Virginia Mathematics Teacher Spring 2017

Dominguez asks Jaxson, “Can you write that as a number sentence on the board?” Jaxson writes 4 + 3 = 7.

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Figure 7: Aisha’s representation using part-whole bar model

Figure 4 : Jaxson’s representation of seven on rekenrek

Mr. Dominguez engages the class in a discussion of the connections among Jaxson’s concrete representation on the rekenrek, his semi- concrete representation of the part-whole bar model, and his abstract representation of the number sentence. Mr. Dominguez sees Aisha’s representation on her rekenrek and asks her to describe her representation (see Figure 6). After Aisha’s explanation, Mr. Dominguez engages the class to represent Aisha’s representation using the part-whole bar model (see Figure 7) and then writing a number sentence (6 + 1 = 7) Again, the class discusses the relationship among Aisha’s concrete representation on the rekenrek, her semi-concrete representation of the part-whole bar model, and her abstract representation of the number sentence. Mr. Dominguez uses Jaxon and Aisha’s thinking to write the equation 4 + 3 = 6 + 1 on the board. He then asks the class what the number sentence means and how can they use Jaxson’s and Aisha’s thinking to make sense of the number sentence. Marcel says, “If you do 4 + 3 first you will get 7 and then you do 6 + 1 you will get 7…so it means 7 is equal to 7.” Many students nod in agreement. Mr. Dominquez challenges the students to find other number sentences that can be written similar to 4 + 3 = 6 + 1. They can use the rekenreks, part-whole bar models, and number sentences to problem solve. The students work independently to develop their own number sentences while Mr. Dominguez circulates and confers with students. Jamal writes the number sentence 5 + 2 = 7 + 2. Mr. Dominguez confers with Jamal to learn about his thinking. Then Mr. Dominguez asks Jamal to create two part-whole bar models in which

lesson, the class used ten-frames to develop basic addition facts to ten. Mr. Dominguez says to his students, “I am thinking of a way to show seven on my rekenrek. Can you show me a way?” All of the students use their rekenreks to show seven. Mr. Dominguez takes note of the different ways students represented seven on the rekenreks. For example, he notes that some students show five beads on the top and two on the bottom, some show four on the top and three on the bottom, and some show six on the top and one on the bottom. As the students work, he asks them to find more than one way to represent seven on the rekenrek. After some time, Mr. Dominguez invites Jaxson to describe his representation of seven. Jaxson describes that he has four beads on top and three on the bottom (see Figure 4). Mr. Dominguez says, “Let’s show Jaxson’s thinking another way by writing it on our part- whole bar model on the board (see Figure 5). So, boys and girls, if seven is the whole, what are the parts Jaxson described?” He calls on Donovan who responds by saying the parts are 4 and 3. Mr.

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Figure 5: Jaxson’s representation using part-whole bar model

Figure 6: Aisha’s representation of seven on rekenrek

Virginia Mathematics Teacher vol. 43, no. 2

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