Fractions and Decimals
Fractions and decimals make up a large part of the fourth grade curriculum.
Fractions and decimals make up a large part of the fourth grade curriculum.
Use the tools below to help create visual fraction models...
Use the tools below to help create visual fraction models...
Learning about Fractions...
Learning about Fractions...
Have your child click on the picture to the right and scroll through the reference sheets to help them learn about Fractions!
Check out the pictures below for more examples and information!
Fractions.pdfStudents learn that a fraction means a part of a whole. The numerator (top number) represents the part of the whole or the number that shows how many equal parts you have. The denominator (bottom number) represents how many equal parts the whole is broken into.
Students learn that a fraction means a part of a whole. The numerator (top number) represents the part of the whole or the number that shows how many equal parts you have. The denominator (bottom number) represents how many equal parts the whole is broken into.
When the numerator and denominator are the same, the fraction represents one whole. We call this a form of one (FOO). For example, 2/2 means that you have 2 pieces out of 2 total, so 2/2 = 1 whole.
When the numerator and denominator are the same, the fraction represents one whole. We call this a form of one (FOO). For example, 2/2 means that you have 2 pieces out of 2 total, so 2/2 = 1 whole.
Students learn that unit fractions are fractions with a one in the numerator, representing one part of the whole. All wholes can be broken up into unit fractions. For example 1/4 + 1/4 + 1/4 + 1/4 = 4/4 = 1
Students learn that unit fractions are fractions with a one in the numerator, representing one part of the whole. All wholes can be broken up into unit fractions. For example 1/4 + 1/4 + 1/4 + 1/4 = 4/4 = 1
When adding and subtracting fractions, the denominators need to be the same. You add or subtract the numerators, while the denominator stays the same.
When adding and subtracting fractions, the denominators need to be the same. You add or subtract the numerators, while the denominator stays the same.
To help students understand this, we teach the students to think of the numerators as adjectives and the denominators as nouns. For example, two slices plus one slice equals three slices, just like two sixths plus one sixth equals three sixths.
To help students understand this, we teach the students to think of the numerators as adjectives and the denominators as nouns. For example, two slices plus one slice equals three slices, just like two sixths plus one sixth equals three sixths.
The denominator always stays the same!
The denominator always stays the same!
Subtraction Examples
Subtraction Examples
Students learn how to multiply a fraction by a whole number in three different ways. They first learn how to use a model, as pictured in the following two examples. They then learn how to use repeated addition to solve, as pictured first below. Finally, they learn how to solve using the formula, as pictured second below.
Students learn how to multiply a fraction by a whole number in three different ways. They first learn how to use a model, as pictured in the following two examples. They then learn how to use repeated addition to solve, as pictured first below. Finally, they learn how to solve using the formula, as pictured second below.
When learning how to compare fractions, students first learn that you can only compare fractions of the same sized whole. For example, we cannot compare half of a small package of skittles to half of a large package of skittles,
When learning how to compare fractions, students first learn that you can only compare fractions of the same sized whole. For example, we cannot compare half of a small package of skittles to half of a large package of skittles,
Students learn how to compare fractions in many ways. As stated above, you can only compare fractions of the same sized whole.
Students learn how to compare fractions in many ways. As stated above, you can only compare fractions of the same sized whole.
They first learn two generalizations:
They first learn two generalizations:
1. When comparing fractions with common denominators, you look to the numerator, and the fraction with the larger numerator is the larger fraction. This is because you have more equal sized parts. For example, 3/4 is greater than 2/4, because 3 pieces are more than 2 pieces. See the first picture below for a visual example.
1. When comparing fractions with common denominators, you look to the numerator, and the fraction with the larger numerator is the larger fraction. This is because you have more equal sized parts. For example, 3/4 is greater than 2/4, because 3 pieces are more than 2 pieces. See the first picture below for a visual example.
2. When comparing fractions with common numerators, you look to the denominator. As the denominators get larger, the pieces get smaller, so the fraction with the smaller denominator is the larger fraction. This is because the pieces are larger. For example, 1/4 is larger than 1/6, because the fourths are larger pieces than the sixths, so one large piece is greater than one small piece. See the second picture below for a visual example.
2. When comparing fractions with common numerators, you look to the denominator. As the denominators get larger, the pieces get smaller, so the fraction with the smaller denominator is the larger fraction. This is because the pieces are larger. For example, 1/4 is larger than 1/6, because the fourths are larger pieces than the sixths, so one large piece is greater than one small piece. See the second picture below for a visual example.
