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February 6, 2017

# The Seven Year Itch: Re-Examining Scale Models

Grades 6–8

Ever want a redo on a lesson? Not because the lesson tanked, but because you suddenly had about eight new ideas that could have made it even better?

In the fall of 2010, I wrote a blog post for Scholastic about teaching scale with 3-D models. In that lesson, students constructed three-dimensional models of their bedrooms based on a 1 inch to 1 foot scale (1:12 ratio). In the post, I mentioned that students could scale up to recreate the walls of a home with stakes and caution tape on the playground.

It was an experience that built the schema for my students, but now nearly seven years later, I realize it could have been so much more. After all, now we have drones!

Recently, I was invited to meet with sixth-grade teacher, Whitney Heckert, to discuss ideas and strategies for her unit on proportional reasoning. As we brainstormed ideas, I mentioned the unit of study I had I done so many years ago. We made some adjustments and what follows are the additions made to the original unit plan.

For Mrs. Heckert, students were asked to create blueprints of their dream home. But first, we decided that in addition to the dream house blueprints the students created, they would be required to determine the height of the walls of their houses, and construct those from card stock and tape. Working on spatial reasoning by taking a 2-D drawing to 3-D with the addition of walls became a new goal for the project.

Students were also instructed to create the walls so they could be lifted (as one unit) from the blueprints. Once the walls were cut out and taped together, they created what looked like a maze; however, they were not permanently attached to the floorplan drawing. Therefore, the walls (now one unit) could be lifted on and off the original floor plan drawing. (Think of the walls like a lid on a pot that could be put on and taken off.) These models would be reference points for the students throughout the unit.

Mrs. Heckert asked the students to determine surface area and calculate how much paint it would take to paint the interior walls. They derived the ratio of bedrooms to bathrooms, exterior walls to interior walls, and rooms with tiled flooring to those with wood flooring. Students easily moved into using the models to make percentage calculations as well.

Next, we thought about perspective. We dreamt big and longed for a drone to capture aerial footage of the dream homes once the students had scaled up their drawings on the playground with caution tape and stakes. This video and the photographs would provide points for discussing and writing about misconceptions and observations. The footage from the drone let the students see that their perspective on the ground is much different from an aerial shot. The aerial footage permitted the teacher to discuss the how imperative it is for buildings to be plumb and square, and what could happen if proper alignment did not happen in the construction of their dream homes.

Our school does not own a drone, but our school district does! All we had to do was make a call. The administrators were more than happy to come and film the projects. Scott Campbell, the Technology Coordinator for our district, made a special trip out and filmed students as they begun the process of mapping out the first floor of their dream homes. We even posed for a “dronie” (instead of a selfie).

Finally, Mrs. Heckert created forms for organizing the thinking of her students, as well as charts for recording calculations and managing data. This had been lacking in my prior unit. When it comes to a unit renovation, collaboration is key. Because of that planning session, several themes arose. These were determined to be the top three:

### 1.     Frame old ideas for current day.

It’s 2017, people. We have awesome technology! As teachers, we worry that the most current technology is out of reach, too expensive. Consider resources that your school district may already have in its possession. Often the technology department has access to some of the newest technology and is willing to come and demonstrate or let you borrow it for a special project.

### 2.     Brainstorm like you mean it.

Collaboration is everything. Leave no stone unturned and consider all topics and connections fair game. As you are thinking through old lessons and units, create an exhaustive list of ideas related to the teaching. The crazier, the better. As you pare down your list, give special consideration to the ideas that seem “too big” and discuss ways you might be able to make it happen. This is where parent connections, business partners, and district level staff can come into play.

### 3.     Get student input.

Embarking on strategies and technology that you have never tried before can be tricky; student buy-in is generally the remedy. Just because the relevance of a new approach is a no-brainer for us, does not imply there is a correlation for the students. With ideas I consider to be a risk, I try to get student input before initiating the changes or additions to a unit of study.

We know that proportional reasoning is the cornerstone of higher mathematics, and is a major concept in middle grade mathematics. Making it come alive with real-life connections and high interest components is key. Sometimes all it takes is revamping an old set of lessons with a good thinking partner.

