Background:On June 15th, my Grade 9 class and I hosted our second annual math fair. What started out as a small idea has grown into a capstone event of their semester. This year, we had 330 elementary school students visit our building to take part in the fair’s activities. Several people (following the hashtag #TDCMathFair2016) commented that they would like to do similar things with their student transitions. This post details the rationale behind the event, how we structured it, what stations we had, and feedback/advice from our exploits.Rationale:I pursued this opportunity with a two-pronged focus. First, I wanted to showcase a …
Continue reading »Category: pattern
Connecting Quadratic Representations
I always introduce linear functions with the idea of a growing pattern. Students are asked to describe growth in patterns of coloured squares, predict the values of future stages, and design their own patterns that grow linearly. Fawn’s VisualPatterns is a perfect tool for this.While stumbling around Visual Patterns with my Grade 9s, we happened upon a pattern that was quadratic. The students asked to give it a try, but we couldn’t quite find a rule that worked at every stage. While I knew this would happen, the students showed a large amount of staying power with the task. The …
Continue reading »Problem Posing with Pills
My class always welcomes conjectures. This is made explicit on the very first day of the semester. This goes for everything from grade nine to grade twelve. As the grades advance, the topics have us venturing into increasingly abstract concepts, but conjectures are always honoured. Certain class structures promote conjecturing more than others. Students offer questions during lectures, but they are often of a surface variety. They notice a pattern that has occurred in three straight examples, or think they have discovered a short-cut. I don’t like using tricks, but if they are “discovered” or “re-invented” (to borrow a term from …
Continue reading »The Discourse Effect
This semester, I’ve been attempting to infuse my courses with more opportunities for students to collaborate while solving problems. This post is designed to examine the shift in student disposition throughout the process.I have noticed an increased conceptual understanding almost across the board and this is reflected in the differing solutions on summative assessments. It is also nice to see their marks grow on these unit tests. I do not believe that paper-and-pencil tests are the best venues for displaying conceptual understanding, but it is awesome when the two intertwine.My unit structureI plan my courses in units of study, and …
Continue reading »Animating Patterns
There is a very strong emphasis on linear relations and functions in the junior maths in my province. In Grade 9, students begin by analyzing patterns and making sense of bivariate situations. The unit–which I love–concludes with writing rules to describe patterns and working with these equations to interpolate and extrapolate.Grade 10 students continue along this path in the light of functions. There is a large degree of abstraction that occurs in a short amount of time, and droves of students abandon the conceptual background (pattern making) in favour of memorizing numerous formulas. (Slope formula, slope-point, 2-point-slope, slope-intercept, etc.)For the …
Continue reading »Dice Sums Task
Dice are familiar tools in most mathematics classrooms. Their use in primary school games allows students to build preliminary notions of number and autonomy. (see Kamii) As the grades progress, dice sums become too simple and the tool is pushed into the realm of probability and chance. There, alongside decks of cards and coloured spinners, it enjoys almost godly status; it seems that there is no better way to calculate odds than to role dice and spin spinners (in outrageous cases—simultaneously). The greatest thing dice have going for them is familiarity. Teachers can use this to upset the thinking of …
Continue reading »Relation Stations
This semester I desperately wanted to improve how I taught linear relations to Grade 9 students. I had tried some interesting activities in the past, but lost patience and ended up drilling them with notation and algorithms. I wanted to find a way to show the students that equations were just explanations of patterns. I began compiling different linear patterns and dug in for the long haul. I stumbled upon a collection of abandoned, square tiles and decided to use them to put students in the center of the pattern making. I began the lesson by dividing the class into groups of three. …
Continue reading »Bike Trail Task
There is two hour parking all around University of Saskatchewan. I once went to move my car (to avoid a ticket) and found that the parking attendant had marked–in chalk–the top of my tire. I wanted to erase the mark so began driving through as many puddles as possible. I then convinced myself to find a puddle longer than the circumference of my tire–to guarantee a clean slate and a fresh two hours. As I walked back to campus, I got thinking about the pattern left behind by my tires. For simplicity, let’s take the case of a smaller vehicle–a …
Continue reading »Using Real-Time Graphs
I have a class of grade nine students this semester that are part of a stretch program. This essentially means that they get 160 hours to complete a 120 hour course. The class is designed to accommodate the transition from elementary school (Grades 1-8) into high school (Grades 9-12) for those students who feel uncomfortable with their math ability. It also affords me a few extra days here and there to stress certain topics. One of my foci this semester has been pattern modeling. Essentially, we work with various patterns and develop generic rules to describe their behaviour. Linear relations will …
Continue reading »Destroying Functions
I have spent the better part of 2 weeks going over various mathematical relationships in my Grade 10 class. They have been represented as tables of values, arrow diagrams, and sets of ordered pairs. Relationships, both qualitative and quantitative, have been defined, analyzed, and graphed. My focus on graphical literacy has been previously detailed on the blog. See the link below for details: http://musingmathematically.blogspot.com/2011/10/graphing-literacy.html Numerous relationships were handled. Students we required to create a family tree and then represent its branches as a table of values and set of ordered pairs. Throughout the various exercises, the words “input”, “output”, “domain”, …
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