Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 38419
Multiplying Fractions With GeoGebra Using An Area
Model
In this lesson, students will derive an algorithm for multiplying fractions by using area models. They will use a GeoGebra applet to visualize fraction
multiplication. They will also translate between pictorial and symbolic representations of fraction multiplication.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Computers for Students, Internet Connection,
Interactive Whiteboard, LCD Projector
Instructional Time: 1 Hour(s) 30 Minute(s)
Freely Available: Yes
Keywords: fraction multiplication, multiplication, fractions, area models
Instructional Design Framework(s): Direct Instruction
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Ind_Prac_Fraction_Mult.pdf
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?
Using GeoGebra, students will be able to use an area model for multiplying fractions and describe patterns in the area model to describe the algorithm for multiplying
fractions; and achieve 80% on the independent practice.
GeoGebra Tube Multiplication of Fractions Applet
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to multiply whole numbers.
Students should be able to represent multiplication of whole numbers using an area model.
Students should be able to recognize that a fraction such as 2/7 actually could be represented as 2 pieces that are each one-seventh of a whole (2 x (1/7)).
Students should be able to multiply fractions by whole numbers.
Guiding Questions: What are the guiding questions for this lesson?
How is multiplying whole numbers like multiplying a whole number by a fraction? (They both can be represented by repeated addition)
What does 2 x 5 mean? (It means 2 groups of 5)
page 1 of 5 What does 2 x 1/5 mean? (It means 2 groups of 1/5)
What does 1/2 x 5 mean? (It means 1/2 of a group of 5)
What does 1/2 x 1/5 mean? (Based on the previous questions, the students should be able to respond that it means 1/2 of a group of 1/5)
Teaching Phase: How will the teacher present the concept or skill to students?
Opener - Open the GeoGebra applet at http://www.geogebratube.org/student/m9781. Present students with this problem: There are 25 students in a class. 15 of them
are boys and 10 of them are girls If two thirds of the boys have brown eyes, what fraction of the class are boys with brown eyes?
Ask the students what fraction of the class is boys? (3/5)
Use the sliders a and b to represent 3/5
Use the sliders c and d to represent 2/3
Have the students write the multiplication problem. (3/5 x 2/3)
Now use the slider to multiply.
Ask students what the overlapping area represents. (2/3 of 3/5)
Ask the students what the product of 3/5 x 2/3 is. (6/15)
Have the students draw the diagram and shade the boxes in two different colors. Have them write the equation above the diagram.
Have the students put the answer back into the context of the problem.
How could you change the model to find 2/3 x 3/5? (Change the sliders in GeoGebra)
Have students compare this to the model they just drew. How is this different from what we did before? (It is now a square with three rows and five columns
instead of five rows and three columns.)
How is it the same as what we did before? (The answer is still 6/15).
Have students draw this diagram and write the equation above the diagram.
What does that tell you about multiplication of fractions? (The order does not matter.)
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Examples: Present the students with the following examples and use the GeoGebra applet to demonstrate the multiplication problem. Have them draw the diagrams and
write the equations
1/2 x 3/4
2/3 x 1/3
1/4 x 1/3
4/5 x 1/2
(Give more examples if they need it)
Ask the students: Do you notice any relationships between the numerators in the problem and the product? What about the denominators in the problem and the
product? (You multiply the numerator by the numerator and the denominator by the denominator).
Have the students write a rule for multiplying fractions.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Give the students the following diagrams and have them write the equations and solutions:
(1/3 x 1/3 = 1/9)
>(2/5 x 2/3 = 4/15)
page 2 of 5 (1/2 x 1/5 = 1/10)
(1/2 x 1/2 = 1/4)
(1/4 x 2/3 = 2/12)
Go over the solutions with students. Ask them if the last fraction can be simplified? (1/6) How can they represent that in the diagram? (There are six groups of two
boxes and one of those groups is shaded, therefore it is 1/6.)
The problems included in the lesson are on the attached worksheet: Independent Practice - Fraction Multiplication
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Ticket Out the Door: Have students
Write a real-world multiplication problem that involves two fractions (on their own
Model the solution using an area model
Apply the multiplication rule developed in class (show their work)
Summative Assessment
Review answers for independent practice.
Review answers on Ticket Out the Door to ensure students have mastered the concept of multiplication of fractions.
Formative Assessment
A. Give the students the following questions (or similar questions) to assess their prior knowledge of multiplication:
1. 2 x 5
2. 3 x 7
3. 8 x 9
4. 6 x 4
5. 5 x 10
B. Draw a model of the following fractions. (If the fraction is in the form n/d, students can draw these models using a rectangle or circle sectioned into d equal pieces
and shade n pieces.)
1. 1/4
2. 2/3
3. 4/5
4. 3/8
5. 2/7
C. Give the students the following questions (or similar questions) to assess their prior knowledge of multiplication of fractions by whole numbers:
1. 1/4 x 2
2. 1/2 x 6
page 3 of 5 3. 2/3 x 9
4. 3/8 x 4
Feedback to Students
As students work through guided practice problems, teacher should circulate and give individual feedback to students. After each problem, teacher can allow students to
share their equations and diagrams with the class. (See below for guided practice questions.)
Present the students with the following examples and use the GeoGebra applet to demonstrate the multiplication problem. Have students draw the diagrams and write
the equations.
1/2 x 3/4
2/3 x 1/3
1/4 x 1/3
4/5 x 1/2
(Give them more examples if they need it)
Ask the students: Do you notice any relationships between the numerators in the problem and the product? What about the denominators in the problem and the
product? (You multiply the numerator by the numerator and the denominator by the denominator).
Have the students write a rule for multiplying fractions.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: 1. Allow students to work in pairs.
2. Teacher can work individually with students as necessary.
3. Allow students to manipulate GeoGebra file.
4. Allow students to model the fraction multiplication using two sheets of patty paper. Have students fold each sheet of paper to model the GeoGebra applet and shade
the correct number of sections on each paper. Then layer to patty paper to see the overlapping sections.
Extensions: Have students simplify the fractions. For example: 1/4 x 2/3 = 2/12. 2/12 is equivalent to 1/6.
Suggested Technology: Computer for Presenter, Computers for Students, Internet Connection, Interactive Whiteboard, LCD Projector
Additional Information/Instructions
By Author/Submitter
Resource aligns with the following standards of math practices
MAFS.K12.MP.6.1 - Attend to precision
MAFS.K12.MP.7.1 - Look for and make use of structure
Use of the following GeoGebraTube resource is acknowledged: "Demo for iPad: Visualisation of Fraction Multiplication" by tzunfung, accessed from
http://www.geogebratube.org/student/m9781, used under Creative Commons Attribution-Share Alike license: http://creativecommons.org/licenses/by-sa/3.0/
SOURCE AND ACCESS INFORMATION
Contributed by: Barbara Perez
Name of Author/Source: Barbara Perez
District/Organization of Contributor(s): Broward
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.5.NF.2.4:
Description
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a
sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create
a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction
side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply
fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
page 4 of 5 When students meet this standard, they fully extend multiplication to fractions, making division of fractions in grade
6 (6.NS.1) a near target.
Particular alignment to:
MAFS.5.NF.2.4b:
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side
lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side
lengths to find areas of rectangles, and represent fraction products as rectangular areas.
page 5 of 5