When comparing fractions with unlike denominators and unlike numerators, students learn the following three strategies:
When comparing fractions with unlike denominators and unlike numerators, students learn the following three strategies:
1. Compare to a Benchmark of One-Half - Think about the fractions in terms of a half. If one fraction is less than a half and the other is greater than a half, then the fraction that is greater than a half is greater than the other fraction. For example, 1/4 is less than 4/6, and I can prove this because 1/4 is less than 2/4 and 4/6 is greater than 3/6. This strategy does not work when both fractions are less than or greater than a half. See the third picture below for a visual example.
1. Compare to a Benchmark of One-Half - Think about the fractions in terms of a half. If one fraction is less than a half and the other is greater than a half, then the fraction that is greater than a half is greater than the other fraction. For example, 1/4 is less than 4/6, and I can prove this because 1/4 is less than 2/4 and 4/6 is greater than 3/6. This strategy does not work when both fractions are less than or greater than a half. See the third picture below for a visual example.
2. Compare using a Model - Students can draw two rectangular models stacked on top of each other to compare fractions. You want to make sure the wholes drawn are the same size, and the parts are drawn equally within each whole. It is easiest for students to draw rectangles stacked on top of each other, rather than circles or rectangles / squares drawn side by side. See the first picture below for a visual example.
2. Compare using a Model - Students can draw two rectangular models stacked on top of each other to compare fractions. You want to make sure the wholes drawn are the same size, and the parts are drawn equally within each whole. It is easiest for students to draw rectangles stacked on top of each other, rather than circles or rectangles / squares drawn side by side. See the first picture below for a visual example.
3. Find Common Denominators and Compare - Once students have learned how to find equivalent fractions, we teach them how to compare after finding common denominators. See the picture fourth picture below for a visual example.
3. Find Common Denominators and Compare - Once students have learned how to find equivalent fractions, we teach them how to compare after finding common denominators. See the picture fourth picture below for a visual example.
Finally, we teach students to check their work with cross multiplication. See the fifth picture below for a visual example.
Finally, we teach students to check their work with cross multiplication. See the fifth picture below for a visual example.
We teach students to find equivalent fractions by using models, and then by multiplying or dividing by one whole.
We teach students to find equivalent fractions by using models, and then by multiplying or dividing by one whole.
Whenever you multiply or divide a number by 1, the value of the number stays the same. This is the same with fractions. Whenever you multiply or divide a fraction by a form of one, the value of the fraction stays the same.
Whenever you multiply or divide a number by 1, the value of the number stays the same. This is the same with fractions. Whenever you multiply or divide a fraction by a form of one, the value of the fraction stays the same.
For example, 1/2 x 2/2 = 2/4, so 1/2 and 2/4 are equivalent fractions.
For example, 1/2 x 2/2 = 2/4, so 1/2 and 2/4 are equivalent fractions.
Fractions with a value that is greater than one are called Mixed Numbers or Improper Fractions. We always convert improper fractions to mixed numbers, rather than leaving them improper.
Fractions with a value that is greater than one are called Mixed Numbers or Improper Fractions. We always convert improper fractions to mixed numbers, rather than leaving them improper.
Students learn how to decompose fractions to convert them between mixed numbers and improper fractions.
Students learn how to decompose fractions to convert them between mixed numbers and improper fractions.
For example: 2 and 2/3 means 3/3 plus 3/3 plus 2/3, which equals 8/3
For example: 2 and 2/3 means 3/3 plus 3/3 plus 2/3, which equals 8/3
and
and
5/2 means 2/2 plus 2/2 plus 1/2, which equals 2 and 1/2.
5/2 means 2/2 plus 2/2 plus 1/2, which equals 2 and 1/2.
See the two pictures below for the formula to convert between mixed numbers and improper fractions.
See the two pictures below for the formula to convert between mixed numbers and improper fractions.
Adding Mixed Numbers
Subtracting Mixed Numbers
Relating Fractions to Decimals...
Relating Fractions to Decimals...
Have your child click on the picture to the right and scroll through the reference sheets to help them learn about Fractions!
Check out the pictures below for more examples and information!
Decimals.pdfReading Decimals:
Reading Decimals:
Relating Decimals to Fractions:
Relating Decimals to Fractions:
*We think of Tenths like Dimes, and Hundredths like Pennies!
*We think of Tenths like Dimes, and Hundredths like Pennies!
