My #1 Math Tip
I’m not even going to make you read this full blog post before revealing the goods, because you’re too busy for that. Here’s my number one math tip: Draw a picture.
No matter what level of math your child is in. No matter how simple or difficult the problem seems. No matter how horrible the student’s (or parent’s!) drawing skills. If your child is stuck and not sure how to tackle a problem - especially a word problem - draw a picture.
If you want to see how this would be done in some sample problems of varying difficulty, read on.
Example: Kindergarten Math Problem Timmy has 3 toy cars. Susan has 5 toy cars. How many toy cars do they have all together?
If your student isn’t sure how to handle this type of problem, ask him to draw Timmy with his 3 cars and Susan with her 5 cars. Or if your student is a tactile learner and you have toy cars at your house, line ‘em up!
Example: Elementary Math Problem Timmy has 8 toy cars, half of which are his favorite color, red. If Susan gives Timmy 3 more red toy cars for his birthday, how many red cars does Timmy have?
This one’s getting a little more complicated, because there’s a math problem involved in the set-up. Step 1: Draw the initial set-up to clearly see how many red cars Timmy has before Susan gives him more. Step 2: Draw Susan’s gift of cars.
Example: Algebra Problem Timmy lives 80 miles due east of Susan. They want to meet for lunch, and agree to meet somewhere between their houses. Timmy travels an average of 60 mph and Susan travels an average of 40 mph. If they both drive for the exact same amount of time, how many miles east of Susan’s house are they when they meet?
Some of you are looking for a paper bag to breathe in as nightmares of high school algebra resurface. But today is different, because you’re going to remember to draw a picture, instead of trying to figure out any equations straight from the words alone.
Your goal is to have a simple sketch that includes all the information the problem gives you. Draw a horizontal line, writing “Susan’s House” on the left and “Timmy’s House” on the right. Label the length of the line as “80 miles.” What else do we know? Timmy and Susan’s speeds. By Susan’s house, draw a right arrow labeled “40 mph,” and by Timmy’s house draw a left arrow labeled “60 mph.” Now you’ve got a simple schematic of how the problem is starting.
The drawing needs one more thing, and it’s what will help your student figure out how to solve the problem. How can you label what you are trying to find? For this problem, we are trying to figure out the distance from Susan’s house to the restaurant where they meet. Even though we don’t know the exact location of the restaurant, remember that the drawing is just a sketch intended to give you a better understanding of what’s happening in the problem. You can pick a spot on the line and draw a little hashmark for the location of the restaurant. (Side note: this is a good time to check on intuition. If Susan drives slower than Timmy and they both drive the same amount of time, do we expect them to meet closer to Susan’s house or Timmy’s house? Draw your hashmark accordingly.)
Label the miles from Susan’s to the meeting point as “x.” I think that the labeling of “x” on the sketch is the most difficult part of the problem. If your student can do this, and understand why they are doing it, they will be well on their way to solving the problem. Your student’s sketch should look something like this:
Notice that your student has done significant work without writing a single math equation. With a sketch in place, they will have a clearer idea of how to proceed and finish.
This works all the way up through the highest levels of math. When I was teaching calculus and a student would come to me for help working through a problem, nine times out of ten, I had them start by drawing a picture. I even followed my own advice when working on my doctoral dissertation. Before any equations were written, I drew pictures. Lots of them.
It’s not often you stumble upon a tip that works at all levels of math ability, so it goes to show you that it’s a powerful strategy. The next time you or your student are stuck on a math problem, give it a try. Draw a picture.
