# Grades 6–8 Math

## Building Equitable Learning Environments for Each Student

Mar 22, 2021

By Danielle Seabold All students can be successful in mathematics. For most mathematics educators, we lean into this. We believe that all students can learn mathematics, that they can be successful. However, as we focus our...

## What Does It Mean to Use Mathematics?

Feb 22, 2021

By William McCallum Our vision at Illustrative Mathematics is a world where all learners know, use, and enjoy mathematics. In my last post I picked up that first verb and talked about what it means to know mathematics. In...

## IM 6–12 Math: Grading and Homework Policies and Practices

Feb 9, 2021

By Jennifer Willson In my role at IM, working with teachers and administrators, I am asked to help with the challenges of implementing an IM curriculum. One of the most common challenges is: how can we best align these...

## What does it mean to know mathematics?

Jan 4, 2021

By William McCallum A world where all learners know, use, and enjoy mathematics. Perhaps the most mysterious verb in the IM vision—a world where all learners know, use, and enjoy mathematics—is the first one: know. Knowing...

## Reading Graphs is a Complex Skill

Nov 4, 2020

Newspapers are full of graphs, far more than 10 or 20 years ago. Indeed, I have a graph to show that! (Source, Priceonomics) And yet I wonder how often readers see graphs as pictures illustrating a point, rather than as...

## Using IM’s Distance Learning Resources to Create a Hybrid Learning Plan

Sep 30, 2020

By Lorie Banks Trying to plan for the 2020–2021 school year has been like trying to fly the airplane while building the wings. I am a career educator—a middle grades math teacher in an urban district in Western...

## Equitable Teaching Practices in IM K–12 Math

Aug 11, 2020

by Tina Cardone The vision of Illustrative Mathematics is to create a world where learners know, use, and enjoy mathematics. This raises the question: Which learners? And what role do the authors of a curriculum play in...

## English Learners and Distance Learning: Math Language Routines

Jul 27, 2020

by Vanessa Cerrahoglu, Jennifer Wilson, and Liz Ramirez We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful...

## New IM 6–12 Resources for Addressing Unfinished Learning and Engaging Students in Distance Learning

Jul 15, 2020

by David Petersen and Kate Nowak In our previous post, we described how we are thinking about planning for next fall. We are also creating some new resources to support users of IM K–12 Math in the fall. Some of this is to...

## Coming Together Around Distance Learning

Jul 7, 2020

By William McCallum I can't imagine what it must feel like right now to be a teacher facing the uncharted territory that is the coming school year. Will I be teaching 100% online, or have some face-to-face interaction with...

## English Learners and Distance Learning: Compare and Connect

Jun 25, 2020

By Vanessa Cerrahoglu, Jennifer Wilson, and Liz Ramirez We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful...

## English Learners and Distance Learning: Co-Craft Questions

Jun 15, 2020

By Jennifer Wilson and Liz Ramirez We envision creating a world where learners know, use, and enjoy mathematics. Knowing and using math goes beyond calculating and evaluating. We create purposeful opportunities for students...

## English Learners and Distance Learning: Clarify, Critique, Correct

Jun 8, 2020

By Jennifer Wilson and Liz Ramirez We want to acknowledge that we are all in different situations that shape how we respond to the call to adapt our teaching to fit a model for distance learning. This impacts the access we...

## Looking Ahead to 2020–21 in IM 6–8 Math and IM Algebra 1, Geometry, and Algebra 2

May 14, 2020

By David Petersen, Lead Curriculum Writer and Kate Nowak, Director of K–12 Curriculum Strategy This school year has been strange and stressful, and there is uncertainty about what next year will look like. Due to school...

## English Learners and Distance Learning: Enhancing Access

May 3, 2020

By Liz Ramirez Which students are experiencing success in today’s “distance learning”? What barriers do other students face? While virtual learning platforms have made it possible for some live instruction to continue...

