# Methods - Shortcuts

Teaching children to use shortcuts to solve word problems is entirely different from teaching them to make models. I have encouraged you to show your children how to model word problems. But shortcuts are something that they should figure out on their own.

### Can My Children Figure Out Shortcuts On Their Own?

Absolutely, yes they can. The videos in this website should help to convince you of that. And, once again, not for one second do I believe that any mathematical abilities that my grandchildren may have are inherited. Based on many years of teaching I believe that almost all children can do the same.

### Why Should I Let My Children Figure Out Shortcuts On Their Own?

If you want your children to be good problem solvers, across all disciplines, in novel situations, you must give them opportunities to figure things out on their own. Finding shortcuts is a good place to begin practicing because it is relatively easy and unambiguous. Shortcuts either do or do not get the same answer that the corresponding model would. To the extent that you show children shortcuts you are depriving them of opportunities to practice figuring things out.

### How Can I Get My Children To Figure Out Shortcuts On Their Own?

Once again, the following is very general advice. I think that the best way for you to understand the methods for helping children to learn shortcuts is to view the videos on the Addition, Subtraction, Multiplication and Division tabs.

• Posing Problems
• Look for opportunities to pose word problems – they are all around. How much change should we get? How many miles is that altogether? How many more plates do we need to set the table? If we each should get 2, how many do we need altogether? If the 3 of you share these, how many will each of you get? With opportunities like these there is little need for stand-alone lessons.
• Mix up the types of problems. One day it can be a Measurement Division problem, the next day Hard Addition. There is no set order.
• Lots of practice isn’t necessary. One or two problems per day, or even fewer, is more than sufficient.

• Helping With Shortcuts
• When you pose a problem, your child will either make a model, or, on his or her own, try to use a shortcut.
• Encourage your child to “think out loud.” It is important that you know the process that he or she is using to solve the problem because it is the processes that you are trying to teach. And it is important that your child learn to articulate his or her reasoning.
• It is sometimes hard to understand children’s methods. This is in part because their arguments are often unusual – you yourself may never have solved a problem in their way. And while the general logic of their arguments is almost always correct, they often make relatively minor errors that can also make their reasoning hard to follow.
• Try to understand what they are doing and help them by supporting their methods. Don’t have them solve the problem the way you would.

• Actively Directing
• There is nothing wrong with suggesting a particular shortcut. The problem is with requiring that shortcut. If your child doesn’t understand your suggestion, let it go - it is only a suggestion. You do not want your children practicing procedures that they don’t understand. That has nothing to do with mathematics.
• If one day your child tries out a new shortcut - say counting by 2's - give him or her a second problem to practice with.
• If your child easily solves a problem using a shortcut, ask if he or she can solve it in another way, or in as many ways as possible. Once again, it is the processes (shortcuts) that are important - not the answers.
• From time to time your child may be completely stuck – apparently unable to think of any way to solve the problem. In that case, remind him or her about making a model. It is really important that children know that modeling is allowed.