Long division that sticks

I recently saw a division problem that a middle school student attempted and her solution looked like this:

Ouch!  She got the format down-- divide, multiply, subtract, bring the next digit down-- and used a remainder; and technically, it is true that 16 x 39 +1023 = 1647 (points for bringing down the 1000 after the fact!), but she missed the point of the process entirely, which is to find the number of times that 39 can go into 1647.

Whether long division, short division, division of fractions, or whatever, students need to know that division asks a question:  How many sets of one number can go into another?  It's easy to get so caught up in the algorithm that the purpose is completely lost.  That's true of a lot of math skills-- it's not enough for the student to be able to run through a procedure; they need to know what they're doing and why.

Many students have a hard time learning long division, simply because there are so many steps involved.  Years ago, my own hands-on girl needed the following method to help make things click:

Materials:

• Colored, 3D numbers: multicolored plastic or wooden magnetic numbers, or play dough, or modeling clay; 
• A markable base to put them on: cookie sheet lined with paper, or magnetic whiteboard; 
• Something to make the math symbols: clay, craft sticks, felt, paper, or pipe cleaners
• Something to mark lines with: dry erase markers, washable markers
• Index cards or other paper

Procedure:

1. Draw 6-8 columns lengthwise on the cookie sheet or whiteboard.
2. Set up the problem:  Construct the long division bracket out of felt, paper or a pipe cleaner, and line up the digits of the dividend in the columns, using a different color number for each digit in the dividend.  The last digit of the dividend should go in the far right column.
3. Write the divisor on an index card or piece of paper.  This illustrates the distinction between the dividend, which is the actual number we are working with, and the divisor, which is the number we're trying to fit into it.  Place the divisor outside of the bracket.
4. As the problem is solved, make a point to line up digits in the columns and match the color of all digits in each column.  I didn't have enough wooden numbers of the same color to complete the division, so I used matching modeling clay to make the numbers I needed.
5. Use popsicle sticks or other neutrally-colored 3D object for the subtraction base lines.
6. If your number set does not include operation signs, make your own subtraction symbols.  It is best to have the student be able to pick up and move a physical subtraction sign.  

By keeping the numbers lined up and color coordinated, place value is emphasized.  When talking with your student,  point out that all the numbers in the same column have the same place value-- for example, in the picture at left, the yellow 1's both mean 1000, the blue digits mean 600 and 500, the red digits indicate 40, 40, 60, 80, and 70, the green digits are 2, 7, 7, 8, and 9.

The benefit to using the moveable numbers is that they are easily picked up and moved around, and the student doesn't have to worry about writing neatly.  If the columns don't line up, a simple push of a finger will fix it.  If a mistake is made, it is corrected as easily as changing out numbers.  They should not be writing anything in this activity, just moving the 3D numbers and symbols.

Have the student practice this procedure over many days.  If she has a hard time remembering the steps of the algorithm, try chanting, "Divide, multiply, subtract, bring it down!" over and over.  You can add in dance moves or hand motions: for "divide," move your hands as if you were separating something into two parts; for "multiply," cross your arms to make an "X;" "subtract" might be pointing away with your thumb as in 'hit the road, Jack,' and "bring it down" could be pantomiming pulling down a window shade or something.  Your student can also come up with her own moves.

Once she's got the procedure down, have the student do the same procedure using colored pencils on notebook paper that is turned sideways.  The column lines are already drawn!

It is important to have the student get in the habit of checking her work.  In this case, point to the original 1647 and ask the student, What two numbers can be multiplied together to get this number? If she understands what she just did, she will know that 39 x 42 will get him close to 1647, but because the solution has a remainder, the remainder 9 must be added to the product to get the final answer.

Getting back to the original problem of the middle school student's division error,  why do you suppose she made the error?  It appears that she did not understand the purpose of the problem to begin with.  If she can learn to see the problem as, "How many 39's are in 1647," that will help her see that "16 remainder 1,023" is a useless answer.  Another way to help her would be to take the card with 39 on it and say, "What could you round this number to that would be easier to work with?"  If she can see that rounding the divisor to 40-- and perhaps also rounding 1647 to 1600-- can give her a good estimate, it will go along way toward getting to the correct solution.

Multiplying vs dividing by fractions: Let's Make Brownies!

