## Tag: direct variation

## Placing Toothpicks

Patterning, Proportional/Direct Variation Linear Relations Patterning is something that comes up early in the Ontario Elementary Math Curriculum during the primary grades often connecting directly to proportional reasoning, and then evolves into direct variation linear relations in the grade 9 academic and applied courses. In both the academic and applied grade 9 courses I teach, I try to integrate proportional reasoning early and often - slowly scaffolding students towards one-step equations and the characteristics of linear relations. Today, I'm going to share out the following 3 act math task that Justin Levack and I filmed last year keeping the grade 9 academic curriculum in mind. In particular, this task can be connected to: ...

## 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...

## Gas Guzzler

Proportional Reasoning / Linear Patterning Real World Math Problem This 3 Act Math Task focuses on the rate of change for proportional reasoning / linear patterning / direct variation linear relations problem. Act 1 - Introducing the Task Getting Ready To Gas Up In the first act, students watch a 30 second video that shows someone pre-paying for gas, selecting the grade of fuel and start pumping. You'll notice in the video that the cost per litre (rate of change) is blanked out on the pump. http://youtu.be/oeMRMWwMk8I Students will then be asked: What is the price of gas? Here are a few images in the case you don't want to load a video / have a slow connection: [gallery columns="2" ids="13655,13656"] Act...

## Stacking Paper

This Task Is Now in a Multi-Touch Book! Grab It! Learn more about what's inside the multi-touch book here. Or, consider accessing these tasks in an interactive way via Google Sites. 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? Stu...

## Bolt

How Fast Is Usain Bolt Running? When introducing slope as a rate of change in my grade 9 academic and applied courses, I used to use a video of Usain Bolt running the 100 m. Fun times, but pretty basic when it came to the question: "how fast is he running?" Dan Meyer manages to provide a video clip that gives us a 300 m race to work with in order to raise the bar slightly, without leaving any students behind. This year, I am working hard to try and move from my typical 4 to 5 tasks per lesson and get down to one that can be extended to multiple concepts. Below, you'll find some resources to go along with this Dan Meyer 3 Act Math Task to assist you when using it. Access Handouts Act 1 - Watch Race, Take Estimates & Workspac...

## 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...

## MPM1D – 4.1 – Direct Variation

MPM1D - Principles of Mathematics - Grade 9 Math Academic Expectations Covered This Section: construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations; compare the properties of direct variation and partial variation in applications, and identify the initial value (e.g., for a relation described in words, or represented as a graph or an equation); Minds On Investigation: Going for a Jog Students will work in their table groups to create a table of values and graph the relationship on a grid. They will then complete the following related to...

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