Jennifer Wilson and Vanessa Cerrahoglu

Having an extended period of time to teach a lesson can be an advantage in a problem-based classroom. Students and teachers can savor the questions that are asked. Activities can breathe in a way that they can’t in a shorter period of time. But questions about planning inevitably arise. We find ourselves asking questions like: Do I simply merge two lessons? What stays? What goes? How do we ensure that we engage our students in the right conversations that will prepare them for the next leg of the journey?

By Noelle Conforti Preszler and Kristin Gray

In the following activity, think about the students in your classroom. How might each respond?

What do you notice? What do you wonder?

This activity is the drafted warm-up of the first lesson in Grade 3, Unit 1: Introducing Multiplication. While we believe the structure of this activity — “What do you notice? What do you wonder?” — implicitly supports equity, it is the word each in the question at the top that has become central to our design of the IM K-5 Math curriculum.

By William McCallum

When I was a child, I used to get puzzle books out of the library. One of the puzzles was the twelve-coin problem, the most difficult of all coin weighing problems. My mother and I worked on it separately at the same time, and she solved it first. Some time later that evening she came into my room to find me in tears of frustration. Instead of helping me, she asked: “Do you want me to tell you the solution?” I said no and she left. I will never forget the joy when I finally figured it out.

Continue reading “What is problem-based instruction?”

Illustrative Mathematics’ high school curriculum is scheduled to be released this summer. This is an exciting time for Algebra 1, Geometry, and Algebra 2 teachers. I honestly am ready to take a job at a school just to have the opportunity to teach with this material (and everyone knows I am always dreaming of being back in the classroom). However, I want to bring light to a hidden gem I think not too many people are aware of that is also part of our high school materials.

Continue reading “Extra Supports for Algebra 1: The Gateway Resources”

By William McCallum

All of our curriculum here at Illustrative Mathematics is released under a Creative Commons Attribution (CC-BY) license, which allows anyone to “copy and redistribute the material in any medium or format” and to “remix, transform, and build upon the material for any purpose, even commercially,” on the conditions that attribution is given and that others’ rights under the license are not restricted. This is both super scary and super exciting.   Continue reading “Realizing the promise of open resources”

By William McCallum

What are extraneous solutions?

A while ago I wrote a blog post about solving equations where I talked about seeing the steps in solving equations as logical deductions. Thus the steps
\begin{align*}3x + 2 &= 5\\3x &= 3\\x &= 1\\ \end{align*}

are best thought of as a sequence of if-then statements: If $x$ is a number such that $3x + 2 = 5$, then $3x = 3$; if $3x = 3$, then $x = 1$. Continue reading “Truth and Consequences Revisited”

Q: What is the fastest way to get a heated debate going about some topic in the IM 6-8 math curriculum?

A: Show people this graph from Lesson 4 in Unit 8.5:

Multiplication is vexation,