Posts Tagged ‘math’

How To Design Stranded Mittens

Saturday, October 9th, 2010

Last night I finished a pair of mittens that I started a while ago.  I love making mittens because they are portable projects, and a rather necessary accessory for the Canadian winter that is quickly approaching.  I like customizing colours and patterns and making sure that my cuffs are long enough.

Really warm mittens are often knit with a stranded pattern in two colours.  The stitch pattern usually includes a maximum of 4 or 5 stitches in a row of one colour.

I knit with a rather tight gauge, using 4mm double pointed needles and worsted weight yarn from Topsy farms.  My general recipe for stranded mittens is as follows:

Decide on a stitch pattern: Colour in some squares on graph paper being sure not to make more than 5 stitches in a row one colour.

Figure out how many stitches and rows are in your pattern repeat:  Choose one point in the pattern and count horizontally and vertically until you have mapped out a repeatable pattern block.

There are 4 stitches and 6 rows in this repeat

There are 6 stitches and 10 rows in this repeat

Decide on how many stitches to cast on: This should be a multiple of the number of stitches in one repeat, and it should fall somewhere between 48 stitches for size small to 54 stitches for size medium/large.

Using the first pattern, the cast on could be (4)(12)=48 or (4)(13)=52 or (4)(14)=56

In the second case it could be (6)(8)=48 or (6)(9)=54

Cast on: Use one colour, cast on the appropriate number of stitches and join in the round being careful not to twist.

Knit cuff: Join second colour and work until the cuff measures 2.5 to 3 inches (depending on your cuff preference).

Thumb Gusset:  Mittens are very form fitted at the cuff, and you need to increase stitches to account for the width of your hand at the thumb area.  The way to do this is to increase 2 stitches every alternate row on the thumb side of the mitten.  The increases will affect the stitch count, and the pattern repeat.  A good work-around is to change the patterning for the thumb gusset.  A checkerboard or striped pattern on the thumb is easy to do.

Continue until the gusset is  17-21 stitches depending on thumb size.  Keep gusset stitches on a stitch holder or piece of scrap yarn, and cast on a full repeat of stitches, or whatever is needed to maintain a consistent pattern across the hand.

Knit Hand: Keep knitting in pattern until the mitten fits up to your little finger.

Decreases: Put the mitten on your hand.  Mark the stitches at the little finger and index finger edges for decreases.  There should be equal numbers of stitches on the palm and back of the hand.

Keeping pattern consistent repeat the following two rows until approximately 16 stitches remain

Row 1:  knit until 2 stitches before the little finger edge.  K2tog in main colour, SSK in main colour.  Knit in pattern until 2 stitches before index finger edge.  K2tog in main colour, SSK in main colour.

Row 2: knit in pattern.  Use main colour over the 2 stitches on the little finger and index finger edges.

Kitchener stitch bind off. video credit: the knitwitch on youtube.

Thumb: pick up and knit (in pattern) the stitches from the scrap yarn/stitch holder, and stitches from the cast on edge around the thumb hole.  I often choose stitches that are not right on the edge of the thumb hole to avoid creating holes around the thumb.  The number of thumb stitches is not critical.  Make it fit your thumb.  Knit in pattern in the round until the thumb is 1.5 to 2 inches long.

Decreases: K2tog in pattern until around 6 stitches remain.  Cut yarn leaving a long tail.  Draw yarn through stitches and pull tight.

Weave in ends

So…Now What?

Monday, March 1st, 2010

The Olympics are done.  The Knitting Olympics are done.  The Ravelympics are done.  Or……are they…..

Ceilidh and Eirinn (Photo credit: Mom)

I had such a good time, I think I will start up another Olympic challenge for the duration of the Paralympics later in March!  Who’s with me?

I’m happy to report that the sales of the Olympic Red Mitten Pattern have been rolling in, and are currently at the $1550 mark raised for the Penguins Can Fly swim team.  I hope that people continue to purchase patterns and knit these mittens through the end of the paralympics.  Maybe we can hit $2010…wouldn’t that be cool?

Who knows….one day maybe some of the Penguins will be swimming in the summer paralympics!

Tonight, during the closing ceremonies, after proudly modeling my gold-medal pattern creations Ceilidh and Eirinn, I sat with no knitting in my hands–for all of about 15 minutes.  It’s at times like this that I wonder if I do have a serious problem, but I was suddenly struck by inspiration to knit more cables for a baby sweater/vest of sorts that I can almost see in my mind.

The trouble with things in your mind is that it’s very difficult to make them appear just like you imagined they would.  I am doing my best though, keeping careful scrawly notes and math written down just in case this project ends up successful enough to share with other knitters out there.

