String Math - Crochet, Braiding, Lanyards

Objective: How knitting works.

Notes: Knitting can unravel. Knitting is worked horizontally and unravels vertically.

Objective: How crochet works.

Notes: Crochet can unravel. Crochet is worked horizontally and unravels horizontally.

Objective: Crochet and knitting can unravel.

Notes: Unraveling is unique to crochet and knitting because it is worked in loops.

Objective: Crochet a chain stitch.

Notes: A slip knot resembles a regular knot except you do not pull the end all the way through. Chain stitch is simply one loop pulled through another loop creating more loops. This is done by wrapping the yarn around the hook and pulling it through the original loop.

Materials: Yarn, Crochet hook, Scissors(optional)

Homework: Practice the chain stitch, you do not need to post a picture of your sampler.

Objective: Crochet a single stitch.

Notes: When working into the chain you will insert your hook under one part of a given V. To build the single stitch you will first insert your hook under the V. Then you will wrap your yarn once around your hook and pull it out from under the V. You will then wrap your hook once more and pull that loop through all loops on your hook, resolving the stitch. When working into any stitch other than the chain stitch you will insert your hook under both parts of the V. When you come to the end of a row add a single chain before turning.

Materials: Yarn, Crochet hook, Scissors(optional)

Homework: Make a single stitch sampler 10 stitches wide and 10 rows tall.

Objective: Finish off a sampler.

Notes: When you have finished your final stitch you will cut your yarn leaving some excess. You will then chain one but pull the yarn all the way through. Pull until tight.

Materials: Yarn, Crochet hook, Scissors

Homework: Finish off your single stitch sampler

Objective: Crochet a double half stitch.

Notes: To do this stitch wrap your yarn around your hook before inserting your hook under the V. Once you are under the V wrap again and pull the loop through the V. You will wrap one last time and pull the new loop through all your stitches resolving the stitch. When turning rows add a single chain to the end before turning.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a double half stitch sampler 10 stitches wide and 10 rows tall.

Objective: Crochet a double stitch.

Notes: To build the double stitch you will wrap before inserting your hook under the V. You will wrap again and pull your new loop back under the V. You will wrap a new loop and pull it through only two loops. Wrap again and pull through the remaining loops resolving the stitch. When you end a row add two chains before turning.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a double stitch sampler 10 stitches wide and 10 rows tall.

Objective: Crochet a triple stitch.

Notes: To build this stitch first wrap twice before inserting your hook under the V. Once you are under wrap your yarn around the hook and pull the new loop back under the V. You will then wrap and pull through two loops. Wrap and pull through two loops. Wrap and pull through the remaining loops resolving the stitch. When ending a row make three chain stitches before turning and beginning the next row.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a triple stitch sampler 10 stitches wide and 10 rows tall.

Objective: Crochet a square or rectangle built from a chain.

Notes: Squares are the same height as they are wide. There are no stitches removed or added to create a rectangle or a square.

Materials: Yarn, Crochet hook, Scissors, Tape measure

Homework: If you do not have samplers already build a sampler of a square and a rectangle.

Objective: Increase or decrease crochet stitches.

Notes: To increase stitches you will stitch multiple stitches into one V. This is added at the beginning or end of a row. To decrease stitches there are two options. My preferred method is to skip the first stitch of a row and work into the second V. The other option is to omit a stitch on the end before creating your chain and turning. This method does not provide a smooth edge.

Materials: Yarn, Crochet hook, Scissors

Homework: Practice increasing and decreasing stitches.

Objective: Crochet a parallelogram and a trapezoid from a chain.

Notes: Parallelograms and Trapezoids both have parallel lines. Trapezoids have one set of parallel lines. Parallelograms have two sets of parallel lines. Slope is documented as the rows over the stitches (rise over run). So if a work increases by one stitch every 3 rows the slope would be 3/1. Trapezoids may have two different slopes for the sides that are not parallel. Parallelograms must have the same slope on both sides.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a parallelogram and a trapezoid. Document your slopes either numerically or with graph paper.

Objective: Crochet a equilateral, isosceles, right, and scalene triangles from a chain.

Notes: Triangles are any shape with three corners and three sides. The equilateral triangle has the same angle for every corner and the same length for every side. With single stitch your triangle will be roughly the same number of rows tall as it is wide. The Isosceles triangle has two sides that are the same length and two angles that are the same. The right triangle will have a "square" angle somewhere on it. This is most simply done by only decreasing one side. The scalene triangle has no rules except to have three corners and three sides. This triangle will have two different slopes.

Materials: Yarn, Crochet hook, Scissors

Homework: Make each of the 4 triangles. Don't forget to document your slopes.

