Chugga-chugga choo-choo!  You can think of a river as a train loaded with water, sand, dirt, and rocks of all shapes and sizes.  As the river-train moves from mountains to the ocean, it drops parts of its load and makes new pieces of land.  Once the river reaches the ocean, its final destination, it is empty.  But what happens to all the stuff it left behind?
 
The Earth's pull, called gravity, tugs on rain or melting ice, pulling it down the hill.  As streams of water come together, they form rivers, which zigzag through the mountains to escape hard rock.  The river picks up loose dirt and rocks, pushing them along and carving a path that look like the letter "V."  V-shaped valleys are valleys with wide sides and narrow bases that are shaped by rivers.  These are different from U-shaped valleys that ice sheets make.  In those valleys, rocks frozen into the ice grind away both the bottom and the sides of the valley.  

It took a lot of water and a lot of time to make the Grand Canyon look like this.


Sometimes river valleys are very steep and narrow, more like the letter "I" than the letter "V."  These narrow valleys consist of hard walls made of rock that the river has carved out from under the top layer of soil.  They are very similar to canyons, but smaller.  This type of place is a gorge, a narrow valley with steep, rocky walls that lies between two hills or mountains.

Watch your step crossing that bridge.
adrian_negoita_2005, CC BY 2.0 , via Wikimedia Commons


Once a river picks up all its rock and dirt "passengers," it has to let them off somewhere.  Some of the rock and soil ride all the way to the end of the line where the river meets the sea.  In these low places, the river spreads out, dumping its load over the shallow part of the beach.  If the sea cannot move all this dirt and rock away from the shore, a triangle-shaped place of rock and dirt is formed, making new coastline.  This is a delta, a flat piece of land that is made when a river meets a quiet body of water like an ocean or even a lake.  

The Mississippi River forms a massive delta in Louisiana where it meets the Gulf of Mexico.
NASA, Public domain, via Wikimedia Commons


Rivers can make new land in other places too, even when there is no ocean or lake to run into.  If a river runs down a mountain and spreads out over a flat place, it slows down enough to let the rock and dirt settle out.  In those places, the river also makes triangle-shaped land shapes, but these are not flat like deltas.  Instead, these triangles look more like upside-down ice cream cones that get shorter and shorter.  An alluvial fan is a triangle-shaped piece of land that is made when a river runs down a mountain and spreads out on an open plain of land, spreading out the sand and rocks it was carrying.

You can't cool yourself off on a hot day with an alluvial fan.
Mark A. Wilson (Department of Geology, The College of Wooster). [1] (User:Wilson44691), Public domain, via Wikimedia Commons


Rivers rush along just like trains, carrying sand, rocks and soil from mountains to flat places and even the sea.  All along the way, the river picks up and drops off passengers.  When it picks up passengers, it leaves behind V-shaped valleys and gorges.  When it lets of passengers, the river can make triangular forms either at the water's edge or on a dry plain.  All aboard!

References:

"Alluvial Fan." National Geographic Education. National Geographic Society, 2013. <http://education.nationalgeographic.com/media/reference/assets/alluvial-fan-1.pdf>

Briney, Amanda. "An Overview of Valley Formation and Development." Geography, About.com, 2014. <http://geography.about.com/od/physicalgeography/a/valleyformation.htm>

"Canyons "" Deep Cuts." National Geographic. National Geographic, 2013. <http://science.nationalgeographic.com/science/earth/surface-of-the-earth/canyons-article/>

"Geography: River Landforms." Bitesize. The BBC, 2013. <http://www.bbc.co.uk/schools/gcsebitesize/geography/water_rivers/river_landforms_rev1.shtml>

Rice, Doyle. "All-time Record June High Tied in Death Valley on Sunday." USA Today. Gannett, July 2013. <http://www.usatoday.com/story/weather/2013/07/01/death-valley-heat-record/2480019/>