Connecting the Dots

Happy Snowy Halloween! Here in Boston, we just had our first snow of the year yesterday. It feels like Mother Nature is reminding us about the upcoming winter.

We would like to take the chance to share some thoughts about “Connections” today.  

A math lesson should not be questions after questions. It is important to take a step back once in a while, to connect the dots between what we are doing today, and how it relates to the big idea.

For example, in Grade 2, students learned about distributive property for multiplication for 3 and 4. In doing 7 x 3, we break 7 into 5 groups and 2 groups, so 7 x 3 = 5 x 3 + 2 x 3 = 15 + 6 = 21

We are focusing on the structure, and not the answers, so we can extend the idea to

  • larger and more confusing numbers (eg 7 x 6 = 5 x 6 + 2 x 6 = 30 + 12 = 42), skip counting can often be tedious and confusing for some kids
  • algebraic structure later, eg (x + y) a = xa + ya

Research has shown that students who are able to see connections will see each incremental idea as an extension, rather than disjointed topics that require more effort. eg subtraction can be seen as the missing addend, factorization is the opposite of distribution, etc. So, continue to remind students to “connect the dots” along the way!

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