Friday, July 15, 2016

Teaching and Learning Divisibility Rules

Important Knowledge, Concept, and Skill: Factors, Multiples, and Divisibility Rules

Introduction: First Impressions
The introduction to a learning experience can last anywhere from 5-15 minutes. It's meant to wake students up to the topic, get them thinking, and make the lesson "sticky" or brain-friendly by connecting the concept to something they know, are interested in, and/or excited and even alarmed by.

"What does a first impression mean?' A first impression is what you notice first.

Students will likely list a number of descriptors of a first impression. Then say what can we know about a person from a first impression? And after that, can we know all about a person by a first impression, essentially, "can we judge a book by its cover?"

Then hold up the number above and ask, what's your first impression of this number--what do you notice? List all that students notice.

After that ask, "What can we know about a number just by looking at it?" And after that short discussion, can we know everything about a number by just looking at it?

After the introduction, share the rationale for the lesson. 

"Numbers are ingredients for mathematical thinking and process. The more you know and understand numbers, the better you'll be able to work with those numbers to describe situations, solve problems, and reason mathematically. Learning about the divisibility rules will help you to understand numbers better. What do you think the term "divisibility rules" means?" Take some ideas, then show the definition card.

One definition you may use is this one:

A Divisibility Rule is a way to figure out the factors of a whole number without performing division, usually by examining the digits.

Teaching and review of multiples and factors is an engaging and valuable focus of the fifth grade math curriculum. Though this focus is more closely matched to fourth grade standards, it's integral to fifth grade standards related to numbers and operations, fractions, measurement, and more.


Day One
Once you've introduced the learning experience and main definition, it's time to explore. A good way to explore is to teach and play Factor Captor online or off. Encourage students to think about their "first impressions" of numbers as they play. Start by playing a simple version of the game with the whole class, then give students time to play at the level they desire with friends.

At the end of the time available gather students, and ask what "first impressions" of numbers they had as they played. Also ask them to share any strategies, patterns, or other observations they made as they played the game.

Days Two and Three (an more possibly)
Review the definition of a divisibility rule, then review the rules below. 

image reference
Watch the video below and singing the song. After that students can practice using this divisibility rules exercise and chart above with classmates.

Once that's complete, students will be ready to play the Factor Game game again. You may even want to encourage students to play the game at home with friends and family members to practice more. At the end of the lesson, add to the chart students made yesterday about game the strategies, patterns, and number observations they made during the game. Ask students if they used the divisibility rules while they played and if those rules helped them to play better.

At this point, you may want to sponsor a Factor Captor Tournament to give students plenty of practice. This tournament provides students with the opportunity to teach one another, practice, and deepen their knowledge and skill. The tournament also provides the teacher with lots of time to coach students with this knowledge, concept, and skill as well as others.

Day Five: Learning-to-Learn Mindset, Behavior, and Science Connection
Before students assess their skills, engage in a conversation about how students can move this knowledge from "short term memory" to "long term memory." This is a good opportunity to teach students about the limited space and accessibility our short term memory has while our long term memory ensures, for the most part, that facts, figures, and concepts are well rooted and easily accessed. You may ask students to think of information they never forget and facts/figures that are easily forgettable, and after that, the students and you can list ways that help us to learn information well--ways to embed that information into our long term memory. Your list will likely include learning tasks such as writing notes, making flash cards, testing one another, making an mini poster or infographic, turning the concept into an image, singing a song, creating a rhyme or poem, acting it out, and teaching the concept to others. Give students time to choose a strategy, work with friends, and learn/study divisibility rules.

Following that, it's time for a quick online or offline assessment like this example. I suggest using Google forms now that they have the new quiz feature embedded right on the forms. That's a quick way to create an assessment to see who knows their divisibility rules and who still needs to study. Allow students to take the assessments as many times as needed until they grasp the learning. Provide extra support where and when necessary.

Blended Learning Resources

Related Videos:
These were a couple of great videos that added to the teaching.