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Grade 6, 7, 8:
Who Are My
Friends?
(@ 5 days)
Overview
View the
Video Introduction
Who
are you? Who are your friends? What do you all have in common, and
how are you different from each other? This unit will help you ask
important questions and
find out the similarities and differences between you and your friends. You
will use math skills to develop a profile of your friends. You will record and analyze the information and data you
gather.
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Enduring Understandings
- important ideas that students should carry with them years beyond the
instruction received this year.
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Data can be used and represented in many forms.
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Data can be used to draw conclusions.
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Data can be used to draw conclusions and make predictions.
Essential Questions
- most important “big picture” questions
students should be able to answer after completing learning activities.
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How would you organize and construct displays of data?
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What conclusions would you make from a variety of data organizers?
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How would you calculate measures of central tendency from a given data
set?
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How would you determine which measure of central tendency best
represents a set of data?
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How would you analyze data and predict future outcomes?
Standards:
Standard 3: Students use data collection and analysis, statistics, and
probability in problem-solving situations and communicate the reasoning used
in solving these problems.
Other Standards and
E-Skills:
Collecting Data
Quantitative and Qualitative
Finding the mean, median, mode, and range
Creating, Interpreting, and Analyzing Frequency Tables, Line Plots,
Stem-and-leaf, Pictographs, Bar Graphs, Histograms, Tables, Line Graphs, and
Coordinate Grid.
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Lessons
Lesson 1: Survey and Graphing Project
Duration: @ 1 class period (45 minutes)
This activity will be
completed when you have finished exploring measures of central tendencies
and data displays. Start thinking about questions that you would like to
know about your friends.
Assessment
Survey and Graphing Project 6th and 7th grade
Survey and Graphing Project 8th grade
Peer Input for the Survey and Graphing Project 6th and 7th
grade
Peer Input for the Survey and Graphing Project 8th grade
Grading Guide for the Survey and Graphing Project 6th, 7th,
and 8th grade
Lesson 2: Collecting Data About Your Friends
Essential Skill: Collecting and analyzing data
Duration: @ 1 class period (45 minutes)
Essential Question: Why it is important to collect data
Activity
When you come into
class, get a pack of post it notes that your teacher has provided, then answer
each of the following questions. Use one answer per post it note.
What month were you born in?
On what day of the month were you born on?
What is your favorite number?
How many pairs of shoes do you have?
How many pets do you have?
How many schools have you gone to?
How many brothers and sister do you have?
What is your favorite sport?
What is your favorite CD?
What is your favorite color?
What do you like to read?
What is your favorite food?
After you have answered the above questions, please place them on the
wall that your teacher has designated for each question.
Teacher: Have a place on the walls to organize the post it
notes for each question. As a class, organize the data for “What month
were you born in?” and “On what day of the month were you born on?” on a
poster paper to show how to group common answers or put the numbers in
order from least to greatest.
Next, break your class into 10 groups. Give each group a piece of
poster paper and allow them to organize one question on to the poster
paper. Each group should report out how they organized the information
and one piece of information that they found from organizing the data.
For example: 3 people have a birthday in December. Keep the posters with the post it notes for the next lesson.
Materials
12 post it notes/student
White board or Chalk board to write questions on
Places to organize post it notes
12 sheets of poster paper
Technology:
http://mathbits.com/MathBits/TISection/Statistics1/BasicCommands.htm
Lesson 3 Title: Which Q
am I?
Essential Skill: Quantitative and Qualitative
Duration: @ 1 class period (45 minutes)
Essential Question:
What is the difference between Quantitative and
Qualitative?
Activities
Use a post it note
to write down a word that begins with Q. (You will share your words with the
class.)
Today we are going to talk about two types of data that can be collected,
Qualitative and Quantitative.
You will have 5 minutes to draw a picture of what you think Qualitative
and Quantitative look like to you. Try to find different words in
Qualitative and Quantitative to get you started. Would anybody like to volunteer to show their picture? Go
to
Regents Prep to see the differences between quantitative and
Qualitative.
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The overall meaning of qualitative is a survey question that gives the
researcher a description or word to answer the question. Quality is a
word that you can find in qualitative. Quality answers for researchers
can help you to remember.
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Use the
Online Stat Book for another definition.
The overall meaning of quantitative is a survey question that gives the
researcher a number to answer the question. Quantity is in the word
Quantitative and quantity is a number. Reference this
Online Stat Book link for another definition.
