## Tag: volume

## We Can Teach By Talking, But Are They Listening?

A few weeks back, I was reading a book called Teaching Minds (Kindle/Hardcover/Paperback or Audible Audiobook) by Roger Schank and really enjoyed it. As a Professor Emeritus at Northwestern University after his faculty experience at Stanford and then Yale, he is known for the quote: There are only two things wrong with the education system - What we teach; and, How we teach it. When I read great books on education, learning, or motivation, I will tweet out quotes that I may want to go back to at a later date. Today, during my grade 9 applied math lesson, I was immediately brought back to the following quote from Teaching Minds: "Once you move to teaching large groups of 10 or more students, you must...

## Mix, Then Spray

Measurement: Volume of Cylinders and Cones This is an attempt to better develop the question by splitting the problem into more than 3 acts, since I found it difficult to make the intended learning goal obvious enough through visuals. Act 1, Scene 1 - Introduce The Problem Act 1 is split into two very short videos. The first, simply shows an empty spray bottle: http://youtu.be/K8d0Ynu1h_Y Act 1, Scene 2 - Introduce The Problem At this point, some discussion regarding where the problem may go could be initiated. In order to lead students down the right path, show the next short clip: http://youtu.be/QIGSG-5pP98 While the question might seem obvious to students at this point (i.e.: how much vinegar/water do you need)...

## Cones and Spheres

How Many Cones Does It Take To Fill a Sphere? In this 3 act math task, the teacher will show short video clips to help students understand where the Volume of a Sphere formula comes from. Similar to the last Volume 3 Act Math Task: Prisms and Pyramids, the intention has been to leave Act 1 of each set very vague to allow for students to take the problem in more than one direction. The teacher can bring light to the learning goal of showing where the formula for volume of a sphere comes from after watching Act 1. Act 1: What's the question? My students usually explore the relationship between the volume of a prism and a pyramid, so this activity is typically considered an extension. To begin, I show students this image: ...

## Prisms and Pyramids

How Many Pyramids Does It Take To Fill a Prism? In this multi-step 3 act math task, the teacher will show three sets of 3 Act Math Style tasks involving comparisons between rectangular prisms and pyramids, triangular base prisms and pyramids, and cylinders and cones. While the intention has been to leave Act 1 of each set very vague to allow for students to take the problem in other directions, the learning goal becomes obvious shortly after seeing the first set of videos. Task #1: Rectangular Prisms vs. Rectangular Pyramids Act 1: What's the question? Show the following short video clip: http://youtu.be/KbWq1PV9Sno I gave my students some time to chat with a partner and come up with some possible questions for this...

## 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 ...