EZ Arithmetic--An Introduction to EZ Math

Mathematics begins with the study of numbers. Beyond a few small numbers that we can recognize at a glance, the study of numbers is based on counting. But counting is not just a part of mathematics, it is a part of our everyday language. We can count forward or backwards, starting with any number. We can count by ones, twos, fives, or tens. We are really quite fluent in our use of counting.





Arithmetic is different. Even intelligent people can sometimes struggle with basic arithmetic. Carrying and borrowing create problems for a lot of people. As an introduction to EZ Math we will look at how to better introduce students to carrying and borrowing.

Addition with carrying requires us to access basic addition facts, know when to carry, and then do the carrying when needed. For students who are struggling to remember the basic facts, all this can be quite difficult.

The standard approach in teaching is to write down little carry numbers. As a teaching tool this illustrates what is happening when we carry. For children, carry numbers mean they do not have to retain as much information in their heads. Unfortunately once learned, writing carry numbers is a hard habit to break. And if we never do anything as difficult as remembering that we are carrying when we do addition, then we will never be able to get very far in the study of math.

Writing carry numbers is only one way to make carrying easier for beginners. In EZ Math we use another. We start with vending machine addition. Add a pair of two digit numbers ending in 0 or 5. If both end in 5 there is a carry, otherwise there is not. We also start with small digits in the tens place. By keeping the addition facts very simple, students are able to focus on learning the process of carrying in a setting where no carry numbers need to be written.

As students become familar with the carrying process, we can introduce problems with larger digits in the tens place. Later we can shift to evens, where we add a pair of two digit even numbers. While harder than vending machine problems, limiting the ones digits to 0, 2, 4, 6, 8 greatly reduces the number of facts students may need to access at the start of the problem, so they will be less tired when they need to remember whether they need to carry or not. Again, we can start doing problems with small tens digits, and only later introduce problems with larger digits in the tens place.

Subtraction and borrowing can be taught in a similar way. We may wish to work through the vending machine problems for both addition and subtraction before proceeding to the evens. Once students become proficent working with these restricted problem types we can proceed we can proceed to the more genral two digit addition and subtraction problems--and then on to working with larger numbers where we might have to carry or borrow more than once.

The challenges you may have learning or teaching math at a more advanced level are not that different from the challenges faced by children and their teachers who need to learn or teach carrying and borrowing. Trying to simplify everything else as much as possible when introducing new concepts makes sense at almost any level.