Adding Strategies

Adding Strategies

4 cards from the game rat-a-tat-CAT

I noticed my little boy, Ethan (6), counting on his fingers when working through his addition homework for first grade.

Counting his fingers was fine when he was first learning to add, but it’s time to work on adding without counting out every value on fingers, toes and other manipulatives. 

What about that number scroll I created and have shown my kids using along with snap cubes? I do think using manipulatives is a valuable learning tool because it helps kids visualize what’s going on.  I also  think it’s necessary for them to practice other strategies so they can figure out answers more efficiently.  This becomes more relevant when the numbers they work with get bigger.  We can still count out (9 + 8) on our fingers, but what if we want to know what (36 + 29) equals?

My goal for Ethan was for him to be able to figure out something like (36 + 29).  I don’t expect him to grind out problem after problem.  Rather, I want to help set the stage, if you will, for the math I know he’ll be doing in 2nd grade.

The steps we’ve been working through to meet this goal are:

  1. Be comfortable adding a sequence of numbers.  For example:  (30 + 6 + 20 + 9) or  (10 +10 + 10 + 10 + 10 + 9 + 6).
  2. Know how to break or combine numbers to make more manageable pieces.  If Ethan is not comfortable working with the numbers 36 and 29, he may choose to use 36 = (30 + 6) and 29 = (20 + 9) instead.
  3. Given any two numbers to sum up, be able to combine steps 1 and 2 to figure out the answer.  Given the sum (36 + 29), Ethan chooses how to break down each number (step 2) and then adds up the rearranged sequence of numbers (step 1).
  4. Know how to check his answer using our number scroll and snap cubes.
  5. Commit to his answer!

A surprisingly fun game 

Adding sequences of numbers

We started by just adding sequences of numbers; we didn’t worry too much about how E was getting to the answer.  We just wanted to get comfortable adding more than 2 numbers at a time.

As always, the more fun we can have with it, the better.  One way we practice adding sequences is by playing rat-a-tat CAT.

When one of the teachers at school recommended this game to me, I couldn’t see the appeal of it.  Each person plays 4 cards, face down.   Players exchange cards with the goal of obtaining the lowest score (sum of the 4 cards).  And that’s it.  I thought the game sounded a little boring and not so mathematically challenging….

Until I realized that adding a sequence of 4 numbers can be a real challenge for little kids.

Until we discovered we could mess with the other players’ cards when we started swapping for their good cards (those are the ones they’ve replaced).

Until I found out how fast this game can really move and how excited the kids get when playing it.

Now we play this game just for fun at the end of the day and I give myself a little pat on the back because I can check off “quality time with kid” and “practice addition” on my mental check-list.

If I wanted to add a little more drill here, I’d deal out 6 or 7 cards and ask Ethan what the sum of the cards are.

How to add 8, 2, 5 and 9 without counting out each value?

Rearranging the numbers by breaking and/or combining them

Now, let’s say we’re comfortable with the idea of adding sequences of numbers and our end combination of cards for rat-a-tat CAT are the ones you saw pictured above: 8, 2, 5 and 9.  How can we add these numbers up without counting fingers or drawing tick marks or counting out each of the handy-dandy snap cubes I love so much?

 Regrouping the numbers to make sets of “10’s”

Most of the kindergartners and first graders I know seem very comfortable counting by 10’s.  I’m pretty sure most first graders know that (10 + 10) = 20, (10 + 10 + 10) = 30, and so on.

They are also not bad about figuring what two numbers add up to 10.  So I think it’s natural to start with these two skills in mind.

Back to our example.  We want to figure out (8 + 2 + 5 + 9).  The (8 + 2) part shouldn’t be a problem.  That’s just 10.  but what about the (5 + 9) piece?  Well, we know that (1 + 9) = 10.  So let’s try breaking the 5 into (4 + 1).  Then (5 + 9) = (4 + 1 + 9) = (4) + (1 + 9) = (4 + 10)

So (8 + 2 + 5 + 9) can be rearranged to look like (8 + 2) + (1 + 9) + 4 = 10 + 10 + 4.
We know (10 + 10) = 20.  We still have 4 to go.  Now go ahead and count the last 4 out (on your fingers if necessary) – that’s 21, 22, 23 and 24.  So (8 + 2 + 5 + 9) = 24.

That was a whole lot of discussion to add 4 small numbers, wasn’t it?  Did it feel like a waste of time?  Keep in mind that the goal is to set up a strategy to deal with summing bigger numbers.

Practicing steps 1 and 2

Once we’ve walked through a few examples with our kids, it’s time to see what they can do on their own.

Deal out a set of rat-a-tat CAT cards.  Hand your child a pile of snap cubes or legos.  If we are adding up the numbers 9, 9, 7 and 4, I’d arrange the snap cubes so we have something like 9 red, 9 orange, 7 green and 4 blue.  Ask your child to explain how he/she is breaking and grouping the numbers to figure out the sum.

