Taxing Math

            Hi.  I’m Bob.  And I’m an alcoholic.

             AA really has the right approach.  You can’t get help until you acknowledge your need.

            “Guys I noticed you were having trouble in math today calculating tax.”  I passed out small whiteboards and markers to Landon, Jeremy, and Ramon sitting at the table in front of me.  All three boys have learning disabilities, and the classroom instructions on moving decimals had sailed right past them.

            “When you did the Restaurant Game, you did a good job adding up your orders, but none of you seemed to know how to calculate the tax.  Before you multiply, you have to turn the percent into a decimal.”

            As each boy got their board, they immediately began drawing on it.  Landon scrawled his name in big loopy letters.  Jeremy drew an alien, and Ramon began pounding dots.  I handed everyone a dry eraser and grabbed a board of my own.

            “OK guys, look up here.”  I wrote 6% on my board.  “I want you to change 6% to a decimal.”

            “I need to go to my locker and get my notes from class,” said Ramon.

            “Just stay here,” I said.  You didn’t take notes.  “I’m going to go over whatever you need.”

            “I already know how to do this,” Ramon objected.  “I just need to get my notes from my locker.”

            You didn’t write a single thing down in class.

            I ignored him and continued, “Think of 6% as six cents.  How would you write six cents as money with a decimal?”

            Landon and Jeremy erased their boards and began writing their decimal version of 6%.  Ramon just continued to stab dots on his board.

            “Ramon.  Come on.  Give this a try.”

            “I don’t need to try.  I already know how to do this.  But you won’t let me go to my locker, so I can’t do it.”

            “If you know how to do it, then just show me a couple on your board.” 

            I waited.  I could see both Landon and Jeremy had written .6 on their boards.  They shielded their work waiting for Ramon to write something.  Ramon finally stopped dotting and wrote 6.0 on his board.

            “You’re almost there,” I said.  I wrote .06 on my board and turned it to show the boys.  “See how if I add a dollar sign to this it looks like six cents.”  To the left of .06 I added a dollar sign.

            “Why do I have to do this?” Ramon argued again.  “I know how to do this.”

            I wrote 8% on my board.  “OK guys.  Now try another one.” I turned my board around.  “How would you write 8% as a decimal?”  

            Landon and Jeremy bent their heads down and began writing, but Ramon was now stomping dots on his board.  I reached over and softly tapped his board.

            “Give it a try please.”

            “Is this right?”  Jeremy turned his whiteboard towards me.

            Jeremy had .08 written.  I watched as Landon finished writing .08 on his board. 

            “Just a sec.  Let’s wait for Ramon.”

            Landon and Jeremy turned and looked at Ramon.  He ignored everyone for a minute, but then stopped his stabbing and wrote .8 on his board.

            “That’s not right,” Landon said showing his board to Ramon.  “Make it look like eight cents.”

            Ramon glanced at Landon’s board, then at his own.  He scrawled a dollar sign to the right of .8, and stabbed three dots over it.

            “Now it’s money!” Ramon growled.

            I dropped my voice to a lower register.  “Ramon.”  I wrote .08 on my board and turned it around.  “This is how you write 8% as a decimal.”

            “Told you,” Landon said triumphantly.

            “That’s how I wrote it,” said Ramon furiously erasing his board.  “I know how to do this.”

            I blew out a little sigh.  As I wrote 3% on my board, I fantasized Ramon standing earnestly in front of me.

            “Hi. I’m Ramon.  And I have no idea how to do my math.”

 

(source)

Dividing Fractions

            “Mrs. Jones, Caitlyn’s grade on her math test was just posted and she didn’t pass.  I studied with her last night.  What’s going on?”

            “I know you studied with Caitlyn.  She told me this morning.  She and I worked on the math every day this week, and she was doing the problems very well.   I was disappointed too that she didn’t pass.”  Caitlyn’s mother struggles almost more than her daughter, over her daughter’s work in school.  It’s unusual to go more than a day or two without a phone call or long email from her.

            “Is she getting the proper accommodations when she tests?”

            Sometimes I feel uncomfortable when people talk about “accommodations.”  We throw out that word like there is a specific set of special things we do and kids suddenly are able to remember things and perform on grade level.  I looked at the reminders still written on the white board.

Change everything to a fraction

Keep, Change, Flip

Word Problems:  What are you dividing?

Put it first

            “Yes,” I answered, “Caitlyn took her test in the Learning Center and we reviewed things before she even started.”

            “I don’t understand why she doesn’t pass a test when I study with her.”

            “I’ll help Caitlyn do the corrections on her test and get those in this afternoon.  Her teacher does give extra points for corrections.”

            Two periods later Caitlyn quietly slipped into the Learning Center.  She shyly handed me her test.  Even though her teacher had used a lime green Sharpie to grade the test, the 58% at the top of the page still looked mean.

