If you don't want to work with plarn but you do want to make a red, white and blue placemat, then try this cotton crochet pattern from Jessie At Home. This is an easy crochet pattern in that it's worked in single crochet stitches only, but you'll have to do some increasing and decreasing since this crochet pattern is made on the diagonal.

Crochet Patriotic Placemat from Jessie At Home
Amber Crochet Placemat Doily
Handmade Crochet Placemats are always fun and a easy crocheting project. Crocheted placemat doilies are always very popular choice for decorating. Crochet doily patterns are great for decorating any corner of your home. Doilies are the most versatile projects you can make. There are so many design and shape options to try them out and of course you can make them in combination of different stitches. Once you have made one you will surely want to make more of them. They are a lovely way to add a personal touch to your home. Add a touch and elegance, style and charming ambiance to your home decor with this pretty Amber Crochet Placemat Doily. I absolutely love making Doilies for home decor and they also make great gifts for your loved ones. The pattern is very simple and easy which is also great for beginners. Materials Used:- 4 Ply Cotton Knitting Yarn 4 mm Crochet Hook Size:- 16 Inches - can be customized to any size

Granny's Scrappy Placemat
My Granny's series features one round granny squares. This makes it really great for using up those tiny bits of yarn in your stash. If you don't need a placemat, use it as a larger doily. You'll need 282 yards of worsted weight yarn. As a placemat, I recommend cotton since it's more durable, but as a doily, acrylic works too. I used Lily Sugar n Cream for my placemat. Alternatively, I recommend WeCrochet Dishie (cotton) or Red Heart Super Saver (acrylic). I have included instructions to make a variety of sizes depending on your preference. This placemat took me about 8.25 hours to complete.

Crocheted Patriotic Basket Pattern
Make your 4th July holiday more creative and fruitful by creating this patriotic crochet basket. Use this basket for decor and presenting sweet treats to your friends on this Memorial Day. Working on this patriotic basket is easier than you think by using a double strand of yarn. Use two-color yarn in a weaving pattern. You can create this basket more proficiently by working in stripes.

Red, White, and Blue Plarn Crochet Placemats
Placemats like these would make a fabulous addition to your outdoor picnic table, especially when celebrating holidays like Memorial Day and the 4th of July. They are made with plarn, an interesting material to upcycle for use in crocheting placemats. This free pattern also comes with instructions for complementary plarn coasters.
Note that it's not recommended to use these placemats for hot dishes, but they're ideal when serving sandwiches, salad, pickles, or other similar picnic fares. Best of all, plarn is easy to make (for free) using readily available materials. And of course, you could opt to use different plastic bag colors to make similar crochet placemats without the red, white, and blue theme.
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Beginner-Friendly HDC Placemat
Here is an easy, basic crochet placemat that anyone could crochet. Even a beginner would have no trouble making this simple design. All that you need to know how to do is half double crochet in rows, adding a simple single crochet border to polish it off.
However, if you are more knowledgable about crochet and want to add a fancy border, this placemat comes with instructions to add a two-round edging consisting of hdc v-stitches and wide puff stitches.