Big Idea: Parts to Whole

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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?

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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.

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Text from Symphony Math Teacher Guide © 2017