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Real World Applications of 3D Measurement
Proportional Reasoning With Volume of a Cylinder and Sphere
In this 3 act math task, students will extend the proportional reasoning and 3D-measurement skills used in the previous task, Guessing Gumballs, to determine whether the gumballs from the short and wide jar will fit into the tall and thin jar. The learning goals for this task include:
- calculating the volume of a cylinder and applying their knowledge;
- calculating the volume of a sphere and applying their knowledge;
- applying their knowledge of proportional reasoning to solve problems.
Act 1, Scene 1: Introduce The Problem
Show students the following video or this photo:
Ask students to talk to a neighbour and come up with some possible questions.
The question I’m looking for here is:
Will the gumballs fit into the tall and thin jar?
Prompt students to make a prediction and be prepared to backup their prediction by discussing with a partner. Will all the gumballs fit? Will it overflow? Will there be a lot of extra space? Will it be a perfect fit?
Act 2 – Give Students Some Information
After students make a prediction, have them discuss with their partner what information they need to make a more accurate prediction.
Then, show this video clip or show these photos:
- Download Photo 1: Jar Dimensions
- Download Photo 2: Gumball Diameter
At this point, students should be able to improve their prediction after using the dimensions to calculate the volume of both jars and determine how much volume the gumballs could “theoretically” occupy.
Act 3 – Reveal the Solution
Once students have shared out their work, updated their predictions based on their calculations, show them the solution:
Related Resources
Guessing Gumballs [3 Act Math Task]
How many gumballs are needed to fill the jar?
Real World Applications of 3D Measurement Proportional Reasoning With Volume of a Cylinder and Sphere In this 3 act math task, students sharpen their proportional reasoning and 3D-measurement skills as they try to determine how many packages of gumballs as well as how many gumballs (individually) will it take to fill the cylindrical jar. The learning goals for this task include: cal...
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. Unfortu...
Prisms and Pyramids [3 Act Math Task]
How many pyramids does it take to fill the prism?
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 direct...
Cones and Spheres [3 Act Math Task]
How many cones does it take to fill the sphere?
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 tea...
Mix, Then Spray [3 Act Math Task]
Where should I stop filling?
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 - 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 A...
How’d It Go?
If you use this task in your classroom, please share your experiences in the comments section! Always appreciative of any improvements that can be made including resources you might want to share for inclusion.
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