IM Certified® Blog
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: Fraction: a...
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...
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...
Time to Noodle
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 popular “use shadows and similar triangles to...
What is an instructional routine?
By William McCallum and Kate Nowak People use routines for all kinds of things. Routines give structure to time and interactions. People like structure. When a child comes home from school, there might be a routine. She expects a snack, homework time, play time,...
Using Math Routines to Build Number Sense in First Grade
By Allison Van Voy When I started teaching four years ago, I had no idea how important number sense was to a student’s math understanding. I was fresh out of college, brand new to teaching, and number sense was not a concept I had learned in my math courses. In my...
Sometimes the Real World Is Overrated: The Joy of Silly Applications
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. What do you notice? What do you wonder? When...
Instructional Materials Matter: Interpreting Remainders in Division
By Jody Guarino We know instructional materials play a key role in student learning experiences but how do we ensure our students are learning from coherent high-quality instructional materials that engage them in critical thinking and provide opportunities to “do...
Adapting Curriculum For Students to Know, Use and Enjoy Fractions
By Melissa Greenwald You know it is time for a change when half of the students in class are lost by the third lesson of a new unit. I teach third grade in a charter school in Philadelphia. We use Go Math! and each year I have followed Chapter 8: Understand Fractions,...
Learning Goals and Learning Targets
By Jennifer Wilson One of your students is asked, “What are you learning about today in class?” How does your student respond? “Nothing” “Math” “The questions on this worksheet” “Deciding if two figures are congruent” During class, one of your students asks you, “Is...