I absolutely LOVE the yarn.  It’s Life DK by Stylecraft, a blend of acrylic and wool.  Easy to care for, and so soft.  I may need to go back to Wool Tyme to get more–there are so many babies to knit for this spring!

Are you gearing up for March 12th when the torch gets re-lit?  The Paralympics run from March 12th to 21st in Vancouver!!

Pattern: Robot Hats

Wednesday, February 24th, 2010

To celebrate the completion of the FIRST robotics build season (meet the team! see our blog!) I have charted and written up the pattern for our unique and delightful robot hats.

Download the hat pattern in .pdf form (full colour charts, photos and instructions)

We wear these hats to competitions, and other events, and they are also regular winter hats to some.  They help unite us as a team, and show our Canadian spirit when we are competing in the USA.  The first hats were knit on the way to the International competition in Atlanta Georgia, on our 22 hour bus ride.

The pattern is based on the Robot Hat pattern that I found on Ravelry last year.  It is knit with any worsted weight acrylic yarn, and 5.0mm needles.  My pattern is fully customizable to fit large and small heads alike based on a small swatch.

Our hats are each unique; the variations have included different stripes, different colours of robots, having a rolled up brim, having pompoms, curlicues, or horns.  We’ve even made headbands too!  Our team challenges each other to come up with more wild and wacky hat ideas, and figure out how to make them.  Each hat has robots on it, and is made from our team colours, and has 2809 (our team number) on it.

Some Math:  We recognize that team members, and mentors and younger supporters all have different sized heads.  It is a good idea to do a gauge swatch and a bit of math to make sure your hat will fit.

Measure the circumference of the head:________________inches.

Make a swatch in stockinette stitch (knit 1 row, purl 1 row) that is at least 2 inches x 2 inches.

Lay the swatch out flat (but do not stretch it), put a ruler on top of it and count how many stitches fit in one inch.  It may be easier to count how many stitches fit in two inches, then divide by 2.

Stitch gauge: ______________stitches per inch.

Generally hats stretch to fit around your head.  Subtract about an inch from the head circumference so the hat will stretch to fit around the head.

Hat circumference = Head circumference – 1.

Hat circumference =_____________

Cast on = Hat circumference  x  stitch gauge

Cast on = ___________________

Cast On the appropriate number of stitches for your hat. Join in the round being careful not to twist.
Work an inch or two in K2, P2 ribbing (more if you are going to flip the brim over)

Change colours as desired.

Knit an inch or two before starting the robot and team number motif.

It is highly recommended to use a spreadsheet or several pieces of graph paper to chart out the entire hat to be sure that everything is centered, and that the robots and team number can all be incorporated.  You can graph out team logos and other different robots if you’d like.


ROBOTS (source)  click for larger image

Try on the hat from time to time to be sure that it is long enough before you start decreasing.  Knit until the hat is long enough.

Decreases: Divide the number of stitches by 4, place markers at each division.  Each round, decrease by knitting together the two stitches that precede the marker.  Each round the total number of stitches will decrease by 4.  Continue until there are about 8 stitches left.  Cut the yarn, draw the yarn through the remaining stitches and pull tight.

Headband Option – Knit in the round.
Round 3 start robots leaving space for team numbers
Round 7 start team logo close to the top
Knit 1 round after robot complete then purl one round, then knit the lining for the headband (same number of rows that you knit for the outside.
Cast off.  Fold headband along purl line.  Sew Cast On and Cast Off edge together


Antenna–instead of decreasing so rapidly, decrease every 3 rows or so, to create a spike at the back of the hat.

Pompom–cut out two circles from cardboard.  Cut out a circle (1 inch diameter) in the centre of each circle.  Hold the two circles together, and wrap yarn around through the middle and around the outside over and over again.  When the circle is full, cut around the outside edge and separate the two cardboard circles a little.  Tie a long piece of yarn around and fasten it tightly around the middle bundle of strings.  Remove the cardboard, and trim the pompom.

Curlicues (source)
Cast on 20 stitches. (The final length of your curlicue will be the same as the length of your cast on row.)  Knit into the front and back of each stitch loosely, ending up with 40 stitches. Bind off purlwise. Here you see the curlicue already curling on the bind off row.  Take your finished curlicue and twist it in the direction it is already curling.

Horns and other structural knitting
Knit with wool and one strand of copper from a copper scrubbie (which is actually knit, so you can unravel it really easily).  You are limited only by your imagination.

