Product Pyramid
These puzzles are the multiplicative version of the Addition Pyramids seen in Stage 4. You are supplied with a target number and a pyramid of numbers.
The challenge
The challenge is to find a path of connected numbers down the pyramid so the product of the selected numbers is the target.
In this pyramid the target is 36, and the red lines indicate the path that works.
These puzzles are easier if you start by doing the prime factorization of the target. Because 36 = 2 × 2 × 3 × 3, these prime factors must be picked up along the path, and this helps guide the search.
Knowing about prime factorizations also makes it much easier to create these puzzles.
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!