I have been thinking about extending the Fraction Talk love ever since I wrote this initial post in June 2015.
I have used them with my grade nine classes as the starter during units on rational numbers. I have taken the larger questions (such as “What possible fractions can be shaded using this diagram?”) as the prompt for entire lessons of student activity. I have used them to create great conversations with grade 7 and 8 students at our school’s annual math fair.
Author: natbanting
I want students to solve systems out of necessity.
I want them to feel the interconnectedness of the two (or three) equations. In the past, I’ve asked small groups to build a functional 4×4 magic square. Soon they realize that changing a single number has multiple effects; this is the nature of the system. Unfortunately, abstracting the connections results in more than two variables. This year, I wanted to create the same feeling with only two variables. (The familiar x & y).
Enter: Alex Overwijk.
[Post Updated June, 2018]
This semester I gave my Grade 12s a term project to practice function transformations. I began by sourcing the #MTBoS to see who had ventured down this road before. Luckily, several had and they had great advice regarding how to structure the task.
I use Desmos regularly in class, so it was not a huge stretch for them to pick up the tool. I did show them how to restrict domain and range (although most of them stuck exclusively to domain).
I gave them the project as we began to talk about function transformations, and they had 3.5 months to complete it. They complained, but the results were fantastic. (…bunch of drama queens).
After an emoji was named 2015 Oxford Dictionary word of the year, I am holding out hope for next years’ candidate:
des-mo-si-fy
/dez-MOH-suh-fahy/
verb
1. to transform the condition, nature, or character of a classroom activity using Desmos.
Let it be known that Sadie Estrella is a Hawaiian treasure.
She made her way north for SUM2015 in Saskatoon and I got the opportunity to learn from her about counting circles (as well as share an eventful dinner).
It is probably good to understand her work on counting circles before reading a couple of ideas I had during her session.
I went to her blog and searched for #countingcircle, and the results can be read here.
I joined a middle years math community organized by my school division. I have a growing interest in the transition of students from middle school to high school because many of the tasks I use or create get at middle years content. I’m wondering what knowledge students come to my room with and what atmosphere it was learned in. Both have huge impacts on how students operate in my room.
I was surprised to hear that middle years teachers lamented that students could not use number lines. I use number lines as a support in my high school classes because I (ignorantly) assumed that this was an accessible tool from their elementary days. As it turns out, what I thought was making things easier for kids to conceptualize, probably was causing cold sweats and night terrors.
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WODB: Polynomial Functions
If you haven’t experienced the conversation stemming from Which One Doesn’t Belong? activities, you are missing out.
As far as I can decipher (#MTBoS feel free to correct me), this all began with Christopher Danielson’s Shape Book centered around this structure.
From there, a crew of tweeps (headed up by Mary Bourassa) established WODB.ca (YES! Canadian) to curate a collection of problems of this format.
My intern just started a unit on statistics with my favourite starter question of all time.
(First blogged near the end of this post in 2011…)
The question is simple: floor is very low, and ceiling is very high.
Create a data set with the following characteristics:
Mean = 3
Mode = 3
Median = 3
Today an amazing thing happened; students put aside the endemic disdain for rational numbers and had a conversation. I’d go further, they weren’t discussing their views on fractions, they were collectively conjecturing–the moves of the room enacted each other. I don’t think that a written document can capture the movement of the body of learners, but I have to try something. Think of it as less of a remembering and more of a re-membering, a reconstruction of a living learning event from the past.
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Integer War
Math 9 poses the specific challenge of pre-assessment. The wave of administrative details (lockers, fees, photos, textbooks, tryouts, etc.) creates a logistical whirlwind for teachers. On top of that, you have no clue who (most) of these new students are, or what their mathematical history is. Our department gives a short pre-skills exam to help with this process, but I like to use the first week to work on integer tasks to really see how the newbies move mathematically–beyond a number on an exam.