Designing A Headband

Friday, February 5th, 2010

Several anonymous knitters met today at lunch to sketch out a plan for a surprise project. The goal was to design a headband that has a complex image on it, and some of these anonymous knitters looked at me strangely when I mentioned words like gauge and thickness of yarn, and stranded knitting, and reading charts.  This post is dedicated to these anonymous knitters, and all other beginners who want to make up their own designs.

Find out the general size of the garment

For a headband, this requires the circumference of the head (wrap a string around your head, then measure the string with a ruler), and an estimation of the width of the band.

Plan of attack

Headbands fit best if they can stretch outward, and knitting in the round will allow for this stretch.  Another option would be to knit a rectangle and sew it up (I avoid sewing things up if at all possible).  Consider how the edges might roll–add ribbing on the top and bottom edge to prevent rolling but to still allow it to stretch.  (I-Cord will not stretch….I learned the hard way on this one)

Choosing the right yarn and needles

If you are planning a really complicated pattern, choose thin yarn and fine needles.  This will let you have detail in your project without the project getting too large.


I don’t like this step, but it is sometimes a necessary step in the design process.  With the needles and yarn that you have chosen, knit a small rectangle at least 2 inches by 2 inches.  Get a ruler, and (without stretching your sample) measure how many stitches fit in one inch.  Measure also how many rows fit in one inch.  Write down your needle size, yarn that you are using, and stitches per inch, and rows per inch.  This will prevent the need for future swatching with the same materials.

NOTE: Stranded knitting with two colours tends to draw in (get tighter) than knitting in one colour.  Keep this in mind if you are going to knit with two colours.  Another option is to use duplicate stitch to add designs on after the headband is knit.

Math Time

To make a headband fit snugly around the head, you need negative ease.  This means that you should aim for the headband to be about an inch less than the head circumference.  If you are doing stranded knitting you might not need so much negative ease, since your knitting will be tighter.

Headband circumference[adjusted to account for negative ease] in inches x #stitches per inch = #stitches to cast on

Desired headband width in inches x #rows per inch = #rows to knit

Chart Time

Get a piece of graph paper, or a fresh excel spreadsheet, and mark off the rectangle that will be the headband (#stitches to cast on is the long side, and #rows to knit is the short side)

Colour in the design on the graph paper.  Each square will represent one stitch.  Think of it like you are creating the pixels of your picture.

Cast on!

Start with ribbing, then add your design according to your chart.  If your design is not symmetrical (like letters or numbers) make sure that your pattern will be the right way up and the right way around.  End with ribbing, and cast off.

I look forward to seeing the finished product!  Get knitting!

Toe Up Socks 101

Saturday, December 5th, 2009

I was asked tonight for a basic sock pattern. This isn’t how everyone knits socks. I know my grandmother shudders at the thought of knitting from the toe up rather than from the cuff down. I know others who learned knitting socks toe up and will probably never knit them cuff down. I’ve done both, and I find this method easier to explain, and more practical to knit.

Benefits of knitting socks from the toe up

  1. you can try it on as you go and make sure it fits you
  2. you can use up all your wool…making the leg of the sock longer or shorter is easier than changing the length of your foot!)
  3. nobody will ask you what you are making….they should be able to tell it’s a sock.

*progress pictures will be taken when I knit another sock*

Basic Socks (Toe Up Version) Socks that are knit to fit!


  • sock yarn (100g) split it up into 2 balls (50g each) before you start–one for each sock!
  • 2.5mm DPNs-double pointed needles (set of 4)

Skills: knit in the round on DPNs (tutorial) , figure of 8 cast on (tutorial), Kfb increase (youtube), picking and knitting stitches (tutorial), K2tog decrease (tutorial), SSK decrease (youtube), K1 P1 ribbing (youtube), cast off (tutorial)

My basic sock recipe (written from memory, please let me know if you get stuck and I will clarify)

Casting on

Using figure of 8 cast on method, cast on a total of 32 stitches (16 on each of two needles).
Divide the stitches so there are 16 sts on needle 1, 8 sts on needle 2 and 8 stitches on needle 3.

It is a little hard to manage at this stage since there are so few stitches and so many needles. Be patient though, knitting socks from the toe up is easier to modify so it fits your foot.

Increasing at the toe

Row 1: Knit all sts.
Row 2: begin toe increases (you will end up with 4 new stitches at the end of the round)

  • Needle 1 K1, Kfb, K to last 2 sts, Kfb, K1
  • Needle 2 K1, Kfb, K to end of needle
  • Needle 3 K to last 2 sts, Kfb, K1

Alternate between rows 1 and 2 until the toe of the sock fits over your toes nicely. This is usually somewhere around 60 sts depending on the yarn, needles, gauge etc. Don’t sweat it though, as long as it is big enough for your foot, that is what matters.