            “How ‘bout you sit at the round table with me, and let’s do your corrections.  We need to figure out what you did wrong.”

            “My mom’s going to be mad.”  

            “No she won’t be.”  Yes she is.

            We slowly worked through her corrections.  She would calculate two problems correctly and forget to flip a fraction on the third problem.  On the next problem she’d flip both fractions.  Then she’d do three problems correctly.  She was correct more than she was wrong.  I made a mental note to sit by her side for the next test and verbally remind her of each step.

            The second page was simple word problems about pizza.

            “Caitlyn, what are you supposed to always do when you have a word problem?”  I pointed to the reminder still on the white board.

            Caitlyn stared at it for a minute, then said, “Figure out what you’re dividing up.”

            “Read these four problems.”

            “Five people have to share one and a half pizzas.  Six people are sharing three-fourths of a pizza.  Eight people are sharing two and a half pizzas.  Twelve people have to share three and one-fourth pizzas.  How much pizza do the people in each group get?”

            “Look at how you did the problems on your test.  Can you see what you did wrong?”

            Caitlyn stared at her work for a minute, then slowly began to smile.  “I divided up people instead of pizzas.”

            “Good job figuring that out.  Now go ahead and fix your answers.”

            Caitlyn bent her head down and began working.

            “My mom’s still going to be mad.”

            “No she’s not.”  Yes she is.

The Lost Year

“I need to be self-sufficient!” Naomi insisted as she covered up her blank paper. 

I wonder who told her that?  

All last semester Naomi had made the "self-sufficient" declaration whenever anyone tried to help her in math class.  My testing confirmed that she was three years below grade level.  So now we were sitting at the table in my room trying to catch up.

“There are eight ounces in a cup,” Naomi read.  “How many ounces are in a pint?” She looked at the bulletin board in front of her.  She looked over at the other wall.  She looked at the computers.  Then she lapsed into her “nothing” look. 

“Naomi, do you need help?” I asked.

“No.” 

“Let me know when you have your answer then.” 

She resumed staring around the room.  I knew she processed things much slower than most students, so it sometimes was a guessing game determining when her “thinking” stopped and her “blanking off” started.

“Naomi, why don’t you read the question again,” I gently asked.  After she read it again, I asked, “Do you remember how many cups are in a pint?”

I waited fifteen seconds.

“No,” Naomi finally answered.

“Look in your reference packet,” I instructed.  Naomi slowly turned the pages of the yellow packet I had put together for her.  She found the illustration showing the cups in the pints in the quarts in the gallon.  

Source of Image

Naomi stared at the illustration for another fifteen seconds.  “Two.”

“OK.  There’s two cups in a pint.  How many ounces are there in one cup?”

“I don’t know!” she snapped.

“They said in the problem Naomi.  Read the problem again to find how many ounces are in one cup.”

Naomi looked back at the workbook and read, “There are eight ounces in a cup.  How many ounces are in a pint?”

Fifteen more seconds passed, then “Eight.”  

“That's correct.  There’s eight ounces in one cup.  A pint has two cups in it.  So how many ounces are there in the pint that has two cups?”  I was doing my slow, articulated speech.  I waited, wondering if I should draw a picture. 

“Sixteen!” Naomi announced.

“You’re right.  There’s sixteen ounces in a pint because a pint has two cups, and each cup has eight ounces.  Eight and another eight make sixteen ounces in all.”

Naomi hunched over her paper as she wrote her answer.

“OK.  You’re ready for the next problem,” I continued.  “Now the next two problems are just calculations that I know you can do, so let me know when you have your answers.”  I watched to see how long it would take Naomi to look back at the workbook.  Instead of looking at the workbook, however, she stared at the bulletin board in front of her. 

After about a minute, Naomi turned to me and asked, “Do the other kids in my class know how to do this stuff?”

“Yes, they do Naomi,” I answered.  I don’t like to point out to Naomi that she is behind other kids her age, but she argues constantly about having to work on math in the Learning Center.  I felt no guilt answering her question truthfully.

“When did they learn all this?” Naomi asked.

“Well,” I hesitated, “They learned it before sixth grade.”

Naomi looked down at her workbook again.  She closed the cover and studied the front of it.  I didn’t see a blank look on her face this time.  She was thinking.  After about 30 seconds she said, “They learned this in fourth grade!”   One of the lessons in her math book had been about Roman numerals, and Naomi had just had her “Ah Ha” moment with the IV on the front cover.

“Yes, they probably did.”

Naomi pondered this for a minute, then slowly opened her workbook again and looked at the next problem.

As she resumed working, I heard her softly mutter, “I wonder what I was doing in fourth grade.”