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# Tech Weigh In

## Direct and Partial Variation Linear Relations

In the Ontario grade 9 applied and academic math courses, students do a lot of work with direct (proportional) and partial variation linear relations. This task was created to assist in adding context to these types of relations and help students build an understanding of both by using intuition, logic, and prior knowledge.

Special thanks to Justin Levack for coming up with the idea and pushing me to actually record this with him when I was running out of steam at the end of the school year!

## Act 1 – Introduce the Problem

Show this video:

What’s the question?

Get your students talking about what they think this math task is going to focus on. Writing the questions out is always helpful.

Here are just a few of the questions that came up today when we used this task for the first time:

• How much does 3 iPads weigh?
• How much does 1 iPad weigh?
• How many scales would weigh the same as the stack of iPads on the table?
• What is the cost per gram/ounce/kg/etc.?

All great questions that should be recognized! While we could try to answer as many questions as possible, today our focus was on the weight of 1 iPad.

Time to make some predictions!

## Act 2 – Giving Some Information

After students are happy with their predictions, start asking students what information they want. In this case, I have pretty specific information, but my students can usually come up with something similar that could help us out.

Show them this video:

Now we can set the students free to work out the problem. At the beginning of the semester, my grade 9 applied students might struggle to get started due to a low level of confidence in math, but today they were done in a matter of 20 seconds or so. They’ve come a real long way!

I also created a Custom Gameshow in Knowledgehook to allow me to get some instant feedback as students worked. The Gameshow Tool now has a feature that allows students to upload their work and then I can display student work samples to consolidate thinking. It was pretty rad!

You can grab a PDF copy of the Custom Gameshow here.

## iPad 2 Weigh In Extensions

Although this is a simple proportion, I try to get students to see the other connections that can be made to linear relations including direct variation. Some additional extension questions could include:

• Is this relationship an example of a direct or partial variation? How do you know?
• Find the initial value and rate of change.
• Determine an equation that relates the weight and number of iPad 2s
• How Many iPads would weigh 27,066 grams?

Since I do these problems back-to-back, students already have a feel for what we’ll likely be exploring. You could try to pull out some more question ideas, but I usually find that the students are already hooked in and are actually more interested in getting to the math. I do, however, try to get some predictions out there just to ensure that they have some way to judge how realistic their answers are.

## Act 2 – Giving Some Information

Show them this video:

The question is: How much does the MacBook Pro weigh in at?

Again, students are now ready to be set free to solve the problem. There is no pre-teaching necessary here. Most students will intuitively be able to determine the weight of 1 iPad Mini and ultimately use the formula for slope of a line by accident as they usually do in Thick Stacks. Let them do it on their own and consolidate later.

Surprisingly, one student even wrote out their solution as a system of linear equations and used elimination to eliminate the MacBook Pro completely:

I found this to be fascinating because I had never even considered this as a potential problem to introduce the concept of elimination to a group of students working with systems. Not my intent at all with this problem, but you bet I’ll be using it in that case from now on!

## MacBook Pro and iPad Minis Weigh In Extensions

Here are some extension questions to complement this partial variation relation:

• Is this relationship an example of a direct or partial variation? How do you know?
• Find the initial value and rate of change.
• Determine an equation that relates the Weight and Number of iPad Minis
• Determine the approximate number of iPad Minis it would take for the entire stack (including the MacBook) to weigh 29,005 grams?

## Access Resources

Check out all of the resources here. Or, you can grab what you want individually below:

• Task #1 – iPad 2 Weigh In – Act 1 [VIDEO]
• Task #1 – iPad 2 Weigh In – Act 2 [VIDEO]
• Task #1 – iPad 2 Weigh In – Act 3 [VIDEO]
• Task #2 – MacBook Pro and iPad Mini Weigh In – Act 2 [VIDEO]
• Task #2 – MacBook Pro and iPad Mini Weigh In – Act 3.1 [IMAGE]
• Task #2 – MacBook Pro and iPad Mini Weigh In – Act 3.2 [VIDEO]
• Slide Deck for Both Tasks [KEYNOTE]

## Student Exemplars

I only managed to grab one photo of student work today (ooops!) so please send your student work my way or add the images in the comments (yes, you can add images!) so others can learn from your students!

Have you tried the task? Let us know how to make it better in the comments!

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

## Share With Your Learning Community:

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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