Rational Numbers: Decomposing Fractions
By Cindy Aossey (KCM) & Funda Gonulates (NKU)
Understanding how mixed numbers can be decomposed into various combinations of whole numbers and
fractions helps students develop a flexible and deep understanding of rational numbers. In this
video, we demonstrate how to break apart and rename the mixed number 2 13 using physical
manipulatives such as pattern blocks to represent quantities. By using the relationship between a
hexagon (one whole) and rhombi (one-third of a whole, or 13), students can see that 2 13 is
equivalent to 2 + 13 or 1 + 43, or even 73. We show different ways to write these decompositions
as addition sentences and finally connect those to multiplication such as 7 × 13. Seeing these
different representations helps students build number sense and develop efficient strategies for
adding, subtracting, multiplying, and dividing fractions.
Targeted Standards: KY.4.NF.3ab, KY.4.NF.4a