Summary:

At the Trotter Elementary School in Boston, Massachusetts, students informally explore properties of addition using dominoes. At the start of the lesson, students are sitting around a large set of wooden dominoes. Mrs. Wright asks her four- and five-year-olds to find single dominoes with pips that add up to four. When one student picks out a single domino with pips adding to eight or "double four" (i.e. 4 + 4), Mrs. Wright takes the opportunity to help children see that they should be thinking "addition" and that the sum of the pips should equal four. Children move from finding sums of four to sums of five. This task also requires that children create pictorial representations of their sums using paper models of dominoes and removable sticky dots. The children realize that the sum 3+2 equals 2+3. The expectation is that they will be able to find all the whole number combinations that equal five and, in so doing, find all instances of the commutative law for a sum of five. Embedded in this discovery is the fact that zero is the identity element for addition (when zero is added to another number the sum is that number, e.g. 5+0 = 5).

Standard Connection:

(Practice Standard)—Common Core Practice Standard #5—Use appropriate tools strategically—is in evidence in this lesson. Instead of using only the tools of "paper-and-pencil" to record addition facts, students can choose to use actual dominoes or student constructed paper models of dominoes as they create their addition facts. These tools are appropriate because they embody the single-digit facts that students are learning. They are appropriate, also, because they provide tactile and visual opportunities for learners to explore sums. When strategically used, these tools will give students a visual representation of the commutative property. By simply turning the dominoes (i.e. actual or paper versions) 180°, students are able to detect the invariance of a sum no matter the position of the addends. Also, when the tools are used strategically, students can "see" the zero property for addition. By allowing children to choose different tools to represent their operational thinking, Mrs. Wright gives tactile, visual, and auditory learners options for expression.

(Content Standard)—Operations and Algebraic Thinking—K.OA—is the content domain that best encompasses the content of this lesson. Using dominoes, students represent addition sentences using objects, drawings, and equations. They are able to "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)." They are just being exposed to the commutative property, which is formally addressed in the Operations and Algebraic Thinking—1.OA domain.

Questions to Consider:

Why are dominoes a good tool to use with young children who are just beginning to understand addition? How do the dominoes help students begin to conceptualize the commutative and zero properties?

5. Use appropriate tools strategically

K.OA Operations and Algebraic Thinking