Q: What is the fastest way to get a heated debate going about some topic in the IM 6–-8 math curriculum?
A: Show people this graph from Lesson 4 in Unit 8.5:
My first years of teaching, I worried my students looked at me much like Ben Stein as the teacher in Ferris Bueller’s Day Off. I cringe to think about the series of monotonous and leading questions I strung together to a room of dazed students slowly wilting in front of my eyes. “Bueller? Anyone?”
NCTM has called for structural and curricular changes in high school mathematics. Learn about how IM’s high school curriculum is aligned with the vision put forth by NCTM to end tracking, implement effective targeted instructional supports, and broaden the focus of teaching high school mathematics beyond college and career readiness.
Supporting high-school students to write detailed, precise proofs is challenging. Learn about some of the design elements that IM used to invite students to a deep exploration of proof.
You will never have to subtract again.
Students sometimes learn about addition and subtraction of integers using integer chips. These are circular chips, with a yellow chip representing +1 and a red chip representing -1. You start with the all-important rule that $1 + (\text-1) = 0$, so you can add or remove a red-yellow pair without changing the number. To calculate the right hand side of the equation in the title, $3 + (\text-5)$, you put 3 yellow chips together with 5 red chips, then remove 3 red-yellow pairs, leaving 2 red chips. So $3 + (\text-5) = -2$. Continue reading “Why is 3 – 5 = 3 + (-5)?”
Having an extended period of time to teach a lesson can be an advantage in a problem-based classroom. Students and teachers can savor the questions that are asked. Activities can breathe in a way that they can’t in a shorter period of time. But questions about planning inevitably arise. We find ourselves asking questions like: Do I simply merge two lessons? What stays? What goes? How do we ensure that we engage our students in the right conversations that will prepare them for the next leg of the journey?
Open House night; cue anxiety and sweaty palms! Hope my students’ parents don’t mind.
I just began my seventh year of teaching middle school mathematics. Middle school is a limbo land filled with prepubescent pre-teens, drama, and students trying to find their individual voice without drawing too much attention to themselves (sigh). There are sixth grade boys and girls in my class who are taller than me, 5’9”. Some of the boys have mustaches while others still look like they’re in third grade. It’s a difficult year for the students. This is their last year before moving onto the even weirder, and much more confusing junior high. Students are anxious about this being the last year of elementary school, and so are the parents; maybe even more anxious than their little boys and girls becoming young men and women. I think it is my job to help ease this transition, and to get them excited about what is to come.
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 works closely with partners 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”
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.