Representing vs. solving; and missing-addend problems

I have seen many lessons in which the distinction between how to model or represent a story problem and how to solve the story problem get confused. This happens especially with story problems in which either the starting value or the change is unknown, a type of...

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...
The choice of numbers matters!

The choice of numbers matters!

I am looking at a lesson research proposal for grade 5 on division of decimal values by a whole number. The problem the team plans to use is 4.26 ÷ 3, and their goal is for students to discover that the same processes they use to model division with whole numbers...
Meaning of ‘3/4’

Meaning of ‘3/4’

How do we want students to understand a fraction such as 3/4? Yesterday I had the privilege of working with an elementary team that is starting lesson study for the first time. They decided their theme would be around developing persistence in their students through...