**PERSONALIZED RULERS**

**MATH / SCIENCE, ****GRADES 3 - 6**

** Lesson Overview:**

In this activity, students use Tinkercad to design their own rulers with custom units and features. The rulers can be designed for fabrication on a 3D printer, or with a laser cutter or vinyl/craft cutter. By combining units of measurement, geometric concepts, and personalization into one ruler, the goal is to foster multi-functional flexibility, fun, and personalized learning in a classroom.

The lesson is structured to follow the Engineering Design Process (EDP), a process widely used by designers in any discipline to tackle challenges. While there are many ways that people solve problems, designers often opt to use the EDP because it offers a roadmap for the project journey and will help them work efficiently and effectively. The process requires that the designer first clearly **Define** the challenge, then **Learn** about and **Explore** existing solutions, before beginning the design stage. This understanding of the problem, combined with the **Design** step requirement of generating at least 3 different ideas, allows for a rich set of creative solutions to draw from choosing a design direction. The designer is now ready to prototype the solution in the **Create** step. An important feature of the EDP is the expectation that the designer will build 2 or more prototypes after the direction is set. This is done by cycling through the **Create** and **Observe/Improve** steps a few times. It is recommended that students have an opportunity for at least 2 design-build-improve cycles. When students feel they have to “get it right the first time” they are less willing to take risks and be creative. On the second and later times through the cycle, they can fix flaws and adopt successful ideas from classmates. Hopefully, the designer will have an opportunity to **Reflect** on the product they created and the process they followed, looking for learning habits and insights that will help in future challenges. The **Share** step involves documentation, publishing, or presenting to affirm the project and inspire others.

Created by: Anya Timchenko, Diane Brancazio, MIT Edgerton Center

**Essential Question(s):**

How are rulers useful in understanding units and measurement? How can students create rulers with units, fractions and geometric concepts that are important to them and fun to use? How can students create custom rulers for specific purposes?

**Skills Taught: **

- Units of measurement, with fractions
- Geometry: Angles
- Geometry: radius, diameter
- 3D modeling in Tinkercad

**Time Required:** 1 - 2 hours

**Materials Needed: **

- For design:
- Sketch paper and pencils
- Tinkercad
- Rulers/protractors
- Miscellaneous prototyping materials (cardstock, foam sheets, markers, etc)

**For fabrication - options:**

- 3D Printer and filament
- Laser cutter and wood or plastic sheet
- Vinyl/craft cutter and cardstock paper

## Step 1: Define

**Context:**

Rulers are common tools used for measurement. To use them effectively, students must understand how the ruler was intended to be used. What if the students chose units and concepts that were important to them and designed their own ruler? How about custom rulers for a specific purpose?

**The problem/challenge:**

Start the activity by sharing project definition, criteria, and constraints with students.

**Definition:**

Students use Tinkercad to design their own rulers with custom units and features. The rulers will be fabricated using the materials and technology(s) specified by the teacher.

**Criteria:**

Students choose 3 of the following to include in their ruler

- Linear scale with subdivisions (e.g. inch and ⅛“, or centimeter and .5 cm)
- Triangles with specific corner angles (e.g. 30°, 60°, 90°, or 45°, 45°, 90°)
- Circles with specific diameters (e.g. ¼“, ⅓“, ½“, ¾“)
- Semi-circles to show radius and diameter (e.g. ¼ inch R and ½ inch D)
- Unit conversions - in text (e.g. 2.54 cm = 1 inch, 12 inches = 1 foot)
- Patterns, for stenciling (e.g. curves, zigzags, semicircles)
- Personal name, logo, or character of choice

**Constraints:**

Overall ruler size

- For plastic rulers made on a 3D printer - approximately 4” x 1.5”, or 10 cm x 4 cm. This size allows them to fit easily in the print bed and minimize printing problems. Print time varies with the level of detail. A moderate ruler should take 40 - 60 minutes to print. Simple rulers with few cutouts will take less time, about 30 minutes or less.
- For cardstock rulers made on a vinyl/craft cutter - less than 10” x 2”, or 25 cm x 5 cm. This size allows them to fit on a standard sheet of cardstock.
- For wood or plastic rulers made on a laser cutter - less than 10” x 2”, or 25 cm x 5 cm. This size allows them to fit on standard sheet stock.

