Cargo swaps: same objects, new places

Every place has an address

Our cargo board has columns A, B and C from left to right. Rows one and two go from top to bottom. Read those labels first. An address names one place, so we can compare that exact place before and after the cargo moves.

Start with the upper-left cell

Look at A one in the before board. It holds a star. A one in the after board holds a circle. The place has stayed the same, but its contents are different. This is one changed cell. We do not need to guess where to look.

Follow the star

Now compare B one. A circle was there before, and a star is there afterward. The star and circle exchanged places. We call that a swap. The star did not grow a second star, and the circle did not vanish into a secret cargo tunnel.

Check the quiet cells too

The triangle, diamond and square stay in their original cells. C two remains empty. These unchanged places matter too: they help us check the entire board instead of stopping after the first exciting clue. There are two changed cells and four unchanged cells.

Pause: a new swap

Imagine a new row with one triangle and one square. They trade places. Pause and answer two questions. How many places change their contents? How many objects are in the row afterward? Say whether you are counting places or objects before giving each number.

Check the two counts

Both places change, so there are two changed places. The row still holds one square and one triangle, so there are two objects afterward. We did not add the before objects to the after objects. Those pictures show the same collection at two different times.

Movement preserves this total

Fun fact: swapping two objects changes their positions without changing how many objects there are. In our big board, there are five objects before and five afterward. A new location is not a new object. That distinction helps us describe a move accurately.

Make your own comparison

Continue to the worksheet below. Trace the swap and explain which places stay the same. Then try Cargo Compare from the games page. Keep both boards visible and compare one address at a time. A careful inspector checks the quiet cells as well as the changed ones.