At the moment, one of our local supermarkets has a slogan: 'Feed a family of four for $15' - and I've been doing that for considerably less for years !
The knack is to look at your whole budget. I know this sounds obvious but many people spend on things which could have ben acquired more cheaply, or not at all, leaving more for food.
Look at vegetables first and creative ways of making cheap meals. If you're not vegetarian, cut down on meats. Never throw anything away. Use wholefoods rather than refined flour and sugars.
One of my families favourites is fried rice. Cook a pan of rice, drain and leave to dry (I usually do it the day before) add a finely chopped onion and a grated carrot. Heat a little ooil in a pan and add any spice you prefer. Toss the rice and veg into the pan and fry vigorously. In the last two minutes, beat up an egg (or two depending on how many you're feeding) and drizzle into the hot rice, stirring all the time. Served with salad if you have it, a little grated cheese (dairy is very expensive here and may be where you live so that's a rare treat). Brown rice is not only slightly more nutritious but less is more filling for hungry kids.
Is that store slogan $15 a day for a family of 4, Large?