## Tag: partial variation

## Placing Toothpicks Part 4

More Patterning and Partial Variation Linear Relations Yet another task in the Placing Toothpicks Series (Placing Toothpicks, Placing Toothpicks Sequel, Placing Toothpicks Part 3) I posted recently. The first task was proportional, followed by a quadratic in the second and a partial variation linear relationship in the third. This task is going to give my students another go at partial variation linear relations. As were the learning goals from the Part 3 Task, here's the grade 9 academic expectations we can make connections to: LR2.02 - I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a v...

## Placing Toothpicks Part 3

Patterning and Partial Variation Linear Relations This task is a follow up to the Placing Toothpicks and Placing Toothpicks Sequel tasks I posted recently. The first task was proportional, followed by a quadratic in the second. This task is going to extend the original task from a proportional (direct variation) linear relation to a partial variation linear relation. That means this task could be used for patterning in elementary or for linear relations in grade 9 academic and applied. Here's the grade 9 academic expectations we can make connections to: LR2.02 - I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly relate...

## Camera Case & Pads of Paper Weigh In

3 Act Math With Partial Variation Linear Relations Here's another task that is a good next step once you've tackled the Tech Weigh In 3 act math task that covers direct and partial variation linear relations. This task gives students another chance to get some exposure to partial variation linear relations and could provide an opportunity for the teacher to begin consolidating the topic by moving towards some more abstract concepts like the slope formula and finding linear equations given two points. Similar tasks to check out would be Stacking Paper, Stacking Paper Sequel and Thick Stacks. Special thanks to Justin Levack again for coming up with the "weigh in" idea and pushing me to actually record this with him when we are all runni...

## Tech Weigh In

Direct and Partial Variation Linear Relations In the Ontario grade 9 applied and academic math courses, students do a lot of work with direct (proportional) and partial variation linear relations. This task was created to assist in adding context to these types of relations and help students build an understanding of both by using intuition, logic, and prior knowledge. Special thanks to Justin Levack for coming up with the idea and pushing me to actually record this with him when I was running out of steam at the end of the school year! Task #1 - iPad 2 Weigh In Act 1 - Introduce the Problem Show this video: https://youtu.be/33TJ8siIYuw What's the question? Get your students talking about what they think this mat...

## Crazy Taxi

If you're an educator on Twitter or other social media, you probably hear a lot about gamification. Well, when you don't have a reasonable option to "gamify" your math class, you can always turn to finding the perplexing math in a game. This is where Crazy Taxi by Jon Orr comes in. Act 1: Introducing the Task This 3 Act Math Task begins with a scene from a "Grand Theft Auto-esque" video game where a man jumps into a taxi and begins what looks to be a joy-ride. The cost of the taxi ride and the distance travelled are displayed; yes, the foreshadowing is probably killing you. https://vimeo.com/70036103 Can't see the video? Click here. After travelling a few kilometres, the game fast forwards and asks the viewer to determin...

## Thick Stacks

Finding the Equation of a Line Given Two Points This 3 Act Math Task is yet another sequel to the Stacking Paper and Stacking Paper - Sequel 3 Act Math Tasks where we look at linear relations with respect to a real world situation involving packages of paper stacked into a tower. While the original task begins with a direct variation requiring only basic proportional reasoning skills, the previous sequel had students looking at a partial variation linear relation with an initial value being the height of a table and were required to use the thickness of one package of paper (slope) and the height of the stack on a table (a point) to determine the height of the table. In this task, students are given two stacks of paper (thus two ...

## Stacking Paper Sequel

Finding the Equation of a Line Given Slope and a Point This 3 Act Math Task is a sequel to the Stacking Paper Real World Math Problem I created a couple weeks back. In the previous task, students were asked "How many stacks of paper will it take to reach the ceiling?" That problem had a sequel that explored the scenario of stacking the paper on a table instead of on the floor in order to see if students understood the concept of the initial value/y-intercept. In this sequel, we will revisit the idea of stacking paper on the table, but take a slightly different approach in order to give students an opportunity to link Finding Equations of a Line Given Slope and a Point to a real world situation. Please note that this is part two of...

## Stacking Paper

Real World Math in Proportional Reasoning and Linear Relations Here's a new Real World / 3 Act Math Task that is related to proportional reasoning and a direct variation linear relation with a partial variation sequel to boot! Please note that this is part one of three tasks in a series: Stacking Paper - Direct Variation (y-intercept equal to 0) Stacking Paper Sequel - Partial Variation (y-intercept not equal to 0) Thick Stacks - Finding the Equation of a Line Given Two Points Act 1: What's the Question? Students watch the first video and begin discussing what the question will be: How many packages of paper will it take for the stack to reach the ceiling? Students can view the first video here: ...

## Math Videos – MPM1D Unit 4 Modelling With Graphs

MPM1D – Principles of Mathematics – Grade 9 Academic Sec. 4.1 - Direct Variation Investigation: Going for a Jog Video discussing the mind buster problem from our section on Direct Variation: Identify the independent/dependent variables. Describe the shape of the graph. Where does it intersect the vertical axis? Write an equation to find the distance, d, in metres, that Susan jogs in t mins. Use the equation to determine the distance that Susan can jog in 25 mins. Consider the distance Susan jogged in 5 minutes. What happens to this distance when the time is doubled? What happens to the distance when the time is tripled? http://youtu.be/NWz9Evab9W0 What Is Direct Variation? A Direct Variation...