Ever want a redo on a lesson? Not because the lesson tanked, but because you suddenly had about eight new ideas that could have made it even better?

In the fall of 2010, I wrote a blog post for Scholastic about teaching scale with 3-D models. In that lesson, students constructed three-dimensional models of their bedrooms based on a 1 inch to 1 foot scale (1:12 ratio). In the post, I mentioned that students could scale up to recreate the walls of a home with stakes and caution tape on the playground.

It was an experience that built the schema for my students, but now nearly seven years later, I realize it could have been so much more. After all, now we have drones!

Recently, I was invited to meet with sixth-grade teacher, Whitney Heckert, to discuss ideas and strategies for her unit on proportional reasoning. As we brainstormed ideas, I mentioned the unit of study I had I done so many years ago. We made some adjustments and what follows are the additions made to the original unit plan.

For Mrs. Heckert, students were asked to create blueprints of their dream home. But first, we decided that in addition to the dream house blueprints the students created, they would be required to determine the height of the walls of their houses, and construct those from card stock and tape. Working on spatial reasoning by taking a 2-D drawing to 3-D with the addition of walls became a new goal for the project.

Students were also instructed to create the walls so they could be lifted (as one unit) from the blueprints. Once the walls were cut out and taped together, they created what looked like a maze; however, they were not permanently attached to the floorplan drawing. Therefore, the walls (now one unit) could be lifted on and off the original floor plan drawing. (Think of the walls like a lid on a pot that could be put on and taken off.) These models would be reference points for the students throughout the unit.

Mrs. Heckert asked the students to determine surface area and calculate how much paint it would take to paint the interior walls. They derived the ratio of bedrooms to bathrooms, exterior walls to interior walls, and rooms with tiled flooring to those with wood flooring. Students easily moved into using the models to make percentage calculations as well.

Next, we thought about perspective. We dreamt big and longed for a drone to capture aerial footage of the dream homes once the students had scaled up their drawings on the playground with caution tape and stakes. This video and the photographs would provide points for discussing and writing about misconceptions and observations. The footage from the drone let the students see that their perspective on the ground is much different from an aerial shot. The aerial footage permitted the teacher to discuss the how imperative it is for buildings to be plumb and square, and what could happen if proper alignment did not happen in the construction of their dream homes.

Our school does not own a drone, but our school district does! All we had to do was make a call. The administrators were more than happy to come and film the projects. Scott Campbell, the Technology Coordinator for our district, made a special trip out and filmed students as they begun the process of mapping out the first floor of their dream homes. We even posed for a “dronie” (instead of a selfie).

Finally, Mrs. Heckert created forms for organizing the thinking of her students, as well as charts for recording calculations and managing data. This had been lacking in my prior unit. When it comes to a unit renovation, collaboration is key. Because of that planning session, several themes arose. These were determined to be the top three:

### 1.     Frame old ideas for current day.

It’s 2017, people. We have awesome technology! As teachers, we worry that the most current technology is out of reach, too expensive. Consider resources that your school district may already have in its possession. Often the technology department has access to some of the newest technology and is willing to come and demonstrate or let you borrow it for a special project.

### 2.     Brainstorm like you mean it.

Collaboration is everything. Leave no stone unturned and consider all topics and connections fair game. As you are thinking through old lessons and units, create an exhaustive list of ideas related to the teaching. The crazier, the better. As you pare down your list, give special consideration to the ideas that seem “too big” and discuss ways you might be able to make it happen. This is where parent connections, business partners, and district level staff can come into play.

### 3.     Get student input.

Embarking on strategies and technology that you have never tried before can be tricky; student buy-in is generally the remedy. Just because the relevance of a new approach is a no-brainer for us, does not imply there is a correlation for the students. With ideas I consider to be a risk, I try to get student input before initiating the changes or additions to a unit of study.

We know that proportional reasoning is the cornerstone of higher mathematics, and is a major concept in middle grade mathematics. Making it come alive with real-life connections and high interest components is key. Sometimes all it takes is revamping an old set of lessons with a good thinking partner.

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