In continually moving forward with our vision of creating a world where learners know, use and enjoy mathematics, the Illustrative Mathematics team is so excited to announce the launch of our official blog! Continue reading “Welcome to the new Illustrative Mathematics blog!”

# 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”

# Fraction & Decimal Number Lines

*By Kristin Gray*

Recently, our 3rd, 4th, and 5th grade teachers had the opportunity to chat math for 2 hours during a Learning Lab held on a professional development day. It was the first time we had done a vertical lab and it felt like perfect timing as 3rd and 4th grade would soon be starting their fraction unit and 5th would be entering their decimal unit. Prior to the meeting, we read the NCTM article, “Identify Fractions and Decimals on a Number Line” by Meghan Shaughnessy, so we started the meeting discussing ideas in the article. We then jumped into playing around with clothesline number lines and double number lines, discussing what they could look like at each grade level based on where students are in the fractional thinking. Continue reading “Fraction & Decimal Number Lines”

# 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”

# Fraction division part I: How do you know when it is division?

*By William McCallum and Kristin Umland*

In her book Knowing and Teaching Elementary Mathematics, Liping Ma wrote about this question and how teachers responded to it:

Write a story problem for $1 ¾ \div ½$.

[Pause here and think about the answer yourself.] Continue reading “Fraction division part I: How do you know when it is division?”

# 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”

# Ways of thinking and ways of doing

*By William McCallum*

Somewhere back in days of Facebook fury about the Common Core there was a post from an outraged parent whose child had been marked wrong for something like this:

$$

6 \times 3 = 6 + 6 + 6 = 18.

$$

Apparently the child was supposed to do

$$

6 \times 3 = 3 + 3 + 3 + 3 + 3 +3 = 18

$$

because of this standard: Continue reading “Ways of thinking and ways of doing”