## The Progression of Fractions

Exploring Fraction Constructs and Proportional Reasoning Fractions are a beast of a concept that causes struggles for many adults and students alike. While we all come to school with some intuition to help us with thinking fractionally and proportionally, the complexity quickly begins to increase as we move from concrete, to visual, to symbolic and from identifying, to comparing, to manipulating. Fractions are formally introduced in the Ontario Math Curriculum when students begin dividing whole objects into pieces and identify these pieces using fractional names (e.g.: halves; fourths or quarters) and continues to promote the development fractional fluency concretely through each grade. Interestingly enough, it is often said that student...

## Making Math Animations With Keynote on iPad

Math Animations Made Easy Using Instant Alpha & Magic Move! Thanks for joining me for a session on creating animations in math class using Keynote on iPad with the Keynote iOS App! In this 90-minute session, we are going to explore an exemplar created using Keynote and then we will provide the resources to piece together our own problem. Math Animation Exemplar: Lawns, Fences, and Fertilizer - Using Perimeter and Area With Unknown Variables https://youtu.be/xpk2mvZX2Ms Also available on YouTube here. What We're Hoping To Create - Setting The Stage: I walk into my office at the board office (beautiful, I know): But the cabinet along the wall has a pretty ugly looking tabletop that would look super flashy in Gran...

## Connecting Relationships to Multiple Strands

Exploring the Relationship Between Diagonal Length and Side Length of a Square It's been a couple weeks since posting, so I thought I need to get back in the swing of things. I've been enjoying a really busy start to semester 2. I'm loving the implementation of the gamified assessment approach I've modified off of Jon Orr and Alice Keeler's work, the spiralled approach to teaching grade 9 applied math that Jon and I are trying after receiving guidance from Alex Overwijk and co., prepping for the third series of full-day PD sessions for the MYCI project, and practicing my first keynote speech coming up in just a couple short weeks. Unfortunately, my blog has been taking a backseat to all of the other "stuff" going on. So while thi...

## Visualizing Two Variable Linear and Non-Linear Relationships

Tables of Values, Graphing Scatter Plots, Describing Relationships and Making Predictions Although generally not the urgent student learning need in most classrooms, working with two-variable linear and non-linear relationships could also be made more visual to help students better understand some of the important pieces that will help with linear equations and beyond. As mentioned in posts previously shared in this visualizing mathematics series, I want students to increase their spatial reasoning skills and better connect concrete representations of math to those that are more abstract. In order to make this visualization relevant for my own students, I created these videos using the data from the Candle Burning 3 Act Math Task: ...

## Visualizing the Maximum Area of a 3-Sided Rectangular Enclosure

Increasing Spatial Reasoning Skills: Optimization of Measurement Although maximizing the area of a 4-sided rectangular enclosure is usually considered quite basic for most students, understanding why maximizing a 3-sided rectangular enclosure does not yield a square can be more difficult. To help address this student learning need, here is the animation created for maximizing the area of a 3-sided rectangular enclosure by using a situation where we must rope in a swimming area at the beach: http://youtu.be/Rie6kF1UZD0 Stage By Stage PDF File Here is a stage-by-stage PDF file for you to grab, if you'd like: [slideshare id=39618132&doc=maximizingareaof3-sidedenclosuresslidedeck-140928100034-phpapp02] Please let me kn...

## Visualizing the Maximum Area of a 4-Sided Rectangular Enclosure

Increasing Spatial Reasoning Skills: Optimization of Measurement In the past, when introducing the concept of Optimization of Measurement, students would complete a series of investigations involving different lengths of rope, fence, etc. and would make connections from the table of values and graph they would produce. While I still intend to do some of the investigations, I want to make them more real and especially more visual to hopefully help students better retain the knowledge and develop a deep understanding. Here's the animation created for maximizing the area of a 4-sided rectangular enclosure: http://youtu.be/lmVxsjIbJhE Stage By Stage PDF File Here is a stage-by-stage PDF file for you to grab, if you'd like...

## Visualizing the Area of a Trapezoid Formula

Visually Understanding Area of a Trapezoid in Multiple Ways While some students are aware that they could find the area of a trapezoid by treating the shape like a composite figure, I wanted to help students better understand where the formula comes from with a visual aid. Here is the next video animation I created in my Visualizing Mathematics series: Visualizing the Area of a Trapezoid Formula. http://youtu.be/YgEIoCMfWrg Stage By Stage PDF File Here is a stage-by-stage PDF file for you to grab, if you'd like: [slideshare id=39606703&doc=visualizingtheareaofatrapezoidformula-animationslidedeck-140927194007-phpapp01] Please let me know if you/your students found this resource helpful to better understand where the V...

## Visualizing the Volume of a Triangular Prism Formula

Visually Understanding Area of a Triangle and Volume of a Triangular Prism About a week ago, I shared my visual animations explaining the "Derivation of the Volume of a Cylinder Formula" and Volume of a Rectangular Prism formula I used in class and students seemed to be able to tie some of the visuals to the work they completed in class. Here is the next video animation I created in my Visualizing Mathematics series: Volume of a Triangular Prism. Feel free to check it out for use in your classroom. I recommend muting the volume and speaking over the video and/or pausing at certain points where necessary. http://youtu.be/a8YLrKTer5M Stage By Stage PDF File Here is a stage-by-stage PDF file for you to grab, if you'd li...

## Visualizing the Volume of a Rectangular Prism Formula

Visually Understanding Area of a Rectangle and Volume of a Rectangular Prism Yesterday, I showed the "Where Does the Volume of a Cylinder Formula Come From?" video in class and students seemed to be able to tie some of the visuals to the work they completed in class. It inspired me to try another one, this time with the volume of a rectangular prism. Here's the result of my latest experiments with animations in Keynote. Feel free to check it out for use in your classroom: http://youtu.be/mHfC8sb1tbQ Stage By Stage PDF File Here is a stage-by-stage PDF file for you to grab, if you'd like: [slideshare id=38754916&doc=wheredoesthevolumeofarectangularprismcomefrom-animation-140905140415-phpapp01] Please let me know if...

## Visualizing the Volume of a Cylinder Formula

Visually Understanding Area of a Circle and Volume of a Cylinder Over the past year, I have been on a mission to try and make some of the formulas we use in the intermediate math courses in Ontario (Middle School for our friends in the U.S.). I think it can be difficult for math teachers to explain where formulas come from because we often think of deriving formulas algebraically. Unfortunately, for our younger students, this might be more harmful than helpful. Specifically, this semester I am teaching MFM1P Grade 9 Applied Math where many of these students come into high school with a sour taste of mathematics in their mouths. Yesterday, we looked at Volume of a Cylinder and began with Dan Meyer's Hot Coffee 3 Act Math Task ...