fun & easy activities for engaging students
TRANSCRIPT
1
Fun & Easy
Activities
for Engaging
Students
Presented by
Elizabeth Howell
North Central Texas College
NTCCC Developmental Education Forum
April 2017
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Want to break up your lecture? Here are a few ideas…
Here are a few tried and true ideas to liven up your classroom. Try one whenever you need to add
some pep to your class. All ideas work for any subject matter.
*ABC Game: Make three sets of problems, A, B, and C. The “A” problems should be fairly easy,
the “B” exercises medium to hard, and the “C” problems TOUGH! Students work independently to
see how many they can answer (hopefully correctly) in a designated time period. 3 minutes for the
10 “A” problems, then another 3 minutes for the 7 “B” problems, and a final 3 minutes for the 2-3
“C” problems. This is great for an opening day activity (new semester, new chapter, etc.). At the
end, students check their answers and the most correct receives a prize!
*Group Quiz: There are lots of variations to this idea. You would think that the students would just
copy/mooch off of the smart kid, but amazingly it doesn’t work that way. Most versions start with
the kids working in small groups (2-4). The quiz problems could be on a preprinted page or on the
board. Version 1: Students turn in one paper with all names on it. Version 2: Students each have to
complete their own paper, but all of the papers are stapled together and you pick one student’s paper
at random to grade. Version 3: Like Version 2 but you pick 1-2 problems from each page at random
to grade. Holiday version: Everyone in the class works together, and every student will receive the
LOWEST grade of any one student. The students are sure to help out their neighbor on this one!
*Pick-A-Problem: Write problem numbers on the board. (I used numbers which corresponded to
problems in a textbook that the students didn’t have.) Students are in groups and are required to
work all problems. To play, each group is allowed to pick a number. The teacher writes the
corresponding problem on the board and everyone works it. The group that picked the number gets
“first shot” at the answer, but if they miss it, the teacher picks another group at random for their
answer. Correct answers earn a point, and the team with the most points wins!
*Scavenger Hunt: Write a problem towards the bottom of a half-sheet piece of colored paper, and
the answer at the top of a different half-sheet of paper. Write another problem below that answer,
and continue until there are 15-20 problems (write the answer to the last question on the top of the
first page). To play, hang the problems RANDOMLY around the room, in your hallway, or around
the school if you can, and put the students in groups. Students need paper to work on, and should
pick a problem to start at. As they complete the problems, they search for their answer and then work
the new problem on that page. Students follow the trail of questions until they have completed all
questions.
*Around the World: Take any problem set, and write/type them on colored paper to post around the
room. Have students start at any problem, and then rotate sequentially to the next problem. You can
also pre-determine the small groups, have the students number off for their starting spot, or do a
random draw to determine their starting spot.
*Matching Cards: Again, take any problem set, and make a set of problems and a set of answers.
Students work in pairs to match the problems with answers, and great discussion ensues!
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*Poker Chips: Let a student draw a chip to determine what kind of homework grade will be taken.
Of course, you can stack the chips toward the outcome you prefer. For example, red could mean no
grade, blue could mean a completion grade only, and white could signify an accuracy grade. If you
use 10 chips total, you can even incorporate a quick review of probability and percentages.
*Magic Squares: Students work alone, in pairs, or in groups to work these puzzles. Cut out each of
the individual squares and rearrange them so that equivalent sides are touching. When finished,
students should have one big square. These puzzles are easy to make, and can be used on any topic
you want. Just be sure to make a copy of the original before you start cutting!
*Relay Directions: Place students in rows of 5-6. Have all students clear their desks except the
students in the back of each row – these students will need a pencil and a blank sheet of paper.
Display one problem at a time on a powerpoint, smartboard, etc. The last student on each row works
the first problem. As soon as they are finished, they pass the paper and pencil to the person in front
of them to work the second problem, and so on until the paper gets to the front of the row. You need
to display the next problem as soon as the first person is done with the previous problem. The
students can only work the problem assigned to them!
When the paper gets to the front of the row, the person on the front quickly checks all problems (and
may need to work the final problem if it’s a short row), and gives the teacher the paper to check all
of the answers. If all answers are correct, that row wins. If any problems are wrong, the teacher gives
the paper back to the person on the front of the row to correct. Do not tell them which one is wrong,
but tell the entire row that they may come to help the person in the front to check/correct the
answers. The first row to have all of the answers correct wins.
