I have taught the second half of a Math 9 Enriched course for the last three years. The students generally finish two-thirds of the curricular outcomes during the first semester (with an different teacher). This alleviates the perpetual nemesis of time, and leaves me with no excuse to stretch the boundaries of what is possible in a classroom.
This is a game that was adapted from a colleague in my department. He can’t quite remember where it came from, but knows there was some influence from his undergraduate days. Nonetheless, he reinvented it to play with his Grade 9s, and this post represents yet another reinvention.
Rationale: Create a game that embeds the skills of adding and subtracting integers into a conceptual decision making structure.
Objective: Insert a set of integers into a 4-by-4 grid so that the sums of the rows and columns is a minimum.
All the students need is the game board and the list of sixteen numbers.
Every student has a gut feeling when it comes to probability, and I feel like I have been too quick to theorize their gut instincts in the past. This year to introduce Grade 9 probability, I decided to exploit gut feelings to introduce the topic.
To do this, I needed a semi-familiar situation, some friendly competition, and a time pressure to make decisions.
To fit these criteria, I invented the Dice Auction.
Surface area is intuitive. Intuition is a natural hook into curiosity. When you think something might (or should) be the case, it begs the question, why? It just seems as though textbooks haven’t gotten wind of that.
Perusing the surface area chapter of the assigned textbook for my Grade 9 math class offers a steady diet of colourful geometric solids all mashed together (at convenient right angles) in various arrangements. Without fail, the questions ask the same thing:
Find the surface area of…
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.
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).