Designs with Number Patterns

This les­son is adapted from a math activ­ity my own kids did in mid­dle school, where they used col­ored string to “stitch” their pat­terns on card stock.  I sim­pli­fied this les­son for my stu­dents (4th grade and up), replac­ing the nee­dle and thread with mark­ers and a ruler.… 

Have you ever mar­veled at the fas­ci­nat­ing pat­terns found in nature??  
I like to intro­duce my stu­dents to these pat­terns by show­ing real life exam­ples of the *Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.), a pat­tern that appears in the spi­rals of sun­flow­ers (which have 55 clock­wise spi­rals and 34 coun­ter­clock­wise spi­rals), pineap­ples (which have 8 seeds in a clock­wise spi­ral and 13 in a coun­ter­clock­wise spi­ral), pine cones, shells, and more.  In this les­son, stu­dents use other num­ber pat­terns to cre­ate inter­est­ing, sym­met­ri­cal designs. 

  • 12 x12 white con­struc­tion paper
  • Ruler with raised or beveled edge (to pre­vent ink from smear­ing when you move the ruler)
  • Fine point mark­ers in assorted col­ors, plus black

1. Fold your paper in half both direc­tions, then open flat.
2. Place the 5” mark of your ruler on the cen­ter point (where your folds cross) and use a black marker to draw a 10” line cen­tered on the fold.  
3. Now turn your ruler and repeat this step on the other fold to make a cross that is cen­tered on your paper. 
4. On each “arm” of the cross, make 5 small marks 1” apart.  Think of the marks clos­est to the cen­ter as being “#1”, then 2, 3, 4, and 5 out to the end of each arm.
5. Use col­ored mark­ers to con­nect all the points in each quad­rant of your paper that add up to six (ex. 1+5, 2+4, 3+3, 4+2, 5+1).  When one quadant is com­pleted, move on to the next.  You may use the same color for each quadant, or try using a com­bi­na­tion of dif­fer­ent colors.
As an exten­sion, exper­i­ment with other num­ber pat­terns and see how your design changes. Or, try this same project on thin card stock, stitch­ing with yarn or col­ored string instead of draw­ing with markers.

*Fib­bonacci (c.1180 – c.1250) was an Ital­ian math­e­mati­cian from the mid­dle ages who is best known for spread­ing the use of the Hindu-Arabic numeral sys­tem (numer­als 0–9 and the idea of place value) and the num­ber pat­tern which became known as the “Fibonacci Sequence”.  Prior to this time, only Roman numer­als were used in Europe!

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6 Responses to Designs with Number Patterns

  1. Robyn January 20, 2011 at 5:44 pm #

    Hi! I am an art teacher for a group of home­school stu­dents and con­stantly try to find way to chal­lenge them! So I was thrilled to come across this project. I have seen it before but hon­estly never knew how to go about it. I have one ques­tion, I do not under­stand what you mean by using dif­fer­ent num­ber pat­terns to see how the design changes. I would really appre­ci­ate you help­ing me under­stand that!

  2. Anonymous January 20, 2011 at 6:32 pm #

    Thank you for post­ing this les­son. I also am a home­school­ing par­ent and am thrilled to find a chal­leng­ing les­son which cov­ers his­tory, math, and art. Coin­ci­den­tally, we’re study­ing the mid­dle ages.
    Thank you.

  3. Anonymous January 22, 2011 at 5:45 pm #

    I just want to tell you how much I love and appre­ci­ate your blog. I teach 5th and 6th graders in a small pri­vate school. I am respon­si­ble for teach­ing my stu­dents art, and while I am an avid crafter, I am not trained as an artist. I have found so many cool ideas on your site — I can’t wait to try them! And I love the math-related ones, like the tes­sel­la­tions and this one. Thank you!!!!

  4. Sherman Unkefer January 25, 2011 at 7:27 am #

    How fas­ci­nat­ing! This post is so intrigu­ing! Thanks for shar­ing this knowl­edge with us.

  5. TeachKidsArt January 25, 2011 at 11:30 pm #

    Robyn, some exam­ples of how you could change your design using dif­fer­ent num­ber pat­terns would be to con­nect each num­ber with “1” on the adja­cent axis (i.e. 1+1, 2+1, 3+1, 4+1), or con­nect each “2” with 2 and 3 on the adja­cent axis, etc. By adding more num­bers you can make more com­plex designs. I’ve kept mine pretty sim­ple since I work mostly with younger kids. I hope that helps!


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