Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 37752
Multiply Fractions and Whole Numbers with Models
Students will multiply fractions and whole numbers through set models and problem solving.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Suggested Technology: Document Camera, LCD
Projector
Instructional Time: 2 Hour(s)
Freely Available: Yes
Keywords: fraction, whole number, numerator, denominator, part, whole, represent, corners game, multiply,
divide
Instructional Design Framework(s): Direct Instruction, Guided Inquiry (Level 3), Cooperative Learning
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Corners Game.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 model the actions that take place in order to multiply a fraction by a whole number.
Prior Knowledge: What prior knowledge should students have for this lesson?
In third grade, students have learned how to fluently multiply and divide within 100 (3.0A.7). Students have also developed an understanding of fractions as numbers
(3.NF)
Guiding Questions: What are the guiding questions for this lesson?
How does your model prove that ½ and of 18 is 9?
How can you model these actions another way?
Can you show me another way to multiply a fraction and a whole number?
How does your model compare to what you're saying?
How does your explanation compare to other student's explanations/models?
How is multiplying a fraction and a whole number different than multiplying two whole numbers?
Teaching Phase: How will the teacher present the concept or skill to students?
Pass out math tools (counters, cubes, paper) to the students then pose the problem "Ms. Vining has 24 cupcakes. She decided to eat 1/3 of the cupcakes and then give
the rest to the students. How many cupcakes did Ms. Vining eat?" As the students are solving the teacher should walk around to monitor student work. The teacher
could select and sequence students to share strategies that would be beneficial to the group. Have a discussion about how the model relates to the problem. Discuss
how the students separated the counters into three groups and one of the groups represents the number of cupcakes Ms. Vining ate.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Have students continue practice with multiplying other fractions and whole numbers using the denominators: 2, 3, 4, 6, 8, 10, 12, 100.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
page 1 of 3 lesson?
Pose the story problems listed below to have students continue modeling multiplying a fraction and a whole number. You will want to move students from using the
counters to drawing a picture and then eventually solving it mentally.
Samantha had 48 oranges. She gave away 3/6 of them. How many oranges did she give away?
3/5 of the class likes baseball as their favorite sport. If there are 15 students in the class, how many students like baseball as their favorite sport?
The students in Ms. Kinney's class used 5/6 of the pencils. Ms. Kinney had 36 pencils. How many pencils were not used by Ms. Kinney's class?
There were 32 students in the fifth grade going to the aquarium field trip. 5/8 of the students did not bring back their permission slip. How many students brought
back their permission slip?
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Post the four "Corners" signs throughout the classroom. Cut out each of the 16 cards. Some have expressions, some have the visual representation. Pass out a card to
each student to solve. Have them decide which corner has their answer and go to that corner. At the corners, students must justify, using words/pictures/numbers, why
they belong at that corner. You could reshuffle the cards and do the activity again. Some students may work in pairs. An additional activity could be for students to pair
up with their match (expression with visual representation), once they are in their corner.
Summative Assessment
Teachers will give feedback at the end of the lesson through a problem posed, during the closure portion of the lesson, with an exit ticket. The exit ticket will give
information about where the students learning is at the end of the lesson and what differentiation still needs to occur based on the results. The teacher will then use the
exit ticket to make a plan for students that still may need extra interventions. The exit ticket question is: "How could you find what ¾ of 24 is?"
Formative Assessment
After the teacher poses the problem, posed during the part 1 teaching phase, they will circulate around the room and record anecdotal notes on index cards in a file
folder to start grouping students by ability level of understanding of equivalent area models.
Feedback to Students
Students will get feedback during the lesson, as the teacher is circulating during the problems posed through guiding practice and independent practice such as: Can
you show me another way to justify your answer? How do you know that Jose is right? How does your model compare to what you're saying? How do you know that
you're right? Is there a way your answer could be incorrect?
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: If students are struggling, continue practice with counters and smaller whole numbers in a small group setting. An example may include finding
2/3 of 9, ¼ of 12, etc.
Extensions: Students could be given larger whole numbers and encouraged not to create a model to solve. An example could be: There are 385 students in the
school. 4/5 of the students got perfect attendance this quarter. How many students got perfect attendance this quarter?
Suggested Technology: Document Camera, LCD Projector
Special Materials Needed:
Preparations may include changing the problems to have names of students from your individual class. Problem solving strategies such as: draw a picture or diagram,
apply logical reasoning need to be practice and reinforced. Materials may include but are not limited to: counters, cubes, paper, corners signs that are attached and
corners game cards cut with one for each child. (You want to have a plethora of tools available in order for students to demonstrate flexible thinking for their
representations).
Further Recommendations: Students should have a sound understanding of fractions of a set in order to model multiplication of a fraction and a whole number.
Make sure to focus on the following Standards for Mathematical Practice throughout the lesson:
SMP 4 - Model with mathematics (students are demonstrating their understanding through multiple representations of fractions as they relate to the whole in order to
compare).
SMP 2 - Reason abstractly and quantitatively (students are reasoning their representation to prove their answer both verbally, using fractions, and pictures).
SOURCE AND ACCESS INFORMATION
Contributed by: Shanna Uhe
Name of Author/Source: Shanna Uhe
District/Organization of Contributor(s): Hillsborough
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the
product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole
number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as
page 2 of 3 MAFS.4.NF.2.4:
6/5. (In general, n × (a/b) = (n × a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models
and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast
beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two
whole numbers does your answer lie?
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
This standard represents an important step in the multi-grade progression for multiplication and division of fractions.
Students extend their developing understanding of multiplication to multiply a fraction by a whole number.
page 3 of 3