Subject(s): Mathematics
Grade Level(s): 5
Suggested Technology:
Computer for Presenter, Computers for Students, Internet Connection, Interactive Whiteboard, LCD Projector
Instructional Time:
1 Hour(s) 30 Minute(s)
Resource supports reading in content area:Yes
Freely Available: Yes
Keywords: fraction multiplication, multiplication, fractions, area models
Sorry! This resource requires special permission and only certain users have access to it at this time.
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 oneseventh 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)
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)
(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 realworld 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
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.
ASSESSMENT
 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.
 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.
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 AttributionShare Alike license: http://creativecommons.org/licenses/bysa/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
* Please note that examples of resources are not intended as complete curriculum.