Adding and Subtracting Fractions

Pattern blocks are incredibly useful learning tools! Today and yesterday we used them to expand our knowledge of fractions. If a yellow hexagon is the whole, then a green triangle is 1/6 because it takes 6 green triangles to evenly fill up a hexagon. Similarly, a blue rhombus is 1/3 because it takes 3 blue rhombi to evenly fill up a hexagon. Finally, a red trapezoid is 1/2, because it takes 2 red trapezoids to evenly fill up a hexagon. 

As children manipulated the blocks, they realized they could fill a hexagon using a combination of blocks. For example, you can fill a hexagon with 1 trapezoid, 1 blue rhombus and 1 green triangle. Therefore, we know that 1/2 + 1/3 + 1/6 = 1. We talked about adding fractional pieces. We learned that we can only add fractions (in our head) if the denominators are the same. For example, we can add 1/4 + 2/4 = 3/4. The denominator of 4 is consistent. In the example 1/2 + 1/3 + 1/6 = 1, the children used a model (the blocks) to solve it. They would not be able solve it mentally because the denominators are not the same. However, some very smart third graders realized that 1/3 + 1/6 = 1/2 (because 1/3 = 2/6) so the same problem can also be solved 1/2 + 1/2 = 1. (Sounds like fifth grade fraction studies, don't you think?)

Challenge your child to solve these addition and subtraction problems:

1/3 + 1/3 =
3/4 + 1/4 =
5/6 - 3/6 =
3/5 - 1/5 =