Composition and Decomposition

As an educator, I am always trying to develop a schema that is accessible to all, flexible and fluent and effective as a framework. Decomposition and composition are two of the most influential constructs in a primary classroom.  Children spend their days mastering  discreet skills/parts and then applying critical thinking as they compose or decompose parts and wholes. (reading, observational drawing, clay, writing, math, handwriting, sports, dance etc.)

Zoey is completing an experience we refer to as "the counting jar.". The basis of counting is composition. We take one jewel, add another and repeat the process until we have counted all of our jewels. She is exploring the sequence of numbers in the context of a number line framework (each line in the numberline is a multiple of five).





As a class, we consider the strategies that help structure our thinking. Are there more jewels than five but less than ten? How many more jewels than ten are in the counting jar?

This work is a prelude to addition and subtraction. We are beginning to add parts together and subtract parts from the whole. We start with games and then begin to formalize the process with the addition, subtraction and equals symbols. 

Cal explained his strategy for this domino. 

He knows that five plus five equals ten and then he added the remaining one. 

Cal decomposed the six into two numbers facilitating his process. 

When writing the number eight  how do we utilize different lines, curves and circles together (composition)? We start with the parts and then construct the whole number.

 The children understand that varying movement and combination of shapes composes other shapes.  We often play the game Fill the Hexagons. The children may use any of the pattern blocks in different combinations to create a hexagon. Each hexagon must look different.

Again, the whole is defined as the sum of its parts.

 A pattern is created with parts (units) combined in a predictable sequence. We often refer to the whole as the pattern train and the parts(unit) as the cars. Students create a pattern using a unit but also identify the number of units apparent in a pattern. The children compose a pattern and then consider decomposition.

Symbols and algorithm  do not hold meaning until children have ample time to explore the  mathematical thinking  present in the process of composition and decomposition.