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## 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...

## Letting students in on the secret in a TTP lesson

The core of a Teaching Through Problem-solving (TTP) lesson involves presenting students with a problem that requires that they learn some new mathematics. For students to focus their energy productively, it helps them to know what that new mathematics is – at least...

## Making sure the problem context supports student learning

I had a delightful opportunity to join a planning meeting with a group of teachers from one of the schools we work with in Chicago. The team was working on a lesson for their 8-year old students about interpreting remainders in problem contexts. Here is how the...

## 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: Recently our team of...

## 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...

## Guide for facilitating post-lesson discussion

We offer this guide for facilitating a post-lesson discussion. Please take a look, and if you use it, please give us your feedback!

## 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...