3 mistakes learners make with volume, each one named and explained.
Volume is the area of the base times how many layers high it goes, which is why every dimension has to be in the product.
A cuboid's volume is worked out from two of its edges, so the answer is an area.
Area is the calculation practised most, and two numbers is the shape it expects.
Question. 4 cm by 3 cm by 10 cm
A common answer. 4 x 3 = 12
The answer. 4 x 3 x 10 = 120
Why. Volume fills a solid, so all three edges have to be used.
Count the numbers you used. A volume always uses three.
The areas of the six faces are added and offered as the volume.
Both are calculated from the same three edges and both describe the size of the solid.
Question. 4 by 3 by 10
A common answer. 2(12 + 40 + 30) = 164
The answer. 120
Why. Surface area is what you would paint; volume is what you could pour in.
The unit decides. Three lengths multiplied gives a cubed unit, every time.
Volume is given as the three lengths added together.
Three numbers appear and adding is the operation that needs no decision.
Question. 4 cm by 3 cm by 10 cm
A common answer. 4 + 3 + 10 = 17
The answer. 4 x 3 x 10 = 120
Why. Volume counts how many unit cubes fit inside, which is a multiplication.
A volume is always much larger than any one edge. If it is not, something was added.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.