For the next relay, have all students move up one seat so the front person will be different each time.
*Sticky Note Matchup: This is a fun way to start class and get the students thinking about math from
the second they arrive. On small sticky notes, write a number or expression. Then on another note,
write its “partner”. For example, in a trig class, I would write an angle measure in degrees on one
note, and a coterminal angle or angle measured in radians on another. Write enough pairs so that
everyone in class will receive a sticky note. Stand at the door as students enter and hand them a
sticky note (mix up the order first!). Once all are distributed, tell students to find their partner! You
can ask students to take their homework paper with them to begin to compare answers once they find
their match, or maybe have a short quiz they can work together with their partner. This works well
for any “matching” topic.
*Stacked Transparencies: Give groups of students a transparency and a marker, and ask them to
create a graph together as a group. When all groups are done, stack the transparencies to show the
entire class whether they agreed (or not) on the graph! Ensuing discussions could relate to good
graphing practices, teamwork, accuracy, and neatness.
*Number Clothesline: Give students a card with a number, and ask them to clip their card on a
prepared clothesline, working with their classmates to determine accurate placement in relation to
other cards being clipped.
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Magic Squares – Factoring x2 + bx + c
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Magic Squares – Factoring ax2 + bx + c
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SLOPE RELAY
1. What is the slope in the equation 3x – 7y = 8 ?
2. What is the slope in the equation 2x + 2y + 2 = 0 ?
3. Find the slope of the line containing (2, 5) and (-3, 1).
4. What is the slope of the line x = 3 ?
5. What is the slope of the line parallel to 4x + 8y = 12?
6. Find the slope of the line y = -4.
SLOPE-INTERCEPT RELAY – Write each equation in y = mx + b form.
1. 2x + y = 7
2. 6x + 3y = 9
3. -4x – y = 3
4. 3x + 7y = 11
5. 4x – 5y = -9
6. -4y – 6 = 2x
GRAPHING RELAY – Sketch a graph of each line.
1. y = 2x+ 3
2. 4x + y = -7
3. 3x + 2y = 6
4. 2x – y = 9
5. 5x – 7y = 14
6. x = -3
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Around the World
Write sets of problems on colored paper and post around the room, the hallway, etc. Students (in
groups of 3-4) rotate around the room and work together on each posted problem. This is a great
activity for review, or simply another way to provide additional practice. Music may be used to
indicate when it is time to move to the next problem.
Domain/Range/Functions
1) Graph 1y x for 2 3x . 2) What is the domain for 2
3( )
6f x
x x
?
3) If 2( ) 1f x x and ( ) 1g x x , find f g x . 4) Find the domain and range of ( ) 3f x x
.
5) What is the domain and range of ( ) 4g x x . 6) What is the range of 2 5y x ?
7) Name the domain and range of the following graph:
8) Name the domain and range of the following graph:
9) If 2( ) 2f x x x and ( ) 5 1g x x , find f g x . 10) What is the domain of 3y x .
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Around the World - Inequality Practice
Solve each problem below, and then choose the correct interval notation.
Problem Work Interval
Notation??
1. 10
1)3(
2
1
5
2
3
1 xxx
2. 3362 x
3. x2 + 4x > 32
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Problem Work Interval
Notation??
4. 04
12
x
x
5. 12 x - 5 = 18
6. 1073 r
**There are more solutions posted than there are correct answers, so look carefully
at the details!
**When you are done, return to the classroom!
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The Bee Problem
Two trains, each travelling uniformly, start towards each other at
the same time along a straight track. One train is travelling at 60
mph and the other at 90 mph. At the start, with the trains 150 miles apart, a
bee travels from one train to the other at a rate of 200 mph. When the bee
reaches the second train, it immediately turns and returns to the first train,
and so on. This continues until the trains meet (and the bee is crushed by
the impact).
How many miles in total does the bee travel?
Solution: Don’t get distracted by trying to track the path of the bee!