Objective: Crochet a kite and a diamond from a chain.

Notes: Diamonds will start from a point and have the same slope and length for all the sides. The kite will also start from a point but it will have different slope and length for the bottom two sides or the top two sides.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a Diamond and a Kite. Document your slopes.

Objective: Set up a round for crochet.

Notes: One way a round can be made is by making four chain stitches. You will then insert your hook into the first chain stitch you made, wrap your yarn around your hook and pull through all loops. You are then ready to chain as many stitches as you need to match the height of the stitch you are using. There are three different possibilities with a round that you are making. A flat circle has exactly enough stitches to make a perfectly round shape without warping. A bell shaped circle has not enough stitches and is therefore curling in on itself. A flair shaped (or saddle, Spanish skirt shaped) circle has extra stitches and is beginning to roll in waves.

Materials: Yarn, Crochet hook

Homework: Practice building a round.

Objective: Crochet a circle worked in a round following a given pattern.

Notes: Begin with a round and follow the number of stitches and stitch patterns in the attached files.

Materials: Yarn, Crochet hook, Scissors, Attached files

Homework: Make a new circle adapting from my original pattern as needed. Document your own stitch pattern using the file attached. I am not looking for exactly perfect circles, I am looking to see your thought process and struggle to solve problems you encounter.

Objective: Make circle patterns.

Materials: Yarn, Crochet hook, Scissors, Attached files

Homework: Build your own circle pattern and test it.

Objective: Make an oval.

Notes: An oval is a circle split in half with extra material in between. Your initial chain will have to have the number of stitches you want the oval center wide as well as a stitch for each apex of your circle halves. If you have a odd numbered circle pattern you will have to choose an even number on either side to split in half. You will never increase the number of stitches in your center section, your circle halves will already be adding any addtional stitches you would need.

Materials: Yarn, Crochet hook, Scissors, Cricle pattern

Homework: Your homework is make an oval. Document the circle pattern you used as well as the number of stitches you added between your circle halves.

Objective: Measure your head and sampler.

Notes: Measure your head where the brim of the hat should hit. Your gauge will need to be measure how many stitches are in an inch as well as how many rows are in an inch.

Materials: Sampler, Head, Measuring tape

Homework: Measure the head you are going to make your hat for. Measure your gauge on your sampler for rows and stitches per inch. Document all of this.

Objective: Calculate the preliminary numbers to prepare for a pattern.

Notes: In this lecture I will explain how to create part I of your pattern. There is an example and a template you may used attached here. I have also included a screen cast (that is in time with the movie) if you wish to visualize the process as the lecture is going or at your own leisure.

Materials: Attached files(printed), Compass, pen or pencil, Calculator(with Pi function)

Homework: Complete all preliminary math for your measurements.

Objective: Complete the bell pattern based on your previous calculations.

Notes: In this lecture I will explain how to create part II of your pattern. There is an example and a template you may used attached here. I have also included a screen cast (that is in time with the movie) if you wish to visualize the process as the lecture is going or at your own leisure.

Materials: Attached files(printed), pen or pencil, Calculator(if your wish)

Homework: Complete all sections of the pattern template based off your measurements.

Objective: Make your hat following your pattern.

Notes: Build your hat following your pattern. Skip counting is your friend. If you have a row of 36 stitches and every 2nd and 3rd stitch are in the same section, then skip count. 3, 6, 9, 12...33, 36. This way you will never loose track of your count by counting two things at once.

Materials: Yarn, Crochet hook, Scissors, Your pattern

Homework: Make your hat following your pattern.

Objective: Tuck in the ends of your work.

Notes: Weave the tails of your work into the main body of the work so that they are hidden.

Materials: Finished project, Crochet hook

Homework: Tuck in the ends of your hat or any other piece.

Objective: Crochet a round square.

Notes: The corners of the square are 90 degree angles. The corner pattern we will be using is 3 double stitches, 2 chain stitches, 3 double stitches. This creates the 90 degree angle.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a square worked in a round.

Objective: Crochet a round triangle.

Notes: The corners of the triangle are 60 degree angles. The corner pattern we will be using is 4 double stitches, 3 chain stitches, 4 double stitches. This creates the 60 degree angle.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a triangle worked in a round.

Objective: Learn the relationships between stitches and angles in rounds.

Homework: Observe the differences between the angles.

Objective: Crochet a round hexagon.

Notes: The corners of the hexagon are 120 degree angles. The corner pattern we will be using is 2 double stitches, 1 chain stitch, 2 double stitches. This creates the 120 degree angle.

Materials: Yarn, Crochet hook, Scissors

Homework: Make a hexagon worked in a round.

Objective: Observe some common errors in my afghan.

