Kindergarten, Operations and Algebraic Thinking

Opinion – CCM grouping, helpful or intimidating

At first glance, the language surrounding this domain is far beyond anything that you and I were exposed to when we were in Kindergarten. Whom is such language for?

“Algebra is the study of mathematical symbols and the rules for manipulating these symbols.” (Wikipedia)

Most of us parents were introduced to the subject called “algebra” in middle school (or its predecessor, junior high school). As the above definition shows, an algebra is a set of symbols and the rules for using them. However, our K-level children are going to be learning the most elementary arithmetic here, not the algebra (per se) that we all love (or not). What gives?

The heading of this CCM standard makes it explicit that, starting at the Kindergarten level, various areas of math will be put into general domains. Rather than being a generality that K-level students need to master, calling it “algebraic thinking” allows CCM to group arithmetic operations under that heading. We will see other examples of this type of grouping in upcoming posts.

Will this particular grouping offer an advantage when the algebra that we all know (or have long forgotten) is introduced later in the program? The originators of CCM thought so; for the rest of us, especially our children, time will tell.

CCM Lesson of the Day: Operations and Algebraic Thinking (K.OA)

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Comment. To me, this is not clear. Represent means to set up the addition (or subtraction) problem. For example, start with two bowls of apples; count the number of apples in each bowl. I imagine that there are 5 in one bowl and 3 in the other. Then, add them together by combining the contents of the two bowls into one bowl.  Solve the addition problem by counting the number of apples in the one bowl; in our example, that would be 8.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Comment. We explained above how to represent and solve an example addition problem. Let’s decribe how to represent and solve a subtraction problem. From the same bowl (of 8), remove 2 apples. Then count the number of apples remaining in the bowl – I expect that there will be 6.

The larger lesson here is that addition and subtraction are extensions of counting. I suggest that you make sure that your child has mastered counting before taking on addition and subtraction.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Comment. The bowls and the apples can work for you here. Start with the number you want to decompose, such as 8, in one bowl. Then, move some number of those into the second bowl. The contents of the two bowls represent your decomposition. Notice that “+” and “=” signs were slipped in above.

For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Comment. Decomposition?

Fluently add and subtract within 5.

Definitions

Add: Combine two numbers, represented by “+”. Example, 3 plus 4 equals 7 which is generally written as 3 + 4 = 7.

Subtract: Remove a number of objects from a quantity, as represented by “-“. Example, 7 minus 4 equals 3 which is generally written as 7 – 4 = 3.

Decompose: Divide a quantity into two or parts. Example, 7 can be decomposed into 6+1, 5+2, and 4+3.

Fluently: from memory?