Division with remainders (mental math)

This is a beginner lesson where we look at visual models to understand the concept of REMAINDERS in division.

The first examples have to do with sharing division, and the latter ones with "measurement" division (where you know the size of the groups). Either way, the remainder is the "leftovers" — the items that cannot be evenly divided into groups.

I also emphasize how we can check a division problem with a remainder by MULTIPLYING, and then adding in the remainder.

All of this is done with mental multiplication and mental math - no long division.

This lesson is meant for 3rd or 4th grade math.

The NEXT lesson is a follow-up lesson, where we practice finding remainders in division. I explain how to find the remainder in single-digit division without using any visual model: we think of multiplication and "test-multiply" until we find how many times the divisor goes into the dividend. Then the difference between the original dividend and the multiplied result gives us the remainder. It's easier to explain with an example than in words!

We will also look at a WORD PROBLEM with Mathy my mascot mammoth. He has lots of puzzle books to pack into boxes... but they don't go evenly. How many boxes does Mathy actually need? The division is 51 / 8 = 6 R3, but the answer is NOT 6, but SEVEN boxes! Why? Because the "leftover" 3 books also need to go into a box. This principle where we also need to pack the leftovers or the remainder amount often throws students off.

Lastly we look at a simple pattern of division problems and see how the remainder increases by ONE each time the dividend increases by one... until you come to an even division.

Division with remainders (mental math)

See also