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 learning mathematics. It is a difficult job because it first involves thinking about how students learn mathematics and then, after choosing a resource, ensure it is being used to best support students’ learning. Our team at Illustrative Mathematics has worked closely with partners such as Khan Academy to align their resources with the IM 6–8 Math curriculum so teachers can feel confident using them in their classrooms to support student learning. In aligning these resources, we keep the focus of how students learn mathematics at the forefront, while considering the type of support the additional resource is providing. Continue reading “Planning for Meaningful Practice”

# What is right about wrong answers?

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 guide to the corresponding answers on each student’s page. I would dole out my x’s and checks with finality and authority. When I got to the end of a page, I would tally a percentage score and enter it into my electronic grade book. I approached every piece of student work as if it were a summative assessment.

# What I Learned Today: Scale Drawings & Maps

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 patient when I ask her again tomorrow), and then I remembered and shared with her:We are working with some teachers who are using the *Illustrative Mathematics 6–8 Math* curriculum. The 7th grade teachers are in Unit 1, Scale Drawings. They are working with scale drawings and maps. Today I learned to look more closely at the scale given for a map.

Continue reading “What I Learned Today: Scale Drawings & Maps”

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

*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 head as I worked through problems with my classmates: *We don’t just teach the algorithm anymore? What do you mean “use representations to build conceptual understanding”? What is an area diagram? What are all of the multiple strategies to solve a problem? How am I supposed to anticipate misconceptions when I have never taught the curriculum?*, just to name a few. Continue reading “The IM 6–8 Math Curriculum Changed My Math Methods Experience”

# 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 scientific notation and irrational numbers. Let’s zoom into a lesson. Continue reading “Fun With Zooming Number Lines in Grade 8”

# 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 from Merriam-Webster online: Continue reading “Untangling fractions, ratios, and quotients”

# 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 Equations)

As students are building their understanding of dilation at the beginning of grade 8 in Unit 2 of the *LearnZillion Illustrative Mathematics 6–8 Math* curriculum, an activity asks students to dilate different quadrilaterals using a given center and dilation factor on a square grid. Here are the results of two of the dilations in that activity involving triangles: Continue reading “On Similar Triangles”

# 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 Math* curriculum and are looking forward to High School and Elementary.

Check out some photos and all of the IM presentations below, including Bill McCallum’s The Promise of Open Curriculum.

Which presentations did you attend and which was your favorite? Continue reading “NCSM and NCTM 2018 Roundup”

# 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