Boxing Technique #2

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Home : 2004 : September : 27

Boxing Technique #2
By df

You just made my day! Glad to be of help, Tanya. Okay...to solve 7,008 - 413 = ?

Once again stress the importance of place value, (and be sure to include that comma in 7,008 - it provides visual place value meaning).
Set
up the problem so that the 3 in 413 lines up in the ones column directly beneath the 8 in 7,008, etc. (I have used graph paper to help students get the idea of this and it helped a few that needed the vertical guidelines.)
Once the problem is correctly in place, then subtract the three from the eight as usual.
Now go ahead and "box" the 7 in the thousands column of 7,008 and

the 0 in the hundreds column of the same number. You should have 7,0 in a box.

It is important those place values replacing the numbers inside the box still line up properly above the box. Subtract the number inside the box by one to 69, placing the 6 above the seven in the thousands place and the 9 above the zero.
(It'll look weird because the comma will still be between the 7 in the thousands place and 0 in the hundreds place. I draw a diagonal line from the upper right corner to the lower left corner inside the box to indicate that I've taken an action - I've reduced the value of the number inside the box by one, and replaced it's value with the 69 in the appropriate place above the box.)
Give the reduced 1 from the boxed 70 to the 0 in the tens column.
Now you can complete the subtraction problem.
Again, check by using addition.

As for two-digit multiplication, once your students have practice with keeping their place values lined up properly using carrying with subtraction, they shouldn't have as much difficulty doing the same thing with multiplication.
The secret with multiplication is multiplying two or three digit number by a single digit.
Once they have that down, then multiply by two digits.
The important thing is to use Zero as a place holder. Zero will act as a place holder for the tens column, the hundreds column, the thousands column.
I use graph paper for this also until students show me they can keep their place values lined up properly.

Have fun!