Descriptions of the Tested Topics Grades 3–4

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.

Challenge your child to become efficient with paper and pencil or mental arithmetic. For this game, your child should use only a pencil and paper, but you can use a calculator. Start simple with single-digit multiplication. List ten problems and say "Go!" See who can find the correct answers more quickly. As your child gets faster and faster, move on to the next level, a two-digit number multiplied by a one-digit number, and so on.

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.

Use this activity to get your child thinking about variables and the relationships between numbers. Ask your child to determine a rule that represents the relationship between two ages of people in your family. For example, your child might be twice your age divided by three. Then ask your child whether that relationship will always be true. If not, find a different rule that will remain true over the years.

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.

Help your child to understand and estimate units of measure. Start by encouraging your child to establish benchmarks for estimating temperatures. How hot is an 80 degree day? Do you need a jacket if it's 50 degrees outside? What can you expect if it's 30 degrees outside? Once you have worked on temperatures, move to other measurements such as height and weight.

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.

Playing games with your child will reinforce the concepts of probability and chance. Encourage your child to play games that use spinners, number cubes, and cards. When children want a certain outcome (for example, "I hope I roll a 2!"), talk about the likelihood of the outcome actually happening. For example, the likelihood that your child will roll a two on a six-sided number cube is 1/6. (Two is one of six possible outcomes.)

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.

Help your child understand the relationships among geometric figures by sorting and classifying shapes and objects. Begin by collecting all kinds of shapes from around the house. You might want to cut figures out of magazines or use a variety of different toys or household objects. Once you have a collection of objects, sort them by different attributes. You can start by separating the flat objects from the three-dimensional. Then sort them by the number of sides each has. Then group any similar objects together. Have your child come up with different ways that the objects can be sorted by their common characteristics.

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.

Multistep math problems or problems that involve working backward are often difficult for students to solve. You can give your child extra practice with these strategies by creating a code. First, think of a word to change to a code. Next, make a code. For example, move every letter to the next letter in the alphabet; i.e., A becomes B, D becomes E, Z becomes A. Or, exchange each letter for its corresponding number; i.e., a = 1, b = 2, c = 3, z = 26, etc. Finally, give your child the word in code. Ask him to figure out your original word by "cracking" your code. If this becomes easy for your child, try a code that involves two 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.

Take advantage of everyday situations with fractions and decimals. At dinner, ask your child to serve the family using fractions. For example, one person might want 1/4 of the meatloaf or the pizza, while someone else may want only 1/8. Have your child prepare the portions according to your mathematical directions. How many portions will there be if the meatloaf or pizza is divided into fourths or eighths? What happens if one person wants 1/4 of the pizza and another person wants 1/5?