include all the possible variations. Your students will catch on quickly!

Use other learning style methods along with this visual worksheet. Auditory learners will benefit from discussing the patterns in the problems and will appreciate a chance to answer orally. It helps to connect learning styles if you encourage them to write their answers in the blanks after giving the correct oral answer. Do any of the following activities with your auditory learner, but talk about what you’re doing and read the problems aloud, or let him talk aloud to himself. Background music is also helpful for auditory students who need it as “white noise” to drown out other noises and help them concentrate, so keep the iPod and headphones handy! If you have any other students nearby who are not auditory learners, they may appreciate being allowed to do their work in another part of the house — my visual/tactile daughter did a lot of lessons quietly in her bedroom while her auditory brother and I discussed his work in the kitchen.

Tactile learners can use manipulatives to help solve these problems, such as small blocks or dry beans. The same group of objects can be used for the entire worksheet by rearranging them to fit each of the various problems. Other helpful items may be individual cereal-box cardboard “flashcards” for each number and arithmetic symbol–students can arrange and rearrange them to see which piece of the puzzle is missing. Tactile learners need to keep their fingers and hands involved during the lesson, so use whatever materials you have available to make that happen, even if that means making the worksheets large enough to hold numbers formed from Play-Doh on each answer blank!

Kinesthetic learners work well with large-scale manipulatives, such as sports balls arranged in groups in the back yard to fit the problems. You can adapt tactile manipulative, table-top methods for kinesthetic learners by making things large enough that they will be using the big muscles of arms and legs instead of just fingers to move items around. Another good kinesthetic learning method is to write large problems on a whiteboard or chalkboard, or use a slick-finish white shower curtain liner as a giant piece of paper on the floor and write on it with wet-erase markers (or use Post-It notes for the answers). Chalk on the sidewalk or driveway is another good stand-by for over-sized writing projects, but don’t forget that your kinesthetic student will also respond well to doing standard worksheets if he can lie on his tummy on the floor to do them! Any method that keeps those big muscles active is a kinesthetic method, so if you want your student sitting quietly in a chair, it’s not a kinesthetic lesson.

Whatever your students’ learning styles may be, it should be their goal to learn how to learn through every style. Therefore, using a few of the above ideas for each student in whatever lessons you do will increase their ability to learn through other styles and increase their overall understanding. Besides that, variety just makes the learning that much more fun!

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