When children plan, build and rebuild structures they develop math skills and learn to focus on solving problems needed all their lives. They learn to think like engineers.
National scientists encourage families to use materials around the home to reinforce the National Science Foundation's program called STEM (Science, Technology, Engineering, and Math) used in schools. For more family math fun see grandparentsteachtoo.org, the authors' books, and podcasts "Learning Through the Seasons" at wnmufm.org.
What to do
Using large blocks or small boxes build a structure against a wall and then outline the wall using blue painter's tape. This becomes a blueprint for young children to follow. Can they rebuild using the outline? Outlines can also be done on the floor.
With your supervision, encourage children to explore fitting nuts and bolts together once you are sure no one in the house will swallow them. They'll love taking them apart and putting them back together.
With adult's help young children can push or pound golf tees into styrofoam packing material or meat trays. They can sort nails and screws and count them out into numbered cups or a muffing tin. They can also bang away with real nails and stryofoam, wood scraps, or a log.
Toothpicks and gum drops
A few bags of gumdrops or miniature marshmallows and boxes of toothpicks are excellent cheap building materials. Show children how to poke a toothpick through a gumdrop and repeat the p process to build. Make a cube with them to start. Sometimes it's helpful for children to build against a cereal box or wall to hold up their structure.
They can build flat structures or 3-D. Explain how to design and build houses, animals like giraffes and dogs. They can make furniture like tables and chairs for dolls, spaceships, and playground equipment. Let them play and explore with a pile of gumdrops and toothpicks. You might want to play a game "Can you make what I make?" another day.
Show children that triangles are stronger than rectangles. Experienced children might make a bridge between chairs. How long can it be before it breaks? How many cars can it hold? Can you make a family Eiffel Tower? How high can a tower or skyscraper be? Will a tower be taller if the base is a larger square and the rest are small squares? Give children an opportunity to experiment and question. Let them know it is OK if a structure breaks and they need to figure out a better way to build and redo.
There are also many commercial snap-together block variations (such as Legos), Tinker toys, train tracks and Lincoln logs for young engineers.