by Dr. Emily Levy
(Originally published in NY Metro Parents, December 2006)
For many fourth grade students, the thought of enduring a three-day-long statewide math exam gives them more jitters than a trip to the dentist. Most would rather wash dishes every night than endure this dreaded test. Yet for any fourth grade student attending a New York public school, this test is mandatory.
The right test taking strategies, however, can help put this anxiety to rest.
The New York State Fourth Grade Mathematics exam, given over a three-day period from March 6-8, helps determine whether students are meeting grade level learning standards. The test consists of three types of questions: multiple choice, short open-ended, and long open-ended. These questions are designed to test students’ content abilities and thinking skills.
To perform well on this exam, students should become comfortable with the format of this test and the different types of questions that may be asked. They can then learn strategies for how to best solve each of these kinds of questions. In particular, students may see the following problems on the test: Representation, Communication, Reasoning and Proof, and Problem Solving.
Representation problems typically involve pictures, charts, graphs, figures, or patterns. They ask students to create a drawing to describe a mathematical concept or to choose a drawing from a series of choices which best represents a given concept. To best solve these problems, students must learn to identify key words. Certain key words, such as “draw”, “create”, “label”, and “shade”, help students identify Representation problems. An example may be as follows:
Jack’s garden is a rectangle that is 40 feet long and 65 feet wide. Draw a rectangle to represent the garden. Label the length of each side.
The student should underline the word draw, since that is the key word which indicates that this problem requires the student to draw a representation of the figure.
Communication problems ask students to communicate an idea or concept. They may ask a student to explain how they came up with an answer or why their answer must be true. Students may be asked to express a mathematical concept in their own words using proper mathematical terminology. To develop proficiency with these types of problems, students should practice communicating mathematical ideas in their own words prior to the test. A sample problem may be as follows:
Two lines are perpendicular. What must be true about them?
To properly answer this question, students must be able to express the definition of perpendicular lines in their own words and relay the properties associated with this mathematical concept. The more practice expressing different concepts, the easier these questions will be.
Reasoning and Proof
Reasoning and Proof problems involve logical thinking. Students must use reasoning skills to prove whether a given statement is true or false. For example:
Richard makes 24 pounds of peanut brittle. He decides to put an equal amount of brittle into 5 boxes. He thinks each box will hold 5 pounds. Is his estimation reasonable? Explain why or why not.
A good strategy for answering Reasoning and Proof questions is to begin with a general statement. This statement should briefly describe the answer, such as “Richard’s estimation is reasonable.” Next, students should provide evidence of their answer. For example, “24 rounds up to 25, and 25 divided by 5 is 5. Thus, Richard’s estimation is likely to be true.” Parents can give students sample questions like this one and can replace the numbers in each problem for extra practice.
Problem Solving questions ask students to analyze a scenario and come up with a solution. They involve more than just recalling a concept or crunching numbers. Rather, students must think, plan, and solve. Specifically, students should use the ORAS strategy, as detailed below:
Operation: Students should decide if the problem requires a specific operation or a combination of a few operations. For example, the problem may require addition, multiplication, or both. Students should indicate the relevant operation(s) with the proper symbol(s).
Relevant Information: Students should underline any numbers that are relevant to solving the problem. They should also cross out any numbers that are irrelevant to solving the problem.
Arithmetic Sentence: Students should create an arithmetic sentence that can be used to solve the problem.
Solution Sentence: Students should come up with a solution to the problem as a full sentence in their minds.
Lisa and her two friends went to a candy store. The price of gummy bears was $3 per pound, the price of chocolate squares was $5 per pound, and the price of butterscotch candies was $2.50 per pound. Each of them wanted two pounds of gummy bears and two pounds of chocolate squares. In total, they had $50. How much money did they have left over for drinks after purchasing their candy?
Students should use the ORAS strategy detailed above to solve this problem. They should make sure to cross out the $2.50, a number that is irrelevant to solving the problem. Parents can create similar problems to the one detailed above and create four lines underneath each problem for each step in the ORAS strategy, so that students can practice problem solving at home.
The fourth grade mathematics test can indeed cause anxiety and lead to sleepless nights. Yet the right strategies and lots of practice can help ease these fears and make the test day more welcoming.