Saturday, January 2, 2016

How I See Addition Facts

Since I've been doing Saturday School with my kids, I've continued to appreciate how intricate is the structure of the addition facts as they play out in the curriculum. Right now, my younger is learning some of the facts from memory and, for some others, learning the strategy of making ten.

At this stage of learning, making ten is a great strategy for a problem like 8 + 5. But the strategy doesn't help you in a problem like 12 + 3. To solve that problem, at this stage of learning, I'd say you want to

  • appreciate the place value structure as 10 + 2 + 3,
  • know from memory that 2 + 3 = 5, and also
  • understand the meaning of teen numbers so that 10 + 5 = 15.

And in general, each region of the a + b map has its own story. This graphic shows the map with different regions color-coded.

Here is a key to the colors:

I use this map to orient myself toward my kids' learning as they progress toward fluency with addition facts and knowing them from memory. For example, the image below shows the worksheet I made for today's Saturday School. (Downloadable PDF here.) You'll see that the worksheet has 36 sums for practice—precisely the 36 sums that are coded yellow above. This is an intense practice day for making ten. Over the past few Saturdays, we established that the partners of 10 (magenta) were down cold, that there was fluency within 10 (red), and that the structure of the teen numbers was well understood (green). These are the key prerequisites for making ten. (Another is the ability to use properties of addition where helpful.)

Previous posts about Saturday School: 1, 2


Nancy McLaughlin said...

May I humbly ask you why you place your addends vertically (on the worksheet) instead of horizontally as in algebraic expressions?
~Nancy Mc

Jason Zimba said...

Hi Nancy - good observation! Thanks for your question. There was no reason, really - just that I had an earlier worksheet prepared that used vertical format, and so the quickest way to get these problems out on a Saturday morning was to type over it.

In general, the rule of thumb in my worksheets is that if I present a calculation in vertical format, then I am asking for a written computation using the standard algorithm. Meanwhile, horizontal format typically means that the choice of method is up to them (mental or written, algorithmic or opportunistic). But those are rules of thumb, not ironclad rules. You'll see both horizontal and vertical formats used in these other Saturday School problems.


Dave Marain said...

Are ten-frames (Japanese origin) still around in US Elem classrooms? I found it effective for both concept development and comfort with sums, differences up to 10.

Jason Zimba said...

Hi Dave - while I couldn't say how common they are, I know that some US curricula do use them, and the workbooks that I have used with my kids at home have used them as well.