Four Easy Reading/Writing Tips

Here are some common reading and writing problems and ways to work on them.  The first two have to do with individual words, the last two with longer passages:

1) When a student reads aloud, he misreads words, substituting similar words, such as "medical" for "mechanical."  Note how the words begin and end the same way-- the brain is tempted to fill in the middle with a word it already knows, especially if the actual word on the page is unfamiliar.   The brain must be trained to look at the middle part, too.

The best way to do this is to have the student divide the word into syllables.  This can be done on paper, underlining or drawing lines on the printed word:  me/chan/i/cal.  (Note: this is a good time to remind the student that ch can represent three sounds: Chocolate, Christmas, and Charlotte.) Using 3-D manipulative letters or tiles is especially helpful, because they move freely and the student can put the word together and apart easily.  Even letters written on small squares of paper can be used.  Alternatively, the word can be written whole and cut up into syllables.  The important thing is that the student becomes so adept at breaking up the word physically that he begins to see the words that way, and breaks them up mentally without thinking.

2) When a student has to spell a long or difficult word,  he may put in the wrong letters, or can't remember which letters are correct.  Have him look at the word syllable by syllable. Practice with 3-D letters as explained above.

Careful correct pronunciation, or over-pronunciation, can be helpful in distinguishing which vowels to use.  For example, "ridiculous" is easier to spell if you pronounce it as rid-ih-cu-lus  instead of ree- dic-you-luss."  “Difficult” is easier to spell if you say diff-ih-cult and not diff-uh-cult.

If a word is particularly tricky,  mentally mispronouncing the word (phonetically) on purpose can help her remember how it is spelled.  For instance, say "deter + MINE"  instead of "deter + men."  "Rendezvous" is easy to remember if you say it in your head as "rehn" "dez" "voos"  instead of "ron" "day" "voo."  "Perseverance" is easier to spell "per + sev + er + ance "  but be careful not to say “enss” at the end. 

The preceding tips were for single-word errors; now, let's look at a couple of common problems students have when reading paragraphs or articles:

3) When a student is called upon to determine the main idea, or central idea, of a passage he is reading, he chooses a sub-point from the passage instead.  The task is harder than it sounds, especially while the brain is still developing abstract thought.  Students must not only read and comprehend the information, but they must mentally sort supporting details from over-riding themes.

To practice this, have students start with easy part-whole exercises, such as "Parts of a house"  "roof" "wall" "window" "door" "foundation."  If you have two identical pictures of a house, and cut one up, the student gets the idea quickly.  Put the whole house picture at the top of the desk, and line the parts up below it.  The idea is for the student to see that the "main idea" includes all of the supporting details.  And each supporting detail is a part of the main idea.

Similarly, you could use "parts of an ice cream sundae" "ice cream" "chocolate sauce" "whipped cream" "nuts" "cherry,"  or "animals on the farm" "cow" "horse" "pig" "goat" "chicken."  Then move on to words instead of pictures.

Finally,  give your student a set of several entire sentences instead of words-- cut them into sentence strips and have your child find the one which works best as the main idea.  Can you pick the main idea from this set?

• Tortoises and lizards, spiders and scorpions are desert inhabitants.
• Many animals make their home in the desert.
• The javelina, or peccary, enjoys the cactus fruit in late summer.
• Jack rabbits hide among the prickly pear.
• Snakes of many kinds roam the desert floor and sun themselves on rocks.
• Coyotes roam the desert in search of prey.

(You picked the second one, right?)  

If your student has trouble sorting the sentences, have her underline 3-4 key words from each sentence.  This will help her focus on what each sentence is about.  In this way, she can see that of the sentences above, most are about individual desert animals.  Only one has the general "many animals" as its topic; this is the main idea that all the other more specific sentences fall into.  Some students will need a lot of practice with this skill.

If the student is supposed to come up with the main idea on his own, or choose between a few given possibilities,  have him write facts from the passage on sticky notes.  Write possible "main idea" choices on a white board.  See which main idea choice can have all facts fit underneath it.

