Thursday, March 14, 2013

Regrouping with Addition Problems

Teaching some math concepts can be difficult.  If you have read this blog much, you know that for Math skills, I like to use the concrete-pictorial-abstract pattern for every skill.  Some basic math, though, needs a creative method to be able to make an idea "stick."  Regrouping, in both addition and subtraction, is one of those skills.

 Regrouping is a better word to describe what we used to call "borrowing" or "carrying over."  It is used in both adding and subtracting where you have to exchange values.


One thing I learned early on when I was a teacher is that children have to value something before they want to learn about it. I have also found that children (as well as adults) value money.  I use money often as a manipulative to teach difficult skills.  As much as possible, I use real coins.  This was very difficult to do when I had 27 students, as it was hard to gather enough coins needed and not worry about theft, but as a homeschooler or as a tutor, I just grab some coins out of our "change cup" which we keep on the refrigerator.  (My husband will never miss anything except the quarters!  And besides, they usually go right back into the cup when the lesson is over)  I discovered that before the child sees the skill itself as important, s/he will value the coins and/or bills that you are using to teach the concept. Either way, it gets their attention and, therefore, makes the skill easier to teach.   Also, when I had to reteach this skill to 4th or 5th graders, they did not feel embarrassed that they did not understand something which they should have picked up in 1st or 2nd grades.  In fact, the students who did not need to relearn this concept were often jealous that they were not included in this lesson! 


Before using these coins in your Regrouping lesson, make sure you have taught your child that a penny is worth one cent and a dime is worth ten cents.  Also help them understand that you can exchange ten pennies for one dime.  They don't have to fully understand that, as this lesson will have the added benefit of helping them understand that also, but it helps if you are not teaching two different new skills at once.  They also need to understand how to add two digit numbers without regrouping.


THE LESSON - Addition with Regrouping


Write the problem on a piece of paper:



Then pull out dimes and pennies.  I usually make sure I have 20 pennies and 10 dimes (per child) as a general rule.


Have the child show you 34 cents using dimes and pennies.  Have some divider to put the dimes on the left side and the pennies on the right side.  (I use the line down the center of my expandable table, but if you don't have that you can use a ruler, a licorice stick, a long toy- anything that is straight). 


About an inch below those coins, using the same dividing line as the 34, have your child show you 28 cents. 


Explain that they just showed you the problem. To add them, push the pennies together and the dimes together.


Now ask if they have enough pennies to trade you for one dime (which you take from the "extras" pile).  They should carefully count 10 pennies and push them to the penny "extra" pile.  You give them a dime, but put it on the dime side.



Tell your child that you have changed the number of pennies and dimes you have, so you need to change the problem to show what you now have.   You added a dime, so you have to write a 1 to the dime side of the problem to show what you just did.


Now count how many pennies are left. Have your child write the 2 under the 8.  (for younger children, or even some older children, they have had hard time lining things up. Draw a line on the problem to separate the ones from the tens, extending it into the answer space.  This will resemble the separating line on the table, which helps).  Tell them you now have 2 "ones" because pennies are worth one cent.  (When I say an important lesson, I usually make them repeat it verbally a few times to make sure they heard me and know it's important). 


Now remind the child that they added a dime and point again to the 1 he added on the paper.  Then have him count the dimes.  Have him write the "6" in the tens column.  Tell him he has six "tens" because each dime is worth ten cents.  


Have him tell you how many "tens" he has.  Then tell you how many "ones" he has.  Then have him read the answer.  Many children, especially at first, will say something like "six and two."  Help them see that if you take away the line, it is "sixty-two."  You write the word "sixty-two" under the answer.



Now go back and solve the problem you just did together.  I use "touch math," so at this point, I or my child writes the dots on the digits of the problem.  (you can skip that step if you do not want to use touch math.  If you don't know about it, look it up.  It is a fabulous method of teaching counting, and it ends up being much more accurate than fingers.  They have some free materials so that you can see where to put the dots, which for me is all that I used from the program). 


Then have them add the ones.  I usually say this several times, trading out the words "pennies" and "ones" so they can connect them in their brain.  Do NOT use the actual pennies at this stage unless your child is completely lost, in which case you probably need to spend more time counting single digits instead of going on to double digits.  Remind them you traded ten pennies for one dime, so they should trace over the 2 in the answer place and the one that you added above the dimes.  Get them to explain to you why that "1" was added.  (Even if you just said the answer, the more your child can explain, the more you know he understood the concept).  We put the dot in the center of that "1" for touch math.


Next, add the tens.  Talk about what they are doing, using the words "dimes" and "tens" often and interchangeably. 


Have them read the answer (which you already wrote in words).  Then have them copy the words below where you wrote them.


