Visualizing Mathematics Related Posts

Counting Principles – Counting and Cardinality


Counting Principles - Progression of Counting and Quantity

A Progression of Counting and Quantity As a former secondary math teacher and intermediate math coach, my new role as K-12 math consultant has led to a wealth of knowledge that I wish I had during my years spent in the classroom. My conversations about student learning needs with intermediate and senior math teachers always seems to come down to gaps in student understanding, however rarely wer...


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The Progression of Fractions


The Progession of Fractions from K-12

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 manipulatin...


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The Progression of Proportional Reasoning From K-9


How Many Doritos Are In A Bag - Consolidation

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 r...


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Connecting Relationships to Multiple Strands


Exploring Relationships - Diagonal Length vs. Side Length of a Square

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...


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Visualizing Proportional Reasoning: Working With Ratios and Proportions


Proportional Reasoning 3 wins to 1 loss Ratio Example

Solving Proportions With The Toronto Maple Leafs Win:Loss Ratio As we began the Proportional Reasoning unit in my MFM1P Grade 9 Math Course, I was beginning to struggle with an idea to extend the idea of visualizing mathematics concepts into ratios, rates, and proportions. What I came up with was using a visual representation of Toronto Maple Leaf wins and losses in order to help scaffold stud...


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Visualizing Two Variable Linear and Non-Linear Relationships


How to Graph Data Points on a Scatter Plot

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 pr...


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Visualizing the Maximum Area of a 3-Sided Rectangular Enclosure


Visualizing Optimization - Maximizing the 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 o...


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Visualizing the Maximum Area of a 4-Sided Rectangular Enclosure


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...


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Visualizing the Area of a Trapezoid Formula


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 ...


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Visualizing the Volume of a Triangular Prism Formula


How to Find th e Volume of a Triangular Prism Starting With Area of the Base

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 Vis...


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