Great article on division with remainders

One of Chicago’s Lesson Study Leaders, Joshua Lerner, wrote a terrific article in NCTM’s journal Mathematics Teacher: Learning and Teaching in PK-12. It is titled, “Recommendations for Teaching Division with Remainders.” From the introduction:...

Fractions as numbers vs. fractions as ratios

A grade 4 team was recently considering the following task for a lesson in which they hoped to have students make a connection between fractions and decimals: What would you say about this? I wrote them two emails about it. First email: What would be the purpose of...

Facilitating a post-lesson discussion

In response to multiple requests, I have finally written up this guide for facilitating a post-lesson discussion, which you can also find on our resources page. I will say that cultivating a good post-lesson discussion tends to be easiest if the planning team has a...

Learning goals should describe cognitive change

A surprisingly difficult but critically important part of designing a lesson is establishing the learning goals. Many teachers write learning goals in the form of behavioral outcomes: “Students will be able to…” Frequently this is what their administrators want, and...