Distributive Property Discussions

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My fifth grade class is in the middle of a unit on pre-algebra concepts.  We explored the different associative, commutative and distributive properties earlier in the week.  Students were able to use the first two with modest success, but the distributive property was causing some issues.  I believe some of the reason is because students were confused with what the parentheses meant, while others needed a visual model to make a better connection.

The class reviewed a few different examples and we went back to a concrete representation.  I find this is the place where solid understanding is developed before we  move to more abstract models.

Students have been use to using base-ten blocks, counters and unifix cubes to put together and take apart numbers.  Students were asked to use cubes to show an understanding of the distributive property.  They used a dice to create a multiplication problem and then split it into two parts.  They then wrote on the desks (who doesn’t love that?) to show multiple number models to indicate the total.

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This student didn’t show the partition, but displayed the different number models

One issue was trying to figure out how to divide or create the partition.  Some students used dice to indicate where to split the model.

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I appreciate how this model shows the different representations

From here, students transitioned to problems involving larger numbers and in an abstract form.  They were more successful this time around.  Students then worked in groups to complete this OpenMiddle problem.  They worked in this task for about 15 minutes using whiteboards in the process.  This was a quality activity that has students trying out multiple numbers to make the equation work.

 

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I’m looking forward to revisiting the distributive property when schools starts back up in January 2020.


Friday was our last day of school for about two weeks.  We’re officially on winter break, but it doesn’t feel like it yet.  I’m sure it’ll sink in on Monday when my alarm clock doesn’t go off at the normal time.

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