Descriptions of the Tested Topics Grades 5–6

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.

Have your child list the multiples of a number. Then, ask him or her to stop while counting and name the corresponding multiplication fact. For example, if your child is listing the multiples of 4 and stops at 32, your child should name the multiplication fact of 4 x 8 = 32. This game can increase in complexity as the numbers get larger. For a new challenge, try this game with multiples of 17.

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.

For practice with patterns, play a guessing game with your child. Think of a number pattern (such as "squaring") and give the first three items in the sequence (1, 4, 9, ...). Ask your child for the pattern and the next three numbers (16, 25, 36, ...). Your child can then make up another pattern and have you guess what it is. The number pattern doesn't need to have a special name; anything with a rule will work.

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.

One element in understanding geometry is identifying lines of symmetry in various objects. A line of symmetry divides a figure so that one half is an exact reflection of the other. You might ask your child to draw a figure with no symmetry at all. Next, ask him to draw a figure with exactly one line of symmetry, then exactly two lines, exactly three lines, and so on. This activity might be difficult at first, but it will become easier for your child to recognize lines of symmetry as he pursues these challenges.

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 collect data, organize the data in a table, and display it in a line graph or a bar graph. For example, your child might collect data about the average high and low temperatures in a given location throughout the year. Your child can collect the data by taking the actual temperature on the first day of each month or find this information by doing research in the library or on the Internet. Then he or she can create a line graph that shows the high temperatures in red and the low temperatures in blue. This graph will show the temperature trends throughout the year.

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 with naming and recognizing geometric terms and shapes by having a scavenger hunt. Use your child's textbook as a resource and make a list of different geometric shapes and terms. Your list might include circle, square, rectangle, and hexagon. It might also include parallel lines, scalene triangle, and rhombus. After you have the list, ask your child to find examples of all of these figures in your home. (You could also have your child make up a list for a sibling and vice versa. They could play as a team or make it a competition.)

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.

One way for your child to practice applying math is to solve riddles. You can create riddles for your child by using the current month's calendar. Choose a number from the calendar and give clues to help your child guess the date. For example, Clue 1: The date is not an odd number. Your child then crosses off all the odd numbers on the calendar. Clue 2: The date is not a multiple of 10. Your child then crosses off 10, 20 and 30. He will continue to cross off the dates that match each clue until there is only one date left.

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.

Encourage your child to ask mathematical questions about everyday situations. Discuss what information is needed to solve each problem. Which store is closer? Which elevator is faster? How many pounds of food did we buy? Discuss with your child different ways of finding solutions to these problems. These skills will build a strong foundation in problem solving that can be applied to algebraic situations.