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Please break into your groups from yesterday and find your question
poster with the data that you organized. As a group, decide whether
your question was qualitative or quantitative and write your decision on
top of your poster.
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Now Quantitative Posters go to one side of the room and Qualitative
Posters go to the other side of the room. Can anybody tell us what is
similar about the posters in your group? Can anybody tell us what is
different about the posters in your group? Do we think we should move
any of the posters to the other group? Why or why not?
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Go
to these
Recommended Websites for more practice on Quantitative and
Qualitative.
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Please sit down in your seat and get an index card. Write your name on
the index card. Then write the word Quantitative on one side and
Qualitative on the other. For you ticket out the door, please write a
survey question for quantitative under the word quantitative and a
survey question for qualitative under the word qualitative. Please hand
them to the teacher when you are dismissed.
Materials:
Post it notes
Lesson 4 Title: Evening out for the class picnic
Essential Skill: Finding the mean
Duration: @ 1 class period (45 minutes)
Essential Question:
How does finding the mean help you in the real world?
Activities
Pick up your “ticket out the door” from yesterday and look over the
feedback. We are now going to take a benchmark assessment on
quantitative and qualitative. You will have 7 minutes to complete the
benchmark. Our class is going to bring in money to have a class picnic. We are
going to count off around the classroom to decide how much each person
should bring. Everybody count off from 1 to 6. All the number ones line
up by the Station #1 sign, the number twos by the Station #2 sign and so
on.
Somebody from station one please read your sign to the class.
Now Station two etc…
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It is fair for Station #2 to bring in $12.00 while
Station #6 only brings in $1.00?
How can we make it fair for the entire class?
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Each person in your group should stack enough
unifix cubes to show how much you should bring for the class picnic.
For example, If you are in group #2 you should have 12 unifix cubes
stacked together.
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Walk around the room and share some of your cubes
with other students or take some cubes from other students so that we
all pay an equal amount for our picnic.
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As soon as you run into a situation when it does
not make sense to share your cubes or take cubes from another person,
please go back to your seats.
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What did we find out? Does everybody have the same amount of cubes? If
we take out the remainder cubes would everybody bring the same amount of
money to our picnic?
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This is called evening out or the mean of a set of data.
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The mean is the average and it is found by adding all the values in
a set and dividing by the number of values.
Example #1:Try to even out the following numbers to find the mean.
6, 15, 10, 5, 6, 8, 6
Try the following problems:
- You are a basketball player and you score the
following points in 5 games: 12, 22, 10, 11, 5 what is your mean
score?
- You are buying gifts for all your teachers and
you want to spend about
$8 per teacher. If you spent $3 on Mr. Jones, $12 on Mrs. Brisben,
and $10 on Mr. Smith did you make your goal?
- If your parents want you to give them a price
for the amount of lunch money that you need a day and you spent $3
on Monday, $5 on Tuesday, $7 on Wednesday, $4 on Thursday, and $6 on
Friday. What would you tell them you needed per day for lunch?
For your ticket out the door explain how evening out and the mean
relate to each other.
Materials:
Benchmark assessment: Quantitative and Qualitative Benchmark Version 1-3, One set of “Evening Out” signs (Stations 1-6), Unifix cubes in the following colors: Blue, Red, Green, Yellow, Purple
Station #1 Chips $8
Station #2 Pizza $12
Station #3 Hot Dog $3
Station #4 Milk Shake $5
Station #5 Pie $7
Station #6 Soda $1
Technology:
Learn to use the
Graphing Calculator.
Lesson 5: Driving Over the Median
Essential Skill: Finding the Median and Range
Duration: @ 1 class period (45 minutes)
Essential Question: How would you explain median and range to a first grader?
Activities
Please pick up your “ticket out the door” from yesterday and look
over the feedback. Does anybody have any questions?
You will have 10 minutes to complete the mean benchmark. When you have completed the benchmark answer the following question on a
post it note and put your answer on the board.
How many letters are in your first and last name?
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We are now going to put the numbers in order from least to greatest. What
do you notice about the number of letters in your names?
What is the highest number? What is the lowest number? What is the span of
letters that we have in our class? This is called the range of numbers. A
range can be written two different ways. One way is 10 - 4 and the second
way is 6 because 10-4 is equal to 6. You should write the range in both
formats.
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Range: The difference between the greatest number
and the least number in a set of numbers.
Now we are going to draw a 3 lane highway on the board. One lane will go
north bound and the other lane will go south bound. I want to know who is
sitting in the middle of the highway.
