Lesson Plan:

General Goals:
The students will have a profound understanding of the area model of multiplication.


The student will gain literacy in reading and interpreting graphs


Specific Objectives:

Upon completion of this lesson the participants will be able to:
1. Identify the factor pairs for a given value.
2. Explain the difference between factors and factor pairs
3. Discuss the difference between discrete and continuous plotted solution.
4. Demonstrate facility with divisibility rules.
5. Understand the significance of the Commutative property of Multiplication for factor pairs
6. Recognize the significance of order in plotting points.
7. Remember the rule for multiplication of negative numbers
8. Recognize factors of a number which will be needed in subsequent lessons on algebraic fractions
9. Understand that each point on the line in the window of the graphing calculator is a solution to the equation.
10. Explain the significance of the area under a curve.
11. Explain that the intersection of the two lines is a common solution to the problem.


Materials Needed
:
Graphing calculator with presentation device
Graph paper

Colored pencils

Procedure:

1 Multiplication as area of rectangle
Each student arranges 12 cubes as a rectangle.
Share out the various dimensions.
Students realize the sides are the factors of 12


.2.Modeling the factors of numbers 1 to 50

Assign each team of three students a selection of numbers. They use blocks to model the possible rectangles. The solutions are recorded on graph paper, cut out and pasted onto cardboard.
The factors are labeled.


3. Looking for patterns

Students stand up if they have a rectangle with a side of 2.
The teacher records the values of the rectangles identified.
Students identify the pattern and create a rule to recognize a number who has a factor of 2. Repeat for 5 and 10.
For sides of 3 and 9 teacher prompts students to add digits and look for pattern


4.Journal entry

Students create Venn diagram with two kinds of divisibility rules: identify ones digit or add digits
Teacher presents problem. There is a rectangle with sides Y and X and YX=24. What could the sides of this rectangle be if I only want whole numbers? Pair share- students brainstorm factors of 24 and list the factor pairs using rules they have created or blocks as a scaffold.


6.Discussion of Commutative property

Teacher records student’s solutions and asks if order counts.


7. Convert factor pairs into ordered pairs in T chart

Teacher models t chart with X and Y as headings defining X as a factor of 24 and Y =24/X.


8. Plot points
Students use graph paper and checks solution with teacher’s graphing calculator
Calculator shows I and III quadrants which leads to discussion of negative numbers


9. Plot y=x

This line is plotted on the same graph paper with different colored pencil.
Discuss if this line goes through any of the points they plotted for XY=24


10. Analysis of points plotted

Students color area from x-axis and y-axis to a single point. Students count colored area and realize no matter which point selected the squares total 24


11. Students repeat the analysis using the equation
YX= 16
Repeat above steps


12. Discuss the significance of (4,4)

Student realize that line X=Y now intersects one of the factor pairs coordinate


13. Discuss the shape of rectangle (4,4)

Connection is made to square number nomenclature

.
14 Students graph XY=36, XY= 48

Independent work


Teaching Strategies

1. Inquiry into problem.
2. Pair and share of factor pairs
3. Technology enhances model of problem
4. Learning log


Assessment/Evaluation

Given a different value for the area of the rectangle, the students are able to calculate factor pairs and graph them on the coordinate plane.


Adaptations/Extensions

1. Learning Disabilities- students can have the blocks and calculators to use as concrete scaffold to find the factors.
2. Gifted students can use the statistics mode of the graphing calculator to plot the factor pairs.


Thought provoking questions

“Why do we study graphs?”
“Which graphs have lines of symmetry?”

 
"Teacher Double Feature"
A competitive grant opportunity provided through a partnership between the Contra Costa County Office of Education and Pacific Bell.
       
       
 


Contra Costa County Office of Education
77 Santa Barbara Rd.
Pleasant Hill, CA 94523

May 2002