Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Learner Express: Modules for Teaching and Learning
A teacher uses real dominoes to help students explore properties of addition. The dominoes are a concrete representation of the lesson's mathematical ideas. This tool helps students develop an abstract understanding of addition. Run Time: 00:03:53
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 and more. This task also requires that children create pictorial representations of their sums using paper models of dominoes and removable sticky dots. When asked to find all the combinations that equal five, the children realize that the sum 3+2 equals 2+3. The expectation is that when children find all the whole number combinations that equal five, all instances of the commutative law for a sum of five will be discovered. 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). This lesson concludes with students writing equations for the domino models.
(Practice Standard)—Common Core Practice Standard #4—Model with mathematics—is in evidence in this lesson. In the early grades, to "model with mathematics" starts with a real-world context then moves from concrete to abstract representations of mathematical ideas. In this class, dominoes are used to represent (model) entire single-digit addends in addition equations. With this representation, students discover that if dominoes are turned 180 degrees they produce sums with addends reversed. This modeling gives students a visual representation of the commutative property. Students move from 3-D to 2-D models of dominoes, created using construction paper and removable stickers. From these models students write symbolic equations for the addition facts found. The implicit addition operation represented on the dominoes is made explicit with plus symbols and equal signs. In addition to discovering the invariance of sum regardless of the position of the addends, students also "see" (visually and symbolically) the zero property of addition.
(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.
Why are dominoes good to use with children who are just beginning to understand addition? How does this tool help students begin to conceptualize the commutative and zero properties?
4. Model with mathematics
K.OA Operations and Algebraic Thinking