## Thoughts on the Back-to-School Problem

Apr 27, 2020

By William McCallum One of the consolations in these difficult times has been tweets and Youtube videos of parents discovering just what it takes to be a teacher. Maybe it takes a crisis like this to restore the respect...

## IM Talking Math 6–8: Resources for Weekly Re-engagement

Apr 8, 2020

By IM 6–8 Math Team This week, IM is launching a new resource to support students and teachers with distance learning. Each week we will publish an open-ended prompt or image that invites math conversation, and a series of...

## Planning for Learning in Spring of 2020

Mar 23, 2020

Some schools are sending home printed packets and establishing teacher office hours by phone. Some are conducting their regular class schedule, but online. And lots are doing something in between. We understand that it is...

## Aggregated Support for the IM Math Community in Spring 2020

Mar 14, 2020

We want to share our deepest gratitude for the work each of you has been doing to protect yourselves, your families, your students, and your school communities, as you face hard decisions about how to support students while...

## Links to Resources for Shifting Instruction Online

Mar 14, 2020

First and most importantly, take care of yourself, your family, and your students. That might not look like doing math, or it might. To the extent that it’s useful, we have curated this list of resources recommended by our...

## Links to Math Resources for Caregivers

Mar 14, 2020

Here is a collection of links the content team here at IM has used with our own students and kids to start mathematical conversations, play math games together, explore new topics, come up with projects, and have fun. There...

## Rethinking Instruction for Lasting Understanding: An Example

Feb 25, 2020

By Kate Nowak How do we help our students build mathematical understandings that endure past the unit test? If we want students to construct strong, reliable bases of mathematical knowledge, our instruction needs to do more...

## Using Diagrams to Build and Extend Student Understanding

Nov 25, 2019

By Jenna Laib and Kristin Gray Take a moment to think about the value of each expression below. $\frac{1}{4}\times \frac{1}{3}$ $\frac{1}{4}\times \frac{2}{3}$ $\frac{2}{4}\times \frac{2}{3}$ $\frac{3}{4}\times...

## The 5 Practices: Looking at Differentiation Through a New Lens

Nov 21, 2019

By Catherine Castillo Our district had seen a downhill trend in standardized test scores in mathematics. This forced us, as educators, to take an intentional look at our teaching practices. The past few years have been an...

## Using Instructional Routines to Inspire Deep Thinking

Oct 13, 2019

We want students to think about math deeply. Creatively. Analytically. Instead, what often happens is that students race towards quick solutions. So what can we do to support this other kind of thinking in class—the slow,...

## Which Vertex is the Center of a Triangle?

Sep 23, 2019

By William McCallum I am sometimes asked what is the secret to the success of our curriculum, what is the special property that sets it apart from other curricula. That question is like the one in the title of this blog...

## Updates to Supports for Students with Disabilities and English Language Learners in IM 6–8 Math

Sep 15, 2019

At Illustrative Mathematics we are committed to creating a world where learners know, use, and enjoy mathematics. We believe that every student can learn grade-level mathematics with the right opportunities and support. Our...

## Preparing for the School Year, Updated with Tips for Staying on Pace

Aug 30, 2019

Last year, we put together some reading to help people get started planning their year with IM 6–8. Now, we have another year’s worth of blog posts to choose from, plus a shiny, new high school curriculum! So once again,...

## Building a Supportive Home/School Partnership

Aug 25, 2019

While families arrive with different school experiences and perspectives on what “doing math” means, they often share common questions: What do I need to know to set my child up for success in math this year? and How can I...

## Co-Creating Classroom Norms with Students

Aug 2, 2019

Establishing norms is critical to creating an environment where all students see themselves as knowers and doers of mathematics. Reflecting on the Illustrative Mathematics mission statement, Creating a world where learners...

## Explicit Classroom Norms to Teach Kids How to Learn From Solving Problems

Jul 29, 2019

This blog post is the fourth in a series of four blog posts exploring the student experience of problem-based learning. The first three posts are available here: (1) “How Do Students Perceive Problem-Based Learning?” (2)...

