Double checking a math problem as a game
Exploring a way to make double checking a math problem into a fun game to play with your kid who loves math
Did you check your work?
It can be difficult to get a kid used to double checking their math problem solving.
When asked to double check they look at their work with confidence and say, "yeah, I double checked."
It can then be annoying as the adult to say, "really? Did you? What did you do? Did you plug the answer back in, did you solve it a different way, did you..."
They don't want to hear that and it can get annoying for the adult to to repeat over and over again.
Trying something different to get the same result
One way we've tried making this into a game is to come up with as many different ways to solve a problem as possible.
Note, we don't do this for all of the problems, just once or twice a math session.
We look together at a problem they solved (the problem, not the solution they wrote up), and I try solve it on my own.
Then I look at the work they did and see what steps they took to go from the initial work to the final work.
A few scenarios occur:
- we both did the same steps and got the same answer
- we both did the same steps and got different answers
- we did different steps and got the same answer
- we did different steps and got different answers
The Double Check Game
Regardless of the scenario, we can play the double check game!
The game is simple: we try to solve the problem as many different ways as possible.
Elementary School Example
Math problem is:
78-57 = ?
So to play the game, we try to solve the problem in as many different ways as possible.
The first solution:
? = 78 - 57
break apart the 57
? = 78 - 50 - 7
? = 28 - 7
? = 21
A second solution:
? = 78 - 57
subtract an easier number from 78
? = 78 - 60 + 3
? = 18 + 3
? = 21
A third solution:
? = 78 - 57
subtract 57 from an easier number
? = 80 - 57 - 2
? = 23 - 2
? = 21
A fourth solution:
? = 78 - 57
count up from the 57
57 to 60 => + 3
60 to 70 => + 10
70 to 78 => + 8
? = 3 + 10 + 8
? = 13 + 8
? = 21
A fifth solution:
? = 78 - 57
break apart the 78 to a number close to 57
? = 18 + 60 - 57
? = 18 + 3
? = 21
A sixth solution:
? = 78 - 57
make the ones digit subtraction easier
? = 78 - 58 + 1
? = 20 + 1
? = 21
A seventh solution:
? = 78 - 57
draw a number line and shift to make the 57 a 60
-------57---------78
move everything up by 3
-------60---------81
? = 81 - 60
? = 21
An eight solution:
? = 78 - 57
draw a number line and shift to make the 78 an 80
-------57---------78
move everything up by 2
-------59---------80
? = 80 - 59
? = 21
A ninth solution:
? = 78 - 57
draw a number line and shift by 50 to make it simpler
-------57---------78
move everything down by 50
--------7---------28
? = 28 - 7
? = 21
A tenth solution:
? = 78 - 57
split by base 10 (left to right subtraction)
? = 70 - 50 + 8 - 7
? = 20 + 1
? = 21
We don't always get to 10 different possible solutions, but we usually find that we can get at least 2 or 3.
Algebra I Example
An example from Algebra I: Finding roots to a quadratic formulas, would involve:
- The quadratic formula
- Vieta's formulas
- Completing the squares
- Treating the quadratic like a parabola and using the parabola equation
=> y = a(x-h)^2 + k to find the roots.
The Double Check Game takes the drudgery out of an important skill
By making the step after solving a problem a fun game and not the drudgery of trying to double check the problem by doing it again, we can start to instill a habit of trying to solve a problem several different ways.
While the kid may groan every once in a while (they want to get on with the next problem and/or topic), it also teaches them different strategies for double checking outside of the normal “plug the answer back into the problem and see if you get a true statement”.
Double Checking Skill Acquired
Ultimately, this helps them mature their “double checking” skills. So in the future they can run through this process by themselves when they are double checking.
Try it soon and let me know how it goes!
Until next time,
Sebastian