Calculate the time it took for the trains to meet:
60t + 90t = 150 Let t = the number of
150 t = 150 hours the trains travel before
t = 1 meeting
In one hour, the bee travelled a total of 200 miles, since its speed was 200
mph.
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The Chicken and the Egg
A dumb chicken named Cluck laid her eggs at the top of a hill. One of her
eggs, Easter, started rolling down the hill. To save her egg, Cluck scrambled down
the hill after it.
Let x = number of seconds Easter Egg has been going downhill
Let f(x) = Easter’s distance down the hill (in feet)
Let g(x) = Cluck’s distance down the hill (in feet)
a.) Easter’s equation is f(x) = 2/3 x. Find the distance Easter has
traveled after 30 seconds and after 1 ½ minutes.
b.) Cluck’s equation is g(x) = 2x-200. Find the distance Easter has traveled after 30
seconds and after 1 ½ minutes.
c.) Has Cluck caught Easter after 30 seconds? What about after 1 ½ minutes? How
can you tell?
d.) Find out when and where Cluck finally catches up with Easter.
e.) The path down the hill is 100 feet long. Who gets to the bottom of the hill first,
Cluck or Easter? (In other words, which came first – the chicken or the egg??
Hahahaha!!! )
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What’s My Number?
This is an activity to use when reviewing classification of numbers.
Write each number of a half sheet of paper or index card and give one to each student:
0.005 2001 4
3
12
3 17.4
12 4
0 1.7 5 2
9
4 7 1 1.6 8
2.4901 38 12 54 5
2
4 5
6 5 2 3 27
1
9 11 7.77 10 15
Here are some sample questions you can ask the students. Tell them they are to hold their number in
the air if their number is:
1) a rational number
2) an even integer
3) a digit
4) irrational but not a radical
5) a natural number that is not a digit
6) an odd whole number
7) a negative radical
8) a real number
9) an integer that is not a whole number
10) a rational number that is not an integer
11) a real number that is neither positive nor negative
12) a nonnegative rational number
13) a real number that is not rational
14) an irrational number that is not a radical
15) a complex number that is not real
16) an odd digit
17) an irrational number that is not real (no one!)
18) a complex number (save this for last since it is everyone!)
I usually give my best students an imaginary number since they are not used nearly as often. I give
my weaker students a whole number or integer so they can get more practice.
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Coding/Encryption Name________________________
Objective: To use functions and inverse functions to demonstrate how written information (text) can
be encrypted and decrypted.
Here is a CODING table for the alphabet. To code a message you would simply replace the letters
of the message with the numbers from the table. Computers use a system like this to capture text as
numeric data.
Encryption changes the coding of the letters according to a particular rule; hopefully
the rule is known only to the person intended to receive the message!
First ENCODE the letters of your first name by replacing the letters with numbers
from the table:
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Choose a simple algebraic function to ENCRYPT your name. It is easiest
to choose a linear function (in the form bmxy ). Write it here:
_________________________
ENCRYPT the letters of your name according to the rule of the function:
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
To DECRYPT your name, you will need to use the INVERSE of your
ENCRYPTING FUNCTION. Find the INVERSE FUNCTION and write it here:
_________________________
See if you can successfully decrypt your name using the inverse function.
In real communications systems many messages are encrypted for security and
privacy. This is not exclusively the domain of spies and the military; private
messages of all kinds need to be secure, especially over a public medium like the
internet or the cellular phone system. Financial information and personal data is
particularly valuable and needs to be protected. Some modern data communication
systems use an encryption system that is fundamentally the same as the one you
are using although the encryption functions are much more complex.
Think of a message you would like to send to a friend; I recommend no more than six words. Then
write a simple function you could use to encrypt it. Write them both in the space below.
On the next sheet write the encrypted message along with the function. Trade sheets with a friend to
decode each other’s messages.
