When studying decimals and the base 10-number system, we can break down the information into a graphic that makes it a bit easier to understand. We start with a square. This represents one whole number. We then divide the square into ten equal parts both vertically and horizontally. When we look at the square now, we count 100 small squares within it. If we were to remove one long rectangle from that square, that would be one tenth of the whole. Removing one square from the tenth gives us one hundredth. Classroom manipulatives for younger elementary school students include actual blocks to represent the base 10-number system. Older students will draw the blocks in their notebooks.
Take for example 5 x 2.5. We can either use the multiplication method to figure out the answer or we can add 2.5 five times. If we wanted to use the pictorial method as mentioned above, we would draw two columns of squares. Each column would contain five squares. These represent the whole number. Next to each row we would draw five small lines. These lines could also be drawn as skinny rectangles. These represent the tenths column. Next, we calculate how many groups of ten lines we can derive from each row, and circle them. This comes out to two groups of ten lines. Draw an arrow from each group of ten around to the bottom of the columns of squares. Since we were able to circle two groups of ten, these each create one whole. In this case, we will draw two additional squares underneath our already existing columns of squares. When you add up all the squares, you now have 12. When you add up the remaining lines that did not get circled, you have five. The answer is 12.5. Check it by doing the multiplication and/or addition methods to make sure you get the same answer. (See graphic above.)
No matter which method you choose, these three methods show you the different ways to analyze and process information. When fifth grade students in New York are given the statewide, standardized tests, they will need to know all three methods. At times, students might question why they need to know this, as it can be confusing at first. If you are the teacher answering this question, try to be as upfront as possible. One student might see the answer more clearly using one method versus another. You never know which method will work best for you until you try all of them. These tests make sure students are able to extract the information and use critical thinking skills in a variety of formats.
When teaching a lesson like this one, try to use three different colors of chalk to make it easier for students to see your work on the blackboard. A SMART Board might work even better to create the graphics digitally and truly enhance the color. Not everyone will get this method right away. Some students may require one-to-one assistance a few times before it sinks in. Use different examples. Be patient. Let students who understand it teach those who do not. Help from peers can go a long way in arriving at the, “Ah ha” moment. Soon, your students will be ready to tackle any base 10, decimal math problem with the power of conviction and the determination derived from all of their hard work!