## Concrete Representations that Give Students a Way to Get Started

Jul 18, 2019

This blog post is the third in a series of four blog posts exploring the student experience of problem-based learning. The first two posts are available here: “How Do Students Perceive Problem-Based Learning?” and “Inviting...

## Realizing the promise of open resources, part II

Jun 17, 2019

By William McCallum In my first post on the topic of realizing the promise of open educational resources, I described the IM Certified program. Our partners offer multiple versions, including a free online version and...

## The Power of Small Ideas

May 21, 2019

By William McCallum, IM President Big ideas are popular in mathematics education, and you can find many lists of big ideas on the web. Some are more thoughtful than others, and I can see how some might be useful for...

## Designing Coherent Learning Experiences K-12

May 7, 2019

By Kristin Gray, Director of K–5 Curriculum & Professional Learning One challenge in curriculum design is considering all we know and believe to be true about math teaching and learning and translating that into...

## NCSM NCTM Recap

Apr 15, 2019

Illustrative Mathematics It was great to see so many of you at NCSM and NCTM in San Diego. 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...

## What is a Measurable Attribute?

Apr 8, 2019

By Kristin Umland,VP Content Development A great conversation I had with the IM elementary school curriculum writing team got me thinking: What is a measurable attribute? That is, when given an object, what can we measure...

## Representing Subtraction of Signed Numbers: Can You Spot the Difference?

Mar 2, 2019

By Greta Anderson & Patti Drawdy, IM Certified Facilitator I read the lesson three times through, but was still unsure why the number line below shows $3 - 7$. My aha moment arrived courtesy of the grade 1 standards....

## Planning Lessons for a Block Schedule

Feb 28, 2019

By Jennifer Wilson and Vanessa Cerrahoglu Update 2020-May-04: IM has created a sample plan for a block schedule for Unit 1 for each of IM Algebra 1, Geometry, and Algebra 2. (In order to make your own edits to the doc, use...

## What is problem-based instruction?

Feb 19, 2019

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...

## Realizing the promise of open resources

Jan 25, 2019

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...

## What is the Time? It Depends…

Dec 18, 2018

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: By Kristin Umland Many of us learned that time is always the...

## The Power of Noticing and Wondering

Dec 3, 2018

My first years of teaching, I worried my students looked at me much like Ben Stein as the teacher in Ferris Bueller’s Day Off. I cringe to think about the series of monotonous and leading questions I strung together to a...

## Why is 3 – 5 = 3 + (-5)?

Oct 31, 2018

By William McCallum You will never have to subtract again. Students sometimes learn about addition and subtraction of integers using integer chips. These are circular chips, with a yellow chip representing +1 and a red chip...

## Engaging All Students in Meaningful Mathematics

Oct 10, 2018

“At the end of the day, this wasn’t about focusing on the objective, it was about making the objective meaningful to him.” The work of teaching is both invigorating and challenging. We want to instill a love of math and...

## Parent Math Night Using Illustrative Mathematics

Oct 3, 2018

Open House night; cue anxiety and sweaty palms! Hope my students’ parents don’t mind. I just began my seventh year of teaching middle school mathematics. Middle school is a limbo land filled with prepubescent pre-teens,...

## Planning for Meaningful Practice

Sep 19, 2018

There is no shortage of available math resources for teachers to use in their classrooms. The difficult and time-consuming job for teachers is weeding through all of the tools to decide which best supports students in...

## What is right about wrong answers?

Sep 4, 2018

When I first started teaching, at the end of each day, I would open my teacher’s guide, grab my pen, and thumb through the stack of completed worksheets. My eyes would dart quickly from the red answers in the teacher’s...

## What I Learned Today: Scale Drawings & Maps

Aug 28, 2018

I asked my 15-year-old what she learned today at school. She paused for a moment and then answered, “What did you learn at school today?” It took me a while to think about what I had learned (which will make me more...