If you don’t want to use cards, you can always roll a die.  Or just assign some numbers for your child to add together.  Use bigger numbers as your child becomes more adept at this skill. 

Today I asked Ethan how he would add the numbers 43 and 24.  He told me he would break 43 into (40 + 3) and 24 into (20 + 4).  Then 40 and 20 make 60.  And he still has 3 and 4 left over.  But (3 + 4) = 7.  So that makes 67 total.  Correct answer.  But even more importantly, a definite understanding of how to break down the problem and solve it.

Using the number scroll to check that (8 + 2 + 5 + 9) = 24
(See post about Val’s Number Scroll  for more details) 
Checking answers on the number scroll

I don’t always confirm if Ethan’s answer is correct or not.  If I know he’s close to the correct answer, I’ll often suggest he check his own work using our number scroll and snap cubes.  Assuming he sets his snap cubes up correctly, he can usually find his own mistakes.

Committing to his answer

Initially, Ethan used to finish every problem with the question, “Mommy, is this the right answer?”  Now he’ll say “Mommy, the answer to this problem is ….”
I want my kid to have the skill to break down these addition problems and to have the confidence to stand by his solution.  Even if his initial solution is incorrect, just having him commit to his answer changes the paradigm a little.
Another example of this is when we’re reading together.  I’ll often stop to check if Ethan knows the meaning of some new vocabulary.  He used to just shrug his shoulders and say “I don’t know.”  But then I asked him to at least try.  It was ok if he didn’t know the exact meaning.  Just start by saying “I think this word means….” and maybe he’d get it correct.  But if he didn’t, no big deal, we could just talk about it.  We tried again.  He gave his explanation of his understanding of new words.  Sometimes he was correct.  Sometimes he wasn’t.  But with each try, I saw him gain confidence in his own ability and understanding.
Same thing math.  That’s why I make him commit to his answers.
And this is what has been going on with Ethan, addition and me. 
Crochet Lessons 2 & 3

Crochet Lessons 2 & 3

After three crochet lessons I am definitely hooked …  ha…

Not ready to start a real project yet, but here’s what I can do so far:

Single crochet.  This results in a nice, tight weave.  I want to use this stitch to make a big basket or tote bag.  Now where can I buy a big spool of leather for not too expensive a price?

Double crochet.  I like this stitch too.  It grows faster than the single crochet but still a has a nice weight to it.

Triple crochet.  I suppose this one is good if you’re short on time and need to finish a project quickly.  But I’m not wild about the airy look of it.  It reminds me of vests from the ’70’s and makes me think about tasseled cords and moccasins.

I learned these 3 stitches and one more, the half double crochet, in the 2 session beginner crochet class at the Lion Brand Yarn Studio (15th Street between 5th and 6th avenue).

By the way, I really like the Lion Brand Yarn Studio.  Bright.  Spacious.  Comfortable.  Lots of inspiring displays.  Super friendly and helpful staff.  And folks are welcome to sit in the store and work on their knitting/crochet projects.  I think the only caveat is that everyone needs to be working with Lion Brand yarn (Correction!  Just found out we are welcome to work with any type of yarn and on any project in the store and can also ask for help.  This is fabulous!)

My class was held in a room upstairs from the main studio.  Most of the yarn stores I’ve been in around the city are a little cramped, so the separate classroom space is a real luxury.  The instructor, Edita, was super.  Organized.  Clear.  Patient.  The only frustrating part was I had to share her with 7 other students.  Instead of signing up for the next level class, I decided to switch to private sessions with Edita.

So many questions for Edita during the first private lesson.  What is a slip stitch?  How do I increase and decrease?  Can we practice reading some of patterns?  What is that popcorn stitch?  Will you show me how to make a flower?

As Edita demonstrated stitches and techniques for me to follow, I had a complete crochet epiphany:  I can sculpt as I crochet!  Amazing!  Edita then tells me lots of other people have figured this out too and it’s called free-form crochet.  Who knew?

At home, I started experimenting by combining the different stitches.  I wanted to make a flower and I wanted to figure out how to work in the round.  Edita showed me how to make petals, but somehow, my efforts look more like coral or maybe seashells than flowers… Still, I rather like the look of them and there’s a liberating feeling to adding stitches as I please.

I think next week I’ll get a little more serious about reading crochet patterns (not so fun) and starting a real project.  But for now, I’m having a good time free-form crocheting.

Snowy Afternoon

Snowy Afternoon

When I say snowy afternoon, what picture pops into your head?

A pristine blanket of white transforming the everyday into something magical?  Children running joyfully about with their sleds?  How about folks rolling snow balls to build snow men?  Perhaps a picturesque little house nestled in the snow with puffs of smoke rising from the chimney?  Something like this cozy idea of winter I saw in a window display while walking down Broadway?

It snowed this weekend.

Then it sleeted.  It may have rained a little as well.  Finally, it snowed some more.  It wasn’t magical.

It was a wet, slippery, dog-poopy mess.

