5th Grade Fractions Unit
Learning Module
- Creator(s):
Learning Module Objectives:
5.NF.A Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.B Apply and extend previous understandings of multiplication and division.
These objectives are standards from the Common Core State Standards for fifth grade.
Prerequisite skills:
Essential Vocabulary for this unit:
Looking ahead:
You can use a common denominator or a common multiple of two or more denominators to write fractions that name the same part of a whole.
A common denominator is a common multiple of two or more denominators.
Strategy 1
Strategy 2
Next, watch the following lesson for more examples:
Read through this lesson as well.
Homework:
Purpose of this update: This module is the foundation for the upcoming modules. With this lesson, students learn what common denominators are and how to use them to find equivalent fractions. This is crucial for them to grasp before learning how to add and subtract fractions with unlike denominators.
Teaching tips: When creating equivalent fractions, students may not recall to change both the numerator and denominator. Thus, it is key to reiterate this particular step.
Extension: Some students may grasp this quicker than others. One way to involve them in a critical thinking activity is to ask them to make a Venn Diagram (similar to the one below) to find the least common multiples of three given numbers.
Objective: Use equivalent fractions as a strategy to add and subtract fractions
To add fractions with unlike denominators you must find a common denominator of both fractions first.
As you watch the lesson below pause it periodically to determine the common denominator of the given problem on your own.
Next, answer the following practice problems:
Homework:
Purpose of this update: In this module, students are asked to solve addition of fractions with unlike denominators. Previously, students have learned the concept of fractions as well as how to find common denominators. Much of this lesson is a review. Next, students will use the foundation from this module to subtract fractions with unlike denominators.
Teaching tips: A common misconception is that students will add the numerator and the denominator across without finding a common denominator. During the whole group lesson, reiterate the important of adding things that are like. The concept of sameness: one cannot add apples and bananas.
ELL suggestions: Provide sentence frames for students to use when responding to questions and make a vocabulary chart to help English Language Learners choose the right words.
When subtracting two fractions with unlike denominators, follow the same steps you follow when adding two fractions. However, instead of adding the fractions, you now subtract.
As you watch the following lesson try to think of the common denominators on your own.
Next, solve the following practice problems and remember to simplify your answers.
Homework:
Purpose of this update: Previously, students learned and practice how to add fractions with unlike denominators. Similarly, they will be following the same steps as above to find the difference of two fractions.
Teaching tips: Many students might have a difficult time with finding common denominators to add and subtract fractions. The ease their understanding, present them with fraction strips such as these:
Other resources: In the following video, a few examples are shown on how to use fraction strips to find the difference of two fractions.
A mixed number is a number consisting of an integer and a proper fraction.
Strategy 1
Strategy 2
Complete the following example problems.
Homework:
Purpose of this update: In this module, students are asked to further their knowledge of fractions by turning mixed numbers into improper fractions to add and subtract them in various ways.
Teaching tips: In this concept, there are multiple steps involved and students may forget to complete a few steps along the way. Provide an anchor chart with steps for students to follow as the one below to help them through the process.
An improper fraction is a fraction greater than one. The numerator is bigger than the denominator.
Strategy 1
Strategy 2
Here, is an example problem and its solution. Watch it carefully and take notes.
Next, read through this lesson.
Homework:
Purpose of this update: In this update, students are asked to rename mixed numbers to find their differences. This concept provides students a way to hone their skills with making improper fractions, renaming, subtraction, as well as simplifying.
Teaching tips: This is a concept that needs much practice due to the many steps involved. Many students will unnecessarily rename fractions, thus, it is crucial to discuss when one should rename and one does not need to. As the previous concept, it would be beneficial for the students to have a visual of all the steps involved in solving these problems. Also, during this module it would be a great opportunity to review the previously learned concepts and vocabulary words.
Other resources:
Objective: Apply and extend previous understandings of multiplication and division
A product is the answer to a multiplication problem.
When multiplying fractions, first multiply the numerators across then multiply the denominators across. If one of the factors is a whole number, then rewrite the number as a fraction with a denominator of one. Lastly, reduce the fraction in its simplest form.
Read through this lesson to view examples.
Next, play this game to practice on your own!
Homework:
Purpose of this update: Multiplying fractions is one of the easier concepts for students to grasp. In this module, students are practice multiplying numerators and denominators across and simplifying their answers.
Teaching tips: When multiplying a fraction by a whole number or a whole number by a fraction, it is not necessary for students to change the whole number into a fraction. Some students will be able to simply multiply the whole number with the numerator and keep the denominator the same. Let students choose their method of choice.
Misconception: On the contrary, students may multiply the whole number fraction and the denominator instead of the numerator or both.
ELL strategies: Visuals are great way to expose English Language Learners to math topics. Fraction circles or equal groups demonstrate understanding of fraction operations.
Here, is an example of a visual representation of multiplying fractions:
Other resources:
Earlier, you were introduced to mixed numbers and how to add and subtract them. In this lesson, you will learn how to multiply mixed numbers.
Recall: a mixed number is composed of an integer and a proper fraction.
Go through this lesson to learn how to multiply mixed numbers.
Watch this video to see Sal work through an example:
Then, complete the following practice problems on your own. If you get stuck, make sure to use the hints to help you solve the problem: Khan Academy - Practice Problems
Homework:
Purpose for this update: In this update, students are again presented with mixed numbers. Now, they will be asked to multiply them by fractions, whole numbers, and other mixed numbers. This skill can be applied to everyday life.
Teaching tips: A potential math talk could include ways in which multiplying mixed numbers are used in everyday life. Such as increasing or decreasing a recipe or finding the total amount of money earned after working a fraction of an hour. Encourage students to think of other scenarios.
Misconceptions: Students may multiply the whole numbers and then multiply the fractions instead of turning them into improper fractions. An anchor chart showing the steps will help students remember the steps such as the one below:
A dividend is the number that is to be divided in a division problem.
A quotient is the answer to a division problem, not including the remainder.
This lesson shows the steps to dividing fractions.
Next, carefully watch this video to view more examples:
Now, your turn to practice! Play this game to answer some problems on your own!
Homework:
Purpose of this update: In this update, students extend their knowledge of multiplication an division of whole numbers to now divide fractions.
Teaching tips: To divide fractions, you must multiply the first fraction by the reciprocal of the other. Another way would be to cross multiply to find the answer. Students may choose any method that they feel comfortable with. A good way to teach students the steps are the phrases: keep, change, flip. You keep the first fraction, you change the sign from division to multiplication, and you flip (find the reciprocal) of the second fraction. This strategy is quite helpful to most.
Other resources: This anchor chart lays out the various steps in a organized form. Creating a handout similar to this anchor chart would be a great resource for students to revisit as they try problems on their own.
For the peer review project, you will be creating a video lesson in which you will solve your own created problems. For the video lesson you will choose five from the following eight topics and a questions pertaining to each topic. These problems should be different than previous ones you have posted on your updates.
Each problem that you present should be followed by a paragraph explaining the problem and solution. Make sure to include vocabulary words and thoroughly explain your thought process.
Topis:
Rubric:
This peer-reviewed project is the final assessment for this learning module. Allowing students to demonstrate their understanding of the concepts using a creative platform strays away from the traditional paper tests. It also allows them to delve into their ingenuity based on their interest. Students will also be able to access their creative work in the future and it will act as an example for future students. Ideally, this work should be assigned by the fourth update so that students have sufficient time to complete the task.
Here is the rubric to assess the work:
This knowledge survey is a formative assessment to provide the teacher with data needed to extend or reteach a lesson. This survey can be used as a pre-test, midpoint check, and an end of the lesson test.