K–5 Math

When is a number line not a number line?

When is a number line not a number line?

By William McCallum The number line is a seemingly simple object: a straight line with two points marked 0 and 1. Those two points are the seeds of great complexity, however. Whole numbers are located at positions marked off by iterating the interval. Fractions are...

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The Art of Reflection

The Art of Reflection

“In times of stress, the best thing we can do for each other is to listen with our ears and our hearts and to be assured that our questions are just as important as our answers.” —Mr. (Fred) Rogers By Kaneka Turner We are never more “on” than when we are teaching a...

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Ratio Tables are not Elementary

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...

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Using Instructional Routines to Inspire Deep Thinking

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...

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Which Vertex is the Center of a Triangle?

Which Vertex is the Center of a Triangle?

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 post, “Which vertex is the center of a...

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

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  By Kristin Gray When I think back to my 8th grade math class, I cannot recall the exact problems I struggled with...

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Realizing the promise of open resources, part II

Realizing the promise of open resources, part II

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 enhanced versions with different options for...

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