Writing a cohesive paragraph requires the same understanding of main idea and supporting details. The only difference is that the student has to decide what details to include in order to support his main idea.  So when your child can easily distinguish between main idea and supporting details, try giving him a set of main idea and supporting details with an added red herring-- an off-topic detail for him to identify and discard.  For example, in the list above,  an off-topic detail would be, "Dolphins prefer the warm waters of the Pacific Ocean."  When he can find one, try giving him a set with more than one discardable detail.  This will help him when he looks at his own writing.  At that point, writing his thoughts on a graphic organizer such as one of these might help him develop his paragraph(s).

4) A student comprehends what he reads, but can't skim for information that he needs quickly.  He doesn't change his reading speed whether he is reading for pleasure or for information.  While most students have been taught to read through the questions on an assignment so they'll know what to look for in the text, they often don't realize that reading every word of the text is not always the best means of then finding that information. Sometimes they just need to know a certain fact.  So they need to be able to focus their search logically.  For example, if a student is looking through a passage for the answer to "How far is the earth from the sun?" ask her what are the most important words in the question.  How far, earth, sun.  What words might be in the answer?  Earth, sun, and some number. 

When the student understands that she is looking for a number and the words "earth" and "sun," she must then be able to skim efficiently through the passage, ignoring everything that isn't a number or those two words.  Just as importantly, having found the words and/or a number,  the student should be able to read the sentence they appear in to verify that it does indeed answer the question.

Skimming is an eye+brain discrimination skill, and takes practice.  It is one of the skills honed in word searches and those 'hidden pictures' games we enjoyed as children.  But there are ways to build proficiency; when the student knows she is looking for numbers, for example, she can try to underline all the numbers. That will help the brain focus.  Also, when looking for a particular word,  she can get a picture in her mind of what that word will look like.  A good way to practice is to pick a page of a book at random and ask the child to find a specific word.  Make it a word that is at least half-way down the page at first; then try other words that may be nearer the top or bottom of the page.  The student should try to find it as fast as possible.

These four tips are not overnight game-changers, but with practice, can make a difference in how well your child reads and performs in school.

Finding the fraction of a number (multiplying a whole number by a fraction)

When students are beginning to work with fractions,  one concept they need to understand is that a fraction involves both division and multiplication at the same time.  It's not as easy to see when using fraction bars or circles, because you're always starting with a fraction of a single thing-- a whole circle or a whole bar.  It is not until you are trying to find the fraction of a whole number that you can see what's really going on.

In this demonstration, I am using pennies and a set of fraction squares that I made from clear plastic page protectors drawn on with permanent markers.  I traced over a piece of graph paper to get my sections even (24 squares x 24 squares).  The same effect could be obtained from squares of paper or drawn a whiteboard, as long as the student has a selection of fractions to choose from.

Now we use our model.

A) What is 1/2 of 12?
B) What is 2/3 of 12?
C) What is 3/4 of 12?

We start with 1/2 of 12, because the student will likely already know the answer, but can also show it with the model.

1. Choose the fraction block that matches the denominator in the problem.  In this case, we are asked about 1/2, so we choose the square that is divided into 2 equal sections (halves).

2. Count out the correct number of pennies (or blocks or beads or whatever you're using) -- 12 in this problem-- and divide them evenly into the sections of the fraction square.  In this case, six pennies go into each of the two sections.

3. Select the number of sections indicated by the numerator-- in this case, 1.  Count the number of pennies in that/those section(s).  So we see that 1/2 of 12 = 6.

To find two thirds of 12, we: 1. Choose the square divided into three equal sections (thirds).  2. Count out 12 pennies and place an equal number of them into each of the three sections of the square (4).  3. Select two of the sections and count the pennies in the sections.  2/3 of 12 = 8.

To find three fourths of 12, we: 1. Choose the square divided into four equal sections (fourths).  2. Count out 12 pennies and place an equal number of them into each of the four sections of the square (3).  3. Select three of the sections and count the pennies in the sections.  3/4 of 12 = 9.

Next, try different whole numbers with various fractions.  Just be sure the whole number is always evenly divisible by the denominator in the fraction.  For example, 3/5 of 15 would be a good practice problem, but we're not ready for 3/5 of 27.

