Big Idea: Parts to Whole

Parts-to-Whole is the big idea that underlies addition and subtraction. The central concept is that there is a whole that can be partitioned into a certain number of parts. If we combine the parts, they equal the whole. If the whole is 8, the parts could be 6 and 2. Combine the two parts (6 + 2), they equal the whole (8). We can change the order of the parts (2 + 6) and they still equal the whole. We can also find several different ways of making a whole (8) out of two parts, such as 7 + 1 or 3 + 5, or three parts, such as 4 + 3 + 1.

A part can be taken away from the whole leaving another part left over. The whole is 8, we take away 5, 3 is left over. A student that has developed in-depth understanding of the Parts-to-Whole big idea can see addition and subtraction as different ways of forming number relationships, often called “fact families,” or, related facts.

Why is Parts to Whole Important?

Understanding how numbers are related to each other signals that children are ready to experience that each number is more than a distinct character; larger numbers, or wholes, are made up of smaller numbers, or parts. When the student sees the iconic 5 dots on a number card, combined with an additional 2 dots, she can count or add on and know there are 7 dots in total. The 5-length bar with a 2-length bar added on takes on the length that is the same as the 7-bar. Two jumps on the number line past the 5 mark, is the same as 2 numbers past 5, which in turn shows that 7 is two more than 5. Children begin by changing a small collection of dots, or bars, or number line jumps, to a larger amount by virtue of more dots, longer bars, or end points farther along the number line.

Text from Symphony Math Teacher Guide © 2017