Monthly Archives: January 2014

Two Birds with One Stone: Adding Tens

            Just recently I have had three older elementary school students come in for help with math, and I realize they need help on addition math facts and place value understanding.  Always looking for work that gets the most bang for my buck, I have used the following process to build both a much stronger understanding of place value and an ability to add ten to any number, an ability that will help so much but is often skipped or just wafted over.

2-digit-white-board

2-digit-white-board from Making Math Real

First, I get out my trusty hundreds chart, a bag of ones and tens from the base-ten blocks, a hundreds chart puzzle and a color-coded recording sheet for two-digit place value from Making Math Real.

I ask the student to build a low, single-digit number (it should be easily subitized so they don’t have to keep re-counting it).  We use a green dry-erase marker to circle the number on the hundreds chart and then we record the number in green on the place value sheet.  Then I make a big deal about putting the green away because we won’t be needing it for a while.  I grab a ten block and also make a big deal about putting down one ten.  I have the student tell me how many blocks we now have.  We find that number on the hundreds chart and circle it in red, and then record the 1 in the tens place.  We go all the way tone hundred and whatever.  Depending on the severity of the disability, it may take a while for the student to see the pattern, but as soon as they do, I ask, totally shocked at their understanding, how they knew that?  What?  You mean when you go straight down on a hundreds chart, you’re adding 10?!?  From then on, I ask them to predict what will be the next number.  Throughout, I ask them how many tens each number has, and then how many ones (not necessarily in that order).  Again depending on the severity of the student’s disability, we may do this for a few days before introducing the hundreds chart puzzle, or it could be later in the same session.

I bring out a sheet of hundreds chart puzzles and build the first single-digit number that is on

Sample Hundred's Chart Puzzle

Sample Hundred’s Chart Puzzle

the sheet.  We go through our now familiar rigamarole.  Then I stop and show them the puzzle and explain that this is the piece of the hundreds chart we just circled and ask them if they can fill it out.  More shock and awe at their amazing ability!  Eventually, I ask if they can predict the answer to the hundreds chart puzzle before we build anything and without even looking on the chart.  Ooh.  “How did you know that?” I ask when it turns out their prediction is true.  Lots of high-fiving ensues.

After a few more days of this procedure, I then bring out the first ten-to-teen sheet (another Making Math Real product).  I reassure them that this is exactly like what they have been doing.  If we need to, we go back to building the numbers.  Most likely at this point, they can do it as a hundred-chart puzzle and then do the adding.  Whoa!  Very exciting.

I take them through a sequence of worksheets that goes from ten to teen to double digits plus ten, to double digits plus multiple tens (23 + 10 + 10 + 10) where we count by tens as they tap each ten (the obvious connection to adding dimes to any amount is worth pointing out and practicing here), to double-digit numbers plus multiples of ten, including crossing over 100 without the procedure of carrying.  Don’t assume that students will be able to generalize to subtracting ten: I go through the whole sequence (hopefully abbreviated) again when we are taking away a ten.

About day six of this procedure with one particular student, he exclaimed, “Wait!  I see a pattern!  We’re just counting by ones, but in the tens place.”  These are the moments that give me chills and make me feel blessed to be a teacher.

In Defense of Pandering

I admit it; I pander.  Scooby Doo, Mighty Morphin Power Rangers, Power Puff Girls, Goosebumps, Baseball’s Biggest Bloopers, Rugrats, Captain Underpants, The Day My Butt Went Psycho, all have graced my bookshelves at one point or another.  Diary of a Wimpy Kid?  Yup.  Hunger Games?  Duh.  Percy Jackson?  Of course.  Divergent?  The day one of my middle schoolers told me she was reading it because her friend told her she had to read it.

The Secret Garden

The Secret Garden

Yes, of course, I have the classics, the books kids should read, the timeless literature, the heart-wrenching drama.  But let’s face it: not every child is ready for The Secret Garden or Lord of the Flies.  And those books that we fell in love with when we were kids?  The Hardy Boys, Catcher in the Rye?  As dated as the slang that made them sparkle so long ago.

