Open Middle®
Directions: I picked 3 dominoes out of a bag and they all had exactly 10 pips, but the same number was not on both sides of any of the dominoes.
Which dominoes could I have picked? Is there more than one answer?
Hint
Typically dominoes come in sets up to double-6, but they can also come up to double-9 or double-12. Consider possible answers for each kind of set.
If one side of the domino had 8 pips, how many pips were on the other side if I had 10 pips altogether?
If one side of the domino had __ pips, how many pips were on the other side if I had 10 pips altogether?
Answer
If it is a double-12 set of dominoes, the answers are:
0 and 10
1 and 9
2 and 8
3 and 7
4 and 6
0 and 10
1 and 9
2 and 8
3 and 7
4 and 6
Source: Brian Kelley
I like this idea, but these solutions do not match what actual dominoes look like.
Hi Janet. I guess their are bigger sets of dominoes than we realized. I thought you were right but wanted to verify and I found this: https://www.amazon.com/Double-Color-Dot-Dominoes-Game/dp/B001D4MIZM/. So apparently these are possible answers.
Yes there are larger sets of dominoes, but typically up to double 6 or double 9 are standard for game-playing. Some cultures will likely have more familiarity with domino games using certain sets (I have mostly played games with double six sets and rarely with double 9 sets).
So depends what students were introduced to before.
For a double 6 set the only solution is the 4:6.
For a double 9 set the other solutions (except the 0:10) come into play.
For a double 6 set, 7 might be a nicer number (1:6, 2:5, 3:4) to start with initially.
Because the intention of this task is to explore partners of 10, I’ve kept the question as is, but added some information in the Hint to indicate that there are different kinds of sets of dominoes.