The chequerboard square needs you to carry a second strand of yarn, and switch between the 2 colours at regular intervals.
You use the same technique to create plaid patterns. This stitch is a great one for getting the hang of colour changes and carrying a second colour.
This pattern is written in US terms, but the UK translation is below.
Double Crochet (dc) = treble crochet
Start by Chaining a multiple of 5 stitches plus 2 stitches for your turning chain
Row 1. In the 4th chain from your hook (turning chain counts as a stitch) make a dc. Dc in next 2 stitches. Dc in the next stitch, but change colour in the final 2 loops.
After each colour change give both threads a tug to make sure they are nice and taught.
*Carry the second colour taught against the bottom of the row. Make 5 dc over the top of the carried yarn* repeat across the row.
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Row 2. With the colour that you used in the final stitch of row 1, make an alternate turning chain in the first stitch. Dc in the next 4 stitches, changing colour in the final 2 loops of the last dc.
Carry the second yarn thread taught against the bottom of the row and dc in the next 5 stitches, changing colour in the last dc. *Make 5 dc over the top of the carried yarn, changing colour in the 5th dc* Repeat between *and*
Change colours in the last dc of the row.
All your colours should be in the same order of row 1.
Row 3. With the colour you changed to at the end of row 2, make the alternate turning chain in the first stitch, and make a dc in the next 4 stitches, changing colour in the last dc. *Make 5 dc over the top of the carried yarn, changing colour in the 5th dc* Repeat between *and* don’t change colour at the end of the row
Repeat rows 2 and 3 for as many rows as you need