Multiplying or dividing fractions by a whole number is pretty easy to demonstrate.  Multiplying and dividing fractions BY fractions, however, can be a confusing business!  The algorithms aren't so bad-- to multiply one fraction by another, simply multiply across the top (numerators) and then across the bottom (denominators), reducing the end result when possible:

Division works the same way, except that the second fraction is "flipped" (inverted) before multiplying:

The typical textbook fraction multiplication model involves shading a rectangle with one fraction horizontally and shading the other fraction vertically.  The intersection is the solution.  That's fine.

1/2 x 2/3 =1/3

Here we have the vertical fraction, 1/2, shaded in pink, and the horizontal fraction, 2/3, shaded in black.  The place where they overlap is the solution-- 2/6 of the rectangle, or 1/3.

Division modeling gets a little trickier.  To model 1/2 ÷ 2/3, you have to show how many 2/3's are in 1/2-- which is not even one, but another fraction.

This lovely box diagram shows 1/2 of the box shaded in pink, and then 2/3 of the box shaded in black.  This time, both fractions are shaded in the same direction (here, vertically).  Again, the overlapping shading gives us the solution-- the difference here is that the overlapped part is measured in terms of the black shaded section-- the overlapped part covers 3/4 of the black shaded area. 

The difference in division modeling is also obvious when the dividend fraction is divided by a smaller divisor fraction.

In this case, the shaded 1/2 section is being divided by the outlined 1/6.  How many 1/6 are in 1/2?  There are three.

Not surprisingly, many students still don't understand what it is they're actually doing when they're multiplying or dividing fractions, so translating it into word problems can be frustrating.  To make the concepts clear, all you need is a fresh-baked batch of brownies, some measuring cups, and maybe some paper and scissors.

First, bake the brownies.  Then, consider this problem:

John made a pan of brownies and shared them with his friends.   They ate half of the brownies in the pan.  After they left, Dad ate two thirds of the remaining brownies.  How much of the original batch did Dad eat?

Is this a multiplication or a division problem?

To help your child understand what's going on, she needs to know two things:

1) The multiplication sign can generally be translated "of" in English.  2x100 means two (sets) of 100, which is 200.  1/2 x 100 means one half of 100, which is 50.

2) Division answers the question, "How many (sets of) _the second number_  are in _the first_?"  100 ÷ 50 is asking, How many sets of 50 are in 100? = 2.  50 ÷ 1/2  asks,  "How many sets of 1/2 are in 50? = 100.

So, back to the brownies-- if we have half a pan of brownies and Dad eats 2/3 OF those,  we can figure out how much Dad ate by multiplying.  1/2 x 2/3 = 1/3.  Dad ate a third of the original batch!

Obviously, to model this with brownies, you'll have to cut the brownies into six even pieces, eat half of them, and then put two thirds of the remainder onto a plate, to see that what's going on the plate is 1/3 of the original pan.

Here is half of the pan of brownies. (Of course, these could also be cookie bars,  rice cereal bars, even gelatin "jigglers," depending on what your students are allowed to eat.)

Here is the 2/3 of the remaining half.  Note that it can also be described as 2/6, but since 2/6 = 1/3, our final answer is 1/3.








So, what would a division word problem look like?  Try this:

John has a recipe for brownies that calls for 1/3 cup of cocoa per batch.  There is 3/4 cup of cocoa in the box.  How many batches of brownies can he make with the cocoa he has?

In this case, we want to know how many sets of 1/3 are in 3/4?  So we divide:

So, John has enough cocoa to make two full batches of brownies and 1/4 of another batch.

A less high-calorie method of modeling fractions is to use measuring cups with water or dry rice. For example, you can measure out 3/4 cup ofto your heart's content. rice, and see how many times you can fill 1/3 cup with that amount.  You will show that 3/4 cup can be divided by 1/3 cup twice, with one fourth of the 1/3 cup left over-- that is, there are 2 1/4 sets of 1/3 cup in 3/4 cup.   Similarly, you can measure out 2/3 cup 1/3 cup of rice, divide it in half and show that the half amount fills a single cup: 1/2 x 2/3 = 1/3.

Another way to model the fractions is by using paper fraction strips.  Print out as many as you need, and then you can model "half of 2/3" (1/2 x 2/3 = 1/3) or "how many 1/4's in 6/8" (6/8 ÷ 1/4 = 3). More on that on a future post.

Whole Brain Writing

I love the Whole Brain Teaching philosophy.  It uses physical movement, oral repetition and response, and visual images to teach.  It is high energy, fun, and highly effective.  I used WBT's Superspeed Math drills and a few other techniques the year before I quit teaching.