**Learning/Product Goals: **

Students will make rulers for their own use, for a specific need defined in the classroom, or for sharing in the classroom.

## Step 2: Learn / Explore

**1. Research:**

Review existing rulers, protractors and other measuring tools. Discuss what they are intended to be used for and how useful they actually are to students. Students list what they like/understand and don’t like /understand about the measuring tools. Look online at other types of “kids’ rulers” or special measuring tools.

**2. Collect: **

Have students create an inspiration page where they sketch and/or document a few of the rulers they like. Include a list of the quantities that the ruler is used to measure.

## Step 3: Design

** 1. Design: **

Students brainstorm ideas using the Project Definition and the Criteria and Constraints specified in the “Define” step. Use the inspiration page created in “Learn / Explore” step as a reference.

**Option A:****draw designs**on how the ruler will look and/or function. Use paper, whiteboard, drawing apps.**Option B:**Build simple models using**crafting materials**(paper, glue, clay, pipe cleaners, etc.) to show look and/or function.**Option C:**Let the students**play around in Tinkercad**to get familiar with the program and make practice models.

It is important that students create at least three different ideas. Many will want to go with their first idea. Encourage them to make life-size sketches of the ruler so they can start thinking about the details, then play around with ideas and see what comes of it. Generating ideas can be hard work, but putting in the time and effort can produce great creative and unexpected results.

*Some examples:*

*Rectangular Ruler (See the Red/Outlined ruler above):*

*4” x 2” rectangle, with ¼” steps, and number at each whole inch.**Shapes varied by diameter.**The shape can be exported at SVG (numbers and name would not come out) to laser cut or as an STL and 3D printed.**To export a detailed SVG file for vinyl/laser cutting make sure the numbers/letters are turned into holes that go all the way through the ruler. Consider size when exporting the shape.*

*Circle Ruler (See the Orange ruler above): *

*The overall diameter of about 4”. The outer edges show all angles that are multiples of 10 between 10° and 80°.**The inside shapes show the diameters. 1” and .33”, and a 90-45-45 triangle.**The “mouth” part of the face measures in inches (.5” per step) on the bottom and mm (5mm) on top.**The shape can be exported at SVG (numbers and name would not come out) to laser cut or as an STL and 3D printed.*

**Triangle Ruler (See the Green ruler above):**

*Two sets on measuring units on the edges. 4” with .25” steps and cm with 5 mm steps.**The overall shape is a triangle with 60-degree angles.**The shapes can be exported as SVG (numbers and units would not come out) to laser cut or as an STL and 3D printed.*

*Semi-circle Ruler (See the Blue ruler above):*

*The shape is based on a 4” radius and shows four angles around the shape: 35 °, 50 °, 55 °, 40°.**The bottom is divided in increments of ¼”, with a number at each whole inch.**The inside shapes show various dimensions including 1”, ½” and ¼”.**The shape can be exported as an SVG (numbers and name would not come out) to laser cut or as an STL to 3D print.*

*Detailed Ruler (See the Purple ruler above):*

*Creating a highly detailed ruler is possible. However, this could take multiple hours to create and then multiple hours to print. Students can use Tinkercad at home, so they could continue adding detail later if desired.*

**2. Choose a Direction: **

Have the students choose a design that meets the criteria of the project. Sketch these designs and emphasize that this is their design “direction” and that the design they create may be different as they learn more about the tools available and iterate through the design cycle.

