## Tuesday, January 31, 2017

### Fraction Study 2017 Begins

It's difficult to employ the kind of project based math classroom without extended support since educators are expected to teach such a large amount of content including lots of vocabulary in the math class. Even though the common core limited the number of concepts for each grade level, it's still a lot to teach between September and April tests. Also there's a depth involved in this teaching that takes time and the numbers of students make it difficult to personalize to meet the many needs.

Greatest Common Factor
Yet, with all that said, I hope to move as well as I can towards a more differentiated, project base math class. I had hoped to teach this lesson yesterday, but a needed review of solid figures model making took precedence, but today we'll try a mini version as we step into fraction study. I'll begin by reviewing factors and finding common factors, then the greatest common factor. We'll use venn diagrams, lists, and discussion as part of the introduction.

After that  I'll have students work in like-skill, friendly groups to figure out which numbers between 0-50 share the most factors. As students embark on that investigation, I'll encourage them to use some or all of the following problem solving strategies:

• make charts
• look for patterns
• consider a systematic strategy so you don't miss any numbers
• consider eliminating some numbers right away (which numbers and why)
• can you think of an algorithm or set of steps to easily figure out the numbers between 50-100 that share the most factors?
As students tackle the problem, I'll observe how various groups attack the problem. I'll watch for team skills, mathematical thinking, use of structure such as charts and lists, and systematic process.

Lowest Common Multiple
Tomorrow we'll look for lowest common multiples (LCMs) by listing 10 multiples for each number from 1-25. Then we'll highlight common multiples. After that we'll look for patterns, trends, and rules related to this with the questions, "What do you notice?"

Practice and Review
On Wednesday we'll have a catch-up day when students organize supplies including scissors, tape, colored pencils, sharpies, and sharpeners for upcoming fraction study and review the concepts introduced with online activities.

Fraction Vocabulary and Models
On Thursday and Friday, we'll review fraction language and models.

Fraction Operation
The following Monday, I'll introduce students to fraction operations using story and models.