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?

Teaching Tips & Tricks

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.  

Teacher/Student Ratio

1.      The best ratio for teaching knitting is 1 to 1.  Then, each student can “pay it forward” and promise to teach at least one other student.  In no time at all, students will be learning to knit exponentially!
2.      If you must teach a larger group at one time, either recruit some outside volunteers or students you have previously taught to achieve a smaller teacher/student ratio.  As an alternative to mentors, project a knitting video or set up videos on multiple computer stations.  Try to have some books with diagrams and/or photos available, too. 

Supplies for Students

1.      Intro letter with resources
2.      Worsted weight, wool yarn
3.      Size 7 or larger wooden or bamboo needles
4.      Gallon size Zip Lock Bags or plastic shoe boxes
5.      If you let students purchase readily available metal or aluminum needles at local discount stores or acrylic yarn that is difficult to knit with, they may experience frustration.  It might be better to take orders for interested students, and place a bulk order from an online source so that good materials are available.   
6.      Some type of notebook to use as a knitting journal/project diary
7.      A crochet hook (around size 7 or 8) for picking up dropped stitches

 Classroom Supplies

1.      Tapestry needles for weaving in ends
2.      Scissors
3.      Rulers or tape measures
4.      Knitting needles in various sizes and types that could be checked out
5.      Knitting books with kid-friendly patterns
6.      Collection of downloaded, free knitting patterns in a notebook or file
7.      Guidelines for how and when students may knit in the classroom or at school
8.      A few crochet hooks (various sizes) for picking up dropped stitches

Set-Up for First Lesson:  Knit a UKO!

1.      Students may want to knit something to wear or use from the first try.  Instead of setting up a goal to knit a scarf or potholder, plan to knit a UKO, an Unidentified Knitted Object!   It won’t matter what mistakes are present or what it looks like.  The UKO will be a  funny keepsake of their first knitting experience.
2.      If possible, prepare knitting kits in Zip-Lock bags.  Previous to class, cast on and knit a few rows onto wooden or bamboo needles with worsted weight, wool yarn.  Let your students learn the basic knit stitch, and give them video links to learn about slip knots and casting on later.  The first class will be so much more successful if you start with the basic knit stitch as the goal. Learning to knit is so much easier if the first few rows have been established.
3.      Stress that mistakes will happen!  Stress that students are training their hands to do something totally new!  Stress that it will become easier as muscle memory is developed!

Learning from Mistakes

1.   If students keep at it and bring back a UKO, you can look at it with them and help them see their mistakes.  In no time at all, students will be able to help each other analyze mistakes in UKOs. If they get frustrated and unravel their UKO while at home, they won’t be able to learn from their mistakes! 
2.      Holes or decreasing stitches indicate dropped stitches or yarn-overs. 
3.      Split or knotted stitches indicate the student is not sliding the needles all the way through the entire loop of yarn.  The needle may be going through part of the yarn and dividing the plies. The needle may not be going through the loop against the other needle.  
4.      Increasing stitches indicate students are wrapping the yarn around the needle in the wrong direction. 

Suggested Order of Basic Lessons

1.      Knit stitch (garter stitch is rows of knit stitch only)
2.      Binding off
3.      Making a slip knot
4.      Casting on
5.      Knit stitch (garter rows)
6.      Purl stitch
7.      Increasing and decreasing
8.      Weaving in ends
9.      Gauge, needle selection, yarn selection
10.  Pick a project!

Questions or comments?


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.  

Knitting Books

Knitting books relevant for the workshop are gathered together in a Knit School Amazon StorePlease remember to support local bookstores and/or yarn shops when possible.  Any revenues from Knit School Amazon Store will be used to support teaching children and teens to knit.

Online Knitting Community

Ravelry is an amazing resource!  If you are a knitter, you have to check this out.  You can search for free patterns.  You can search for a pattern and see what yarns other people have used.   You can keep track of your own projects, stash, needles, books, etc.  AMAZING! 

Online Knitting Videos

The following sites have multiple teaching videos.  For other videos, search knitting terms, projects, and abbreviations on You Tube for a plethora of how-to videos!  Find one that works for you.
Guidelines for Teaching Kids to Knit 

Curriculum Guides 
Knitting and Math 
Higher Math, Science, and Artistic Knitting: Inspiration  
Inexpensive Knitting Supplies
  • for inexpensive natural fiber yarn and knitting needles (including good quality circular needles) 
  • for inexpensive wooden and bamboo needles made by ChiaoGoo (the needles used at the workshop—9 inch size 7, 8, and 9 single point needles)
Please remember to support local yarn shops when possible! 

Just For Fun!  

Questions or comments?