Whole Brain Writing is a free download at Chris Biffle's  Whole Brain Teaching website.  To get it, create an account on the website (free!) and download the material from the "Goodies" menu.  It is presented as a slideshow, but is very easy to follow.  In fact, you could easily use the slideshow as the basis for your own classroom (or your own child's) writing curriculum.

The program starts out giving definitions and accompanying hand gestures to teach parts of speech. There are also hand gestures to teach sentence rules (capitalization and end punctuation), topic sentence, paragraph, and essay.  Students practice 'oral writing" with these gestures-- answering questions in complete, capitalized and punctuated sentences-- and are challenged to support their answers with gesture-emphasized "because" statements.  The function of the gestures is not unlike Signed English-- which is a bridge between ASL, with its unique vocabulary, grammar and syntax,  and the English that deaf students learn to read.  WBT's "oral writing" is a similar bridge between students' spoken language and the written conventions.

The program then provides several activities with graphic organizers for expanding students' thinking and writing from brainstorm charts to complete essays.  These include WBT Brainstorming, the Genius Ladder, and Triple Golders.

WBT Brainstorming takes students through creating "who, what, when, where, why, how" questions about their topic and then answering them in a way that can create complete, organized essays.

The Genius Ladder is presented as a game that helps students develop a simple sentence into a more complex, descriptive one, adding details and "extenders," and organize the sentences into paragraphs.  It reminds me of the step-by-step approach of Andrew Pudewa's Institute for Excellence in Writing (IEW), and I suspect it would work for the same type of student.  Pudewa starts his students out writing "key word outline" notes from published material, and they end up writing detailed original sentences with specific "dress-ups" in organized paragraphs and essays.  In WBT's Genius Ladder, students move from the "blah sentence" to the "genius paragraph."

With Triple Golders, students begin with simple, scaffolded sentence frames and learn to create detailed sentences that they can expand into tightly organized paragraphs and essays.

And about that grammar... Superspeed Writing is an activity that helps students practice constructing sentences using various parts of speech, beginning with "I see a (noun)," and ultimately completing "Article adjective noun, appositive, verb adverb prepositional phrase conjunction rest of sentence."

As if that wasn't enough, Biffle provides a fun, low-stress method for getting students to notice their own errors and not meltdown when their errors are pointed out to them.  For red-green proofreading, students mark each other's papers, once with a red marker to identify an error ("less perfect skill"), and once with a green marker ("more perfect skill.")

And as with all WBT programs, it is the individual student's progress that is celebrated, not just the top banana.  So everybody stays motivated.

Here's another activity, called SuperSpeed Reading, that is a fun way to drill sight words in a large classroom.  It is similar to WBT's Superspeed Math, which I have used with success to drill math facts.

If you are at all interested in adding these hands-on, whole brain activities to your writing classroom, check out the Whole Brain Teaching website!

Adding negative numbers

Negative numbers can be confusing to some students, because they don't see them often in real life. Modeling can help.

Real life examples of using negative numbers occur on thermometers,  altitude, and ocean depth:

• If the temperature is 10*F and drops 15 degrees, that is 10 + (-15) = -5*F.   If the temperature is -5*F and drops 7 degrees, that is -5 + (-7) = -12*F.
• If a plane flies at 45,000 feet above sea level, and descends 15,000 feet, that's 45,000 + (-15000) = 30,000 feet.
• If a submarine descends to 290 meters, and then ascends 50 meters, that's -290 + 50 = -240 meters.

If your student has trouble with these calculations, here are some hands-on models you can use to help him.

1. A number line.  Make a reusable paper number line, with numbers from -20 to 20 or farther. (Here's a link to printable number lines.   The ones with negative numbers are labeled as "integer lines.") The student can use a button, eraser, or some other marker to show what happens in the equation.  Add positive numbers by moving to the right, add negative numbers by moving to the left.
2. Hopscotch number line.  Use some chalk and a sidewalk to make a number line, and the student becomes the marker.  
   
   To model 5 + -7, the student stands on 5 and hops backward 7 places to stand on -2.
3. Beads on a string.  Make a "numberless line" of beads on a string, with the center bead being "zero."  (If you'd prefer to have the numbers labeled, have the student make clay polymer beads and write the numbers on with a permanent marker after baking.)  To model -3 + -4,  hold the -3 bead and move 4 beads to the left to land on -7. 