Do 3 - 4 more problems, then stop for the day.  You want to give your child time to "stew over" the method of solving the problem.  This should be done  3 - 5 times per week for at least 2 weeks (about 5 problems per day) before you use problem with hundreds in them.  After a few days, you can start having problems with a hundred in the answer, but you will need to have a dollar to trade for ten dimes.  Use the pennies and dimes every day, but as your child understands the concept better, you will find that they are using them less and less.  It's okay for them to like playing with the manipulatives (the dimes and pennies), as long as they are using them correctly to solve the problems.  He will stop playing with them as he gets excited about solving the problem correctly.  It shouldn't be rushed because this will actually hurt the learning process. 


Don't use the virtual money (meaning the programs on the internet) until AT LEAST 2 weeks of successfully using the real or play pennies and dimes.  Anything online requires a higher level of understanding and your child will lose a lot of the value of this type of learning if you ignore the physical money and go straight to the virtual world.


Have fun!

Monday, March 4, 2013

Fighting in Schools

In my twelve years of teaching public school, I found that many teachers and administrators had very strong, unshakable philosophies of fighting, and many differed from each other. Now, none that I knew of encouraged it. While I have heard a news story here and there where a teacher wanted children to fight, for whatever psychological reason they had, I did not know anyone with that idea.  However, some stories recently in the news brought up some memories of discussions about fighting, and they just make me all the more glad I am homeschooling.


One principal at a school where I taught made the most sense from any other principal I've known.  She said that if a child is hit by another child, they get one "free punch" to protect themselves.  At that point, they need to leave the situation or they will be in trouble also.  Now, this sounds strange to many people, and I heard her defend her position to many, many parents and teachers who thought any child who punched another child was in the wrong, but she knew why she said it and she stood by this philosophy numerous times in my presence.  She said that a child has a right to defend him/herself.  I agree.  She said that if someone punched her son, she would want her son to stand up for himself.  Now, if he stayed and egged it on or continued punching, that was a different story.  I have to say that I agreed with her then, a little hesitantly, and I fully agree with her now.

Most schools, though, have what they call a "no tolerance" policy on fighting.  I hate any blind "policy" which ignores facts before the punishment is given.  I do not agree with fighting, I think there are many situations where it can be avoided, but there are times when another person is focused on a fight and there is only one way to get out of it - one good, solid punch, then run.

About 10 years ago, my husband (a black belt in Tae Kwon Do) had a friend who was either a 2nd or 3rd degree (I forget which) black belt in TKD.  He was also a teacher at a local high school, and he frequently was assigned detention duty.  One day, he said a teacher actually put two bullies in detention (most of the teachers were afraid of them so it did not happen often).  They came in and sat down with no problem, but they decided that it was time for them to leave about five minutes early.  Our friend, while an extremely tough fighter, is only about five foot six, so when these two six foot "plus" guys surrounded him on their way out the door, he had to look up to them to block their path.  He calmly told them they weren't going anywhere, to which they told him differently.  Knowing a fight was likely to happen and that most of the staff had already gone home, he immediately dismissed the rest of the detention students and distracted these guys as they left.  He said as the others left a little early, they continued arguing and he instinctively turned his body, automatically lining them up for one good, swift kick a piece, in weak points.  Then, he said, he planned on running out the door as fast as he could before they got up! Fortunately, these guys were a little smarter than they seemed and something in the teacher's stance told them that he had a plan and they would not be happy if they tried anything.   As the last students left the room, they sat down.  He kept them the remaining five minutes and another minute or two, then let them leave.  Our friend said he did not breathe a sigh of relief until he was in his undamaged car, driving away from the school. 

Other teachers, though, feel differently about bullies.  Teachers of the same philosophies tend to group together.  I have taught in schools, or just met teachers from schools, who refuse to stop a fight.  They say that they do not want to be hit, so they will call the office and wait, watching while the weaker student gets pummeled.  Unfortunately, I've talked to parents of those same schools (in events having nothing to do with education) who say they know the teachers are there to protect their children if needed.  Some teachers will - I did, and I know many others who have done it or who are perfectly willing to if needed - but many teachers will not. 

The last example I want to share is what started all of these thoughts this morning.  In the news last week was an incident on a school bus in Florida.  The event and the school's response completely and totally infuriates me to the point that I will just let the local news tell the story, as I can already feel my blood pressure rising and I'm not even telling the story!


While this real hero was punished, we also have these stories for school suspensions:

That 5 year old is a terrorist??!!

Then there was this 5th grader, suspended for her "dangerous weapon":

Oooohhhhh!!!  I can feel my blood boiling now, so I will stop, but I know that you know other news stories that would easily fit in this.

My daughter, who has special needs, was once threatened when she was in 1st grade at recess.  Another special needs boy (also in 1st grade) stood up for her and was pushed down for his trouble.  The bullies eventually left.  My daughter told me about it that night, so I called the teacher the next day to get the entire story.  The teacher had no idea what had happened and neither did the assistants.  A week later, we had a play date set with this family and I was able to talk to the boy's dad.  The dad (a single parent) still had no idea about the incident, but he knew his son (not as verbal as my daughter) had come home wanting to fight with everyone. that day and for a couple of days after that.  Even though I had told the teacher, she still had not told him about the incident.

These events were not the reason why we started homeschooling, but they are just more reinforcement that I'm glad that we are.