Knitting the foot
When your sock can cover your toes nicely, stop increasing. Knit every stitch around and around and around and watch your sock grow!

Knit until the sock goes up to about the middle of the arch of your foot (the longer the foot, the longer this will take. I am jealous of those with dainty feet…but I digress)
Increases before the heel
Row 1:

  • Needle 1 K all stitches
  • Needle 2 K1, Kfb, K to end of needle
  • Needle 3 K to last 2 sts, Kfb, K1

Row 2: Knit all stitches in the round

Alternate between row 1 and row 2 about 12 times.

Pardon my mathiness, but you’ll be creating a right angle triangle with the perpendicular sides running along the floor and up your leg, and the hypotenuse going along the top of your foot. Your goal is to have the side of the triangle that is going up your leg be about 1.5 inches long.

Setting up for the heel

You need to shift some stitches around before you make the heel. Currently needle 1 is holding all of the stitches for the top of the foot, and needles 2 and 3 are holding the stitches for the bottom of the foot, and the sides of the foot (the triangle stitches).

  1. Slide half of the stitches from needle 1 (the top of the foot) onto needle 4 (the empty one).
  2. Shift the triangle stitches (the ones that you increased) from the ends of needles 2 and 3 onto the ends of needles 1 and 4.
  3. This leaves a much smaller number of stitches for the heel (probably around 30 stitches, depending on gauge etc)
  4. Put all of the heel stitches on one needle.
  5. We will now call the heel stitches needle 1, and needle 2 and 3 will be the ones holding the stitches on the top of the foot.

Ok, that probably sounded difficult.  I promise you that it is easier to do, than it is to write down.  You should have about 30 sts on needle 1 (heel), and about 60 stitches split evenly between needles 2 and 3.

Knitting the heel flap

Working back and forth on needle 1 only

Row 1: K1, SSK, K to last 3 sts, K2tog, K1

Row 2: Purl all stitches

Repeat rows 1 and 2 until about 6 stitches remain.

Turning the heel

Pick up 12 (or so) stitches from the SSK decrease side of the heel. Knit the heel stitches, then pick up and knit 12 (or so) stitches from the K2tog decreased edge of the heel flap. (it should be about 12 stitches, but could vary based on your gauge. Just be sure that you pick up the same number on each side)

You should now have about 30 stitches on the heel needle.

Another bit of rearranging stitches (here we go again….moving stitches around!)

Slip the first half of the heel stitches onto needle 4 (the empty one). Slip the “triangle stitches” that we had moved earlier, onto the end of needle 4.

Slip all of the “top of the foot” stitches onto one needle. This should leave the remaining “triangle stitches” on another needle ready to be knit.

Pretty soon this will look like a sock….I promise!

Finishing the heel

You have just knit the heel stitches, and have not knit the triangle stitches on the needle to the left.

Turn the work (the wrong side will be facing you)

Row 1: Purl until one stitch before the triangle stitches. Purl the last heel stitch together with the first triangle stitch. Turn the work

Row 2: Knit until one stitch before the triangle stitches. K2tog with the last heel stitch and the first triangle stitch. Turn the work.

Alternate Row 1 and Row 2 until all of the triangle stitches have been incorporated. You should be back to almost the same number of stitches that you had in the foot.

Knitting the leg

knit in the round until the sock is almost as long as you want it.

Making the cuff (you need an even number of stitches….increase or decrease to make it so!)

K1 P1 ribbing in the round for an inch or two.

Cast off loosely, and sew in the two ends.

Put on that sock….march around proudly….then cast on for a second one

Family of Red Mittens!

Monday, November 16th, 2009

I’ve been working on red mittens since Saturday. Today I drafted a child version of the pattern!

Remember the one mitten?

In my knitting history, I’ve improvised many designs, but I’ve never attempted to write down the instructions in a way that anyone else could follow. My usual method involves a recipe card, and cryptic scrawling, a bit of a graph for patterns, a few numbers for size. This works well provided I finish mitten 2, or sock 2 soon after completing the first one. Otherwise it becomes an exercise in deconstructing the first mitten/sock, and hoping that in the end it really doesn’t matter if it’s an exact matched set, because, well that’s just proof that it’s hand made, and a guarantee that all of my results are unique!

and then there were two

Drafting up this red mitten pattern has challenged me to slow down, and be deliberate about how I am knitting. It’s easy enough to know how to do something, but the wording of it is a challenge that I’ve been working through these past few days.

An issue I’ve never really dealt with is sizing. My usual theory is to knit the garment, and find the person that it will fit. I’ve done enough knitting, that now I’m pretty good at guessing what needles go well with what yarn.

