Lesson Overview:
For my lesson, the students were
able to manipulate linear graphs of equations in slope-intercept form to identify
the relationship between the independent (x) and dependent (y) variables. The content
we focused on was that a function can have several solutions for y, but each
one has to be unique to each x and y depends on what we substitute for x. In addition, as the x values increase in an
equation with a positive slope the y value also increases. Similarly, as the x values
in an equation with a negative slope increase, the y values decrease. I added
negative x values and slope in my final lesson plan.
Lesson Implementation:
First, we had an open discussion on
the definition of a function and what the variables mean. Then, I did an
example with the equation y = 4x + 5. We looked at the slope and y-intercept of
the line and created a table to compare the x values. We also looked at the
direct relationship between our x values and our slope. I did a more advanced
example with y = - 1/2x
– 8. Students actively participated and came to the board to answer questions
on the Smartboard while recording observations in their notes.
Lesson Reflection:
The software program was the main
focus in this lesson. It allowed students to manipulate a graph whereas in past
lessons they used stand still images. This technology made the lesson more
interactive and the students were more engaged in their discoveries. Learning
was able to take places socially as a group by discussing observations, analyzing
the data and making connections.
Although GeoGebra is a great program
for plotting points and graphing equations, not everyone could participate at
once since the only set of laptops in the school was taken for the week due to
testing.
My intentions for this lesson were
not only to manipulate a graph and an equation, but apply this information to the
real world. In my examples, I used situations like going bowling or changing
temperatures over a given time. The students could then apply the equations of
these situations to the graph. Also, I wanted to introduce my students to an
advanced software program that would be comparable to what they would use if
they went into careers like engineering. I used this program in my undergraduate
math class and I found that many of the tools are would be useful in teaching
the curriculum in my classroom.
Their reaction and engagement was
more than I expected. They love to learn new tools to use in the classroom;
therefore, this was perfect in maintaining their attention. They were intrigued
as I plugged in points on the graph and watched them appear before their eyes.
Some questions they had concerning
the graphs were: “What if the number is negative?” and “What if y is 0?” If the
questions related to the content, I told them, “Let’s try it out!” I want to
encourage curiosity. I love when they think outside the box, so I get excited
and we answer their questions together.
The class received an average of 95%
on the assessment at the end of the lesson. Based on classroom observations,
student responses, and the assessments, the students seemed to comprehend the
content of the lesson. I will test them again in the unit test to ensure
retention.
Narrative:
Student 1: “What if y is zero?”
Teacher: “Everyone take a second to
think about that silently. We continue to plug in different values for x, but
what if we plug in a number for y?”….”Ok, let’s try it on the graph. Student 1,
on which axis would we look for a y value?”
Student 1: “On the y-axis.”
Teacher: “Great. Let’s go to zero at
the origin. Now let’s move along the graph to find where our line intersects
the line y = 0. Student 2, what x value am I at?”
Student 2: “Negative 16.”
Teacher: “That’s correct, we would
describe that point as (-16,0). That’s the great thing about graphs instead of
doing the work algebraically we can simply look at the graph and work backwards
to find our answer. We can continue to do this to find unlimited solutions to
our equations.”
Narrative Reflection:
The student was able to use the
graph to work backwards plugging in a value for y and finding x. He identified
that we need to look at the y axis first to do so and our answer is right there
on our graph. This process can be repeated to find unlimited number of
solutions.
