Twist on an old puzzle and our number scavenger hunt

who: J1, J2, J3
when: after lunch, before violin lessons
what did we use: mini-white board and things around our neighborhood

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Digit Substitution

You've seen these puzzles before: there are triangles, squares, and circles that represent digits in an arithmetic equation and you need to figure out which digit is represented by each shape. During a recent RightStart Math session, J1 got a couple of these. The puzzles were fun, but standard, each with a unique answer. We decided to add two twists.

How many answers?
The first twist was to find how many answers there are to this puzzle. You can see us mid-work, having already identified two choices for the circle and several options for the other two shapes.
The point is that it invites the kids to think carefully about the abstract relationships between the values that the shapes can have.

Build your own
I always love reversing a puzzle and having the kids build their own puzzles. I opened with the challenge to see if they could create a puzzle with no solutions. Initially, they draw the shapes at random and assume there's no solution. However, once we worked through a couple, they started to notice patterns and to carefully plot their strategies for making the puzzles impossible. Also, it led to discussions about what should be allowed as a solution: can a number have a leading zero, is it ok if two shapes represent the same digit, can we allow a shape to represent a negative number or a number larger than 9, etc.  Really cool thoughts that transcend the specific puzzles we suggested to each other.

Our number scavenger hunt

J3 went looking for numbers around our neighbourhood the other day. This was suggested long ago on Kids Quadrant last September, but I didn't really appreciate how good it would be for us until we started. Here are pictures J3 took of our finds from 1 to 4.

One swimming pool (that is soo big)

Two black metal pieces to open the door

Three plastic bottles (prior to us doing a civic duty and helping clean up)

Four light switches

Except the first, all pictures were taken by J3. We also found an office chair that has 5 wheels, but the picture didn't quite capture it.

Playing this game, J3 was really excited to count everything in sight. I was a bit surprised that she seemed to have very little prior expectation about whether any particular group would meet the target we were seeking, so we will make sure to play this again soon.