After enough practice, the student should recognize that what she is doing is dividing the whole number by the denominator and then multiplying that product by the numerator.   At this point, she can try using mental math to solve similar problems with larger whole numbers..

2/5 of 100 (40)
3/8 of 64 (24)
4/7 of 56 (32)
9/10 of 120 (108)

Finally, the student can be told that in math, "of" is generally translated "x" (multiplied by).  So 2/5 of 100 is actually 2/5 x 100, and so on, for the rest of the problems.

Getting a perspective on decimals

In my years as a 6th grade teacher, I found many students who had trouble with decimal operations. They could read the numbers: "three hundred sixty-one and two hundredths," but then they'd get a problem such as 65.001 x 3.2 and come up with an answer like 2080.032, with no idea of why their answer made no sense.  Addition, subtraction, and especially division all seemed quite hard.  Their difficulty came because they didn't understand decimals enough to be able to estimate their answer to see if it made sense.  For example, in the above problem, 65.001 might as well be plain old 65 and 3.2 is pretty close to 3, so the answer should be pretty close to 65 x 3.  Even a ballpark estimate of 70 x 3 = 210 should tell the student that 2080.032 was way off.

It's easy for students to get confused about decimals, or even not understand the significance of where the decimal is placed.  After all, when a decimal number is written, all the digits appear to be the same size and that little dot is awfully small-- surely it can't be that important!  And for the many students who have trouble with whole number place value, the concept of decimal numbers can be almost meaningless.

So before introducing decimals, be sure your student has a firm grasp on place value.  For example, in the number 222, the digits are the same, but their value is completely different.  A student should understand that 222 is the same as 200 + 20 + 2.  (Writing it this way is known as expanded notation, because the number is expanded into the digits' actual values.)

If a student can write a number in expanded notation, but still seems to have trouble keeping digits lined up when adding or subtracting, it might be helpful to use manipulatives.  Here's a link to paper base ten blocks that can be cut out.

At left are some base 10 blocks (these are from the  MathUSee basic set, but others work as well) illustrating what 222 looks like.

That's all fine and dandy, but what do you do to illustrate the relative size of decimal numbers?





One way is to use base ten blocks, only this time the largest block represents "one" and each smaller segment is a decimal number.

 To match the previous set of base 10 blocks, I have made a giant "one" (out of paper and foam board) and colored it the same color as the original "one."  It's as if the original one is being seen through a magnifying glass.

Here we see 2.222; notice the large blue "decimal" that matches the scale of the blocks.










Of course, the giant blocks don't match the scale of the original whole number blocks, so when you want to model what a whole number with decimals looks like, we have to go smaller.  For this we can use modeling clay in a shade that matches the original "one" block.  (If the student performs this activity himself, it may leave more of an impression, but either way it's one he'll remember.)

Here we see a "one" block and a block made of clay, approximately the same size.

Using a knife, cut the clay block in half, and then cut each half into 5 pieces.  You have now divided one into tenths.  Roll up each tenth into a ball.

Next, take one of the tenth balls and roll it into a snake that you can cut into ten tiny pieces.  These are your hundredths.  Roll them into little balls.

At this point, the student should begin to see just how different a hundredth is from a hundred!

 It's almost impossible to divide the tiny hundredth ball into thousandths, so for the .001 place value, I use a pencil or marker of the same color to draw dots on the paper in the thousandths place.  (White boards are a good base for this!)

Here you can barely see the pencil marks, but we have 0.222 illustrated.

Now, when we put the blocks all together, it is easy to see what 222.222 really looks like.  At this point, it would be good to discuss with the student how significant the placement of the decimal point is.

And, of course, have the student practice writing and illustrating various numbers.  Can he model 256.3?  256.03?  256.003?  Which is bigger?  Can he write the correct number when you place various numbers blocks in the columns?

Most importantly, can the student see why estimating with whole numbers can help him get the decimal placement right in his final answer?  Those tiny little pieces of clay can be ignored long enough to get a ballpark idea of what the solution will be.

Subtraction: Borrowing, renaming, whatever you want to call it.

