Descriptions of the Tested Topics Grades 7–9

Below are descriptions for all the tested topics in Math and an activity that you can do with your child to address each topic.

Numbers and Operations

This topic focuses on whole numbers, fractions, decimals, percentages, ratios, and proportions. It addresses the properties of numbers and the operations used to compute (addition, subtraction, multiplication, and division) and to solve problems. All of these concepts relate to a student’s number sense.

Encourage your child to look for integers, fractions, and decimals in familiar places. For example, your child can practice working with percents in everyday situations involving sales tax, discounts, and tips. Whenever your child accompanies you to the store, have her estimate the amount of tax that will be added. Your child can also help you determine the amount that a waiter should be tipped.

Algebra and Functions

This topic focuses on recognizing and describing patterns that have numeric and/or geometric features. When a child notices that house numbers increase while walking down the street, he is noticing one of these patterns. This topic teaches students to express these patterns using variables (such as x or y) and to translate sentences into variable expressions. Recognizing patterns and variable expressions is important for many areas of mathematics.

Play the simple game "Who am I?" Here's an example. "Five more than I am is 17. Who am I?" (The answer is 12.) Your child will need to work backwards to answer this question. You can make the game more difficult as you play it. A more difficult version is the following: Seven more than half of me is 13. Who am I? When your child gives an answer, make sure he or she puts it back into the original statement to check that it works.

Measurement and Geometry

Students learn to use standard units of measurement, like inches, ounces, and hours, and to talk about amounts that otherwise would be described as “a little,” “a lot,” or “way too much.” This topic focuses on understanding units of measure for time, length, area, volume, temperature, and weight, in both the customary and metric systems. This topic also focuses on the building blocks of geometry: points, lines, and angles. Students should be able to identify and describe various two- and three-dimensional figures and such characteristics of those figures as angle size, side length, and parallel and perpendicular sides. Children show an early understanding of geometry by using shapes in their drawings, and by recognizing the shapes of road signs, buildings, and sports equipment.

When opportunities arise in your home to think about perimeter, area, and volume, ask your child to get involved. For example, if you want to frame a picture, what information do you need? The size of the picture matters, but what aspect of size? The area or the perimeter? And should the measurement of the frame be exactly the same size as the picture? When making orange juice from concentrate, what size of pitcher should you use?

Data Analysis: Statistics & Probability

This topic focuses on being able to read and compare the data in tables, charts, bar graphs, line graphs, circle graphs, and line plots. Students should ask questions, collect the data needed to answer the questions, and display their results. This topic also includes finding the probability of chance events by considering the relationship between favorable outcomes and total outcomes. What are the chances of rolling a six? What are the chances of choosing a red king from a deck of cards? What are the chances of winning the lottery? These questions can all be answered by using probability.

Ask your child to look at a graph in a newspaper or magazine and describe the information that is presented. How are the stated conclusions supported by the evidence in the graph? Sometimes conclusions are made that are not particularly evident in the data display. Encourage your child to be critical of these situations and to decide what reasonable conclusions can be drawn.

Conceptual Understanding

When learning geometry, students name figures and describe their properties. When learning about computation, students add chips or blocks. In these and other areas of mathematics, we ask students to give definitions and show examples to explain the definitions. Students who participate in these activities are demonstrating Conceptual Understanding.

Ask your child to describe household objects using geometric terms. For example, have your child identify all of the geometric characteristics of a window. He may say that it is a rectangle (or possibly multiple rectangles), that it has two pairs of parallel edges, two pairs of perpendicular edges, and four right angles. Refer to your child's textbook to make sure the terms are being used correctly.

Procedural Knowledge

When students approach a math problem, they are expected to use appropriate procedures to solve for the correct answer. Once they fully understand number concepts, they will develop the essential tools — processes and steps to be followed — for solving problems efficiently. Choosing the best method for solving a problem and communicating the results of the method are addressed in Procedural Knowledge.

Create a three- or four-step treasure hunt for your child. It's best to work backward when creating treasure hunts. First, choose the location for the treasure. Second, write a clue for that place. Third, choose a place to hide the clue. Repeat these three steps until you have three or four clues written and hidden. When your child becomes comfortable working through these treasure hunts, have her create one for a friend or younger sibling. By creating a treasure hunt, your child will get better at working backward through math problems and solving problems with many steps.

Problem Solving

A strong measure of mathematical skill is the ability to solve math problems in real-life situations. Situational problems challenge students to form questions and apply appropriate procedures to produce reasonable results. They apply to a variety of real-life contexts, from buying groceries to determining the percentage of students who watch scary movies. Problem Solving requires students to combine their mathematical knowledge of concepts, procedures, and reasoning with their communication skills.

Help your child pose mathematical questions about our world. Which train will get us where we want to go the fastest? Which box of cereal is the best buy? When thinking about questions like these, figure out what information is needed to answer them. The solutions to these problems are often based in algebra, which is the study of patterns and unknown values. Solving these kinds of problems will give your child experience with important algebraic ideas.