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Common Core math tests visualization skills

Three different ways to figure out the same problem tests students math skills.
Three different ways to figure out the same problem tests students math skills.
© 2014 Suzanne Brodsky

“There is more than one way to solve this problem, and you need to know all three of them for the test.” This is one excerpt you might hear emanating from a fifth grade classroom as the teacher prepares her students for the New York State standardized math test. In the past, students were taught only one way of figuring out the answers. The Common Core now presents new ways to decipher the same information. The skills needed to solve these problems require looking at the numbers and translating them into lines and circles. For some, that is a rather tall task to accomplish.

Take for instance, 3 x 0.24. Parents today may have learned to solve this problem by lining up the 3 underneath the .24 and then multiplying the numbers. The decimal is then moved two places to the left, resulting in an answer of .72. The second method is to do straight addition. We could line up .24 + .24 + .24 one underneath the other and then add up the numbers. Most students understand both of these methods and can do them with relative ease.

There is a third method to approach the above problem. This is part of the Common Core. It involves creating a visual representation of the numbers using lines and circles. After we do that, we add, regroup and figure out what we have left over. Using the example above, start by creating three rows of two lines and place them one underneath the other. This represents the tenths column. Then, draw a line down the right hand side of these rows. To the right of the line, create four small circles to correspond with each row of lines. This creates a total of 12 small circles. These represent the hundredths column. Next, count ten of those small circles. One group of ten creates one tenth. Draw a big circle around those ten. Next, draw a big arrow from that all encompassing circle to the other side of the line and place it next to the bottom row of lines. That creates one whole tenth that we add to it. In looking back at the small circles, there are only two left that we did not circle. This is not enough to create another group of ten. Count up how many lines we have. This is the number that gets placed in the tenths column. Next, count up how many circles we have left over. This number gets placed in the hundredths column. We then move the decimal two places to the left (since that is where the decimal was in our original number). That gives us our final answer, which is .72. (Please see the graphic above for the actual work.)

Some students can comprehend this method easily. Others have a much harder time trying to visualize it. Teachers take a tremendous amount of time in the classroom trying to gets these points across. Students must understand that they will be tested on all three of these methods when it comes to the state tests. Although it may seem a little daunting at first, the process gets easier with practice. After a point, all three of these methods will be rote and the students can move on to the next topic. Just try not to scare them when it comes to lattice math!