Common Core Math – 3rd Grade

Common Core gets a lot a press these days and most of it results from the fact that it is not ‘what we are used to’.  When most adults went to school, math was a series of ‘rules’ and ‘processes’ that we executed in order to ‘solve’ a problem.  The premise behind Common Core is that students should develop and understanding of math concepts so that, when faced with problems of a complex nature, they have the mathematical understanding to ‘figure it out’ rather than relying on a series of steps that may not necessarily apply.  The ‘rub’ lies in that it makes what seems to be ‘simple math’ into a complex task that makes no sense to the parents at home trying to help with homework.  Regardless of your feelings, here’s some information that may help parents understand the standards and provide some insight as to how to ‘help my kid with his homework’.

The standards: Operations and Algebraic Thinking Strand


Represent and solve problems using multiplication and division.  So…

  • 3 x 5 = 15…..not because we memorize that fact, but because we need to understand that this represents 3 groups, each containing 5 objects.
  • 15 ÷ 5 represents 15 objects shared amongst 5 groups equally…how many are in each group?
  • As third graders, the students are expected to be able to ‘do’ the above for any problem involving a total up to 100.  This includes using drawings to represents the groupings, arrays and equations where a number is missing (for example:  5 x ___ = 15)

This standard is why you see your child drawing arrays (columns and rows of objects) to represent the groups of objects.  Why not just memorize the facts?  Because rote memorization does not provide understanding.


Understand the properties of multiplication and division and the relationship between multiplication and division

  • 4 x 6 = 24 and 6 X 4 = 24.  So, this explains why your child is asked in his homework to ‘draw the arrays’ which show that this is true.  Students are asked to ‘prove’ that 4 x6 = 24, not just ‘know it’.
  • 3 X 5 X 2 can be worked out by adding together 3 x 5 = 15 and then multiplying the 15 x 2 to equal 30.  
  • 3 X 5 = 15 and 3 X 3 = 9, so 3 X 8 = 24.  Understanding that this ‘works’ explains why your child is asked to draw those arrays and combining them to see that when two arrays come together they can ‘prove’ that 3 x 8 = 24.
  • When posed with 15 ÷ 5 = ____, we don’t ‘know the answer’ because we memorized it, but because we know that the problem represents 5 x ____ = 15    The process helps students understand that division problems are just multiplication problems with a missing number (relationship between multiplication and division)


Math Fluency 

This is the standard that expects that all 3rd graders can multiply all one-digit numbers, from memory,  with fluency, and, since they understand the concepts of multiplication, they will be able to fluently divide, as well.


Solve problems using the 4 operations, and identify and explain patterns

  • Solve two-step problems and be able to represent those problems using equations.  Students should be able to begin using letters to represent the unknown quantities.  So, given the problem:

Sally is 4 years older than Robert.  If Robert is 12, how old is Sally?

The student should be able to write that S = R + 4. So, if Robert is 12…

S = 12 + 4, and so, Sally is 16. 


  • This standard also expects that 3rd graders can begin seeing patterns in numbers and can explain ‘why’ it is true.


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