Exchanging Exercise




To prepare the child for problems with exchanging
To develop the understanding that 10 of any hierarchy is equal to one of the next hierarchy


Knowledge of the decimal system, and ability to count to 9, identify quantities to 9999, and match quantities with corresponding numerals


4 1/2 to 5 1/2 years


The tray of golden beads is placed at the top of the felt covered table.
From the tray, the teacher takes beads from each hierarchy and places a pile of mixed quantities in front of the child.  The teacher needs to be sure that the total quantity of beads in the pile is not greater than 9999.  This can be accomplished by placing only a few thousands in the pile.  She leaves a number of beads in each hierarchy on the tray so they can be used for exchanging.  The child is usually interested in the pile of beads.  The teacher can say something to the effect, "We have a lot of beads there don't we?  Let's see how many we have."



The child discovers that in order to count the beads, he must separate them into their hierarchies of thousands, hundreds, tens, and units.  After the child has done so, the teacher asks the child to count the units into a small container, such as the lid of a small box.

The child begins counting, and when "ten" is reached, the teacher stops and shows him that since 10 units is the same as a 10 bar, he can exchange the ten units for a ten bar from the tray.  The teacher shows him to place the ten bar above the other tens to show that this ten bar was received by exchanging.


The child continues counting the units, exchanging for a ten bar each time ten units are counted.

 As we can see in the photo above, the child received three ten bars by exchanging.  After the units are all counted, the teacher asks the child to count the tens he got from the exchange process.  These tens are then added to the other pile of tens, and the child begins to count them.  When the child has counted 10 tens, the teacher stops him and shows him how to exchange the tens for a hundred square from the tray.  The hundred square is placed above the pile of hundreds on the mat. The child continues counting tens, exchanging for hundreds whenever he has 10 tens.

After the tens have all been counted, the child will count the hundreds which have been exchanged to see how many he got.  These hundreds will then be added to the original pile of hundreds and the child will count these.
When 10 hundreds are counted, the teacher will show him how to exchange them for a thousand cube, and the child will continue counting and exchanging until all the hundreds have been counted.  The child can then count the thousands and restate the total amount.
(Note: Make sure the number never goes higher than 9,999 at this stage.)