4.  Poker chips.  A classic manipulative for teaching negatives in many math classes  is a set of poker chips.   Positive numbers are represented by one color, and negative numbers with a different color. The two colors cancel each other out.  So to model -8 + 5, you might place 8 red chips on the table and then 5 blue chips.  Match up all the red and blue pairs that you can,  and you are left with 3 red chips, or -3.  So, -8 + 5 = -3.

NOTE:  Most students will catch on that adding negative numbers is like subtraction.  When they make that discovery, introduce this idea:

Subtraction = adding the opposite.

The opposite of every positive number is its negative counterpart.  This will be an important concept when it comes to understanding how subtracting negatives works.   More on that later in a future post, but for now, if you have to model the subtraction of negative numbers, think of taking away debt.  For instance,  -10 - (-3) can be thought of as "Bob owes me $10, but I'm taking away $3 of that debt because he helped me wash my dog.  So now he owes me $7."  So you could have 10 index cards each labeled "PAY ME $1.00"  to represent -10.  Then take away three of them to represent - (-3).  There will be seven PAY ME  cards left, representing a total of -7.

Or, using the poker chips, you can set out 10 red (negative) chips and subtract (take away) three of them, leaving 7 negative chips.

Teaching with "the Spectrum" in mind

One of my favorite online discoveries this year has been the guys at Asperger's Experts.  They are Danny Raede & Hayden Mears, two young men who were diagnosed with Asperger's (an autism spectrum classification) early on and now have a business offering dvd's and online consultation to people on the autism spectrum and their families.  They also have a number of helpful videos that are free online.   I love their insights.  Of course, a lot of the information they share is what parents of children with Aspergers/Autism instinctively know and practice every day.  But as teachers, we don't live with the students and don't always have insights into their behavior.  In fact, there is a whole lot of misunderstandng and invalid assumption out there.  So, without plagiarizing any of their material,  I will share a few of their ideas:

1.  Too often, people who work with a child on the spectrum focus first on social skills, communication and academic achievement because those are the most obvious issues.  According to AE, however, the child is not receptive to learning these things because he is "deep in defense mode."  The focus needs to be on getting him out of defense mode first.  Then the learning will follow.

2. Defense mode begins as a sensory overload.  A child on the spectrum has way more going on in his head than it may appear-- his senses are amplified and can bombard him like a hurricane when people around him feel only a gentle mist.  Too much noise, odor, visual stimulation, touch, tastes... things that a neurotypical person might not even notice can cause the affected child extreme distress.  The AE's "Sensory Funnel" at left shows how this overwhelming sensory input can be the bottleneck for the child's growth.  Carly Fleishmann, a teen with autism, describes the overwhelming visual input: "I take over a thousand pictures of a person's face when I look at them."  She also explains that her shrieking and hand-flapping is often a response to the sensation of ants crawling all over her body.  Imagine how hard it would be to focus on social skills when your brain is under that kind of attack!

The distress can be neurological, but it can also be due to physical issues; the AE guys note that gastrointestinal tract problems are common to children on the spectrum, and suggest that the vagus nerve may play a role.  (I'm not sure whether gastrointestinal issues trigger the vagus nerve or the other way around... chicken/egg... all I know about the vagus nerve is that I was told mine was "overactive" because it causes me to faint under certain conditions, but that's another story.)  This may be why dietary changes help some affected children.  A child with both autism and food sensitivities will likely feel the effects of the food reactions more keenly than a neurotypical child. Removing the offending foods can cause great relief.

3. The key to teaching a child on the spectrum, according to AE, is to get them out of defense mode.  AE estimates that 95% of an affected child's energy is spent defending from perceived threats-- initially from sensory overload, but as the child gets older some of the threats become anxiety-based-- more on that later.   But that leaves only about 5% of the child's energy left for daily functioning-- everything from getting dressed to doing homework.  No wonder meltdowns are so common!

4. For younger children, getting them out of defense mode means you try to reduce sensory issues as much as possible.  So you have to identify what the issues are, and accommodate them.  Noise-blocking headphones, soft tagless clothing,  fragrance-free detergent,  dependable routines-- whatever can be done, avoiding triggers in every way possible is the basic game plan.  Some families find that homeschooling provides a more controllable environment for their children.  Brick-and-mortar school does provide a dependable routine, but this advantage can be offset by the sensory overstimulation of a bright, noisy classroom with all its bells and smells.

