IM Certified® Blog

Fun With Zooming Number Lines in Grade 8

Fun With Zooming Number Lines in Grade 8

By Charles Larrieu Casias The number line is an anchor representation that threads through the entire middle school curriculum. For this blog post, I want to focus on a creative use of the number line in grade 8 to explore...

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Untangling fractions, ratios, and quotients

Untangling fractions, ratios, and quotients

By William McCallum In everyday language, $\frac{a}{b}$, $a\div b$, and $a : b$ are all different manifestations of a single fused notion. Here, for example are the mathematical definitions of fraction, quotient, and ratio...

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On Similar Triangles

On Similar Triangles

By Ashli Black The fact that a line has a well-defined slope—that the ratio between the rise and run for any two points on the line is always the same—depends on similar triangles. (p.12, 6–8 Progression on Expressions and...

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NCSM and NCTM 2018 Roundup

NCSM and NCTM 2018 Roundup

It was great to see so many of you at NCSM and NCTM. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below. We enjoyed the conversations we had with those of you that are using the IM 6–8...

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Time to Noodle

Time to Noodle

By Kate Nowak This task is the first part of the culminating lesson of unit 2 in grade 8, which is about dilations and similarity. (You will need to create a free teacher account to open the link.) It is a variation on the...

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What is an instructional routine?

What is an instructional routine?

By William McCallum and Kate Nowak People use routines for all kinds of things. Routines give structure to time and interactions. People like structure. When a child comes home from school, there might be a routine. She...

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Learning Goals and Learning Targets

Learning Goals and Learning Targets

By Jennifer Wilson One of your students is asked, “What are you learning about today in class?” How does your student respond? “Nothing” “Math” “The questions on this worksheet” “Deciding if two figures are congruent”...

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Warm-up Routines With a Purpose

Warm-up Routines With a Purpose

By Kristin Gray As a teacher, curiosity around students’ mathematical thinking was the driving force behind the teaching and learning in my classroom. To better understand what they were thinking, I needed to not only have...

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Adapting Problems to Elicit Student Thinking

Adapting Problems to Elicit Student Thinking

By Jody Guarino As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical...

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A Fraction Unit Does Not Always Begin With Lesson 1

A Fraction Unit Does Not Always Begin With Lesson 1

By Jared Gilman As I sat down at my local coffee shop to plan my upcoming 5th grade unit on fractions, a wave of dread spread across my body. I started having flashbacks to last winter, when my students’ frustrations with...

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Why We Don’t Cross Multiply

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...

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Using the 5 Practices with Instructional Routines

Using the 5 Practices with Instructional Routines

By Robin Moore As a coach, how can I help teachers structure their lesson-planning in order for students to unpack their mathematical understandings? This question is always at the forefront of my mind as I reflect on my...

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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...

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How the 5 Practices Changed my Instruction

How the 5 Practices Changed my Instruction

By Alicia Farmer I am the type of teacher you want on your teaching team. I am the person that can remember vast amounts of details, predict potential obstacles, and meet any and all deadlines.   My organized personality is...

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Not all contexts have the same purpose

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...

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Welcome to the new Illustrative Mathematics blog!

Welcome to the new Illustrative Mathematics blog!

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! Our blog will be...

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Info Gap Cards: The Hidden Gem

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...

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Fraction & Decimal Number Lines

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...

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Respecting the Intellectual Work of the Grade

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,...

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Reflection & Discussions in Grade 8, Part 1

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...

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Ways of thinking and ways of doing

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

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Misconceptions about Multiple Methods

Misconceptions about Multiple Methods

By William McCallum You may have noticed that I am back to publishing regular blog posts! My goal for now is a blog post every second Wednesday. I am now also trying to answer forum questions promptly. I want to thank the...

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The Structure is the Standards

The Structure is the Standards

Co-authored by Bill McCallum, Jason Zimba, Phil Daro You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will...

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