Number Patterns
Players: 2 or more
Ages: 4 and up
Cost: Free!
Math Ideas: Sequences, skip counting, linear functions
Questions to Ask:
What would the next number in this pattern be? What would the tenth number be?
How many numbers do you need to figure out the missing number?
Different contexts call for different games. Some of my favorite board games, although fun, require a lot of time and space to play.
We don't often have the ability to take over the whole kitchen table with a multi-hour Monopoly session. As parents, sometimes we just need something to keep our kids distracted in the car for a few minutes so they'll stop arguing about which song from Moana to listen to next.
Number Patterns is a perfect mini-game for these situations.
How to Play
To play, just list a sequence of numbers, including a blank. Ask your kids to figure out the missing number. Some examples below:
5, __, 7, 8
11, 13, 15, ___
2, 6, __, 14
17, __, 39, 50
You'll notice that these puzzles became more difficult. The first puzzle is perfect for my 4-year-old daughter. The next couple of puzzle keep my first grader thinking hard. That last question is a legitimate challenge for anyone, even adults, especially if they don't have any paper handy.
Like I said, it's a mini-game. There's not a lot more to explain. There is, however, a ton of math to discuss!
Where's the Math?
The beauty of Number Patterns is that you and your child can find interesting math to discuss, no matter how old they are.
For our youngest kids, there is a challenge simply in remembering the relative locations of numbers to each other. Your child might be able to count to 8, but if you ask them "what comes after 7?" or "What comes just before 9?" they may get stumped. In that case, number patterns are a great game to strengthen their conception of the order of numbers.
Early elementary will get introduced to the idea of skip-counting, which is where you count by 2s, 3s, or some number other than 1s. Skip-counting shows up all over elementary math, helping kids understand multidigit numbers (count by 100s, count by 10s) to multiplication (4*5 can be thought of as "count by 4 five times").
And of course, number patterns are just a variation on arithmetic sequences, which your child will learn about in middle and high school. Of course, you don't need to ruin the fun of the game by saying the phrase "arithmetic sequences" out loud. Just let them be pleasantly surprised when they reach Algebra 1.
Questions to Ask
The beauty of Number Patterns is its flexibility: each puzzle is an opportunity to have a math conversation, and you can follow your child's lead to see what they want to talk about.
My favorite question to ask is "Can you come up with a number pattern to ask me?"
I firmly believe that people learn ideas more deeply when they approach them from multiple angles. Solving a number pattern requires a certain amount of thinking, but developing a number pattern that is solvable is even more challenging. Consequently, the payoff for your child's understanding is greater.
For older kids, I like to ask "What would be the tenth number in this pattern?"
If you ask that question enough, with enough different patterns, your kids might even come up with some shortcuts to identify the tenth number in a pattern. Then you can ask about the 100th number, or the 43rd number, or whatever number you want.
Sometimes I like to have fun with my kids and give them a pattern like "5, blank" and then argue about whether this pattern is solvable. It tends to lead to the question "How many numbers do you need to know in order to solve a number pattern?"
The main thing to keep in mind when playing with your child is to keep them challenged without making them frustrated. Give them plenty of time to think before you give them a hint. When you want to jump in, give them another 20 seconds. Then when you really want to jump in, give them another 10.
If they don't want to play anymore, let it go. You'd rather they have positive memories of Number Patterns so that a few days later, while they stare out the window, they ask "Can you give me another number puzzle?"