5. A child in defense mode needs a "safe place" of his own.  This is a physical place with as few sensations as possible, or at least controllable sensations.  AE  recommends including an item in this place that makes them feel safe-- a flashlight, stuffed animal, etc.-- and perhaps something weighted.  (One of the AE guys used to use a beanbag chair that he would place on top of himself.)  So maybe the child has a room that he has decorated himself (controllable visual sensation), with headphones to block noise and a flashlight to keep him safe, and a beanbag chair to lie under.

6. The child in defense mode needs to increase his trust in the world around him. Routines develop trust.  He also needs to develop trust in relationships, beginning with the people in his life.  "Frequent, personal, positive, low-risk" interactions will build the kind of relationship a child needs.  Not surprisingly, those kinds of interactions will build trust in ANY relationship with ANYBODY, but, to be honest, the child in defense mode may not naturally inspire this kind of treatment.  It is easy as a parent to become overwhelmed, or as a teacher to focus on unwanted behaviors, and forget that there is a child in there.

7. Not all threats are sensory.  AE explains that as some children with Asperger's/Autism grow, they may begin to spend a lot of energy on defending against all the "what if"'s they can possibly imagine, making endless "contingency plans." This is Murphy's law on steroids; the Boy Scout motto gone horribly wrong.  As they fixate on worst case scenarios, their anxiety builds.  Because a lot of this anxiety is based on their lack of trust in their own ability to cope, it can be combatted by helping the child document evidence to the contrary-- recognizing his own successes,  maybe even running an experiment to see, for example, just how many times he spells a word correctly vs incorrectly.

8. As the child matures, Raede and Mears recommend building up his tolerance for sensory or situational triggers with "purposeful, voluntary exposure."  Voluntary means the child agrees to it-- whether to earn a reward or prepare for the unpleasant certainties of the family trip to Disneyland-- and purposeful, of course, means there's a goal in mind or a reason for it.  So Mom and child agree ahead of time that every time he handles an unexpected event without a meltdown, he earns ten points (toward a reward), and then on the way to the park she purposely but unexpectedly stops by the grocery store instead of going straight to the park.  No meltdown = ten points.  

9. Anger is often an issue. AE describes the formula for anger as "What should be is not what is."  In other words, the child has expectations, assumptions, or rules that are not met, and a meltdown occurs.  As the child develops trust in you, you may discuss with him whether his "rules" are fair or valid.  Is it valid to make a rule that you only get ten math problems for homework, or might there be days when there's more to practice and review?  Of course, such a discussion is not possible when the child is stuck in defense mode, so trying to argue with a child in the middle of a meltdown, as parents will attest, is counterproductive.  As you would when communicating with anyone, discuss the issue when everyone is calm and relaxed.

10. Avoidance is another topic they cover.  Avoidance, according to AE, is the main motivation for playing video games obsessively.  It can also lead to isolation and refusal to participate in certain activities.  For younger children, you may just have to "play their game."  Allowing a child to avoid interacting with noisy people at the family reunion by letting him sit in a corner playing on his tablet or reading a book may give Aunt Susie conniptions, but it will preserve your child's sanity.  As he matures and grows in trust, he can build his tolerance for unpleasant social situations at his own pace. Other avoidance issues may be connected to past traumas-- a scary dog, perhaps-- or based on imagined contingencies.  Sometimes calculating statistics can help relieve the anxiety-- how many times have we been to the store without being attacked by ninjas? And sometimes logic just gets in the way:  one of the AE guys relates how he relieves his fear of flying by imagining a solid support under the airplane as it flies.

The Aspergers Experts have a lot more detail on their website and videos, including personal examples and stories.  They are definitely worth a look for any teacher who has a student with an autism spectrum personality.

Playing with roots to build vocabulary

Want a painless activity that can improve working vocabulary, reading comprehension, spelling proficiency, and future SAT scores, all at the same time?  Here you go!

One of the quickest ways to build English vocabulary is to learn how root words, prefixes and suffixes work together to build words.  A child who knows the word mutation, for example, can more easily remember the meaning of immutable if he recognizes the part of the Latin root "mutare" in both words, and knows the function of the prefix "im" (as in possible/impossible).

(Note: A root is the basic part of the word from which its main meaning comes.  In English, many of our word roots come from Latin or Greek.  An affix is a piece of a word that can be placed before or after a root to modify its meaning.  A prefix comes before, a suffix after.  In the word removable,  re is the prefix, move is the root, and able is the suffix.)

