Classroom ideas using technology: a snowflake in winter. (2024)

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When I was a child in a land Jar away, I scooped up snowflakes andstared at them in wonderment and awe. So meltingly ephemeral. Gone in aninstant. And yet there, in the palm of my hand, I held all eternity. Buthow can that be?

The 'Snowflake Curve' was first conceived of by theSwedish mathematician Helge von Koch in 1904 (Wikipedia, 2017). It hasan area that can be bounded by a circle, and yet it has an infiniteperimeter. But how can that be?

Snowflakes falling in Brisbane, Australia would likely make newsheadlines during any season of a given year, even during winter. Year 8students at Ormiston College which is located in Brisbane, have madetheir own snowflakes--of a kind. Using the programming language Scratch,all Year 8 Mathematics students wrote code to construct Koch'sSnowflake Curve (Figure 1).

Student activity

As an initial exercise, Year 8 students were challenged toconstruct Koch's Snowflake Curve manually by first using colouredpencils and isometric paper. Students were then required to codecommands using Scratch to trace out the same curve pattern that they hadmanually created on the isometric paper. Figure 2 provides sampleScratch code constructed by a student, with additional commentsexplaining how they produced the curve.

Having produced the curve using Scratch, students were thenrequired to add some artistic flair and make a contribution to a classPowerPoint display. Figure 3 shows an example of how a student employedadditional commands to the script to make the snowflake multi-coloured.

An enthusiastic teacher demonstrated how to use the "playsound" function in Scratch, so that the curve would be drawn to themusic of "Winter" from Vivaldi's Four Seasons. Amazingly,Koch and Vivaldi went very well together!

Another student made multiple copies of their computer generatedsnowflake and, using PowerPoint, created a delightful animation ofgently falling snowflakes (Figure 4).

Summary

When a few more winters have passed, Year 8 Ormiston Collegestudents will be challenged to use their knowledge and skills from thisexercise with the topic, sequences and series. Students will bechallenged to consider, and explain the mysteries of the Snowflake usingthe additional knowledge from this mathematics topic with previouslylearnt concepts. Year 8 students are congratulated for achieving whatthey have by engaging in this activity, given the many varied andartistic contributions that they were able to make. Just as eachSnowflake has an infinite perimeter, they too are each individuals withan infinite inner potential.

Note

Activities outlined in this article, were given to students as anassessment which counted for a small percentage of the semester gradefor mathematics. A copy of the student activities are summarised in theAppendix.

References

Wikipedia. (2017, March 25). Koch snowflake. Retrieved 25 April2017 from https://en.wikipedia.org/wiki/ Koch_snowflake

Scratch, (nd.). Scratch. Retrieved 25 April 2017 fromhttps://scratch.mit.edu/

Appendix

Student worksheet: Creating the Snowflake Curve activities

The Snowflake Curve was first described by the Swedishmathematician Helge von Koch in 1904 (Wikipedia, 2017). It resembles asnowflake and that is why it is sometimes called the "SnowflakeCurve". It can be constructed by first drawing an equilateraltriangle and then adding more equilateral triangles at the centre ofeach side. Figure 5 identifies the first four iterations of theSnowflake Curve.

Activity 1

Using coloured pencils and isometric paper, complete the followingmanual steps to create a Snowflake Curve.

1. Draw the Snowflake Curve up to the fourth iteration.

2. Colour in your Snowflake Curve to make it look unique andattractive.

3. Write your name on the back of the paper.

Activity 2

Using Scratch, write some code to complete the following:

1. Construct the third iteration of the Snowflake Curve

2. Construct up the fourth iteration of the Snowflake Curve.

Note: be sure to use the "Make a Block" facility inScratch, so that your code is efficient.

Activity 3

Create a PowerPoint slide that displays your Snowflake Curve in animaginative, and artistic manner.

Caption: Figure 1. Year 8 Ormiston College students display themysterious snowflake.

Caption: Figure 2. Student comments added to explain how the codeused produced the curve.

Caption: Figure 3. Sample multi-coloured snowflake and Scratch codecompleted by a student.

Caption: Figure 4. Screen capture of a student created animation ofthe falling snowflakes.

Caption: Figure 5. The first four iterations of the SnowflakeCurve.

The Snowflake Curve sample marking schemeActivity 1: Snowflake Curve on paperAccuracy /2Design /IActivity 2[a]: Snowflake Curve using Scratch for third iterationNote: no need to print this, just show your teacher your SnowflakeCurve and the code that produced it.Accurate Snowflake Curve produced /2by some form of Scratch codeActivity 2[b]: Snowflake Curve using Scratch for four iterationNote: submit hard copies of your code and the resulting pictureAccurate Snowflake Cuive /1Scratch code showing the use of "Make a Block" /2Activity 3: Powerpoint slidePowerPoint slide contributed to class collection /1Artistic merit /1TOTAL /10

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Classroom ideas using technology: a snowflake in winter. (2024)

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