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Core Curriculum

Upper Elementary Math Lessons

Elementary

Number Theory

• Place Value and Whole Numbers ...This unit focuses on place value of whole numbers through 1,000,000. It also touches on comparing whole numbers, ratios, ordering whole numbers, and rounding whole numbers.

• Whole Number Place Value...Numbers are made up of the digits 0-9. All digits in a number have a place. Their place determines their value, or what they are worth. If you are buying a video game and it costs $65, the 6 is in the tens place. The value of the 6 is $60.

• Decimal Place Value...Decimals help us to understand the exact value of a number. If one game costs $10.95 and another game costs $10.75, we can use decimals in money to figure out which game costs less. If you are 4 feet tall but your friend is 4.5 feet tall, your friend is taller than you are.

• Factors and Multiples ...This unit covers finding factors and multiples of whole numbers. There are lessons about finding common factors, prime numbers, and composite numbers. There are also lessons on comparing and ordering whole numbers.

Addition and Subtraction

• Properties and Problems ...It is important to understand the different relationships and properties of addition and subtraction. Learning these properties helps us to solve problems that come up in daily life. This will be helpful in future math classes as well. Estimating an answer rather than solving an entire problem is helpful when hurrying through daily chores. It is also important to know basic addition and subtraction facts in order to complete tasks quickly and correctly.

• Addition and Subtraction with Whole Numbers and Decimals...Addition and subtraction is used often in daily life, both with and without decimals. Understanding how to solve these problems correctly can make everyday chores, such as paying bills or cooking, easier to accomplish.

Multiplication and Division

• Applying Facts...It is important to understand the different rules and relationships of multiplication and division. Learning these rules and relationships helps us solve problems that occur while shopping, such as deciding how many boxes of fruit snacks we need to have enough for our entire class, as well as in the kitchen when trying to cut a recipe in half. Practice will help you become proficient in multiplication and division. This will make future math classes easier, as multiplication and division are used in all math classes from middle elementary on.

• Multiplication of One- and Two- Digit Numbers...Learning the basic math facts is very important for success in all future math classes. Multiplication is used in algebra, calculus, geometry, and problem solving. Multiplication is also used in everyday life. Although the problems continue to get more difficult, the steps to multiplication will remain the same. Whether you want to balance your checkbook, decide how many packages of pork chops to buy, or determine the square footage of a house, knowledge of how to correctly multiply is essential.

• Division...This unit covers division, with and without remainders. It also focuses on estimating quotients, dividing with zeros, and dividing 2 and 3 digit quotients.

• Working with Multiplication of Whole Numbers...Multiplication is based on repeated addition. After learning how multiplication works and memorizing the multiplication tables, harder problems are easier to solve. As you work up to harder and harder multiplication problems, you always solve the problem the same way, no matter how large the numbers are. Also taught in this module are estimation and a review of rounding. Estimation is a great way to figure out problems as well, when you do not need to know the exact result. All you have to do is round up or down according to the rounding rules, and then multiply the number, and place the correct number of zeros on the end.

• Working with Division of Whole Numbers...This lesson explains division of whole numbers. Included in this lesson are patterns in division, estimating quotients, dividing by one- or two-digit numbers, and interpreting remainders.

Fractions

• Investigating Fractions...Investigating Fractions reviews the definition of a fraction, how to identify its parts, and how to create visual representations of a fraction. In addition, the student will explore how to identify and name fractions, rename mixed fractions as improper fractions, and compare fractions and mixed numbers.

• Working with Concepts of Fractions...Several different ways of showing fractions are explained, as well as the problem-solving strategies associated with each one, including mixed numbers, improper fractions, and fractions on a number line.

• Manipulating Fractions...This module explains how to add and subtract like and unlike fractions. Included in these lessons are steps on estimating sums and differences, as well as adding and subtracting mixed numbers. Also, we will go over subtraction of fractions using renaming.

Decimals

• Exploring Decimals...This module covers an introduction to decimals up to and including the thousandths place. Students will learn how to properly write and name decimals, as well as compare them. In this module, you will also learn how to locate decimals on a number line and put them in the proper order.

• Operations with Decimals...This module is a continuation of decimals. It shows how to round decimals, estimating sums and differences and also how to add and subtract decimals.

Exploring Algebra

• Introduction to Algebraic Concepts...This unit teaches basic foundations of algebra, including lessons on patterns, variables, and linear equations. There are also lessons on order of operations and problem solving.

Geometry

• Spatial Reasoning...This WebLesson explains locating points on a number line, exploring lines/line segments/rays, locating points on a basic coordinate grid, symmetry, rotations/reflections/translations, and determining congruent figures.

• Basic Geometric Figures...This unit focuses on geometric figures, both two- and three-dimensional, as well as exploring different angles, exploring triangles, exploring quadrilaterals, and symmetry.

• Comparing and Classifying Geometric Figures

• Perimeter, Area, and Volume...The geometric shapes around us have dimensions that can be measured. The perimeter of an object is the sum of the lengths of al of its sides. The area of an object is the number of square units needed to cover its surface. For a three-dimensional object, you can measure its volume by multiply its length, width, and height. You can also measure its surface area by adding the areas of the faces that make up the object. Being able to measure the dimensions of objects is useful for many things like figuring out how your new furniture will fit into your room or the amount of wrapping paper you need to wrap gifts. We often use geometry without thinking about it.

• Transformations

• Tessellations

Measurement

• Capacity...We can describe measurements using both the U.S customary system and the metric system of measurement. Volume, capacity, and weight are three important quantities that you will measure. Because you will encounter units from both systems of measurement, it is important to know the units and how they relate to each other.

• The Customary (English) System...Students review US customary units of measure, practice converting between different measurements, and identify the amount of elapsed time between two different times. US Customary Units of Measure: Exploring Units of Length, Weight, Capacity, and Temperature, and Exploring Elapsed Time

• The Metric System

Introduction to Data Analysis

• Organizing and Displaying Data...This module shows students how to display data in tally charts, bar graphs (including double-bar graphs), pictographs, and line plots. It also covers data represented by a single number: the mean, median, or mode. Students only find medians of data sets with an odd number of values.

• Displaying and Interpreting Data...This module focuses on four types of data displays: bar graphs (including double-bar graphs), line graphs, histograms, and circle graphs. Once students have explored the graph types individually, they study when to use each type.

• Investigating Probability...Probability reveals the chance of something happening. Theoretical probability tells what should happen. Experimental probability tells what actually happened.

Problem-Solving Skills

• Using Problem-Solving Skills...This Module will cover many problem-solving skills including the 4-step method, finding patterns, learning how to make tables and graphs to solve a problem, as well as a few other strategies.

• More Problem-Solving Skills

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