A 1
B 2
C 3
D 4
E 5
F 6
G 7
H 8
I 9
J 10
K 11
L 12
M 13
N 14
O 15
P 16
Q 17
R 18
S 19
T 20
U 21
V 22
W 23
X 24
Y 25
Z 26
Space 27
! 28
? 29
@ 30
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Message Sender: ____________________________
Encrypted Message:
Message Receiver: ___________________________
Decrypted Message:
A 1
B 2
C 3
D 4
E 5
F 6
G 7
H 8
I 9
J 10
K 11
L 12
M 13
N 14
O 15
P 16
Q 17
R 18
S 19
T 20
U 21
V 22
W 23
X 24
Y 25
Z 26
Space 27
! 28
? 29
@ 30
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ACTIVITY #1
Here is a secret message from me. This time see if you can “crack the code” without my giving you
the encoding function.
Helpful tips: The encoding function is a linear function. Try looking at the differences between
coded numbers to find the encoding function.
51 103 75 47 91 119 135 127 47 91
23 27 127 23 127 95 75 55 31 63
39 91 95 131
A 1
B 2
C 3
D 4
E 5
F 6
G 7
H 8
I 9
J 10
K 11
L 12
M 13
N 14
O 15
P 16
Q 17
R 18
S 19
T 20
U 21
V 22
W 23
X 24
Y 25
Z 26
Space 27
! 28
? 29
@ 30
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ACTIVITY # 2
Here is a secret message from me. This time see if you can “crack the code” without my giving you
the encoding function.
Helpful tips: The encoding function is a linear function. Try looking at the differences between
coded numbers to find the encoding function.
142 92 152 102 122 62 42
107 92 152 117 22 32 92
152 27 42 77 77 157
A 1
B 2
C 3
D 4
E 5
F 6
G 7
H 8
I 9
J 10
K 11
L 12
M 13
N 14
O 15
P 16
Q 17
R 18
S 19
T 20
U 21
V 22
W 23
X 24
Y 25
Z 26
Space 27
! 28
? 29
@ 30
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Answers to Coding/Encryption Activities
Activity #1:
The equation is y = 4x + 19. The message is: HUNGRY? GRAB A SNICKERS!
Activity #2:
The equation is y = 5x + 17. The message is: YO QUIERO TACO BELL!
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E X ☺ P O
Choose 24 of the following 30 answers and fill in your EXPO card at random. Mark out each
answer as you go so you know which answers have been used.
28x 1356x 34x y 416x 4 4x y
6 10x y 10
8
x
y 8 35x y 6x 43x
2x y 8 103x y 44x 1620x 7 6x y
2 3x y 4 512x 7x 222x
42x 56x 5 1614x y 76x 816x
62x 62x 327x 4y 15x
Expo1
FREE
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EXPO 1 Problems:
5
5
4x
x 7 8x x
422x 2 42 x x
3 7
6
28
7
x y
y
57
4
x y
y x
8 20x x 4 45x x 12 2
5 2
x y
x y
3y y
47
32
2
2
x
x
224x
9
2 3
xy
x y
87x
810
5
x y
y x
10 15
2 5
24
8
x y
x y
23 5x y 2 52 3x x 7 94 5x x
56
2
x
x
3
3x 3
2x
25
4
x
y
4
xy 128 7x x
9
3
8
4
x
x
5 53 9x x
27 13
19 10
20
4
x y
x y 4 4x x 4 11 52 7x y xy
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E X ☺ P O
Choose 24 of the following 30 answers and fill in your EXPO card at random. Mark out each
answer as you go so you know which answers have been used.
8 8 1
8
1
8 2 2
17
72 14 14 27 4 4
128 27
8
8
3
5
7
5
2
1
16
1
2
1
2 318x
2
1
8x
3
2
x
14
11
x
y
6
7
x
y 14 10x y 1ax 2 1ax 2 1ax 2ax
FREE
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EXPO 2 Problems:
1
38
125
3
532
3 22 3 5 26 3x x
38 64x 3 1
a
a
x
x
32 3
24 1
x y
x y
3
2
3
2 3
3
32 2
4
4 2
2 5
x y
x y
2 43 32 8x x
1 0 2t t ax x x x
3
416 2
4
1
2 32 2
3
5 2 1 4x y x y
7 53
3 32
2
3
9 x x
x
1
249
25
13 3
2 22 4x x
2
2
3
64 2
8
3
430 8x 32 4
2
3
a
a
x x
x
2 2a ax x
1
34 8x
3
3 4
5 2
16x
x x
3
211 125x
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L O ☺ G O
Choose 24 of the following 28 answers and fill in your LOGO card at random. Mark out each
answer as you go so you know which answers have been used.
