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Lesson objective: Understand that a number can be decomposed or taken apart in more than one way.
Students bring prior knowledge of decomposition from previous work with K.OA.A.1 and K.OA.A.2. This prior knowledge is extended to include a more broad definition of "take apart" as students develop an understanding that a number can be taken apart in more than one way and still maintain a total equal to the original set. A conceptual challenge students may encounter is that arrangement or size may affect the quantity of the set or total.
This concept is developed through work with direct modeling using tiles, which can be bundled, piled and grouped as a single unit to support counting and cardinality. Connections to written work by transferring designs to paper or graph paper and coloring in or circling the smaller parts they see within the total further develop students' understanding of decomposition.
This work helps students deepen their understanding of equivalence as they experience that organization and order do not matter for equivalence. The number of objects in a set is fixed no matter how it is arranged and counted, and different sets may have the same number of objects.
Students engage in Mathematical Practice 7 (Look for and make use of structure) as they explore different arrangements of five tiles and share how the design can be seen or explained in terms of smaller parts of the total, such as groups of two or body sections of an imaginative animal.
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