Cinder cones are volcanic features that are found at volcanic sites where there has been some form of fountaining activity. Fire Fountains are where lava has been ejected during an eruption up into the air where it cools and falls to the ground as solid or even semi-solid particles. Those particles are what we call cinder.
Because the viscosity of lava - how 'runny' it is - is a function of its chemistry, cinder cones tend to form in locations where runny lava's mix with magmatic gases and form fountains. So the vast majority of cinder cones form on volcanoes with basalt magmas, as molten basalt is very runny. For example, the islands of Hawaii, which have all been made from the eruption of basaltic lavas, have many examples of cinder cones. In fact, hawaiian-type eruptions are classified due to the existence of fire fountains.
The typical cinder cone found in almost all textbooks is a circular hill with a distinctive crater in its middle. However, it is rare for such a beautiful structure to be built up as cinder cones form at the whim of the prevailing winds. As a fire fountain erupts, its particles are blown downwind to be deposited. So it is more typical to find lopsided hills with fans of debris thinning out downwind.
Cinder cones are often seen as being the final last gasp of a volcanoes life. In Hawaii, they form capping features on older volcanoes and then post-eruptional last 'blasts' after the main volcano has become extinct. Famous Dimond Head on Oahu is an example of one of these
So most cinder cones are just a part of a greater volcano, rather than been seen to be a separate or individual volcano. They represent an eruptive event that was part of the greater volcanic period.
Cinder cones also provide useful materials for humans. They have provided glassy materials for ancient to make stone tools, through to modern uses as road gravel, landscaping stone and even put into propane grills as 'volcanic stones'.
If you want your students to build a cut-out model of a cinder cone, you can download this B&W one from the USGS created by my friends Tau Rho Alpha and Leslie Gordon. Or even the color version Tau and I created a few years later.
GEOetc's Field Adventures to Hawaii provide you first-hand experience on these and many more volcanic features. If you love volcanoes, then there is no better way to come ane experience them for yourself than to be a participant on one of our trips.