I’m not so keen on knitting swatches, so it’s been interesting!

I knit a mitten, and found out that it would fit a large hand. Then I altered the stitch count, and changed the needle size so it will make a mitten to fit a smaller hand. It is hard to imagine the math required to develop a child’s mitten, so after a little careful estimation, I cast on, and just went for it. These are the results! 

Cute eh?

Knit Night

Saturday, November 14th, 2009

Today is Friday the 13th, and it is a good day!

I went to see the Handloom Weavers and Spinners show and sale (still running Saturday and Sunday 10-4). If you are in the Kingston area, check it out. There are some very beautiful items.

My art of the day is the continuation of the puffy mittens, and the appreciation of the complexities of the weaving I saw today!

There were wall hangings, and polar bears…

handwoven bears

handwoven bears

….Felted Angels dressed in handwoven garments…

…beautiful wooly blankets…

…delicately patterned scarves…

…lots of handspun yarn…

…and the cutest little sheep ornaments…

I have belonged to this group in the past, and learned a lot from the knowledgeable instructors who taught me how to spin, and weave

my first weaving

learn to weave workshop--scarf in progres

After getting totally inspired, I headed off to knit at Wool -Tyme, where you will be able to find me on any Friday the 13th.  There were snacks, and coffee and cider, and lots of keen knitters, and beginner knitters.  I enhanced my yarn stash with a lovely skein of Cascade 220 in red.  New mittens are in my future!

dinosaur mitts

dinosaur mitts

There were some interesting projects being worked on this evening:  Dinosaur mittens, a baby bear suit, earflap hats, shawls, a tea cosy, and some were knitting their very first socks.

being mathy

being "mathy"

Anne, at Wool-Tyme challenged us to determine the number of stitches used in this garter stitch afghan.  We were all given an opportunity to be “mathy” and figure it out.  The winner got to choose any skein of yarn, or any set of needles!  (it is now that maybe being swatchless is not the best plan!  I’m not used to such calculations).

puffy mittenthe puffy mitten is getting bigger

The puffy mitten made an appearance, and grew a thumb hole and got a lot longer.  I enjoyed showing others about this thrumming method, and we all marveled at how fast hands heat up when they are surrounded by fleece.  I have to keep reminding myself of how big these mitts need to be!  Lots more knitting to do.

I hope you all had a very productive and creative Friday the 13th!

P.S. Congratulations to Lisa, Noor and Ru who are the three participants in Pay it Forward!

Bring on the math!

Sunday, November 8th, 2009

Remember when your high school teacher told you that math was important, and that you’d use it in your daily life when you grow up?

I have reached the point in the pattern where I am supposed to decrease until I get to the correct number of stitches which can be determined by a mathematical equation. (Don’t be scared by the math. It is a very useful calculation which I have tried to explain)

getting bigger!

getting bigger!

Let S be the correct number of stitches in the brim

Let R be the number of stitches in an inch

Let H be the circumference of your head (in inches)

S=R x (H-2)

What is (H-2)? We subtract 2 inches to create “negative ease” so the hat must actually stretch to fit on your head, and will fit snugly.

How do I determine H? I wrapped a piece of string around my head, and then used a ruler to measure the length of string. H=21 inches.

How do I determine R? I counted the number of stitches in 2 inches and divided by 2 to give me the number of stitches in one inch. R=5.5 sts/inch


The hat came with me to watch Nukariik, a throat singing duo. Click on the picture to see them in action!

Substituting into the equation

S=5.5 stitches/inch x (21 inches-2 inches)

S=5.5 stitches/inch x (19 inches)

S=104.5 stitches

The pattern then says to adjust this number to the nearest multiple of 8.

That’s easy, 8×13=104.

I currently have 120 stitches on the needles, so I will need to decrease a total of 16 stitches.

I am decreasing 8 stitches each row, so I will need to do 2 decrease rows. Logical, right?

these are the real colours in the sunlight

these are the real colours in the sunlight

I finished the hat tonight after singing a choir concert (another art form that I have enjoyed for most of my life). Here I am trying the hat on and attempting to take a decent photograph.

not so slouchy, but it is done!

not so slouchy, but it is done!

I’m currently blocking the hat around a dinner plate. I like how the circles of colour are so clear.

blocking the hat

blocking the hat

I have arranged with a friend to have a proper photo shoot tomorrow. Hopefully it will be a nice day!

Thanks to all who have followed the creation of this hat. I hope you are enjoying my daily art as much as I am. I’m looking for inspiration for tomorrow’s post. Is there anything you want to know?? Any good crafts I should try??