Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 28336
Using Models to Add Fractions with Unlike Denominators
This lesson is specific to adding fractions with unlike denominators. It requires students to already have a working knowledge of adding fractions with
common denominators, and equivalent fractions. Subtracting fractions with unlike denominators will follow in a subsequent lesson, as the two should
be taught on separate days.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Interactive Whiteboard,
Overhead Projector
Instructional Time: 1 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: fractions, unlike denominators, adding, fraction strips
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
FractionStripsBlacklineMaster.docx
FractionStripsColorMaster.docx
AddingFractionsWorksheet.docx
AddingFractionsWorksheetAnswerKey.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to use models to show how to add fractions with unlike denominators.
Students will be able to explain verbally why the fractions with unlike denominators can be added (explanation needs to include mention of equivalent fractions).
Students will be able to replace given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like
denominators (for example, 2/3 + 5/4 = 8/12 + 15/12= 23/12).
Students will be able to use fraction strips to model (but not necessarily explain) the formula a/b + c/d = (ad + bc)/bd.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should come to this lesson able to:
find equivalent fractions
add fractions with like denominators
use and be familiar with fraction strips
Guiding Questions: What are the guiding questions for this lesson?
How can you use models like fraction strips to add fractions with unlike denominators?
How do you know those fractions are equivalent?
Why did you rename that fraction with that denominator?
How can you use equivalent fractions to add fractions with unlike denominators?
page 1 of 4 How can you use common denominators to add fractions?
Teaching Phase: How will the teacher present the concept or skill to students?
1. Warm up for the activity by reviewing how to model adding and subtracting fractions with like denominators using fraction strips. Write 2/6 + 3/6 on the board.
2. Ask: How many sixths fraction strips do you need to show 2/6? (2) How many do you need to show 3/6? (3)
3. Have students place fraction strips for 3/6 next to fraction strips for 2/6.
4. Ask: How many sixths fraction strips show the sum of 2/6 +3/6? (5) What is the sum of 2/6 + 3/6? (5/6)
5. Repeat this activity using other examples of adding fractions with like denominators, such as:
1/4 + 2/4 =
3/5 + 1/5 =
1/8 + 4/8 =
6. Next, pose the following problem: Amelia was using strips of ribbon for her costume for an upcoming play. She had ½ yard of blue ribbon and ¼ yard of red
ribbon. How many total yards of ribbon does Amelia have? Is there a way to use the fraction strips to prove your answer?
7. Circulate around the room to observe how students are solving the task. Take note of students that make the common error of adding denominators - this strategy
should be shown first. If no student shows ½ + ¼ = 2/6 then say "I saw a student last year do this … can you explain what they did and if that works?" Highlighting
this common error first promotes deeper understanding of why fractions of the same size (same denominators are needed). Students should be able to point out
that in this attempt the student added the numerators and added the denominators. Have a student demonstrate with fraction strips if this is true. Be sure it is
shown as placing ½ and ¼ next to each other. Have students explain what they notice about that length (longer than what was started with, more than half way to
one, etc.) Then have them show 2/6 fraction strips. Ask what they see now (less than one-half). Ask, "How can we combining two amounts and end up with a
length shorter than what we started with? Does that make sense? (no) Can we just add numerators and denominators? (no) Why not? (the denominator tells the
size of the strip or fraction, numerator how many pieces of that size fraction you have)
8. Keep the 1/2 strip and a 1/4 strip under the 1-whole strip on the whiteboard (students may do the same at their seat). Have a students that came up with the
correct amount explain what they did with the fraction strips. They should point out that they had to trade strips to find equivalents. Ensure that precise vocabulary
is being used (numerator, denominator, equivalent, etc.). If no student has the correct solution begin step 9.
9. Ask students to find fraction strips, all with the same denominator, that fit exactly under the sum of 1/2 and 1/4. Think aloud as you look for strips that will fit,
explaining why some won't work (these are too long/short, these work but they aren't the same denominator, etc.). As students name equivalents, record the
statements on chart paper or white board. If they say something like, "I saw ½ was the same length as three sixths" the write ½ = 3/6 to reinforce equivalent
fractions. Also record comparative fractions as well (3/6> ¼).
10. Discuss why fraction strips for fourths fit under the fraction strips for both 1/2 and 1/4. (because four is a multiple of 2)
11. Model how to determine if there are any other denominators that will fit under the fraction strips for 1/2 and 1/4. Students may work with their own fraction strips
as you model this for them. (Determine that fourths, eighths, and twelfths will all work).
12. Revisit the concept of equivalent fractions: 6/8 and 9/12 are equivalent to 3/4.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
1. Continuing to use their fraction strips, students will add 1/2 + 1/3. Teacher walks around the classroom, encouraging students to line up fractions strips accurately
so they can find the correct answer.
2. Once students find the answer, encourage them to work together to find 3/5 + 1/2. Pull students who are struggling into a group for reteaching before they move
on.
3. Ask: Why do we place fraction strips that all have the same denominator under 3/5 and 1/2? (the denominators have to be the same to add the fractions) Once the
students arrive at the answer, briefly discuss renaming fractions into mixed numbers (i.e., 11/10 = 1 1/10...) Students should be able to see this concept with their
fraction strips, because the fraction strips will fit exactly under the 1 whole strip, with 1/10 strip left).