4 27 2
13
1
3 2 8
2
3 3
17
3
1
32 4
3
5
0 1 3
2
2
7 3
11
5
1 5
6
1
2 5 15 2
1
36
1
8
1
4 64
FREE
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LOGO Problems:
3log 81 5log 125 3
15log 15 2
1log
32
1
log100
1
2
log 16 3log 10 2 2log 4 log 16
9 3log log 27 3 2log log 8 5 5log 1 log 125
1
3125
27
1
29
4
3
29 3
532
5
416
8log 2x 6log 2x 36
log 225
x 2 74 16x x
2 125
5
x 2
3 19
3
x
x
4log 16 2 2x 3log 27 3 6x
7
1log 2
49x 4log 1 2x 4 4log 1 log 5 2x
2 2log 3 log 3 3x
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Graphs and Equations MATCHING
25
26
27
28
29
Factoring MATCHING
k2 + 6k – 16 (k + 8) (k – 2)
2p2 – 7p – 4 (2p + 1) (p – 4)
y2 + 6y + 9 (y + 3) 2
x2 – 10x + 21 (x – 3) (x – 7)
10x2 – 13x – 3 (5x + 1) (2x – 3)
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y2 – 16 (y + 4) (y – 4)
64p2 – 49 (8p + 7) (8p – 7)
6b – 9 + 2ab – 3a (a + 3) (2b – 3)
5x3 – 35x –14y + 2x2y (x2 – 7) (5x + 2y)
2x2 – 7 prime
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A Leaky Bottle Experiment
Each group needs a timekeeper, water-level reader/bottle holder, and recorder
Fill the bottle so the water level is below the curve at the top
When the timekeeper says “go,” uncover the hole and let the water run freely
The timekeeper calls out time every 10 seconds
The water-level reader reads aloud the water level to the nearest millimeter
The recorder records the data
Stop measuring when the water level reaches about a centimeter from the hole
1.) Enter the data into your calculator and look at the scatterplot.
Describe in words what your graph looks like and draw a quick
sketch. Write a conjecture about what types of functions might fit
the data.
2.) Find regression equations for 2 different types of functions that
fit the data reasonably well.
3.) Decide which of your models is the best fit, and explain why.
4.) Use your best model to predict when the container would be
empty.
TURN IN ONE REPORT WITH ALL THE MEMBERS OF
YOUR GROUP WRITTEN ON
THE TOP.
Be sure you have explained everything thoroughly – this will be a
group grade, so be sure all members are satisfied with the finished
product!
Time
(seconds)
Height of water
(cm)
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
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Concept Attainment – Even and Odd Functions
The purpose of this activity is for students to discover the characteristics of odd and even functions.
Copy and laminate the two sheets of pictures on the following pages. Then cut the pictures and give
a set of pictures to each group of 2-3 students. (You will need a set of pictures as well for later in the
activity.)
First, ask the students to “group” the pictures with no further directions.
After a time, tell the students that there are three groups. Allow them to discuss and regroup, if
necessary.
Then, tell the students that there will be 5 cards in one group, 4 cards in another group, and 3 cards
in the third group.
Now that the students have attempted to classify the pictures, discuss the cards one at a time and
group them correctly (odd, even, or neither) with the students.
After the cards have been properly sorted, discuss types of symmetry with the class and introduce
the concept of even and odd functions.
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x x
x x
x x
y y
y y
y y
34
x x
x x
x x
y y
y y
y y
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MATH0305
Howell
Work together to crack the code and find the message below from Mrs. Howell.
1. Factor each expression using what we have covered so far.
2. Match the answer to a letter.
3. Write the code letter in each blank having that exercise number.
Good luck!
