Making A Mobile
The setup
You are given some weights and a design for a mobile that has some attach points. The challenge is to put at most one weight per attach point so the mobile will balance along every arm. Assume the wires are weightless. Each arm in the mobile is a lever that needs balancing, so these puzzles are an extension of the Lever Balance puzzle given earlier in this Stage – practice those puzzles before starting these.
Simple example
Start with the simplest mobiles, which are just levers in the air. Above is a solution for putting the weights from 1 to 4 on this mobile to balance it. This works because (2 × 4) + (1 × 2) = (4 × 1) + (3 × 2).
More complicated example
Use the total of the weights below it to balance each side of the top wire (1 + 3) × 3 = (4 + 2) × 2.
Go to the Stage 5 Bonus Material for more examples and a longer discussion of mobiles.
Helping your child
Puzzles are meant to be challenging and to take time, so please don’t ruin the fun by telling your child how to do them. These puzzles are chosen so that you can create them easily and then have fun solving them together.
If your child gets stuck on a puzzle, you have several options. You can, of course, give very small hints, if you can think of things that won’t give away the puzzle. You can suggest looking at smaller or simpler versions of the puzzle. Encourage your child to be bold in their ideas, even if sometimes they lead to dead ends. We all learn a lot from our mistakes and dead ends! Let your child know that it is perfectly okay not to solve a puzzle on the first (or second or third) try, and that useful ideas may occur to them if they leave the puzzle alone for a day or two.
These puzzles are meant to be fun and to teach problem solving. One of the greatest mathematical pleasures is that AHA moment, after many false starts and much wrestling with a problem, when the answer is finally discovered – be sure to let your child experience that feeling of discovery as many times as you can!