Lesson Topic: __Functions____________ Grade level:__6-9_______
Length of lesson: __50 min___
Stage 1 –
Desired Results |
||||||||||||||||||||||||||||||||||
Content Standard(s): Represent and
analyze real-world and mathematical problems using numeric, graphic and
symbolic methods for a variety of functions. |
||||||||||||||||||||||||||||||||||
Understanding (s)/goals Students will understand: ·
How to
move between the different function representations. ·
How to
use functions to solve real world problems. |
Essential Question(s): ·
Have any of you ever
been to a sports game when the crowd starts to do the wave? ·
Is there a difference
in how long it takes the wave to be completed and the number of people? Why? ·
What would you call
this relationship and what exactly is the relationship? |
|||||||||||||||||||||||||||||||||
Student objectives (outcomes): Students will be able to: ·
Demonstrate
that they can take the problem apart and move between the different
representations of functions. ·
Describe
the behavior of the graph or function in their own words. ·
Apply
their knowledge of functions to other similar problems. ·
Compare
different functions and their behaviors. |
||||||||||||||||||||||||||||||||||
Stage 2 –
Assessment Evidence |
||||||||||||||||||||||||||||||||||
Performance Task(s): ·
Given
information students will be able to graph functions on graph paper. ·
Students
will be able to create tables of information relating to the problem or function. ·
Students
will be able to find an expression that describes the given function. ·
Students
will be able to compare the graphs of several different functions. |
Other Evidence: ·
The
students will have completed the given activity. ·
They will
discuss their results together in groups or as a class. ·
They will
complete a short homework assignment that gives them more real world problems
that they need to solve using functions. |
|||||||||||||||||||||||||||||||||
Stage 3 –
Learning Plan |
||||||||||||||||||||||||||||||||||
Learning Activities: http://www.learnnc.org/learnnc/lessonp.nsf/Approved_By_Grade/9A96C834FBB3EB4A85256BF200678D88 ?opendocument http://www.pbs.org/teachersource/mathline/concepts/earthday/activity3.shtm
(I used the activity from this lesson plan for my lesson plan so that I could
go into more detail about what would take place) http://www.shodor.org/interactivate/lessons/fm3.html Materials and resources:
Introduction:
(5-10 minutes) ·
Anticipatory Set: I will ask my students whether they
have been to a sports game in which the crowd has begun to do the wave. From there we will talk about their
observations and reach the conclusion that the length of time it takes to complete
the wave and the number of people involved is a functional relationship. Once they know this I will ask, “Can
anyone give me an example of a function and how it may be seen in the real
world?” or “Can anyone give me an example of something that is not a
function?” From there I will
tell the students that we are going to build on yesterday’s knowledge and
learn more about moving between different functional representations, using
functions to solve real world problems, and describing the behavior of
different functions. ·
Rationale:
We will be learning a great deal about functions because they describe
different real world phenomena.
For example, functions help us understand population growth and decay
so we can predict future population levels. This may help us save certain species of animals. Functions can also be used to
describe financial situations in the real world. Savings accounts and the interest that is gathered on them
deal with functions. So
functions are all around us even if you may not notice them. Once the students have learned this
they will be more able to talk about the different graphing transformations
that take place with functions at a future time. Body: (40-45 minutes) ·
Presentation/Modeling: We will have already talked about functions in
general. So the students will
work on an activity that furthers their functional knowledge. The students will simulate the
population growth and decay that is present in a fish pond. I will place them in already assigned
pairs and each pair will get a cup of M&M’s and some graphing paper. The M&M’s will represent the fish
in a pond. 1. The
students will count the fish in their pond and record that number under year
0 in the population decay chart.
2. Then
they will pour the fish onto their desk. Fish that land with an “M” up represent fish that died or
were caught during the first year.
They will set these dead fish aside and count the number of live fish
and record the number below year one.
From there they will put the live fish back in the cup, shake them,
and pour them out again to record the number of fish that are still alive for
year two. They continue to do
this until they have completed eight trials.
3. Once
the students have finished their trials I will ask them, “What patterns are
you beginning to see in your tables?”
“Why do you think these patterns are taking place?” 4. From
here the students will have to graph their data on graph paper and describe what
they are seeing from the graph.
I can ask things like, “What type of behavior are you seeing in your
graph?” “Is it increasing, decreasing, or remaining constant?” Why do you think this is happening?” 5. From
their graph the students will attempt to come up with an expression that
describes their data. They may
have to tweak their original equation to come up with a closer approximation. At this point I will ask them what
equations they came up with and how they changed their first guess to closer
approximate an equation for their data. 6. This
same situation can be repeated to learn about population growth if there is
enough time. Instead, have the
students start with only two fish in their pond and when they pour them out
they add a fish for each “M” that lands facing up. They repeat this eight times. ·
Guided Practice: Much of this activity is guided practice since the
students had learned about the basic components of exponential functions the
day before. So throughout this
activity I would be walking around the room observing student work and
answering any questions that they may have. We would also do the first several steps together so that
the students would understand their experiment. The class would also discuss the patterns and expressions
that they were finding as a group.
Students can get into bigger groups and discuss their equations,
graphs, or tables. ·
Feedback and Correction: I would give the students feedback and corrections when we
first started the activity and when we were having group discussions. I would know if they were ready to
move on by the answers they would be giving me and the work that they have
shown. For example, if they know
that the data they are finding is an exponential function and they can come
up with an equation then will know that they are ready to move on. ·
Independent Practice: The students would then be given several charts,
equations, or graphs and have to move to the other function representations
to show that they know how they are related. Conclusion: (5 minutes) ·
Review:
So we have learned that functions can describe real world phenomena
and help us understand the world around us. We now know how to move between the different
representations of functions and describe their behavior. “So what are some of the different
function representations?” “What
kind of behavior took place in our experiment?” “How does this behavior compare to the behavior of other
functions?” ·
Preview:
Tomorrow we will learn more about function equations and the different
transformations that can be obtained.
This will further help us understand the behavior of functions. ·
Remember that you have 6 problems to finish for
tomorrow. |