1. 2a – ab + 2b – b2
2. m2 + 4m – 12
3. x2 – 1
4. 2x2 – 18
5. w2 – 9w + 20
6. 5(x – 2) + y(x – 2)
7. 5x3y7 + 15xy3
8. 49a2 – 4b2
9. x2 – 10x + 21
10. -12x2 +3x
11. a2 +13a + 40
12. 9x2 – 49
13. 6ax – 9a + 2bx – 3b
14. w2 – 12w + 36
15. 16 – 9y2
16. 2x2y + 3xy – 4x – 6
___ ___ ___ ___ ____ ____ ____ ____ ____ ___
10 9 12 13 9 8 3 13 9 11
___ ___ ___ ___ ___ ___ ___ ! ___ ___ ___ ___ ___ ___ ___ ___
2 13 13 16 13 14 4 7 13 13 1 6 5 6 14
___ ___ ___ ___ ___ ___!
15 6 14 4 9 1
Code Letter Answer
A (x – 7)(x – 3)
D 2(x + 3)(x – 3)
E (3a + b)(2x – 3)
G (7a + 2b)(7a – 2b)
H 3x(-4x + 1)
K (2x + 3)(xy – 2)
M (4 + 3y)(4 – 3y)
N (w – 6) 2
O (x – 2)(5 + y)
R (x + 1)(x – 1)
S 5xy3(x2y4 + 3)
T (a + 5)(a + 8)
U (w – 4)(w – 5)
V (3x + 7)(3x – 7)
W (m + 6)(m – 2)
Y (a + b)(2 – b)
FACTORING PRACTICE
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37
Group Activity: Mean, Median, Mode, Range, and Midpoint DIRECTIONS for TEACHERS
Divide your class into two separate groups, one consisting of the women and the other consisting of the men. Each group is to select a recorder to write the group’s results. As a group, carry out the following tasks. (You may want to devise a way to allow the members of the groups to provide personal data anonymously.)
1. Record the number of members (n) in your group.
2. Collect shoe sizes (x) and heights in inches (y) for all members of the group.
3. Compute the mean, median, and mode(s), if any, for each set of data.
4. Identify the range and midpoint.
5. Plot a scatter diagram for the x,y data collected
6. Find the equation of the line. Now re-combine your two groups into one. Discuss and carry out the following tasks.
1. If possible, compute the mean of the shoe sizes for the combined group, using only the means for the two individual groups and the number of members in each of the two groups. If this is not possible, explain why and describe how you could find the combined mean. Obtain the combined mean.
2. Do the same as in item 1 above for the median of the shoe sizes for the combined group.
3. Do the same for the mode of the shoe sizes for the combined group.
4. Do the same for the range and midpoint for the shoe sizes for the combined group.
5. Fill in the table below, pertaining to shoe sizes, and discuss any apparent relationships
among the computed statistics.
Number of
Members
Mean Media
n
Mode Range Midpoint
Women
Men
Combined
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Group Activity: Mean, Median, Mode, Range, and Midpoint
As a group, carry out the following tasks. Please select a recorder to write your group’s results. 1. Record the number of members (n) in your group. n = __________ 2. Collect shoe sizes (x) and heights in inches (y) for all members of the group.
Shoe Size (x) Height (inches)
(y)
3. Compute the mean, median, and mode(s), if any, for each set of data. Shoe size Height Mean: Mean: Median: Median: Mode: Mode: 4. Identify the range for each set of data. Shoe size: Height: 5. Using the smallest and largest shoe sizes as the endpoints, calculate the midpoint of the segment that would connect them in a graph.
39
6. Plot a scatter diagram for the x,y data collected. Think about how to label the axes based on your data.
7. Find the equation of the line that approximates the data. Now re-combine your groups into one class. Discuss and carry out the following tasks. 8. Compute the mean of the shoe sizes for the combined group, using only the means for the two individual groups and the number of members in each of the two groups. 9. Find the median of the shoe sizes for the combined group.
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10. Find the mode of the shoe sizes for the combined group. 11. Find the range for the shoe sizes for the combined group. 12. Using the smallest and largest shoe sizes for the combined group as the endpoints, calculate the midpoint of the segment that would connect them in a graph. 13. Add the data for the other group to your scatter plot above (in #6). Does it appear as if the line approximating the data would be moved based on the new data? 14. Fill in the table below, pertaining to shoe sizes, and discuss any apparent relationships among the computed statistics.
Number of
Members
Mean Media
n
Mode Range Midpoint
Women
Men
Combined
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Quadratic Formula Puzzle
x = b
2b ac4 a2
x = b
2b ac4 a2