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Core Curriculum

6th Grade Math Lessons

Secondary

Decimals

• Introduction to Decimals...Numbers are an important part of life. You use numbers to calculate how much a new video game costs, how much you weigh, what your temperature is when your are sick, and how long to cut boards to build a tree house. When you think of your age, that is a whole number, but not every number is a whole number. Decimals are numbers that allow us to write numbers of all sizes smaller than one. We use a decimal point to show parts of a whole. Our decimal system of numbers is based on the number ten. In ancient times, people counted using their ten fingers or ten toes. This is where the decimal system began. A decimal is a special number; it contains a period or a point in the number. The portion to the right of the decimal point represents a fraction, or a smaller part of, of a whole number. For example, the numbers 2.1, 12.78, and 0.0124 are all decimals.

• Get to the Point; Decimals...Multiplying decimals is just like multiplying whole numbers. After you multiply, then you figure out where to put your decimal point. We multiply decimals all of the time. Has your class ever ordered pizza for lunch? Your teacher probably multiplied the number of students in your class by the number of slices they could eat. Then, multiply the number of pizzas you need to feed the whole class. Once you have that number, then you must multiply the cost of the pizza – which usually has a decimal point – by the number of pizzas you will order. In order to divide decimals, always make sure that the divisor is a whole number. There are easy steps to follow when solving division problems with decimals. Even long numbers are not difficult when learning the steps to dividing decimals. Exponents are a shortcut method that represents how many times a number is multiplied by itself.

Fractions

• Introduction to Fractions...We use fractions in a variety of settings. Chefs measure ingredients in a recipe in fractions of a cup. Carpenters measure wood in fractions of an inch. Sale prices are reported in terms of fractions of the cost- as in buy one, get one half off. One of the most important skills to learn is how to compare fractions. When comparing fractions with the same denominator, the fraction with the bigger numerator is the larger fraction. When comparing fractions with the same numerator, the fraction with the smaller denominator is the larger fraction. When comparing fractions with both a different numerator and a different denominator, first you have to use multiplication to make the denominators the same.

• Operations with Fractions...The rules for operations with fractions are covered, including addition, subtraction, multiplication, and division. Decimal conversion is also discussed.

Basic Algebra Concepts

• Introduction to Algebraic Concepts...The basic operations used for equations are covered, as well as those used for evaluating expressions. The properties of addition are also explained.

• Understanding Expressions...Expressions containing multiplication and division, with a particular focus on evaluating with known variables, and expressions showing powers of ten.

Data Analysis and Probability

• Methods of Displaying Data...Several methods for displaying data are covered, including bar graphs, histograms, line graphs, and stem-and-leaf plots.

• Data Analysis...The world is full of information. Television, the Internet, magazines, books, and radio are sources of information about our world. Information is useless unless it is organized and accurate. Statisticians organize and interpret data which, to most of us, would be either too difficult to understand or too time-consuming to read. One measurement that helps us understand data is average. Think about your own grades. Averages are used to measure how well you are doing in each course. Based on that average, you are assigned a grade. Statistics and averages are used in almost any area of life you can think of – medicine, science, the news media, and elections are just some examples.

• Roll the Dice; Exploring Probability...What are the chances of rain tomorrow? What are the odds of winning the lottery? What is the likelihood of lightning striking? All of these questions refer to probability. A probability is a numerical measure of the likelihood of an event. For example, what are the chances of an event where you will meet someone who has the same initials as yours today? A probability can range from 0 to 1. If we assign a probability of 0 to an event, this indicates that the event will never happen, like the probability of rolling a 7 on a single dice. A probability of 1 means that the event will always occur; such as the probability of rolling a number less than 7 on a single dice. A probability of 0.5 or one-half means that it is just as likely for the event to occur as for the event not to occur. So the the probability of rolling an odd number on a single roll of a die is half, or 0.5. Probability is a discipline that is very useful in real life. In fact, just about everything you do involves a certain amount of risk. If you have ever had surgery, the doctor probably informed you about the chances of having complications. When you decide to get in the car, there is a chance that you will be involved in an accident. The chance of surviving that accident increases by wearing a seatbelt. Some occupations involve more risk than others do. For example, a dentist has a safer job than a police officer does.

Number Theory

• Exploring Numbers and Operations...This module covers identifying prime and composite numbers, finding a composite number’s factors and prime factorization, and using divisibility rules. These concepts are combined to teach how to calculate the greatest common factor (GCF) and least common multiple (LCM) of groups of numbers, and how to apply these concepts to real world situations.

Measurement

• Customary Units...Have you ever heard of a fathom or a parasang? How about a rood? Believe it or not, these are older units of measurement. The metric system has replaced most of these older units, but some of them have survived today, including ounces, feet, inches and pounds. These are some of the U.S. customary units, which are the non-metric units of measurement used in the United States. Being able to take and record measurements using U.S. Customary units is an important skill. You will need to know the units used to describe each measurement and the relationships between them. U.S. Customary units of length and distance include inches, feet, yards, and miles; units of capacity include cups, pints, quarts and gallons, while units of weight include ounces, pounds, and tons. We use ounces to describe both capacity and weight.

• Metric Units...This module introduces students to the metric system, metric units, and metric prefixes. Students learn to convert among metric units by moving a decimal point. Students are introduced to scientific notation, and learn how to use it to express large and small numbers.

Introduction to Algebraic Functions

• Introduction to Functions...Functions are introduced, primarily in the form of input-output machines and sequences. The order of operations is also discussed.

• Introduction to Equations and Inequalities...This module introduces students to the basic concepts of algebra including appropriate terminology. Students are taught how to solve basic equations for an unknown variable. The module also introduces students to inequalities.

Integers and Rational Numbers

• Introduction to Integers and Rational Numbers...This module introduces students to integers and the number line. Students learn how to add, subtract, multiply, and divide integers. The module challenges students to use integers to describe familiar situations.

Basic Geometry Concepts

• Introduction to Geometric Properties...The study of the shapes in the world around you is just beginning. This module has introduced you to some of the basic geometric shapes and their properties. You know a little about some pairs of angles, and about how to find the area and circumference of a circle. Look at the shapes that surround your world. As you do so, you will probably see some more complex shapes, formed by a combination of the basic shapes you have begun to study. You may begin to see that these shapes share some of the properties we have discussed.

• Geometric Concepts...From simple shapes come complex and fascinating designs. As shapes are repeated, reflected, and rotated, they can form eye-dazzling patterns. Many kinds of patterns, from simple checkerboards to detailed mosaics, are based on the same principles. Now that you have learned about symmetry and transformations, complicated designs may make more sense. You may notice more patterns in the world around you. Perhaps you may even appreciate their beauty in a new way.

• Exploring Polygons...Perimeter and area are commonly used measurements. You can find the distance around any shape by measuring the length of each side and finding the sum of the lengths. You can find the area of figures by using a formula. Shapes that are not regular polygons can be divided into pieces that are regular polygons. Then you can find the area of each piece and add all the areas. Landscapers, architects, artists, and engineers are some of the professions that use perimeter and area measurements. Look around and you will see geometric figures everywhere.

Ratios, Proportions, and Percents

• Introduction to Ratio and Proportion...In this lesson, students will explore the relationship between ratios and proportions. They will learn how to write equivalent ratios, set up a proportion to solve an equation for an unknown, and how to solve different types of word problems involving scale drawings and maps.

• Corresponding Percents, Fractions, and Decimals...This module introduces the idea of percentages, and teaches how to convert between percents, fractions, and decimals. It covers how to find a specified percent of a number and how to find what percent one number is of another. The module uses examples applying these concepts to real world situations.

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