Reading teachers from kindergarten through college are faced with a dilemma:  give kids books we know they’ll enjoy, or give them what’s “good for them?”  Here are two things to consider.  1) A book a kid loves easily and immediately can serve as a gateway to the rest of the world of literature, especially for reluctant readers.  2) The best and most amazing book, introduced too soon, can inoculate against said book and all its ilk for the rest of a person’s life.

I mean, how many adults (and you may be one of them!) experience a visceral and violent reaction to Dickens because they were forced to read Great Expectations in high school?  “Ugh!”  They tell you.  “Dickens is the worst!  That language!  It makes no sense.  And it goes on and on.  I hate it.”  Admit that you are reading him for fun and they shudder.

A typical student's reaction to Dickens (http://truthiness43.blogspot.com/)

A typical student’s reaction to Dickens (http://truthiness43.blogspot.com/)

Look: Dickens is an amazing writer.  He writes with some of the most expressive and beautiful prose there is.  His descriptions are cinematic in their scope and grandeur, biting social satire and incredible human empathy.  And he is wordy as all get out and very, well, Victorian.  That cinematic imagery reads to most high school freshman like the teacher in a Charlie Brown special: mwah mwah mwah mwah, mwah mwah mwah mwah.  If you’re lucky, the top readers of the class enjoy the book, but the reluctant readers?  You’ve just proven to them again that reading sucks.

Reluctant readers already hate reading.  Why?  Because it is hard for them.  Anytime a student tells me a book is boring, I translate into “too hard for me to enjoy.”  Either the sheer act of decoding the words on the page is laborious enough to take away the brainpower necessary for comprehension, the vocabulary or syntax of the passage is unfamiliar and thereby erects a wall between the reader and the meaning of the text, or the reader has trouble visualizing what they read.  In any case, reading is too effortful to allow the student to get lost in the book.

Reluctant readers may not even know what they are missing.  A freshman girl one time lowered her voice conspiratorially and asked, “Be honest.  Do you actually enjoy reading?”  I was shocked that she didn’t get that enjoyment, nay, love, was the motivator for everything I was teaching her.  She was shocked that anyone actually liked this whole reading thing.

Now, take one of these kids who think reading is a total must do kind of thing and give them a book about something they love and already know about.  First of all, you’ve instantly given them internal motivation to read.  Secondly, you’ve given them a chance to use their domain-specific knowledge to support their comprehension.  Huh?  You are tapping into what they already know about, so that they can use that to help them understand the text.

I worked with a middle school boy whose mother told me, “I don’t care what grades he gets.  I just want him to choose to pick up a book now and again.”  We started brainstorming what wouldn’t be too terrible (forget the word “enjoyable”) for him to read.  He finally told his mom and me that if he had to waste his time reading, at least he wanted to learn something from it.  No fiction!  Our routine became simple: review and teach phonics and morphology and then Google something he was curious about and read it.  One day, we read a comparison of aluminum bats, carbon fiber bats and wooden bats.  Another, we read about Belgian Waffles and the special pearl sugar needed to make them come out just right (supremely entrepreneurial, he wanted to set up a competing shop near the Belgian Waffle booth at the farmer’s market).  A third, we read about the Corvette Z06 Carbon Limited Edition.

I never could have guessed his varied interests.  But once he was reading because he had a “need to know” as Maria Montessori called it, he naturally employed all the comprehension strategies of good readers: monitoring his comprehension, making predictions, checking out unknown vocabulary and unfamiliar syntax, visualizing, asking questions of the text and reading with the purpose of answering them.  Slowly, he started applying these skills to fiction.  One day he came in amazed and excited because he had found a fiction book he was actually enjoying: Alex Rider.  He told me it was the first time he had been able to picture what was happening in a story, and agreed that it made it much more fun.  Eventually, he even started to apply these strategies to assigned reading. Reading about what interested him became the gateway for him to learn to be interested in what he had to read.

fairies

One of Many Fairies Book Series

So, even though we all want our kids to love Treasure Island, or Anne of Green Gables right off the bat, we have a lot to gain from taking a deep breath, asking them what they want to read, and even offering them Captain Underpants or one of the endless Rainbow Magic Fairies Book Series.  After all, what we really want is for them to learn to love reading, not to learn that reading is a painful drag that grown-ups, inexplicably, make you do.