Why is 3 – 5 = 3 + (-5)?

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)?”

Planning Lessons for a Block Schedule

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?

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Parent Math Night Using Illustrative Mathematics

Open House night; cue anxiety and sweaty palms! Hope my students’ parents don’t mind.

Photo Courtesy of Robert Eiselstein

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.

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What is right about wrong answers?

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.

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What I Learned Today: Scale Drawings & Maps

I asked my 15-year-old what she learned today at school. She paused for a moment and then answered,  “What did you learn at school today?”

It took me a while to think about what I had learned (which will make me more patient when I ask her again tomorrow), and then I remembered and shared with her:We are working with some teachers who are using the Illustrative Mathematics 6–8 Math curriculum. The 7th grade teachers are in Unit 1, Scale Drawings. They are working with scale drawings and maps. Today I learned to look more closely at the scale given for a map.

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Building a Supportive Home/School Partnership

FAMILY NIGHT DOWNLOADABLE

 

By Kristin Gray, Jenna Laib, Sarah Caban

Open House. Back-to-School Night. Family Welcome. Math Night. No matter what the name of the event that launches the school year, family members will arrive at your school with the same burning questions: What do I need to know to set up my child up for success in math this year? and How can I continue to support them throughout the school year? Continue reading “Building a Supportive Home/School Partnership”

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