Newspapers are full of graphs, far more than 10 or 20 years ago. Indeed, I have a graph to show that!

Continue reading “Reading Graphs is a Complex Skill”# The Story of Grade 5

*by Sarah Caban*

From the start of the year, we want students to know they are capable of engaging in grade-level mathematics.

In the Opportunity Myth (2018), data shows that there is an opportunity gap for historically marginalized students—often students of color—between the grade-level expectations laid out in standards and students’ opportunities to engage with this content in their math classes.

Continue reading “The Story of Grade 5”# Equitable Teaching Practices in IM K–12 Math

*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 shaping the experience?

Continue reading “Equitable Teaching Practices in IM K–12 Math”# Coming Together Around Distance Learning

*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 my students? Will I be teaching synchronously or asynchronously for most of the school year? How will I get to know my students and how will they engage in one another’s ideas? How will I get to know my students’ families? How can I give them manageable guidance to support students this year? Most of all, where can I get help with all these questions?

# IM Talking Math

*By Kristin Gray*

Most importantly, I hope everyone is taking care of themselves, their families, and others as much as they are able to during this time. With schools and districts pushing instruction online with a quick turnaround, everyone is experiencing unprecedented change.

# Ratio Tables are not Elementary

*By William McCallum*

In grade 3, as students start to learn about multiplication, they think about products like 6 x 7 in terms of equal groups. 6 x 7 is the number of things when you have 6 groups with 7 things in each group. They might start out calculating that number by drawing a picture of the 6 groups and counting how many things they are. They might use a 6 x 7 array to organize the count. They might then see that the total number is 7 + 7 + 7 + 7 + 7 + 7 and do the additions 7 + 7 = 14, 14 + 7 = 21, etc. From there they might learn to simply write down the multiples, doing the additions mentally:

7, 14, 21, 28, 35, 42

Continue reading “Ratio Tables are not Elementary”# Using Diagrams to Build and Extend Student Understanding

*By Jenna Laib and Kristin Gray*

Take a moment to think about the value of each expression below.

What do you notice? How would you explain the things you notice?

If you are like us, or the students in Ms. Stark’s grade 5 classroom, you may have noticed many things. Things such as each expression has the same denominator, or the way in which the values increased as the problems progressed. When students notice these things, we often ask, ‘Why is that happening?” but it can be challenging to explain why beyond the procedure one followed.

Continue reading “Using Diagrams to Build and Extend Student Understanding”

# Building a Math Community with IM K–5 Math

“I’m not sure this is working. Only five of my students are participating and commenting each day. The rest sit there and look at me.”

*By Tabitha Eutsler*

This was my conversation with our math coordinator after my first few days of teaching IM K–5 Math^{TM} with my third graders. Those five students were having great conversations. However, my other students just sat there wide-eyed, silent, and staring blankly at their papers. I felt lost. Was this the best for my students? Could we survive a whole year of math like this? I wanted my students to love math and have a deeper understanding of mathematical concepts. How would this get them there?

Continue reading “Building a Math Community with IM K–5 Math”

# Creating an Accessible Mathematical Community with IM K–5: the power of “yet” for students and adults

Does the perfect elementary math curriculum exist? Armed with a growth mindset and the Alpha IM K–5 curriculum, teachers in Ipswich Public Schools push their thinking to reach all mathematicians.

*By Maureen D. O’Connell*

I preach growth mindset daily. When my students say they can’t do something, they almost always add their own “…*yet.*” However, walking this walk as an elementary school teacher is another story. Creating, mastering, and modifying curricula to reach each and every student—in every content area—is a daunting expectation. We hold ourselves to near impossible standards.

# Using Instructional Routines to Inspire Deep Thinking

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, deep kind?

*By Jenna Laib*

One way is through instructional routines like “Which One Doesn’t Belong” and “Notice and Wonder.” These routines give structure to time and interactions. Within the structure, there are opportunities to have time to think deeply and a predictable way to share and deepen thinking with partners and the whole class.

Continue reading “Using Instructional Routines to Inspire Deep Thinking”