Before being introduced to fractions, children have developed a one-to-one relationship with counting numbers. As a result, most children face difficulty in fully conceptualizing fractions. However, a thorough understanding of basics can help children to better grasp the concepts of fraction. I often like to start with using a pizza pie. It seems that a great number of people enjoy that tasty stuff. A standard large pizza pie broken into 8 slices. Starting this unit off with a pizza party always makes it a bit more successful because you can always refer back to those 8 slices. We try to include visuals as much as possible. Are there any fraction-based skills that we are missing? Please let me know.
- Add and Subtract Mixed Numbers With Like Denominators - You will need to learn to evaluate two points of the entire value.
- Addition and Subtraction Between Whole Numbers And Mixed Numbers - This is start point for learning operations between mixed numbers.
- Add and Subtract Unlike Mixed Numbers - This indicates that there are different denominators in the fraction portion of the mixed value.
- Adding and Subtracting Decimals and Fractions - You will need to jump back and forth between the different formats that are presented to you.
- Comparing Fractions and Equivalence - You will determine if a fraction is greater, less, or equal to another fraction.
- Comparing Fractions with Like Numerators or Denominators - This seems straight forward, but the goal is to understand how relevant a value is.
- Comparing The Size of Fractional Products - Estimation skills will come in very handy here.
- Comparing Mixed Fractions - Obviously, it starts with the whole number and then progresses to the fraction.
- Creating Fractions from Story Problems - You will need to look deep into some these problems to find inconsistencies.
- Decimal Notation for Fractions (10 or 100 Denominators) - This is just a slightly different way of looking at these values.
- Denominators of Tenths and Hundredths - These denominators make the transition to decimals or percentages very easy.
- Dividing Mixed Numbers (As Improper Fractions) - The basic procedure is to multiply the whole number by the denominator.
- Division of Whole Numbers By Fractions Word Problems - These are very rare problems, but they do often appear in the real world.
- Division of Fractions by Whole Numbers Word Problems - Have you ever wondered if you could slice a fraction into pieces?
- Estimating Sums and Differences with Fractions - Your aim should be to see how far off the numerator and denominator are off and then go from there.
- Express Whole Numbers as Fractions - The simple answer is to put a one over the whole number.
- Fraction Addition (Like Denominators) - In this case we learn to add the numerators.
- Fraction Subtraction (Like Denominators) - These will remind you of straight subtraction if the denominators are the same.
- Fraction Multiplication (Unlike Denominators) - I sense a little cross-multiplication in your future.
- Fraction Division (Unlike Denominators) - Make sure students have mastered the multiplication operation first and then they will be much more comfortable with this.
- Fraction Operations Review (All 4 skills in one) - Every operation is looked at and gone over here.
- Fraction Word Problems (Add and Subtract Only) - It seems very simple, but for many students it is far from it.
- Fraction Word Problems (w/Mixed Operations) - You may need to read these problems several times to get a solid understanding of what they are asking you for.
- Fractions and Whole Number Multiplication - The focus here is on the top value of the fraction and the whole number.
- Fractions and Whole Numbers in Words and Visuals - We look at a wide variety of methods to understand both types of values.
- Fractions of Integers - This will help you calculate a smaller portion of an integer.
- Fractions to Mixed Numbers - We show you several different ways to convert these values.
- Interpret and Compute Quotients of Fractions - Students will learn how to setup these problems, which is more than half the battle.
- Interpretation of Fractions - We observe fractions that are around us everyday in many different situations.
- Making Equivalent Fractions - Given one value match it with another fractional value.
- Operations Between Fractions and Whole Numbers - We cover the major operations and even a little order of operations.
- Products of Top Heavy Fractions and Integers - We stay away from mixed numbers here and instead; we work with improper fractions.
- Products of Fractions and Mixed Numbers Word Problems - We start out simple and it progresses as we get into the material.
- Products of Fractions and Whole Numbers in Word Problems - Make sure students are well versed on converting mixed numbers to improper fractions first.
- Products of Mixed Numbers - You will see some familiar situation here.
- Products of Whole Numbers and Fractions - Your focus here should be between the whole number and the numerator.
- Recognizing Equivalent Fractions - This will help you learn to observe and even make baking a little easier for you too.
- Rectangles with Fractional Sides - If you ever take on a wood construction project, these skills are invaluable.
- Reducing Fractions - What factor fits both the top and the bottom?
- Represent a Fraction on a Number Line - This really makes the concept much more approachable for students.
- Represent Mixed Numbers on a Number Line - You will need to break whole numbers into lengthy sections.
- Sum and Difference Fraction Word Problems - You would find problems like this in your kitchen whenever you try to cook anything.
- Sums and Differences of Like Fractions - This indicates that the denominators are all the same over these operations.
- Understanding Visual Fractions of Shapes - This is where we section apart the shapes.
- Understanding Visual Fractions - This is fractions of groups or items.
- Understand a Fraction on a Number Line - You should start with a number line that at least breaks things into equal parts as your denominator.
- Unit Rates and Ratios of Fractions - We look at a measure of how fast or slow something occurs.
- Whole Number and Mixed Number Operations - You can put the whole number over one, if it makes you feel better.
- Word Problems with Fraction Division - As you read through these problems, you will realize how often you use these skills.
What is a Fraction?
A fractional number or a fraction represents a part or portion of a whole. Fractions are a way to split a whole into equal parts. Fractions are identified with a slash drawn between two numbers. The number that is written on top of the slash is known as the numerator, and the one written at the bottom of the slash is known as the denominator. The denominator shows the number of equal parts in which something is divided. The denominator tells you how parts there are in one whole unit. The numerator represents how many equal parts are to be considered. For example, if a fraction is 1/2 of a cake, the denominator 2 shows that the cakes has been divided into two equal parts, of which 1, that is the numerator, is in consideration. In other words, 1/2 also means 1 out of 2 equal parts from the whole cake.
There are three basic types of fractions. They are classified based on difference between the numerator and denominator value or if they contain a whole number. Here is a quick rundown of the different types:
1) Proper - A fraction with numerator less than or smaller than the denominator is known as the proper fraction. These are very common and the form we will work with the most. For example, 1/2 , 3/4 , 9/11.
2) Improper - These are fractions with a numerator greater than the denominator. For example, 11/9, 5/3 , 21/7. As a result of this top heaviness, they are always equal to greater than a whole number.
3) Mixed - These have a whole number part as well as the fractional part. For example, 3 1/2, 5 3/4.
When we are evaluating fractions there are several different features you should be aware of:
Unit Fractions - They are classified as such when they contain a numerator of 1. They are named that because they indicative on one unit or slice of the overall whole.
Equivalent Fractions - These are when two values are the same or same portion. For example 4/8 and 1/2. You can cut a cake into 8 slices or 2 slices, but it is how much of that cake that you take that determines the part of the whole that you have.
Like and Unlike - You will hear these terms a great deal when we make our to working with operations. Like fractions share the same denominator such as: 6/8, 2/8, and 5/8. Unlike do not have the same denominator such as: 4/7, 1/2, and 3/5.