Exchange
(Ages 5 – 7)
Understanding place value and regrouping is a critical prerequisite for all math operations. In her wisdom,
Maria used this understanding as the basis for multi-digit operations – ranging from primary level bank game to
elementary operations with decimals.
Of course, “changing” is initially done under a teacher’s guidance. It is critical that the child understand that 10
units equals a “ten”, 10 tens equals a “hundred,” and 10 hundreds equals a thousand.
Using the golden beads, place value blocks, or the stamp game, place a random quantity before the child. For
example, give the child 1 thousand, 14 hundreds, 6 tens, and 13 units.
Starting with the units, the child changes the 13 units to one ten and 3 units.
Now there are 1 thousand, 14 hundreds, 7 tens, and 3 units.
The child changes 14 hundreds to 1 thousand and 4 hundreds. Now the child has 2 thousands, 4 hundreds, 7
tens, and 3 units or 2,473.
On the following pages you will find instructions and two sample exercises from the series Exchange from
Conceptual Learning Materials (www.conceptuallearning.com). Rename is a more advanced series that
prepares the child to subtract from a minuend with zeroes.
Exchange Matching Set
1. All pieces on each sheet are designated with the same number code in the lower right corner and should be cut
and stored in the same drawer or envelope. Each sheet is comprised of ten pairs for two-part matches or eight
sets of three for three-part matches. Each of the Exchange, Rename, and Equivalence sets consists of a series of
ten different exercises.
2. The student may work either at table or on the floor. If working on the floor, it is recommended that he or she
lay out the work on a small mat. Carpet samples or rectangular place mats work well.
3. Each exercise consists of eight or ten problem cards to be matched with one or two other pieces. The
exercise below shows a sample problem set. As a guide in laying out the work, it is recommended that the child
place all the cards labeled "1st" in a vertical column as illustrated below.
4. The child then matches the card designated "2nd" to the first card.. Young children will use the golden beads,
place value blocks, or stamp game to figue out the simplified value. Older children may abstract some of the
matches, but should still use manipulatives when needed.
5. Young children may do only two or thee matches in a session. Older children may be ready to all 10 matches
at a sitting.
1st
2nd
92
8 tens, 12 ones
Exchange 1
1st
Exchange 1
2nd
94
8 tens, 14 ones
Exchange 1
1st
Exchange 1
2nd
99
8 tens, 19 ones
Exchange 1
1st
Exchange 1
2nd
32
1 ten, 22 ones
Exchange 1
1st
Exchange 1
2nd
22
1 ten, 12 ones
Exchange 1
1st
Exchange 1
2nd
42
1 ten, 32 ones
Exchange 1
1st
Exchange 1
2nd
56
4 tens, 16 ones
Exchange 1
1st
Exchange 1
2nd
53
4 tens, 13 ones
Exchange 1
1st
Exchange 1
2nd
60
4 tens, 20 ones
Exchange 1
1st
Exchange 1
2nd
63
4 tens, 23 ones
Exchange 1
Conceptual Learning Materials
www.conceptuallearning.com
Exchange 1
Copyright 1994 Dianne M. Knesek
1st
2nd
12 tens
120
Exchange 4
1st
Exchange 4
2nd
21 ones
21
Exchange 4
1st
Exchange 4
2nd
21 tens
210
Exchange 4
1st
Exchange 4
2nd
21 hundreds
2100
Exchange 4
1st
Exchange 4
2nd
13 ones
13
Exchange 4
1st
Exchange 4
2nd
13 tens
130
Exchange 4
1st
Exchange 4
2nd
13 hundreds
1300
Exchange 4
1st
Exchange 4
2nd
20 ones
20
Exchange 4
1st
Exchange 4
2nd
20 tens
200
Exchange 4
1st
Exchange 4
2nd
20 hundreds
2000
Exchange 4
Hands-on Development Sets for School and Home
Exchange 4
Copyright 1994 Dianne M. Knesek
Exchange 04