Dividing with Fractions

Rules that Expire

Vocabulary:

MVIMG_20190127_122542

As students explore math they begin to make rules, and they expect their work to obey these rules. As students progress they bump into math where their rules does not work anymore. This is an opportunity to explore how to alter the rule to accommodate this new information.

A rule that expires this week is that division always makes your dividend smaller. Students will discover that 5 ÷ 1/3 = 15. This quotient will initially be a bit disorienting as it breaks a rule they have created.

Students can make sense of this by exploring what 5 ÷ 1/3 is asking them to do. This expression is asking them to find out how many 1/3s there are in 5 wholes. This connects to the work you did with them last week converting fractions. An example of a model you may see is below:

MVIMG_20190127_123410

In this example 5 was broken into thirds, and then the thirds were counted.

At this point we are not yet teaching an algorithm, but we can ask students to start looking for patterns they see. The algorithm will be further explored in coming posts.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s