Provisional Crochet Cast On
This provisional cast on (PCO) is worked with a crochet hook over a knitting needle using a piece of smooth waste yarn; the waste yarn is removed later by unravelling the crochet chain produced during the PCO. The stitches picked up from the PCO edge are finished as the pattern directs. When these stitches are picked up, there is always one less stitch picked up than the number originally cast on since the stitches are picked up between the original stitches.  
Cast On - Step 1
Tie a slip knot 6" / 15cm from the tail end of the waste yarn.
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Cast On - Step 2
Place the slip knot on the crochet hook.
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Cast On - Step 3
Place needle parallel to crochet hook, waste yarn behind needle.
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Cast On - Step 4
Bring hook over needle, then to the left and under the yarn, to catch the yarn with the hook.
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Cast On - Step 5
Pull hook with waste yarn through loop on hook.
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Cast On - Step 6
Bring waste yarn between the hook and needle then under needle to the back.
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Cast On - Step 7a
With the yarn in front of the needle, catch the yarn with the hook.
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Cast On - Step 7b
Pull hook with yarn through loop on hook.
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Cast On - Final Chain
Repeat Steps 7a and 7b four or five times to create a short crochet chain (this helps to identify the end from which to undo the PCO later and makes unravelling the chain easier). 
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Cast On - Finished
Cut the waste yarn leaving a 6" / 15cm tail and pull the tail end through last chain lightly. This tail will have to be pulled out of the chain again when the chain is unravelled later so a tight knot is not desired. 
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DON'T FORGET the final step: to attach the working yarn (below)!!!
Attach Working Yarn 
Using working yarn, knit one row. Turn. You are now ready to work the first row of the pattern. 

Picking Up the Provisionally Cast On Stitches 
Stitches may be picked up mounted with right (first) leg at the back of the needle or with the right (first) leg to the front of the needle. To place the right (first) leg of the stitch at the back of the needle (Combination style), pick up the right (first) leg with the needle tip; to place the first (right) leg at the front of the needle, pick up the left (second) leg of each stitch with the needle tip. (This may seem counter-intuitive but, remember, once stitches are picked up, the work will be turned upside-down to work the PCO stitches.) 
 
In the picture at right, knit stitches from the first row of knitting with the working yarn are highlighted in pink. Stitches to be picked up later are the ones formed between and below these knit stitches. Look for stitches that form an upside-down V (shown in green at right). The gold-coloured needle tip in the Step 1 picture below is pointing at the first (right) leg of such a stitch. Notice that it is not the first yarn strand in this row that is picked up but the second yarn strand which forms the first (right) leg of the stitch (or third yarn strand which forms the second (left) leg of the stitch). 
 
There will always be one less stitch picked up from a PCO than the number of stitches originally cast on because the picked up stitches are seated between the cast on stitches. 
 
Please note, in this example, the initial work is not finished before picking up the PCO stitches. Most often the item would be finished before picking up the PCO stitches and therefore only one needle would be in use.
Picking Up - Step 1
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The gold-coloured needle tip is pointing to right leg of first stitch to be picked up. If the right leg of each stitch is to be mounted to the back of the needle (Combination style), pick up the right leg of the stitch; if the right leg of each stitch is to be mounted to the front of the needle, pick up the left leg the stitch. (This may seem counter-intuitive but, remember, once stitches are picked up, the work will be turned upside-down to work the PCO stitches.)
Picking Up - Step 2
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Pick up the right (or left) leg of each 'inverted V' stitch with the needle tip. Small insert shows all stitches picked up (1 less than original cast on number).

Push stitches onto the needle an inch or two (2.5 – 5cm) to make sure they don't slip off while the PCO chain is unravelled.
Picking Up - Step 3
Pull the tail yarn back through the last crochet chain to allow the chain to unravel.
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Picking Up - Step 4
Gently pull the tail yarn to unravel the crochet chain.
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Picking Up - Step 5
Unravel the chain all the way across the bottom; this frees the PCO stitches.
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Picking Up - Step 6
When the last chain is unravelled and only the slip knot is left… 
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Picking Up - Step 7
gently pull the yarn ends to undo the slip knot.
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Picking Up- Step 8
Notice that the yarn is 'caught' in a side loop of the last knit stitch of the first knitted row…
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Picking Up- Step 10
There are 12 stitches cast on originally in this example and 11 stitches picked up from the Provisional Cast On.
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Picking Up - Step 9
simply pull the waste yarn out of this side loop. This is often misinterpreted as a missed cast on stitch; it is not.
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The work can now be turned upside-down and the PCO stitches finished as directed in the pattern. 
 With working yarn, begin pattern using cast on stitches.