September 9, 2019

It is always fun to do a Number Talk with Preservice Teachers!!!!
I want them to get really versed and comfortable with it. I want them to recognized each others
strategies and pull out the various domains and properties of mathematics.

The NT for this week was a little more challenging from the week before. Again, we are using
dot images to build multiplicative strategies and to strengthen algebraic thinking like order of operations and the properties.

This first image included 15 dots. This one was pretty simple. You can subitize 5 because of the prior knowledge with dots on dice and playing cards.  PTK said she saw 5+5+5.  PTE skip counted by 2 until 12 then counted on until she arrive at 15.  PTC said he multiplied 3x5 because he saw three groups of 5.


The second images was a little difficult. PTC said she saw 5 +4 +5. Then added left to right. 
PTK said she saw 5 +3+3+3. Then added left to right. 

The third image was a doozy. PTK said she saw 5 x 3+3+3. She multiplied first then added 3 to get 18. Then she added 3 to 18 and got 21.  PTE saw 8 +5 +8. Again added 8+5 first. Then she added 8 to 13 and got 21. PTC saw three groups of 5 and then 6 or 3 x 5 + 6. He multiplied 3 x5 and added 6 to  15.

Themes: All three PT showed some multiplicative reasoning. This included skip counting like PTE did in the first image and knowing three groups of five like PTC in  images one and three.  PT relied heavily on additive reasoning. This evident in all three images. The goal is to provide opportunities for PT to develop higher reasoning strategies and naturally develop the properties of addition and multiplication. These two strategies can solving problem more flexibly and efficiently. 




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