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 students 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 teachers
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?
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