A fifth grader was having trouble with this problem:

                                                                                                                        The student knew there was borrowing, aka renaming, involved, because the top number ended in two 0's, and neither 1 nor 5 can be subtracted from 0.   However, his method of renaming made me suspect he was unclear on just what was being renamed or borrowed from.

This was the student's solution.  Can you spot two errors?

         

Here we see the student has attempted to cover his bases by renaming the digits all the way across the top.  He ends up with an incorrect answer, however, because the pattern he has learned is to turn zeroes into tens and subtract one from the digits on the left.

Using a whiteboard with colored markers,  the student works through the problem.  When he gets to the end, I call his attention to the hundreds column: did he need to borrow anything to subtract 3 from 7?  No?  Okay, so let's erase the 6.  In fact, let's start over.

This time, I guide the student through the "borrowing" one step at a time:

1. Can 1 be subtracted from 0?  No.  We need to borrow from the left column to turn 0 into 10.
2. We can't borrow 1 from 0, but we CAN go one more column to the left and borrow 1 from 80.  what is 80-1?   It is 79.  So we mark out the 80 and write 79 above it, then put the 1 above the last 0.
3. Now we start to subtract:  10-1= 9, 9-5= 4, 7-3= 4,  7- 0 = 7.  Final answer: 7,449.

After a few times practicing with the whiteboard, it's time for a change of pace.  So we build another problem with 3D letters.  In this photo, we are using magnetic numbers on a paper-lined cookie sheet, and the paper has columns marked on it so we can line up the numbers correctly.  (Try asking the student why the numbers need to be lined up carefully.  What could happen if the top and bottom numbers were misaligned?)

This time, we guide the student through the process:  

1. In the ones column, you have 3 - 6.  Is that doable?  No, you must borrow from the tens column on the left.

2. The tens column has a zero!  No tens to borrow; go left again.

3. The hundreds column has a zero!  No hundreds to borrow; go left again.

4. The thousands column has a 5.  Change it to 499+1 (4990 + 10), use the 10 to turn the 3 into a 13.  Now subtraction can proceed.

By keeping all the digits within a column the same color, it becomes clear where the "1" is being borrowed from.

If the concept is still unclear, it may help to have the student perform the following exercise:

  You'll need a box of 500-1000 craft sticks, a bag of 50 or more rubber bands, a large sheet of paper, a regular lined paper, and markers  Prepare the sticks by bundling about 45 sets of ten sticks.  Leave the rest loose.  Then bundle 3 sets of 100 sticks by putting 10 sets of the 10-stick bundles together for each set of 100.

Prepare the large sheet of paper by folding it into three columns, and labeling the columns left to right, "hundreds," "tens," and "ones."

1. Give your student 364 sticks as pictured (3 hundreds, 6 tens, 4 singles.)  Show her that each small bundle is 10 and the large bundles are 100.

2. Have her place the sticks on the sheet of paper in the appropriate columns.

3. Ask her how many sticks there are altogether.  Have her write the number down on a separate sheet of lined paper (or a white board.)

4. Ask the student to write below 364, "-295."

5. Ask the student to take 295 sticks away from her collection of 364 to see what the result is.

If she starts by taking the 2 hundred bundles away, she'll be unable to complete the subtraction. She has to start with the ones.

When she starts by trying to take away 5 ones, she will not have enough ones.  What is the solution? Borrow a 10 bundle.  Now the 4 is 14.  If she breaks apart the 10 bundle, she can take 5 from 14 and have 9 single sticks left over.

She now has 5 bundles of ten (50), but needs to subtract 9 (90).  Solution?  Borrow a hundreds bundle.  Now she has 15 bundles of ten (150).  When she separates the hundreds bundle, she can subtract 9 of them (90) and have 6 (60) left over.

She now has two hundreds bundles left over.  When she subtracts those, there are none left.  What she does have left is 6 bundles of ten and 9 singles, equalling 69.

5. Have the student work the problem on the lined paper, this time writing in the borrowed digits and marking out/changing the required donor digits.  Her answer should again be 69.

With enough practice, the student should see the correlation between borrowing from the next highest bundle of sticks and borrowing from the digit on the left.