Mathematical Thinking: Problem Solving for Grades 4-5

This class is for students in Grades 4-6 who are working on a 4th grade level or above.  To be successful in this class students should be able to:
-fluently add/subtract large numbers
-add/subtract fractions
-multiply 3-digit numbers by 2-digit numbers
-divide 3 digit numbers by 1-digit numbers

This is an ONGOING CLASS, meaning students can join and leave at any time.  However, students who join for multiple weeks build confidence and important problem-solving skills through repetition and collaboration with peers. 

While this class can supplement ANY math program, it is a natural fit for anyone currently in  a Singapore Math program.  I pull a lot of problems and strategies from the Dimensions Math Curriculum. We will go over some word problems from the 4A/B and 5A/B workbooks, however it is NOT necessary for any student in this class to purchase those workbooks.  All problems will be posted separately on the virtual whiteboard or in the classroom.  This class pairs well with my Mathematical Thinking 4A, 4B, 5A, and 5B courses. 

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APPROACH TO PROBLEM SOLVING
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Problem solving is not always a linear process.  Students must first make sense of the problem and then choose the best strategy to solve it.  And of course, there is not just one way to approach any problem.  Each problem we work through is different from the last.  I do this to help kids focus on the PROCESS of problem-solving, as opposed to giving them "tricks" for solving one particular type of problem.  For example, we don't work on problems that all focus on addition, where students just learn to pull out the numbers in the problem and add them together.  Instead we might have a missing addend problem and then one that focuses on multiplication and then one that deals with fractions.  In this way, students learn to visualize what is happening in the problem and start to think about what they need to do to attack the problem.  

In this class, I help students visualize the problem by having them draw, use bar models, or create charts.  Once they wrap their heads around the problem, we work through it together as a class as I build on THEIR ideas and guide them to a solution.   Sometimes students have no idea how to begin.  Sometimes they get stuck on a strategy that won't lead to a solution.  Working through these challenges is all part of learning how to problem solve.  One of the major components in this class is for students to explain their thinking.  In this way, students both learn from each other and become aware of their own mathematical thinking as they solve problems.   

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STRUCTURE OF CLASSES
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In each class, students work through 2-3 different problems together, which are chosen based on the needs and level of the students in the class. Though the problems change from week to week, the structure generally remains the same. 

1- Students are presented with a problem posted on the whiteboard.  Each problem is different from the previous one, because the focus is on the PROCESS of problem-solving, not learning an algorithm for solving them.  
2- Students spend a few minutes drawing or writing information they think is important to the problem.  
3- I pose the questions "What do we know about this problem?" and "What do we need to know?"
4- Students suggest ways of solving while I organize and annotate their ideas on the whiteboard.  This guided discussion is key to helping them learn to solve word problems, because working through challenges helps them gain new ideas to try on the next problem.  

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SCHEDULE OF CLASSES
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Classes are ongoing and will meet every week as scheduled below.   There are no topics that we focus on each week, since we are instead focusing on the processes used with different types of problems.  

SUMMER 2024: August 1 - September 26

FALL 2024: October 17-December 11

WINTER 2025: January 6 - March 14

SPRING 2025: April 3 - May 29