Math: Place Value
Place Value Spiral
an orange, cut into it at the top, and peel it cross-wise, in a spiral shape.
Kind of pretty, isn't it? But don't eat the pretty spiral peel - eat the
delicious fruit! Drink - what else? - orange juice to go with it.
Old spiral notebook with at least 10
Scissors | a bit of Scotch tape |
In later grade school on through
middle school, it can get tricky to keep track of place value. Mixing up the
correct place values can make you get a lot of math problems wrong.
In the early grades, when you're mostly working with
one's, 10's and 100's, you can keep things straight. But when the numbers get
big, the challenge gets big, too.
Here's a simple device you can make
to help. You recycle an old spiral notebook, and use it to visualize place
value in dealing with those huge numbers.
Count 10 blank pages in the old
spiral notebook. Remove all other pages. Count twice to make sure, before you pull
out the other pages, because you will need exactly 10. You can use the extra
pages as scratch paper.
Now go back to those 10 pages still
attached to the wire spiral binder in the notebook. Cut away all but the two
inches closest to the spiral binding. Discard the rest of the paper and re-use
as scratch paper.
Now take the scissors and cut every
two lines, from the edge of the paper where you just cut, to the punched holes
that the spiral wire goes through. You should end up with 15 stacks of 10 little
rectangles apiece, attached to the spiral wire in one or two holes. See:
This finished Place Value Notebook
shows the U.S. federal debt as of one
Spoken aloud, it would be sixteen
15 billion, 769 million, 788
thousand, 215 dollars. Wow!
You should be able to flip the
little pieces of paper around on the wire spiral so that all 15 little
rectangles can be flipped.
Now put all the stacks in place, so
that you have all 10 rectangles stacked up in the 15 rows.
Underneath the top left one, on the notebook cover
cardstock, write hundred-trillions.
Under the next stack, write ten-trillions. Next,
Repeat with hundred-billions, ten-billions, billions,
and then hundred-millions, ten-millions and millions, and then hundred-thousands,
ten-thousands and thousands, and finally, hundreds, tens and ones.
Now on all 15 little rectangles
across the notebook, write a 0 inside each rectangle.
When you've done that, flip all 15 over out of the
way. You will have 15 new, blank rectangles. In each of hem, write a 1. Then
flip all of them over, and on the next blank rectangle, write a 2.
Continue on to the number 9.
When you have your Place Value
Notebook complete, now you can ask someone (an after-school program leader? a
parent? a sibling? a friend? A mentor or tutor?) to say aloud a number to you,
and you can show how it looks on your Place Value Notebook. The adult or friend
should check your work and make sure you're getting the answers right.
Start with a single-digit number,
like 8. You should flip all 14 of the other rectangles up and out of the way,
and only show the 8 on the "ones" rectangle.
Maybe the next number is 27,491.
Leave the rectangles representing the place values of hundred-thousands on up
out of view, and just use the ten-thousands and smaller to display that number.
Be careful when you're flipping the
little rectangles, that you don't tear them. If you do, a tiny piece of Scotch
tape can repair the holes so that the rectangle will stay in place.
You may want to play with this
device for a few days, and then put it away for a month or so and take it back
up again for review.
Once you have place value down pat
through the trillions, and never get any wrong, pass the device on to a younger
student. That's your "place" - to share "value" with others!