Gaining Knowledge


Adding and subtracting are math concepts most people learn at a young age. Although we start by learning simple math problems, we still develop an understanding of the concepts. For example, if there are 5 sheep on a farm and 2 get lost there are now 3 sheep on the farm; if there are 2 cows on a farm and the farmer buys 2 more cows, then there are now 4 cows on the farm. These simple math problems help students to understand the idea of adding and subtracting. As we get older we begin to learn more complex problems like 159+253=412. This may be easy to understand for most people, but may be very confusing for a student who has no idea what they are doing. How does 9+3=2? This is a question a student may ask because clearly 9+3 does not equal 2; it equals 12. In this case we use the idea of “carrying” numbers, and if it were a subtraction problem we may have to use the idea of “borrowing” numbers. What is a good way to teach a student to “carry” and “borrow” numbers? How can we help a student understand how to add and subtract numbers? I have learned great ways to answer these questions and gained a better understanding for adding and subtracting numbers.

A great way to teach a student to “carry” and “borrow” numbers is to use manipulatives. Using a manipulative is a hands-on-way to get students involved with math. For the standard adding and subtracting problems we use base-ten units; therefore, we will use base-ten pieces for a manipulative. The base-ten pieces include: flats (100 units), longs (10 units), and units (1 unit). For the problem 159+253=412, we will use 1 flat, 5 longs, and 9 units to show the number 159; we will use 2 flats, 5 longs, and 3 units to show the number 253. After we decide what base-ten pieces we need for the problem, we then begin “carrying” units. In this manipulative we show “carrying” by exchanging units for longs and longs for flats. The first exchange in this problem is to exchange 10 units for 1 long; the second and final exchange is to exchange 10 longs for 1 flat. Once the exchanges are done, we are left with 4 flats, 1 long, and 2 units. 4 flats is equivalent to 400, 1 long is equivalent to 10, and 2 units is equivalent to 2; therefore, if we add 400+10+2 we get 412. This is time consuming, but it is a great way to explain addition and subtraction. Although this is an example of addition, the same idea is used when using manipulatives to show subtraction. The pictures provided may help to clear up any confusion about adding with base-ten pieces.

Hands-on-activities are great ways to get students involved in the math problems, but there are also other options. Technology is growing very quickly; therefore, there are dozens of online websites that have interactive games and manipulatives to get students involved in math problems. This is a great way to stay updated with new opportunities available for teaching math concepts. National Library of Virtual Manipulatives is a great website that has a bunch of activities. This website allows you to download different manipulatives for free! This is a wonderful way to enhance any classroom.


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