Our question today was: we have two cakes.  Period B ate some pieces of one cake.  Period C ate some pieces of the other cake.  How much is left?  Is it enough to offer to period D?

We counted 6/18 pieces eaten from one cake, and 6/16 eaten from the other.  We simplified fractions to 1/3 of one and 3/8 of the other have been eaten.

Knowing what we know about fractions and common denominators, we were able to solve the problem.  But we also looked at the problem visually.

If we divide a cake in three parts, and colour in one of those parts to represent 1/3, and the second cake we cut into 8 parts and colour in 3 of them to represent 3/8.  To compare the cakes and add up the pieces, we need the pieces to be the same size.  We divide each cake into 24 (3 one way and 8 the other).  We can then add up the 8/24 and the 9/24 to make 17/24.

We know that 17/24 were eaten, but to start with we had 2 cakes!  2 cakes have 48/24 pieces.  We know we have one whole cake left over, and 7/24ths of the other.

We looked at how to convert mixed numbers and improper fractions.

We looked at improper fractions for multiplying as well.  This visual model shows the multiplication of 3 and 2/7 by 1 and 1/2.  If you are not converting to improper fractions, you can still multiply, but you need to remember that it’s more complicated than just multiplying whole numbers and multiplying fractions together.  This grid shows all the multiplications broken down, and then added together at the end.

Good work today!