## The IM Curriculum Changed How I Think About Math Instruction

Aug 21, 2018

Growing up we usually think we are either a math person or not a math person. But, in preparing for this year I saw a picture that said ‘How to be a math person: Step 1: Do math Step 2: Be a person’ and I really started to...

## Planning to Use Pre-Unit Assessments

Aug 13, 2018

[bctt tweet="Time to start a new unit! What do you need to know before your students enter the room? " username="IllustrateMath"] NCTM’s Principles to Actions names several productive beliefs about assessments that will...

## IM Preparing for the School Year

Aug 6, 2018

There are always so many things to do in preparation for a new school year. At this point of the summer, to-do lists start getting made, materials get purchased, rooms are organized, and math class planning begins....

## Building a Supportive Home/School Partnership

Jul 24, 2018

By Kristin Gray, Jenna Laib, Sarah Caban Open House. Back-to-School Night. Family Welcome. Math Night. No matter what the name of the event that launches the school year, family members will arrive at your school with the...

## Building a Mathematical Classroom Community

Jul 23, 2018

Classroom environments that foster a sense of community that allows students to express their mathematical ideas—together with norms that expect students to communicate their mathematical thinking to their peers and...

## The Intersection of Fraction Talks and Clothesline Math: Formative Assessment and the 5 Practices

Jun 12, 2018

By Jenna Laib My sixth graders are weary of pre-assessments. No matter how many times we discuss the goal of a pre-assessment–for me to learn more about their current strategies and understandings, so that I can design...

## The IM 6–8 Math Curriculum Changed My Math Methods Experience

Jun 4, 2018

By Anna Polsgrove When I first started the Math Methods course at University of California, Irvine, all of my ideas on how to learn math took a complete 180. During the first two months, a million questions swirled in my...

## Fun With Zooming Number Lines in Grade 8

May 21, 2018

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...

## On Similar Triangles

May 7, 2018

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...

## NCSM and NCTM 2018 Roundup

Apr 30, 2018

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...

## Time to Noodle

Apr 16, 2018

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...

## Sometimes the Real World Is Overrated: The Joy of Silly Applications

Mar 26, 2018

By Charles Larrieu Casias One of the cool things about math is that it can provide powerful new ways of seeing the world. Just for fun, I want you to open up this lesson from the grade 8 student text. Take a quick skim....

## Warm-up Routines With a Purpose

Feb 27, 2018

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...

## Why is the graph of a linear function a straight line?

Feb 6, 2018

By William McCallum In my last post I wrote about the following standard, and mentioned that I could write a whole blog post about the first comma. 8.F.A.3. Interpret the equation $y = mx + b$ as defining a linear function,...

## Why We Don’t Cross Multiply

Feb 6, 2018

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...

## Vocabulary Decisions

Jan 18, 2018

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...

## Not all contexts have the same purpose

Jan 2, 2018

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...

## Info Gap Cards: The Hidden Gem

Dec 12, 2017

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...

## Respecting the Intellectual Work of the Grade

Nov 30, 2017

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,...

## Assessment Principles in Illustrative Mathematics 6-8 Math

Nov 24, 2017

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...

## Reflection & Discussions in Grade 8, Part 1

Oct 12, 2017

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...

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

Aug 16, 2017

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...

## Truth and consequences: talking about solving equations

Jul 19, 2017

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...

## Misconceptions about Multiple Methods

May 24, 2017

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...

*to the IM Blog and Newsletter*

#### RECENT POSTS

- The Joy of Fluency April 5, 2021
- A Circumference By Any Other Name… March 31, 2021
- Building Equitable Learning Environments for Each Student March 22, 2021
- Explorations in IM K–5 Math: Challenges for Curious Students March 2, 2021
- What Does It Mean to Use Mathematics? February 22, 2021

#### Categories

- Grades 3–5 (61)
- Grades 6–8 (73)
- Grades 9–12 (51)
- Grades K–2 (41)
- Grades K–5 (8)
- Professional Learning (41)