What do we call the island in the middle of the road?
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Can anybody guess who will be sitting on the median of our highway?
How can we find out? We are going to take our post it notes and put one the
lowest number on one side and the largest number on the other side. Can we
keep doing this process?
If we have an odd number of students in our classroom the median will be
standing by itself. If we have an even number of students then we will need
to find the mean of the two numbers.
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Median: The median is the number that falls exactly in the middle of a set
of data when the data are arranged in order from least to greatest, or the
mean of two middle numbers when the set has two middle numbers.
Find the median of the following data and explain in writing why that number
is your median.
Do not forget to put your numbers in order.
Example #1 1, 13, 2, 7, 4
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What number is your median? What is your range?
Example #2 5, 2, 8, 12, 11, 7
What number is your median? What is your range? What was different about
Example 2 from Example 1?
Practice problems: Find the median and the range for the following problems.
1. 8,42,13,7,50,91
2. 0,1,1,1,0,1,1,0,0,0
3. 8,6,9,5
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After you have completed finding the median and
range for 1-3, come up with a real world situation where you would get
the numbers that were collected for each number. For example, if I had
collected numbers 3, 2, 1, 1, 0, 4 My question could be “How many times
do you eat out during the week?”
When you are done the class will discuss problems 1-3.
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Your ticket out the door: On one side of the index card explain how to
find the median of a set of data. On the other side, explain how to
find the range and how to write it in two different formats.
Materials:
Post
it notes (small), white board or chalk board to write down the question,
wall space to organize the post it notes.
Technology:
Lear to use the
Graphing Calculator
Lesson 6 Title: Spaghetti ala Mode
Essential Skill: Mode
Duration: @ 1 class period
Essential Questions: Why would mode be helpful in your life?
Activities
Pick up your “ticket out the door” from yesterday and look
over the feedback. Does anybody have any questions?
We will be completing 2 benchmarks today, one on Median and the other
benchmark on Range.
You will have 15-20 minutes to complete both benchmarks. When you have completed the benchmarks please take 2 pieces of spaghetti and
break each piece into 3 varied lengths.
Now we are going to break into groups of 4 people.
After you are in your groups, put your spaghetti in order from the shortest
to the longest. Are there any pieces that are the same size? Please slide
the spaghetti that has the same length above the other spaghetti.
Today we are going to talk about the mode of a set of data. The mode is the
number that appears most frequently in a set of numbers. There may be one,
more than one, or no mode.
Who can tell me the mode of their spaghetti? How many pieces have the same
length? Does anybody have a group with more than one mode? Does anybody
have a group with no mode?
Now can your group find the median of your set of spaghetti? How did you
find it? Do you need to keep your spaghetti in the same order as the mode?
Now we are going to practice finding the mode from a set of data. On your
white boards, answer the following questions.
Example #1 Find the mode 2, 4, 7, 1, 2, 5, 4, 8, 4
Example #2 Find the mode 4, 7, 1, 9, 3
Example #3 Find the mode 3, 7, 0, 1, 0, 7, 4, 9, 1
Please put your boards up to show me what your answers are. Can somebody
tell the class how they got the mode for Example #1? Example #2? Example #3?
On your white boards, please tell me the median of each set of numbers.
Please put your boards up to show me what your answers are. Can somebody
tell the class how they got the median for Example #1? Example #2? Example
#3?
On your white boards, please tell me the mean of each set of numbers.
Please put your boards up to show me what your answers are. Can somebody
tell the class how they got the mean for Example #1? Example #2? Example #3
Practice finding the mode and median for each of the following problems.
- 1, 7, 2, 8, 4, 5, 9, 2, 4,
- 4, 8, 23, 6, 3, 4, 23, 9
- If Ms. Sue sells her cookies for the following
prices, what is her mode and median cost?
$4, $6, $8, $2, $2, $1,
$4, $1, $1, $8
- What is the mode and median price for the
following candy, $1.25, $0.50, $1.00, $1.00, $0.50, $0.25, $1.00
Can someone explain #1 to the class? #2? #3? #4?
Your ticket out the door - On one side of the index card, tell me what
mode and median have in common. On the other side of the index card,
tell me what makes mode and median different.
Materials:
2 pieces of spaghetti for each student,
Options: String or Pipe cleaners can also be used,
student white boards,
rags for erasers
Technology:
Learn to use the
Graphing Calculator.
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