Saturday, June 18, 2011

Knitting & Math Problems


This is a compilation of resources created for a workshop I developed on knitting and math called "Knit it, Solve It!" for the Mississippi Arts Commission's 2011 Whole Schools Institute.  

Gauge problems:

  • Using your UKO in progress and/or using a swatch at your table, practice measuring garter stitch gauge.

  • Pretend you have designed a pattern for a simple garter stitch placemat.  Your gauge on size 8 needles is 5 stitches per inch.  How many inches wide is your placemat when you cast on 60 stitches? 

  • If your classmate’s gauge is 6 stitches per inch, and he/she casts on 60 stitches, how wide would the placemat be?  Would you change to a larger or smaller diameter needle to achieve the correct gauge?

  • If another classmate’s gauge is 4 stitches per 1 inch, and he/she casts on 60 stitches, how wide would the placemat be?  Would you change to a larger or smaller diameter needle to achieve the correct gauge?

  • If you cannot change needle sizes to get the correct gauge, how could you modify the pattern to make a set of placemats that are all the same width? 

Transformation Design with Triangles:  Using translation, reflection, rotation, and/or symmetry, create a design for the triangles provided.  If you like, transfer your design to graph paper and/or create a border.  What are the measurements for your design? How many triangles will you need?  How many squares? 

Blanket Problems:

  • Perimeter/Area Problem:  What is the perimeter of this blanket?  What is the area? 

  • Stitch Problem:  Approximately how many stitches are in this blanket? 

  • Time Problem:  About how many hours (or days) did it take someone to make this blanket using the estimated stitches and area of the blanket from the previous problem and an average time of 20 stitches per minute?

Note:  To achieve an even more accurate idea of time, one would need to consider the different amounts of time it takes to execute different kinds of stitches in the blanket.  Picking up stitches and binding off stitches takes almost double the time of a simple knit stitch.  Then, we would have to consider how long it takes to weave in ends.  

It might be interesting to ask students to keep a detailed log of time spent knitting  on a project and compare this time with an estimation of time worked out from measurements and average stitches per minute. 

  • Cost Problem:  How much would it cost to make this blanket? 

                        Factors to consider: 
      • yarn costs $2.99 ball (20 balls used)
      • shipping costs $15.00
      • needle cost: $19.99
      • tapestry needle: $.99
      • time compensation:  (use time from previous problem and agree on a fair wage to use)

  • Weight Problem:  If this blanket weighs approximately 3 lbs, how many balls of yarn at 2.5 ounces each did it take to make the blanket? 

  • Yardage Problem:  If a ball of yarn is 122 yards each and a blanket uses 20 balls of yarn, how many yards of yarn are in the blanket?  If the yarn from the blanket were unraveled in one continuous piece of yarn, how many miles long would the strand of yarn be?  (1 mile = 1760 yards) 

Design a Problem to Solve!  With prior knowledge or knowledge from today’s workshop, what problem can you think of that would be appropriate for the grade/grades you teach?

Questions or comments?

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