Tuesday, February 21, 2017

Semester Two Learning Outcomes

Below you will find the Semester Two intended learning outcomes for all subject areas.  Click on the links to view and download the documents.  If you have any questions about these learning outcomes, please contact your child's homeroom teacher, our PYP Coordinator (Michael Hughes), or our Elementary Principal (Sandra Mulligan).

Thursday, February 9, 2017

What are these new multiplication methods?

After deeply exploring and understanding how multiplication and division work, third graders have started to learn different methods of multiplying multi-digit numbers. If you've glanced at your daughter's work, however, you might notice that her methods are probably different from the way you learned multiplication when you were in school. So...what's up with these strange, new multiplication methods?



First, it's helpful to think of the advantages of "traditional" multiplication. These methods are prominently used for two main reasons: speed and efficiency of space. That is, you can multiply quickly and not take up too much paper. For students learning to multiply for the first time, we have a more important goal: understanding.

Great mathematical thinkers don't simply memorize facts and algorithms. Great mathematical thinkers are able to think about numbers flexibly, possessing a deep understanding of place value and the base-10 system. They can take numbers apart and put them back together. They can solve problems in more than one way. We call this number sense, and students who have it will be in excellent position for future mathematical success.

So, rather than multiplying quickly and efficiently, we break numbers down. For example, see how Yumi and Noushin show their knowledge of place value and extended facts with the "partial products" method.



Check this link for an ever-growing list of examples. It gets trickier when you multiply 2 digits by 2 digits, but the "window method" helps students to take numbers apart and put them back together. Yuka explains the process with great clarity:


This method has gained popularity amongst students, click here for a full list of tutorials. Eventually, students can multiply 2 digits by 2 digit with the "partial products" method, which Miyu enthusiastically explains here: 


Another method you might not be familiar with is the "lattice method". While it's not as helpful for breaking down place value, many third graders enjoy using it as well. Lucy shows how it works here:



As each student's number sense develops, we can move towards applying their mathematical skills to problem solving and real life mathematical challenges. We will keep practicing different forms of computation; however, our next unit of math will focus on geometry (shape and space).