If you're homeschooling a kid or, god forbid, kids during this pandemic, you're undoubtedly looking for ways to burn off some energy, for them and for you! Box jumps at home can be a fun way to do that, and constructing a box from a half-sheet of plywood is fairly straightforward.
The box is usually called a plyometrics box, plyometrics being a fancy word for jump training. The vertical jump is an excellent measure of the power you can generate, power meaning speed and strength expressed simultaneously. Like VO2max, the vertical jump is considered a good measure of your natural genetic potential because it doesn't respond well to training. Put another way, you would need to spend a lot of time and effort to get fairly incremental improvements in both your VO2max and vertical jump. Box jumps aren't strictly measuring vertical jump because you're also drawing your feet up to land in a squat position, but that's a nitpick.
Box jumps are still worth doing, just make sure you're doing it for the right reasons. What are the wrong reasons? Glad you asked! Don't use plyometrics for strength or conditioning unless you really have no other options. Strength is a general adaptation (i.e. don't do stupid things like practicing throwing with a dumbbell or "functional training")and is best acquired under a barbell. Conditioning is a specific adaptation (don't run long distances to prepare for interval-based sports and vice-versa), and although you can certainly do box jumps as intervals it will also accumulate a lot of impacts that you probably don't need.
So what are the right reasons? Well, box jumps are fun, both for kids and adults, meaning it doesn't seem like so much of a chore. Box jumps train a natural movement pattern, one that adults in particular are prone to lose as they age and forgo the running and jumping they did as kids. Box jumps are mentally challenging and thus will build confidence and courage, because standing in front of a box set at a height that stretches your abilities requires you to fully commit; don't underestimate the joy to be gotten from landing a high jump you weren't sure you could! And finally, even though you might not end up with a five-foot box jump you can still improve your jump to the limits of your natural potential.
The box in the picture above is made from a half sheet of plywood, 4×4 feet and 3/4 inch thick. We used sanded plywood from Lowes because we're lazy. It's 16x19x24 inches, giving you three heights for jumping. Standard plyo boxes are 20x24x30, which weighs more, takes up more space and requires a full sheet of plywood. This guy gives instructions for making three different sizes, and although none are the half-sheet version we built the process is the same. Our 16x19x24 box used six cut pieces, two of each: 16×24, 17.5×24 and 14.5×17.5. You can see in the picture how they're arranged to get to 16x19x24. Here's the cool thing: you can get extra height out of your box by building a simple cradle out of a single eight-foot 2×4. It will hold the box in it's tallest position and can raise it to at least 32 inches or so, depending on how high you screw in the legs.
For training we do two warmups: first, stand in a standard jump position, heels about six inches apart, arms down and back and hinged slightly at the waist. Explode upward on to your tiptoes without leaving the ground, reaching your arms upward and holding that stretched out position for a few seconds. Drop quickly back into the jump position, and after you've done a few reps bring your feet off the ground as you're dropping. Second warmup: same as the first but actually jump, trying to bring your knees up as far as possible in front of you.
When you start jumping, just progress from the lowest comfortable height where you know you can land it, do 2-4 jumps and increase the height. Try to land softly on the balls of your feet, bending your knees with good lower back control, both on the jump up and more importantly the jump down. Limit your volume to a few reps at each height. You can either step down off the box, or walk off it if you're OK with the impact of landing. Bonus tip: remember to limit forward motion while jumping, as that increase forces and difficulty.
Some basic safety tips: round the corners of the box to eliminate sharp edges. Make sure it's on a level surface. Aim for landing on the center of the box. Make sure there's nothing you can fall into in the immediate vicinity. And watch your arm swing: we cracked our hands pretty hard on the box by swinging our arms straight forward as we jumped, a mistake we will not repeat. Be safe out there!