Building a collection of word parts is an easy hands-on method to study roots and affixes.  It's kind of like Legos for literacy.  All it takes is some index cards, colored markers or pencils, and a notebook.   The cards are color coded to make them easer to use.

1. Write (or have students write) prefixes and suffixes on index cards, one affix per card, using one color for prefixes and a different color for suffixes.  For example, orange for prefixes,  blue for suffixes. Here's a list.  Prefixes should be written against the right side of the card, and suffixes up against the left, so they can build words more easily.  At the bottom of each card, students should write the meaning of the affix.

2.  Have students make cards for common Latin and Greek roots. Here's a list of roots.  Red may be used for Latin, and green for Greek.  The meaning of the root should be written at the bottom of the card.   Just do a few at a time.  You might want to focus on roots that appear in words he will encounter in his studies, or just pick some that you think he might hear or read frequently.

3.  Give the student a short list of words that can be made by combining the roots and affixes that they have written.  At first, you may want to start with pairs: for example, predict, encrypt, and decorate can all be made from two cards each.  Three cards are required to make predictable, misanthropy, encryption, and redecorate.  Have him find the pieces of the word in his card collection and assemble the words from the list.  The object of this activity is to help the student recognize both the root and the affix in a word.

4. Tell the student that the meanings on the cards are only clues to help figure out the actual definition of the word.   "Redecorate" does not mean "again ornament process," but it might be thought of as a process of ornamenting a place again.  Still, that's awkward!  Ask the student how each clue helps figure out the word.  Perhaps you might use an ornament of some sort to decorate. "Encryption" might be "a process of causing something to be hidden," as long as the thing being hidden is information, such as encrypting a message in code. Let the student try to guess what the word might mean based on the clues, and then look it up in the dictionary and see how the ideas compare.

5. Continue to add to the student's vocabulary base by giving him new roots to use.  Be sure to have a list of actual words that he can make with them!  Otherwise he'll end up making nonsense words like "precrypty." (Granted, some kids might get a kick out of making up nonsense words, and that can be great as long as they also make up a logical definition, matching the meanings of the roots and affixes, to go with it.  Perhaps "precrypty" could describe the expression on somebody's face when they're about to tell a lie -- i.e., hide the truth:  Mary's eyes became suspiciously precrypty when her mother asked her how the lamp had broken.  But this word play might only be confusing to some students.  You probably know whether your child would enjoy it or not.)

6. Later, when a student learns a new word in his regular studies, have him look it up in a dictionary that includes the etymology, or history of the words.   An online dictionary would generally include the word origins.   Some may be from other languages, such as German.

You may need to help the student find the root.  In the example at left, the root is that part of mutabilis that is also found in immutable--  mutab.  (If you follow the link to mutable you would see that the main root is mutare, so the root could also be thought of as muta.   Muta is the same root in mutate and mutation.)  Use these new roots to make new cards.   Choose a new color for language origins other than Greek or Latin-- perhaps brown for German, and yellow, pink or black for somewhere else.

7. When the student discovers new affixes, have him add those to his collection.  He should check the dictionary to make sure it is a legitimate affix, and be able to give at least two examples.  For instance, "ex" can be found in "exchange," "exhaust" and "excommunicate," and each time the dictionary identifies it as meaning "out."

8.  Challenge the student to come up with as many real words as he can find in the dictionary that are made with the roots and affixes he has.  He may keep a running list in a notebook, organized alphabetically by the root.  So under "decor," he might list the derivatives decorate, redecorate, decorated, undecorated, decorative, etc.   Perhaps he could set a goal and get a reward for the first 25, 50, or 100 words.  But the words have to be found in the dictionary-- "exdecorate" doesn't count!

Want a similar experience, without having to do so much work?  Read on:

There are some great vocabulary-building workbooks that use roots, but for hands-on fun, nothing beats a good game.  One that we used in our homeschooling days was Rummy Roots.  It's a card game that introduces both Latin and Greek roots, and gives students practice in forming new words.

A  more comprehensive vocabulary curriculum is  Vocabulary Vine, which has students specifically studying the roots and related words, and then provides several games the students can play to reinforce their new knowledge.

Whatever way you go, learning to use roots and affixes provides a huge boost to academic success. The student begins to build new vocabulary words by recognizing familiar parts in newer, perhaps longer, words.  Spelling improves because the student can see the patterns of the roots and affixes used over and over again.  Comprehension improves because the student is making idea connections between words that are related, and SAT scores improve because the student's verbal skills are greatly enhanced.