Content Objectives
As stated in the Common Core State Standards, one of the critical areas of focus in the fourth grade is fractions. Students are expected to be able to understand how fractions are built from unit fractions and they need to be able to compose and decompose fractions in terms of unit fractions. These understandings then need to be applied to various operations. The objectives of my curriculum unit are to develop the student’s conceptual understanding of fractions. With this knowledge I want them to apply it to word problems and be able to clearly articulate and represent the process of adding and subtracting fractions with a fixed denominator.
The “Unit”
The “unit” is an essential understanding in fractions. When working with fractions, it is always important to identify what the unit is. The fraction tells the size of another quantity in relation to the unit. For example, if there are 24 bottles of soda in a case and the unit is one case, then a 6 pack represents one fourth. However, if the unit is one bottle then a 6 pack of sodas represents 6. Another example could be used with time. For example, if the unit is an hour, then a day represents 24. If the unit is changed to a week then a day represents 1/7. Other measurements such as inches/feet/yards and centimeter/meter require students to understand the size of the unit being looked at. The unit allows us to know how to express the relationship between two quantities. These examples show how it is important for the student to identify the unit in the problem. Then numbers are used to express other quantities relative to the unit. Being able to identify the unit and recognize how other quantities are related to it is essential to understanding the meaning of fractions.
Unit Fraction
A unit fraction is any fraction that has a numerator of one. If any whole is broken into b equal parts, and then each part equals the unit fraction 1/b. The fractions one half, one third, and one fourth are all unit fractions. The denominators of these fractions tell the size of the unit. For example, the denominator of three in one-third tells us that it takes 3 unit fractions to make the whole. Students need opportunities to build this understanding through the use of manipulatives and visual models. Through these practices they need to be able to identify the unit, which continues to build their understanding of the whole.
General Fraction
A general fraction represents multiple copies of the unit fraction. This means that if I have three copies of, say 1/5, then I would have three fifths, expressed symbolically as 3/5. Students need to understand how to look at a general fraction as one number, that expresses the size relation between the fractional amount and the whole. Through the process of decomposing, students will develop the understanding that general fractions are composed of unit fractions.
Adding and Subtracting Fraction with Like Denominators
Adding and subtracting fractions requires the understanding of joining and separating pieces of a whole. In this unit we will only be looking at fractions with a common denominator. As the standard states, students should also be able to use visual models and equations to represent these problems. Student’s previous work with equations to solve problems involving whole numbers is applies as they work with equations involving fractions and mixed numbers.
In this unit I will be creating a bank of problems from a scenario that kids would relate to and then change how I use the numbers in each set of problems. I want students to become more comfortable analyzing the word problem and discussing the process they used to solve it. Through this process I want the students to use the concrete and pictorial representations they use when working with fractions. By the end of the unit I want the students to have the ability to write their own word problems.
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