Subject / Course: Math / TC Name: Steven Huynh
Grade Level: 7/8 / Date: October 26th, 2010
Topic: Stem and Leaf plots/Histograms / Time of Class: 40 minutes + 40 minutes
AT Name: Greg Foreman / Room # / Location: 20
1. Instructional Expectations and Opportunities
a)  Expectations:
·  “organizing data into intervals; displaying data using histograms...” (pg 109)
·  “collecting and organizing categorical, discrete, and continuous data; displaying data in relevant frequency tables” (pg 97)
b)  Goal(s) for the lesson:
Students will understand how to construct a stem and leaf plot. (Grade 7)
Students will understand how to determine the median and mode from a stem and leaf plot.
Students will understand how to construct a histogram. (Grade 8)
2. Preassessment and Accommodations/Modifications
Preassessment: / Accommodation/Modification:
Academic Needs:
Behavioural/Social/Emotional Needs:
Physical Needs:
Diversity Needs: / 7/8 class are all IEP (exceptional). Their end assignment is different. These students require higher level thinking questions:
·  It takes a long time to make a stem-and-leaf plot. Why bother? Why not just calculate the average and call it a day? Because a computer sorts faster than it can divide – a computer can only really add and subtract and make guesses. But with a good algorithm (set of instructions), it can very quickly sort things and find the median. And if the data is already sorted, finding the median is almost instantaneous.
A few students in 7/8 class require “real-world” examples or else the math is not relevant. A theme that is working is, “How companies use math to try to trick you and/or take more of your money.”
Grade 7 class has two students (S. and M.) that are IEP. They may require more one-on-one time.
Many students have low reading comprehension. Some students will benefit from writing key words or concepts on the board.
C. is easily distracted. During the lecturing part of the lesson, ask him quick, simple questions to keep his attention.
N. often asks unrelated questions. Be careful when he answers and cut him off if needed.
n/a
No ESL students.
Students are aware of the importance of diversity.

3. Learning Environment

On the board will be the raw data (any order).
Students work alone but volunteer for questions.
Be prepared to put chart paper on the whiteboard with magnets (or tape).

4. The Overview (Agenda) for your lesson:

1. Intro. of Stem and Leaf plots
2. Look at real data, frequency tables, and stem-and-leafs.
3. Why bother with Stem and Leafs; assignment.
4. Intro. to histograms
5. The difference between histograms and other graphs.
6. Why bother with histograms? Assignment.

5. Resources and Materials for your class

Write on the board the following numbers in any order really:
35 4 9 23 26 49 55 0 8 17 0 36 2 6 0 10 12 27 0 32 15 14 0 11 4 7 0 8 6
Chart paper tables and graphs (frequency table, stem and leaf, histogram)
Magnets to hold up the papers (tape works).
Textbook: Nelson Mathematics 7, Nelson Mathematics 8
Students need writing utensils and math work books.

6. Content, Teaching Strategies, for Lesson

Time / Teaching or
Assessment Strategy / Detailed Description
5 min / Introduction / Write “Stem and Leaf Plots” on the board.
“When I first started talking about this unit, I mentioned mean, median, and mode (and if you don’t know what those are yet, that’s okay – we’ll talk about them soon). That’s not what today’s lesson is about. Instead, we’re going to explore a certain way of organizing data so that we can easily determine the median and mode. Today, we’re going to explore Stem-and-Leaf Plots.
Grade 8’s, I know you’ve probably already done this so just bare with me. I’ll come back to you and we’ll talk about another way to organize data.
15 / Minds On / Put on the board the chart paper that has our data (see above).
“So here I have our data. These are the total amount of goals scored by every single Toronto Maple Leafs player from the 2007-2008 season to the 2008-2009 season. Obviously, the data is a mess and we’re going to need to sort it somehow before we can use it. Now, a good way to do this is to make a frequency table. That is, I’m going to set an interval and count how frequently something falls into it. For example, let’s say my intervals are at five. I might make a table that looks like this...”
Put on the board the chart paper that has the data in a frequency table with interval 5.
“So here we can begin to actually see where the data actually falls and we can see some trends. For example, we could probably ballpark what the middle number may be. We can also see what would be rare to see someone score in a season while playing for the Leafs.”
“Now this is pretty quick and easy to make. I just set up my table by writing my intervals and went number by number and putting a tally where it belonged. So for example, I took this number, saw it fit in this interval, put a tally in it, and then crossed it off on the raw data. I kept doing that until I was done.”
“But there’s a problem with this kind of table. What might a limitation be of a frequency table?”
·  Not accurate enough, hard to pick good intervals, etc.
“Great. Luckily for us, there’s another table we can do called a Stem and Leaf Plot. I’ve already made one for this data and rather than just tell you how to make one, we’re going to come up with how to do it.”
Put up the Stem and Leaf plot. Ask students what the difference is and how you would instruct someone in how to make it. Write these things on the board.
5 / Conclusion / “So that’s a Stem and Leaf plot. But so what? Yeah, we saw that it’s more accurate than a frequency table but who cares? Does anyone actually use these things in the real world? Short answer, no. Long answer, kind of.”
“Computers are really fast at sorting and, in fact, calculating a median is usually faster than calculating an average. And that just comes down to the fact that a computer can only really add and subtract – division and multiplication are done through a series of approximations and estimates that are actually really complicated and I won’t get into that today.
15 / Application/
Introduction for Grade 8 / “Grade 7’s, your assignment is page 100-101, #6, 10-13”
“Grade 8’s, we’re going to organize our data in a different way but using the same idea of intervals to show them. This particular graph is called a histogram.
So rather than throw definitions at you, I’ll just show you a histogram for this data. Now, when I show this to you, you’ll see that it looks a lot like another kind of graph but there are a few key differences.”
Put the histogram on the board. Write on the board, “Histogram vs. [Bar graph]”
Draw a Venn diagram with Histogram in one and Bar Graph in the other. Take ideas as to what features are similar/different. If possible, feed them the term “bin” for the name for intervals.
5 / Consolidation/
Application / “Histograms are useful when it’s most important to show data in intervals. In fact, a lot of things in our lives are grouped in intervals. For example, your grades all function in intervals. It would be a lot more helpful to show a graph to see how frequently students got a B+ or an A rather than how many got a 78 or an 85.”
Are there any questions, comments, or concerns about histograms?
“Alright, your assignment is page 106-107, #5, 6, 8, 9.”

7. Reflections: To be completed after you have taught the lesson. (In this section, you will assess the effectiveness/ineffectiveness of your lesson and of your teaching.

a) Effectiveness of your lesson.

Include 2 or 3 lesson elements that were effective/ineffective. What went well, what could have gone better? How was the pacing of your lesson? Were your teaching strategies effective? Were all students engaged? Did the students accomplish your goal? Did your assessment strategies work?

What do you need to learn more about? What do you need to work on when planning your next lesson? Should you discuss something with your AT or your FA?

What was effective/ineffective about your lesson / How do you know? / What steps will you take to improve?

b) Effectiveness as a Teacher:

Include 2 or 3 comments about your effectiveness as a teacher or areas that could be improved. You could comment on your ability to manage the class, use higher order questions, your questioning technique and your ability to have the participation of all students. How effective was your oral and/or written communication? Were you able to adjust your lesson plan as required?

What was effective/ineffective about you as a teacher? / How do you know? / What steps will you take to improve?