Thursday, October 29, 2015

Thursday Tool School: Computational Fluency Math Tools

Last week, I talked about using Base 10 blocks to develop a conceptual understanding of multiplication of larger numbers. Today, I would like to talk about how to use Base 10 blocks to do the same with division. 

When students first begin to multiply and divide with larger numbers, we often jump to using the algorithm too quickly. However, students really need time to develop these skills so that they have a solid foundation for the algorithms later. Today's post will offer some ways a Base 10 model can be used to connect to the algorithm. 

In the model below, the illustration shows a step-by-step model of how an understanding of the division process is developed through using Base 10 blocks. 

  • Notice the regrouping of the hundreds in the first step. Instead of allowing students to think that "7 doesn't go into 3," the model helps them understand that because we cannot divide 3 hundreds into 7 groups, we must regroup the hundreds into tens, add them to the two original tens for a total of 32 tens, and then separate them into 7 groups. 
  • From here, students see that the remaining 4 tens are then regrouped into units and added to the four original units for a total of 44 units. 
  • Finally, students are able to see that once the 44 units are divided into 7 equal groups, there are two leftover units. 
  • When the value of each group is counted, we have 4 tens and 6 units, or 46. There are two remaining units that will not be separated into the 7 groups.   

Sound Off! The traditional algorithm is shown below. Compare this process to the one above. What connections do you notice? What language is necessary to better support our students' understanding of the division process. 


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