Ratio Tables are not Elementary

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

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Using Diagrams to Build and Extend Student Understanding

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 \frac{2}{3}

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. 

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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.”

This was my conversation with our math coordinator after my first few days of teaching IM K–5 MathTM 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? 

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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. 

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. 

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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?

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. 

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First Impressions: The First Units in IM K–5 Math

“I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.”

― Maya Angelou 

When I think back to my 8th grade math class, I cannot recall the exact problems I struggled with or exact things the teacher said or did, but I can distinctly remember how I felt each day walking into that classroom: anxious. From the very first day of school, I struggled, and my feelings of failure and self-doubt only compounded as the year progressed. I just could not keep up. While many, many years have passed, and details have faded from my memory, I have never forgotten how badly I felt about myself as a learner of mathematics each day.  

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