Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 49127
Decomposing Fractions
Using circle fraction manipulative students will investigate adding fractions by decomposing them into their smallest parts.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Suggested Technology: Microsoft Office
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: addition, fractions, decomposing, investigate
Instructional Design Framework(s): Structured Inquiry (Level 2)
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: Confirmatory or Structured Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
By the end of this lesson the students will:
understand that decomposing a fraction and then adding it with like denominators is a joining to form the same whole.
be able to use circle fractions to compose and decompose fractions with like denominators.
be able to record their decomposed fractions as an equation.
strengthen their ability to form a viable argument by explaining their work and justifying their reasoning.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should have prior experience with:
the meaning of fractions and what a numerator and denominator represents.
decomposing or breaking apart numbers.
working with circle fraction manipulatives.
Guiding Questions: What are the guiding questions for this lesson?
How does breaking apart or decomposing a fraction help in your understanding of adding fractions with like denominators?
What do we already know about adding fractions with like denominators?
How will using the circle fractions help us to decompose our fractions with like denominators?
What evidence do you have that supports your answer?
Could you explain that in a different way?
Another example of that is...
Introduction: How will the teacher introduce the lesson to the students?
Begin by passing out a set of circle fractions to each student giving students about five minutes to take out of containers and play/manipulate them. At this time have a
review conversation about fractions with the class asking questions such as:
What does it mean to have 2/3?
Are there other ways to show 2/3?
page 1 of 4 Are all 2/3 the same size?
Student Responses could include:
2/3 is when you have a whole split into three "equal" pieces and you only have two of those three pieces.
I can show 2/3 by placing 4/6 on top or 4/12 on top of that.
No, because it depends on the size of the whole.
Discuss with the class what decomposing a number means. They just did a warm up on it so use that as your example.
Pass out the Decomposing Fraction worksheet to each student and do number one together as a class walking them through each step as described below.
Note: This worksheet is a two part worksheet "Decomposing Fractions" on the first page and "Fraction Investigation" on the second page. When using it in the class I
would copy it front to back.
Write "Decompose 2/3" on the board and ask students to show 2/3 using their circle fractions. Ask students "What individual parts is 2/3 made up of"? Show them that
you have 1/3 + 1/3 and that together when you join these equal parts you have 2/3.
Have students pair up and work together completing the remaining four questions. If a group finishes early let them make up their own problems and write them down
on their paper.
When the class has completed the worksheet let students share their papers with the class reviewing the answers. Please note the student provided a description on
this answer sheet, not an explanation or justification. Stating that he/she broke apart and added and got the same answer describes what he/she did. The justification
would be that the answer is the same because we did not add anything to the parts or take anything away from the parts.
Focus on questions four and five as they have multiple answers that they could have recorded.
Ask students "Why do these two questions have multiple answers"?
Student Answer:
In number four there are seven 1/8 pieces. There are several ways to make the number 7. I can add 1+6 or 2+5, which is why there are many answers.
In number five there are six 1/10 pieces and also several ways to add in order to get the number six, like 3+3 or 4+2.
Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be
used to answer the question(s)?
Students will complete an investigation worksheet in which they are given two statements and asked to prove whether they are true or false. Then they will explain
and justify their answer based on their circle fraction drawing and answer.
Have students complete the two question Fraction Investigation worksheet independently, which is the second half of the decomposing fraction worksheet.
Remind students to use their circle fraction manipulatives drawing out the fractions, labeling them, and creating an addition sentence with the decomposed parts they
have in front of them.
Analyze: How will students organize and interpret the data collected during the investigation?
Students will be required to write their explanation for whether they were in agreement or disagreement with the statements provided. Once students have completed
their investigation, they will pair up with a partner who is also done and compare their responses.
Remind students beforehand that you expect to hear Math talk such as:
I agree with the statement because the parts of the fractions are equal.
I disagree with the statement because when I drew out the fraction parts they were unequal.
I have a question about ________....
I have something to add to what you said....
