## OTF Connect – Making Connections Between Proportional Thinking and Fractional Thinking

Ontario Teachers Federation Connect Webinar December 5th, 2016 Make connections from the relational thinking behind proportional reasoning and represent these number relationships as fractions. Join Kyle Pearce as we explore fractional thinking using tasks that are contextual, visual and concrete in order to examine fraction constructs, uncover multiple representations of fractions, and discover different perspectives that build the conceptual understanding behind the rules for multiplying and dividing fractions. Replay the webinar and access OTF Resources here. Resources Related to This Session: Slide Deck OTF Connect - Making Connections Between Proportional Thinking and Fractional Thinking from Kyle Pearce Download the S...

## The Progression of Proportional Reasoning From K-9

The Foundation and Development of Multiplicative Thinking Proportional Reasoning is a big idea that is connected in some way to all mathematical strands and stretches across many grades in the Ontario mathematics curriculum. While many focus on the importance of proportional reasoning for students in junior and intermediate grades, I believe that we can see the early development of proportional reasoning in kindergarten and primary grades when students begin unitizing, grouping, and fair sharing. In this post, I'd like to briefly explore some of the progression of proportional reasoning across the Ontario mathematics curriculum. Paying Attention to Proportional Reasoning The Ontario Ministry of Education has done a great job releasing ...

## Solar Panels

Proportional Reasoning With Green Energy This is a 3 Act Math Task that focuses on "Green Energy" proportional reasoning questions related to solar panels in order to address proportions both visually using area models and proportions written as equivalent fractions. Special thanks goes to Dave Raney from CPE Inc. for allowing us to use his video and photos as well as Kathleen Quenneville, Energy & Environmental Officer at GECDSB for her feedback to create problems around solar energy. Act 1: Introduce the Task Show students the act 1 video. https://youtu.be/TVNelm5Xgtk Then ask students to do a rapid write of what they notice and what they wonder. Students will then share out their noticings and wonderings while ...

## Calvin’s Clearance

Working With Percentages to Estimate & Calculate Discounts The following lesson resource material provides Real World Math Problems that were created with the Grade 6 Ontario Mathematics Curriculum in mind, but can be used in all intermediate grades to reenforce an understanding of percentages and discounts. Throughout the lesson, students are asked to estimate the cost of each item of clothing after a discount is applied while encouraging the use of friendly numbers and their understanding of percentage as a part (percentage) of a whole (out of 100). Students will then be able to take their estimate and complete the calculation with a calculator to compare their estimate with the actual result. Learning Goals: After our Real Wo...

## OTF Connect – Exploring the Progression of Proportional Reasoning From K-9

Ontario Teachers Federation Connect Webinar October 26th, 2016 Students begin using proportional reasoning early in their mathematics learning journey when they begin to think of the magnitude of numbers relative to another rather than in absolute terms. Join Kyle Pearce as we explore the progression of proportional reasoning throughout the primary, junior and intermediate math classroom by using tasks that are contextual, visual and concrete and spark curiosity in students. Replay the webinar and access OTF Resources here. Resources Related to This Session: Slide Deck OTF Connect - Exploring The Progression of Proportional Reasoning From K-9 from Kyle Pearce Download the Slide Deck in the following formats: Portable Do...

## Fast Clapper

Using Real World Rates and Proportional Reasoning The following 3 act math task shared by Nathan Kraft (@nathankraft1) involves proportional reasoning with opportunities to address learning goals around rates, proportions, rates of change and creating equations. Jon Orr and I have used this task in presentations a number of times over the past few months and many have asked us to share our slide deck and other resources with a summary. So, here we go! Act 1 - Sparking Curiosity Show the following video: https://youtu.be/wT_d2GOEm_0 *Note that this is an edited version of Nathan's video where I have blacked out the number of claps. You can always add. You can't subtract. I typically give students a prompt to jo...

## 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: ...

## R2D2 Post-Its by @MrOrr_geek

Applying Area to Proportional Reasoning Thus far in the spiral, I haven't made it to measurement yet. Today, we're going to touch on area and lead us into an exploration of area formulas over the next day or so. Jon Orr's R2D2 Post-It Notes 3 Act Math Challenge is a nice low floor task that works with area of a rectangle and proportional reasoning. Here's the Act 1 video we show the students: http://youtu.be/IbAhJ8T98UE Can't see the video? Click here. Here's the question we eventually settle on: Determine how many post-it notes it will take to cover the board? My students came up with some predictions including: Alex - 888 Jaden - 700 Olivia - 688 Cole - 756 Grace - 900 Lowwwwza - 950 S...

## 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...

## Why We Must Model The Interconnections in Math

An Example of Tricks and Quick Fixes Leading to a Dead End Recently, my students were just starting their weekly assessment that interleaves/spirals our math learning goals from the year. The first problem was taken directly from an EQAO Standardized Test open response release question about unit rate: My students have been working with ratios, rates, and proportional reasoning delivered in various contextual problems throughout the year including some unit rate problems sprinkled in. As soon as my students began solving this problem, they went straight for the strategy that they've likely been using since grade 6 and the strategy that I used to teach for years - division. While division does work, it is only useful when there ...