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
1. Students will complete the first set of exercises on the AddingFractionsWorksheet.docx (Here's the AddingFractionsWorksheetAnswerKey.docx) in finding the sum of
fractions with unlike denominators by completing exercises that show a picture of the fractions strips (AddingFractionsWorksheet.docx or
FractionStripsColorMaster.docx) they've been using. Students may still use the fraction strip manipulatives to arrive at their answer. Have students try the following
problems independently or in pairs:
1/2 + 3/8= (4/8 + 3/8 = 7/8)
1/2 + 2/5 = (5/10 + 4/10 = 9/10)
3/8 + 1/4 = (3/8 + 2/8 = 5/8)
3/4 + 1/3 = (9/12 + 4/12 = 13/12, or 1 1/12)
2. After doing these problems independently, stop and check as a class. Students should be able to demonstrate how they arrived at their answer using their individual
whiteboard and fraction strips. Students who miss one or more exercises from the above exercises may be retaught in differentiated instruction (see
"Accommodations" below).
3. Once students have completed the above exercises successfully, they may move on to the next series of independent practice exercises on the worksheet that does
not include pictures of the fraction strips (though they may continue using fraction strip manipulatives).
2/5 + 3/10 = (7/10)
2/3 + 1/6 = (5/6)
5/8 + 1/4 = (7/8)
1/4 + 1/12 = (4/12)
1/2 + 1/5 = (7/10)
3/4 + 1/6 (11/12)
1/2 + 3/10 = (8/10)
1/2 + 1/3 = (7/6, 1 1/6)
7/8 + 1/4 = (9/8, or 1 1/8)
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students will respond to the following prompt as a means of completing the lesson: "Explain how using fraction strips with like denominators makes it possible to add
fractions with unlike denominators."
Lead a discussion of student responses, coming to the explanation: "The strips for both fractions need to be the same size. Finding like denominators is done by trying
smaller strips so they can all be the same size."
page 2 of 4 Summative Assessment
The teacher will determine that the students have attained understanding and a working proficiency of adding fractions with unlike denominators based on the
outcome of their independent practice. They will not move on to independent practice until they are comfortable and showing understanding in the guided practice
portion of the lesson. Once in the independent practice portion, students should be able to demonstrate a clear understanding of the material by adding fractions with
unlike denominators, on paper and with the use of fraction strips as models. The teacher can observe the student working with the fraction strips to achieve their
answers, and review their final answers on the independent practice answers.
Formative Assessment
The teacher will assess student understanding and prior knowledge before the lesson by reviewing addition of fractions with like denominators, as well as reviewing
equivalent fractions. Sample questions may include:
3/8 + 4/8 = ?
3/4 + 2/4 = ?
Name three equivalent fractions for each of the following:
1/2 = _____ = _____ = _____
4/6 = _____ = _____ = _____
5/3 = _____ = _____ = _____
Quick student responses using individual sets of fraction strips on an individual whiteboard will also give the teacher a formative assessment of the students' prior
knowledge and understanding. Adding fractions with like denominators, and creating equivalent fractions, will be needed throughout the lesson. The teacher will use
the information gathered at the beginning of the lesson to form ability groups, and to differentiate by ability.
Feedback to Students
Student performance will be reviewed informally throughout the lesson (as the teacher walks through the classroom and "spot-checks" their responses and work
with fraction strips), and more formally at the end of the lesson when classwork is completed and reviewed as a class, guided by the teacher. Students will grade
each other's work as the teacher models the thought process involved in solving each problem. The teacher will "think aloud" about each problem, showing each step
via ELMO or document camera as the class follows the steps on another student's paper, checking for mistakes as they review. This provides each student the
opportunity to observe the problems being solved correctly, to be watchful of common mistakes, and to quickly see their own mistakes (when their corrected paper is
returned at the end of the review). The teacher will collect and review each paper as a means of educative assessment.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
For students who are struggling with the use of fraction strips, give them a worksheet with the fraction strips already drawn. Students may shade or color the correct
amount to represent the answer to each question.
For students struggling with finding the common denominator, introduce the idea of "trading" one strip for strips with same denominator. For example, in the exercise
1/2 + 3/10, students may trade the 1/2 strip for 5 1/10 strips, then add all of the 1/10 strips together, to arrive at the answer 8/10 (or 4/5).
Students who are having difficulty may also benefit from using the "Adding Fractions" resource included with this lesson in the Related CPALMS Resources section.
Extensions:
A possible extension of this activity is to add fractions with unlike denominators using a number line. The number line should be between 0 and 1, with answers
equaling less than 1.
Another extension is to have students add fractions with unlike denominators using circles as the 1 whole, shading spaces on the circle to represent the two fractions.
Suggested Technology: Document Camera, Computer for Presenter, Interactive Whiteboard, Overhead Projector
Special Materials Needed:
Individual whiteboards
Fraction strips
AddingFractionsWorksheet.docx of problems listed in the (can also be written on white board)
Additional Information/Instructions
By Author/Submitter
It should be noted that the practice of reducing fractions to lowest terms is no longer emphasized in the Common Core. This is due to the fact that the fraction in
lowest terms is not always the easiest to understand or to use. A good example is any fraction over 100, which can often be much more easily converted to a percentage
than the lowest terms version of the same fraction. Students should instead become proficient at finding equivalent forms of a fraction and choosing the equivalent version
that is best suited for the particular situation or problem.
This lesson addresses Standard for Mathematical Practice MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others as students have to justify their
strategies as well as explain why common errors are not mathematically correct.
SOURCE AND ACCESS INFORMATION
page 3 of 4 Contributed by: Jennifer Mahurin
Name of Author/Source: Jennifer Mahurin
District/Organization of Contributor(s): Manatee
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.NF.1.1:
Description
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
page 4 of 4