Place Value & Graphing 

We have been focused on working with two and some three digit numbers and recognizing the value of each digit within a number.  Students have also worked on different ways to represent the same number.  For example, they have shown multiple ways to show the number 137 by using one hundred, three tens, and seven ones.  They know they could do with one hundred, two tens, and seventeen ones.  Understanding these different ways to represent the same number is the foundation for our later work with addition or subtraction that requires regrouping (the borrowing or trading technique from when we were in school).

We have worked heavily with addition and subtraction with two digit numbers with a strong focus on how we found our answers.  Students could show their thinking (their work) with pictures, equations, or number lines.  We are working to find more efficient ways than using pictures.  As we work with larger numbers, heading towards 4 digit numbers, we do not want to be bogged down with drawing large numbers.  Students are transitioning to more efficient methods.  We have also focused on writing equations that match the problem.  This means we are showing our understanding of what the problem is asking of us.  At this point in our work, most of our subtraction problems are written as addition equations with a missing addend.  For example, 100 - 25 = ____ if often written as 25 + ___ = 100.  Later, students will become more fluent with using either equation.

An interesting note about equations!  Two of Muddy Brook's teachers (Jessic Redman, 4th grade and Mary Berle, 3rd grade) are part of a state committee to work on the math MCAS.  We have learned that the state is not accepting the vertical alignment of numbers as an equation.  It could be a strategy to work with numbers; however, if a problem asks for an equation to be written it must be written horizontally.   We have carried over this expectation in our classrooms in effort to better prepare students for both the MCAS and their future in math.

We have been working with pictographs and line plots.  Pictographs can be challenging because students often forget to look at the key to see what the value is of each picture used in the graphing.  Pictographs usually use one picture to represent 2, 5, or 10 items in 3rd grade.  The value of the picture is not limited to those numbers, it just the common place for our work at this age.  Line plots are a way to graph numerical data.  We have collected data on how many pockets we were wearing on a given day, then taken that data and displayed it in a line plot.  The line plot allows us to analyze the data more easily because the data in organized sequentially and visually.  The challenge is in using precise, accurate language to describe the data.