All of the following Common Core standards involve an understanding of part/whole relationships. Notice that the word equation is mentioned in only three of these standards, and in those standards it is only one option that students can use to represent addition and subtraction. In actuality, using an equation may not be developmentally appropriate for most kindergartners. What they should be doing in order to meet the standard, is show addition and subtraction in terms of the part/whole relationships of numbers.
For example, if you ask a child to show combinations of 10 with colored plates, as shown in the previous video, and he/she can tell you all of the different combinations that make ten, they have just solved a problem involving addition to 10 or subtraction from 10 using a drawing. This meets Core Standard K.OA.A.3 without solving any abstract equations. "To really understand addition and subtraction, we must understand how they are connected... By modeling addition and subtraction situations and then generalizing across these situations, children are able to understand and represent the operations of addition and subtraction... Children who commit the facts to memory easily are able to do so because they have constructed relationships among them and between addition and subtraction in general, and they use these relationships as shortcuts. When relationships are the focus, there are far fewer facts to remember, and big ideas like compensation, hierarchical inclusion, and part/whole relationships come into play. Also, if a child forgets an answer, she has a quick way to come up with it" (Fosnot and Dolk 2001)
It would be difficult to overstate how important part/whole relationships are to a kindergartener's mathematical development. I highly recommend looking into the books that I have used as sources in these discussions if you would like more information as well as some great lessons on teaching part/whole relationships. Our Interactive Math Worksheets for March also include some activities designed to develop this skill. Tomorrow we will discuss some of the number sense skills that are on the horizon for kindergartners.