## Step 4: Create

- Before starting to model, set the grid units to inches or millimeters as desired. Set the snap to your smallest unit of measurement, (e.g ⅛” ¼”, 5 mm, or 1 mm).
- Pull in a shape which will be used as the body of the ruler. This can be a circle, half circle, triangle, square, rectangle, etc.
- Click on the shape and scale it to the desired
**length and width**. Keep in mind the constraints of your 3D printer, vinyl/craft cutter, or laser cutter. See the recommended sizes in the**Constraints**section of**Step 1: Define**. - Set the
**height**of the shape to ⅛” or 3 mm. - Create the
**increments**by bringing in a hole or solid blocks, and arranging them by the desired unit of measure, then grouping with the ruler base. - Pull in shapes and change the dimensions as desired. Students may need to calculate side lengths to get the angles for their desired triangles. Turn the features to hole and group with the ruler base.

To create a right triangle within a given angle (A), use the wedge shape and rotate it to be flat on the workplane. To create the appropriate angles, set the sides to 1, tan(A) and scale from there. For example, to create a 30, 60, 90 triangle, set the sides to 1 and tan(30). For isosceles triangles use the roof shape, rotated to its side.

Image: the Blue shape is the Wedge and green shape is the Roof.

7. Personalize the ruler by adding text and/or shapes for names, initials, logos, etc. Text/shapes can be dropped on top of the ruler to create embossed features. For engraved features change the text/shape to a hole and group with the ruler. Raise the feature up a bit if the text/shape has features that will otherwise fall through.

Note that rulers exported as SVG files will only include the outline of the part (including interior features, but will not include embossed or engraved features. To export a successful SVG, make sure the letters and numbers are cut through the ruler before exporting.)

## Step 5: Observe, Improve, Iterate

- Try out the new rulers! Have some fun measuring things. Encourage students to share their creations and come up with things for each other to measure.
- It’s a good idea for students to have an opportunity for at least two design-build-improve cycles. When students feel they have to “get it right the first time” they are less willing to take risks and be creative. On the second time through they can fix flaws and adopt successful ideas from classmates.
- Provide stopping points for the class where students can observe, evaluate, and document their design.
- Create documentation guidelines for students to record their thoughts and progress as they work through product iteration cycles. This can serve as a formative assessment.

- A description/sketch of the design
- How well the design met the project definition, criteria, and constraints
- What students liked about their design
- What students want to improve on the design
- Suggestions for improvement

**Possible prompts:**

## Step 6: Reflect

**Reflect: **

After the design and build time is over, have students reflect on the process and product. This reflection is similar to the one in the “Observe, Improve, Iterate” step but now includes reflection on the process as well.

** Possible prompts:**

## Step 7: Share

Give the students an opportunity to share their personalized rulers with the class or some other community. Options for sharing include presentation, demonstration, blog or online post, video clip, physical display, family events, and maker fairs, or in the use for which it was intended.

## Step 8: Resources

** “THING” Checklist: **

To ensure you get a quality 3D print, go through the list before tinkering and printing.** (See images above)**

**Tutorials:**

Basic Tutorial- 3:27 mins, will explain the basic shape moving, plain orientation, scaling, and grouping.

2D to 3D design - 5:52 mins, showing how to clean up SVG files and create them into extruded 3D shapes.

Advanced shape generator - 19:46 mins, a demonstration on how to create your own free-form shapes in order to make custom designs.

## Step 9: Project Extensions

** Examples: **

- Students create a
**custom unit**of measurement for their rulers. They use the new rulers along with standard unit rulers to measure and record data for classroom items. Once students have that data, they can analyze, compare, and share what trends they notice in their data. They may use base ten multiplication and division to convert their custom units to standard units to make comparisons. They may also discuss whether their custom ruler would be a good measurement tool for measuring additional items (i.e. a car, the distance from their desk to the classroom door, the school track, a cup of water, etc.) and they can make suggestions for the correct units of measurement that would be needed to measure the specified items. - Students learn about systems of measurement across different cultures or time periods, including
**non-standard systems of measurement**, and include this information in their rulers, perhaps as the total length. - Students discuss units of measurement that are
**not physical dimensions**, such as money, temperature, color, or weight. They may look at the different increments used in the various systems and debate the merits of conforming to a universal system of measurement. - Add
**Unit conversions**. Inches to centimeters, fractions to decimals, Fahrenheit to Celsius, mm to cm to m (and so on).

## Discussions