Math problems that ask a student to demonstrate understanding of graphing and proportional relationships will ask him to look at points and lines on graphs to find the slope and solve word problems relating to the data shown. Questions about relationships between changing variables as related to real-life problems might be shown in graphs or word problems.
Examples of math problems that challenge a student's understanding of exponents and fractions require multiplication of numbers with exponents and multiplication of fractions. For example, "Write the number 833,000 in scientific notation." Or, "Write 4.08 as a fraction." Or, "Add 3/4 + 1 1/2 + 1/2 + 1 1/4." Students must also know how to solve algebraic equations and identify associative, commutative, reflexive and distributive properties.
Math problems that test a seventh grader's knowledge of geometry involve visual shapes. She will need to understand the Pythagorean theorem to solve problems about plane and three-dimensional shapes. The student will be asked to find the length of segments and measurements of angles using limited information about the shape, plot coordinates on a grid, identify lines that are perpendicular and parallel and will require the calculation of the volume and area of a shape using a limited number of given measurements.
Math problems that test understanding of probability will ask the student to look at a chart or scatter plot, find median and mean averages and make a prediction. Problems typically replicate real life situations, such as the finding of a purchase price, weather averages, sports score averages or traffic speed.