Why We Don’t Cross Multiply

By Kate Nowak
(co-authored with Kristin Gray)

“Ultimately, the goal of this unit is to prepare students to make sense of situations involving equivalent ratios and solve problems flexibly and strategically, rather than to rely on a procedure (such as “set up a proportion and cross multiply”) without an understanding of the underlying mathematics.”
Illustrative Mathematics 6–8 Math, grade 6, unit 2, lesson 12

Continue reading “Why We Don’t Cross Multiply”

Vocabulary Decisions

By Bowen Kerins

A wide-ranging team worked together to develop the Illustrative Mathematics Grades 6–8 Math curriculum. Many of the authors were and are experienced teachers of Grades 6–8, while others are experienced high school teachers.

My own experience is as a high school teacher, then a high school curriculum writer. One of the ways the IM team’s experiences led to a higher-quality product was the discussion around language and terms used throughout the three grades. Continue reading “Vocabulary Decisions”

Not all contexts have the same purpose

By Nik Doran

We sometimes use familiar contexts to understand new mathematical ideas, and sometimes we use familiar mathematical ideas to understand what is going on in a context. We do both of these things by looking for parallels between the familiar and unfamiliar structures. I want to highlight two places this happens in the Illustrative Mathematics 6–8 Math curriculum. (It’s easy and free to sign up to see the teacher materials.) Continue reading “Not all contexts have the same purpose”

Info Gap Cards: The Hidden Gem

By Sadie Estrella

May 2016 seems so long ago. I actually had to look it up on a calendar because I really thought it was more than 1.41666years ago. That was when I officially started this journey with Illustrative Mathematics. Our kickoff meeting was in Chicago. I was pumped to learn about this new adventure I was embarking on (and honestly quite scared too). One of the things I distinctly remember taking away from that meeting was this idea of an Info Gap. I hadn’t learned much about math language routines just yet but this Info Gap thing sounded really cool. Continue reading “Info Gap Cards: The Hidden Gem”

Respecting the Intellectual Work of the Grade

By Kate Nowak

A thing that I think we did really well in Illustrative Mathematics 6–8 Math was attend carefully to really deep, important things that adults that already know math can easily overlook. For example, what does an equation mean? What does it mean for a number to be a solution to an equation? What does it mean for two expressions to be equivalent? (This is an example of the crucially important foundational understanding that gets short shrift when we rush kids through middle school math.) Continue reading “Respecting the Intellectual Work of the Grade”

Assessment Principles in Illustrative Mathematics 6-8 Math

By Bowen Kerins

A wide-ranging team worked together to develop the Illustrative Mathematics Grades 6-8 Math curriculum. As Assessment Lead, it was my responsibility to write and curate the Shared Understandings document about assessments we used throughout the writing process, and I thought you might be interested to read some of the key features.

This quote drives a lot of the ideas about assessment:

“You want students to get the question right for the right reasons and get the question wrong for the right reasons.” – Sendhil Revuluri Continue reading “Assessment Principles in Illustrative Mathematics 6-8 Math”

Reflection & Discussions in Grade 8, Part 1

By Ashli Black

Woo, blogging! As I start work on high school curriculum, I thought I would go back and revisit the grade 8 units that I’ve spent the past 18 months working on and share some of my favorite things. This gives me a chance to think about what sorts of things I really want to keep in mind as I write new stuff and gives folks a way to take a peek “under the hood” at how some activities came about. A new curriculum can be a daunting thing to jump into, so hopefully this is a friendly way to dip toes in. Let’s start in grade 8, unit 1, shall we? Oh, and some of the links are going to be to the online curriculum, which you’ll need to sign up for. Signing up is free and you can do that here.

Continue reading “Reflection & Discussions in Grade 8, Part 1”

Truth and consequences: talking about solving equations

By William McCallum

The language we use when we talk about solving equations can be a bit of a minefield. It seems obvious to talk about an equation such as $3x + 2 = x + 5$ as saying that $3x+2$ is equal to $x + 5$, and that’s probably a good place to start. But there is a hidden assumption in there that the equation is true. In the Illustrative Mathematics middle school curriculum coming out this month we start students out with hanger diagrams to represent such equations: Continue reading “Truth and consequences: talking about solving equations”

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