Circles, Circles, Circles


Circles

This lesson adds engineering with littleBits to a more traditional study of the formula for finding the circumference of a circle, making a math lesson into a STEAM design challenge. Students first design circle drawing machines before analyzing the diameter and circumference of circles their inventions draw to approximate the value of pi.

Objectives:

Students will be able to:

– Approximate the value of pi by comparing the relationship between circumference and diameter of circles
– Design and build a working circle machine using littleBits

Assessment:

– Analyze student understanding by collecting student work. Use attached documents to partner with students for assessment:

SCAMPER Checklist: Students use this checklist to ensure thorough brainstorming
Documentation Report: Students document problems they encountered and solutions they used during the design process

Standards:

NGSS Science and Engineering Practices

– SEP2. Developing and using models
– SEP3. Planning and carrying out investigations
– SEP4. Analyzing and interpreting data
– SEP5. Using mathematics and computational thinking
Common Core Math Standards

– G: Geometry

Duration: 1-3 days of 45 minute classes

GRADE LEVEL

Middle School (ages 11-13)
Elementary (ages 8-10)
High School (ages 14-17)

DIFFICULTY

Intermediate

SUBJECT

Art/Design
Math
Engineering

MODULES & ACCESSORIES USED (8)

slide dimmer (1)
dc motor (1)
button (1)
power (1)
servo (1)
wireless receiver (1 channel) (1)
wireless transmitter (1 channel) (1)
powerSnap (1)

OTHER MATERIALS USED (6)

cardboard 1
Rubber bands 1
Glue 1
Tape 1
Paper 1
other available building materials 1

ADDITIONAL FILES
https://lb-community.s3.amazonaws.com/uploads/user/72565/2eb4bdc8-e569-4aab-85d6-5b87d29f22da.docx

https://lb-community.s3.amazonaws.com/uploads/user/72565/c54cde5f-8b9b-47c4-b933-47f8b039acba.docx

LESSON GUIDE

STEP 1 : Introduce

(10 minutes)

Start by showing your students the circle created by Spiral Bot, an invention on the littleBits Project Page. Ask them what they notice. Some will likely volunteer that the circle is close to perfect.

Tell students that in this lesson, they will be creating a different machine that creates “perfect” circles. Explain the lesson objectives. Make it clear that the lesson will give students an opportunity to iterate through Invention Cycle, as well as create a sampling of circles for the class to analyze.

Take this opportunity to see what students already know about pi and the ratio between the circumference and diameter (or radius) of a circle. While many may already be familiar with the formulas, explain that in this lesson, students will approximate the value of pi by analyzing the relationship between circumference and diameter in the circles their machines create.

STEP 2 : Create

Circles1
Picture 2

(10 minutes)

To start your students’ brainstorming process try one or both of the following suggestions:

1. Give students time to create circles with compasses. Ask them to think about how they could use littleBits to mimic a compass. Review the geometric measurements in a circle including the diameter, radius, and circumference.
2. Ask students to create basic circuits with power, button, and DC motor. While maybe not essential, the DC motor will likely be a popular Bit in many circle drawing machines.

Creating circles with compasses and getting their hands moving by building basic circuits will likely kickstart your students’ imaginations, getting them started inventing their own circle drawing machines.

STEP 3 : Play

(10 minutes)
After creating the basic circuit outlined above, give students time to play with the Bits. Playing with the DC motor will give them time to think about they can use it to build their circle machines.

At this time, you may want to introduce supporting craft materials. Consider supplying the basics (cardboard, paper, tape, glue, rubber bands) along with additional supplies students can be creative with (tinker toys, math manipulatives, recycled plastic, etc.).

This is also the time to start conversing with students to support students in the brainstorming process. Consider asking questions like:
-How will you attach a pencil to the DC motor?
-Will you place the paper below or above the machines?

STEP 4 : Remix

Circles2

(30-60 minutes)
Free students to create their own circle drawing inventions. Give them the time and space they need to be creative. Expect that many of their first creations will fail. Encourage students to learn from these failed attempts.

Partner with students to help assess their progress during this stage. Ask students to complete the SCAMPER Checklist to document their brainstorming ideas. Students can also fill out the Documentation Report to identify problems they encountered and solutions they designed. Both files are attached to the lesson.

STEP 5 : Share

Circles3

(10 minutes)

Beyond using the Invention Cycle to come up with a unique designs to draw “perfect” circles, this lesson requires students to analyze the circles their machines draw. Even though time may be short, it is important to give students an opportunity to share what they have created. Try using a gallery walk strategy. Instead of spending considerable time having students present their inventions to the whole group, gallery walks can occur in as little as five minutes.

Ask students to leave their circle machines on their tables and then walk around the room, viewing what others created. Asking students to give others feedback on post-it notes can save time as well as build community and boost confidence. Make sure to establish clear ground rules for the types of feedback allowed on post-its. At the same time, observing what others have created can give students ideas for invention in this or other projects.

Adjust the gallery walk to fit your needs. For example, you could have half of the class stay by their inventions to answer questions while the other half walks around. After a set amount of time, students switch places, giving all students a chance to share about their machine as well as check out what others created.

During the gallery walk, take the time to look at what students have created as well as observe the quality of feedback students are giving to each other.

STEP 6 : Review

Circles4

(10 minutes)

Now analyze the circles. Ask students to measure the diameter and circumference of their circle(s). Students will have to problem solve to measure the circumference. One possible solution is to use string to approximate the circle and then use a ruler to measure the length of string.

Afterwards, ask students to divide the circumference by the diameter. Collect these results as an entire class. Based on your sampling size and the accuracy of student measurement, you should have a close approximation of pi. Discuss any outliers to see if you can discover the cause of error.