Homework: Keep these ideas in mind when you make your own afghan.

Objective: Find some inspiration to be creative in your stitch choices.

Homework: Your homework is to make your afghan following one of the polygon patterns (triangle, square, or hexagon). Please try different stitches and share your work with us.

Objective: Observe that a strand disappears from sight.

Notes: With any given braid one strand will disappear behind the rest of the work and not be visible.

Objective: Observe the similarities and differences between weaving and braiding.

Notes: Weaving contains a pattern of over and under that is observable in braiding as well. Braiding is done diagonally. Weaving is worked horizontally and vertically. Because braiding is worked this way all strands share the tension through the work. In the weaving the one strand (pink) has full control of the tension. It is the primary strand in the weaving vs. the shared work of the braid.

Objective: Braid a traditional three strand braid.

Notes: The three strand braid has a pattern of moving strands from the bottom to the top in a pattern of right, left, right, left. This over and under pattern of moving from the bottom to the top should remind you of the weaving.

Materials: ribbon(or other string), a way to anchor your end

Homework: Make a three strand braid. Only post if you need feedback these are a little hard to see.

Objective: Braid a traditional four strand braid.

Notes: The four strand braid has a pattern of moving strand from the bottom to the top in a pattern of left, left, right. The even stranded braids will have a mismatched set of movements. As you can see there are two left ward movements and one right hand movement.

Materials: ribbon(or other string), a way to anchor your end

Homework: Make a four strand braid. Only post if you need feedback these are a little hard to see.

Objective: Braid a traditional five strand braid.

Notes: The five strand braid has a pattern of moving strand from the bottom to the top in a pattern of left, left, right, right. When you weave this it will become very apparent how similar this is to traditional weaving.

Materials: ribbon(or other string), a way to anchor your end

Homework: Make a five strand braid. Only post if you need feedback these are a little hard to see.

Objective: Observe the difference of inward and outward turning on a french braid.

Notes: When you turn inward you will notice that the new strands coming in will be the "columns" of the part of the braid. In effect the new strands are covering the sides of the braid. When you turn outward you will observe that the braid is on top of the new strands coming in creating a ridge. The new strands do not cover up the "columns" of the braid that we talked about in the disappearing strand.

Objective: Braid a half french three strand braid.

Notes: Adding small amounts of additional hair (or yarn) is what defines french braiding. The half french only adds strands to one side.

Materials: Wig or a friend's head

Homework: Your optional homework is practice the 3 strand half french braid on a friend or a wig.

Objective: Braid a full french three strand braid.

Notes: The full french braid adds strands to both sides of your braid whenever a new strand is moved to either side.

Materials: Wig or a friend's head

Homework: Your optional homework is practice the 3 strand full french braid on a friend or wig.

Objective: Braid a full french four strand braid.

Notes: The four strand french braid adds strands to both sides. The sides will still appear different since one side will always be turning inward and one side will be turning outward.

Materials: Wig or a friend's head

Homework: Your optional homework is practice the 4 strand french braid on a friend or a wig.

Objective: Braid a full french five strand braid.

Notes: The five strand braid adds strands to both sides. Notice that like the three strand braid both sides will be inward turning or outward turning.

Materials: Wig or a friend's head.

Homework: Your optional homework is to practice the 5 strand french braid on a friend or wig.

Objective: Braid a three strand braid that curves back and forth.

Notes: This curved or turned braid I found to be much easier when using a stiff material like the lanyard string. I have provided a photo of my lanyard string 3 strand braid here so you can see more clearly the movement of the strands. Please note the one strand that remains unchanged going straight throughout the work unturned. Your homework for this lesson is make a curved 3 strand braid. If you happened to purchase "The Complete Guide to Needlework" the rug making section can also show you how to use three strand curved braids to make oval or rectangle rugs.

Materials: Ribbon(or other string), a way to anchor your end

Homework: Make a curved 3 strand braid.

Objective: Braid a four strand braid that curves back and forth.

Notes: This curved or turned braid I found to be much easier when using a stiff material like the lanyard string. I have provided a photo of my lanyard string 6 strand braid here so you can see more clearly the movement of the strands. Please note the strands that go straight through the work unturned.

Materials: Ribbon(or string), a way to anchor your end

Homework: Make a curved 4 strand braid.

Objective: Braid a five strand braid that curves back and forth.

Notes: This curved or turned braid I found to be much easier when using a stiff material like the lanyard string. I have provided a photo of my lanyard string 6 strand braid here so you can see more clearly the movement of the strands. Again observe how the strands are traveling through the work.

Materials: Ribbon(or string), a way to anchor your end

Homework: Make a curved 5 strand braid.

Objective: Apply the concepts you have learned into a complete work.