Another example of that is....
What evidence do you have that supports your answer?
Could you explain that in a different way?
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Ask students who would like to share their work and explanation with the class correcting any errors or misconceptions as you progress through the worksheet. An
example of their work should look similar to the answers. The answer on this document is a description, not an explanation or justification. When the student said
he/she took apart the fraction, added and got the same answer, they are describing what they did. The justification or reasoning behind why this works is because we
did not add anything to the parts or take anything away from the parts so the answer is the same.
Teacher Tip: Note the difference between asking a student to describe and explain their reasoning. When a student describes they are just telling, but when they
explain they are being asked to identify why what they did works mathematically.
Complete the lesson by reviewing the guided questions:
How does breaking apart or decomposing a fraction help in your understanding of adding fractions with like denominators?
What do we already know about adding fractions with like denominators?
How will using the circle fractions help us to decompose our fractions with like denominators?
Why
Possible Student Responses:
By breaking apart the whole fraction into its smaller pieces I see them better when adding.
I now know that I can break apart fractions to make it easier to add.
I know that I can combine fraction parts to make a larger fraction.
Using the circle fractions helps me visualize and see the fraction parts better in order to add.
End with an Exit Slip on a sticky note:
write a plus sign for something that you learned or was helpful in your learning.
write a question mark for anything you still have question on.
page 2 of 4 Summative Assessment
During the investigation, students are asked to agree or disagree with two statements and explain and justify their reasoning. This explanation will be used as their
Summative Assessment as this is an introductory lesson on the topic.
End with an Exit Slip on a sticky note:
write a plus sign for something that you learned or was helpful in your learning.
write a question mark for anything you still have question on.
Teacher Tip: Note the difference between asking a student to describe and explain their reasoning. When a students describes they are just telling, but when they
explain they are being asked to identify why what they did works mathematically.
Formative Assessment
Start with students prior knowledge of being able to decompose whole numbers. Begin with a whole number "Number Talks". A video on what this would look like in
your classroom is available on YouTube.
Teacher Example
1. Gather students all together in a group.
2. Instruct students to think of as many ways as they can to solve the problem. They are to indicate this with the number of fingers placed in front and close to their
chest.
3. Write the number sentence on the board and allow students to solve mentally.
4. Call on students to give their answer and reasoning of how they solved the problem mentally. Note: doing the algorithm in their head is not what you are looking
for.
5. Repeat as needed.
Being able to decompose whole numbers will lead right into decomposing fractions and this will make a strong connection piece.
Feedback to Students
Throughout the practice and investigation, the teacher moves from group to group asking questions and providing immediate specific feedback on the students'
progress. Simple, open ended questions or statements such as "What have you found out in your investigations so far?" and "Explain to me whether you agree or
disagree and why," help students review and communicate their understanding aloud to you.
This investigation helps students start developing important communication skills by asking them to provide support using their circle fraction manipulative and their
understanding of decomposing numbers. Discussions with their partner as well as the teacher provide important feedback that allow students to revise and improve
their explanations.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Pull a small group to work with individually.
Have students only work with the benchmark fractions.
Limit the number of problems that the student has to solve.
Extensions:
This lesson can lead right into subtraction of fractions and Adding and Subtracting Mixed Numbers.
Suggested Technology: Microsoft Office
Special Materials Needed:
Students will need circle fraction manipulatives.
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in the following the Mathematical Practice: MAFS.K12.MP.1.1 Attend to precision.
SOURCE AND ACCESS INFORMATION
Contributed by: Monica Friske
Name of Author/Source: Monica Friske
District/Organization of Contributor(s): Brevard
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each
page 3 of 4 MAFS.4.NF.2.3:
decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8
+ 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent
fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and equations to represent the problem.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
This standard represents an important step in the multi-grade progression for addition and subtraction of fractions.
Students extend their prior understanding of addition and subtraction to add and subtract fractions with like
denominators by thinking of adding or subtracting so many unit fractions.
page 4 of 4