Far too yucky to play outside.  We doggedly trudged through our Saturday morning routine, but by afternoon, were more than ready to just go home and stay home.

Jin went straight to the TV to catch up on sports news.  We gave Simon permission play with his 3DS for as long as he pleased.  I assumed Ethan would join him.  Wonderful.  All three of my guys plugged into something.  This meant I could snuggle into my favorite chair in my bedroom, watch a movie and do some knitting.  Quiet alone time in the midst of my family.  Love it.

But before I even finished knitting my first row, Ethan was at my side ready for some Mommy-Ethan time.  Could I read him a book?  Watch some cartoon network with him?  How about I tell him a story?


So I told E about how my brother and I used to make nests for ourselves on our parents’ bed.  As we talked, we rolled up my comforter and I showed him how to push it into a U-shape.  We used pillows to complete the circle of his nest.  Lounging on the bed means getting back into pajamas.  And he’d need some company in his nest.  Little boy made trips back and forth between our bedrooms until he had everything he needed for his new game. 

When he was ready, he paused for a moment to assess his set-up, then jumped into the middle of his nest where he surprised me by contentedly playing with and reading to his “baby birds” for a good two hours.  Amazing.  Once again, adding a little story or idea to an ordinary activity saved the day.

I picked my knitting up once again (the other wristlet for next week’s giveaway), half watched my movie and half listened to E read aloud to his stuffed animal audience.  Simon wandered in and made himself comfortable in a corner of the room so he could enjoy his video games in our company.

Our snowy afternoon wasn’t as I would imagine.  No frolicking in the snow.  No cold wet cheeks.  We spent it inside.  Dry.  Warm.  A little lazy.   Alone but together.  Completely ordinary.  But special too.  It was a good afternoon I want to remember.



Copying from Modigliani’s Madame Pompadour 
Painted by Val Chan
Acrylic on Paper (12 inches by 17 inches)
In my most ambitious daydreams of all, I am a fabulously talented and disciplined artist whose works are vied for by galleries and collectors everywhere.
In my reality, I am a complete hacker.  I draw and paint only when I feel like it.  I try to copy from works I especially admire.  And I seriously doubt any gallery will ever want my work.  Instead, I”m playing out my little fantasy with “the Gallery” section in this blog.  Hope you don’t mind.

Portraits.  That what I wish I knew how to paint.  To have the technical skill to recreate someone’s likeness with brushes and paint.  But also the ability to capture and express a person’s spirit and character and then to make it breathe and live on canvas.

How does the artist evoke an emotion?  What is it that makes the difference between a person’s eye glossing right over the picture versus stopping someone in her tracks and then dragging her into the painting?  I just don’t know.  But I do know it’s something.  And I wish I had it.  I keep chipping away at it.  A class here.  Some more instruction there.  Trying for discipline.  And originality.  But for now … I copy.

Beginner Crochet

Beginner Crochet

From Lesson 1 – Chain and Single Crochet
I took a beginner’s crochet class yesterday (at Lion Brand Yarn Studio ) and discovered that I really dig crocheting!
As a child, I owned two crocheted items:  a white “lacy” hat and a bright red and white patterned poncho.  Not sure who made them, but I recall intensely disliking both pieces (Momsy – hope you either didn’t make them, or that you’re not reading this…).  I didn’t care for that that more-hole-than yarn look.  I didn’t like the red and white contrast.  Hated tassels then; still can’t abide them now.  By the age of six, I’d developed a prejudice against any type of crocheted item.  I associated crocheted anything with ugly designs and macrame plant holders the grown-ups seemed so fond of making.
I’ve recently had a change of heart about crochet.  I was initially intrigued when I started seeing pretty crocheted flowers on hats and sweaters.  Then I noticed the granny squares I’d so disliked on my poncho pieced together as a scarf (and in colors I actually liked).  Beautiful.  The colored trim around knit headbands at the holiday market?  Crocheted.  A better way to piece together knit squares?  Crochet.  So many of the handmade items that caught my eye turned out to be crocheted.
Time to learn this needle craft.
Yesterday was my first crochet lesson.  We learned how to make the foundation chain and the single crochet stitch.  The swatch you see here is my very first attempt at crocheting!  It’s our homework assignment.  Not my choice of color.  And only single crochet over and over and over…. but I’m starting to get the rhythm of the hook and feel of keeping the right tension on.  Maybe I should just keep going until this is big enough to make into one of those little zippered rectangular pouches … if only I knew how to sew lining and a zipper….
I’m looking forward to next week’s lesson.  Can’t wait to learn double crochet, slip stitch, work in rounds… and everything else!
The feel of this craft is different than knitting.  It makes me want to experiment with using rope or string or ribbon.  I came across a set of instructions on how to crochet storage baskets.  Wow.   I’ve only just attended my first class and I’ll need to be patient with myself, but I’m utterly fascinated with the crocheting possibilities and can’t wait to make my first project!