Download rms titanic - Mangham Math

ACCELERATED MATHEMATICS: CHAPTER 8
Measurement & Data
RMS TITANIC
Royal Mail Steamer Titanic
MEASUREMENT & STATISTICS UNIT COVERING:
•
•
•
•
•
•
•
•
•
Mean, Median, Mode, and Range
Line, Bar, Double Bar, Circle, and Pictographs
Constructing Circle Graphs
Measures of Variation, Quartiles
Box-and-Whisker Plots
Scatter Plots, Stem-and-Leaf, Venn diagrams
Line Plots, Histograms, Scatter Plots, Frequency Tables
Customary Units
Metric Units, Time, Rulers
Created by Lance Mangham, 6th grade math, Carroll ISD
TITANIC SCAVENGER HUNT
1.
Where was the Titanic built?
London
Belfast
New York
2.
What was the Titanic made of?
Wood
Steel
Fiberglass
Soap
Bananas
Tugboat
600 tons
34,614 tons
5,892 tons
8
121
23
Medical
Officer
Captain
Head Cook
2
30
10
Cats
Snakes
Roosters
Southampton
Cobh
Belfast
Dogs pooped
on the deck
Luggage
deck
End section
of a ship
40,000
24,000
61,000
Sea gulls
Morse code
Telephone
25 couples
6 couples
12 couples
18 minutes
11 seconds
37 seconds
15. How many life jackets did the Titanic carry?
2,225
3,560
900
16. How long did it take the Titanic to sink?
2:40
1:15
4:10
One
Two
Four
28 degrees
40 degrees
12 degrees
3.
4.
How did the shipyard workers launch such a
huge ship into the water?
How much coal did the Titanic carry on her
maiden voyage?
5.
How many women worked on the Titanic?
6.
Who greeted third class passengers when they
came aboard?
7.
How many dogs were aboard the Titanic?
8.
9.
What other animals did passengers bring on the
Titanic?
The last stop before Titanic’s maiden voyage was
Queenstown, Ireland. What is the name of that
city today?
10. Why was it called a poop deck?
11. How many eggs were on the Titanic?
12. How did a ship receive messages in 1912?
How many passengers were on the Titanic for
their honeymoon?
How long after Frederick Fleet saw the iceberg
14.
did the Titanic hit it?
13.
At the bottom of the Atlantic, how many pieces
is the Titanic in?
How cold was the water the night the Titanic
18.
sank?
What were the last things taken aboard the
19.
Carpathia?
17.
20. Who found the Titanic?
Food
Jim Cameron
Titanic’s
lifeboats
Leo
DiCaprio
Luggage
Bob Ballard
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-1: Statistics Vocabulary Part 1
Name:
7
7
17
17
25
Mean – The mean of a set of numbers is the same as the average. To determine the mean, add up all of
the numbers and divide by the quantity of numbers.
MEAN =
7 + 7 + 17 + 17 + 25
= 14.6
5
The mean is 14.6.
Median – The median of a set of numbers is the middle number when the numbers are lined up from
greatest to least. In other words, half of the numbers are more than the median and half of the numbers
are less than the median.
7
7
17
17
25
17 is the median of this set of numbers.
If two numbers are in the middle, the median is determined by averaging those two numbers.
Mode – The mode of a set of numbers is the most common number in a set. If two or more numbers are
the most common, all of those numbers are the modes. If all numbers in a set are in equal amounts,
then there is “no mode”.
The mode of the set of numbers above is 7 and 17.
Range – The range of a set of numbers is the difference between the smallest and largest numbers.
The range for the set of numbers above is 18 (25 − 7) .
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-2: Statistics Vocabulary Part 2
Name:
Variation is the spread of the data. If there is a lot of variation it means the numbers are spread out all
over the place. If there is little variation it means the numbers are all pretty similar. Range is one way
we have already learned to measure the variation.
With large sets of data it is often helpful to separate the data into four equal parts called quartiles. The
quartiles are used to find another measure of variation called the interquartile range. This is the range
of the middle half of the set of data.
Students in math class are divided into 4 groups with one-fourth getting the grade of a D, one-fourth C,
one-fourth B, and the best one-fourth get an A.
DDDDDDDDCCCCCCCCBBBBBBBBAAAAAAAA
This is the
median. It breaks
the group in half.
This is the lower quartile.
It breaks the bottom half in
half.
This is the upper quartile.
It breaks the top half in
half.
Lower Quartile – The median of the lower half of the data.
Upper Quartile – The median of the upper half of the data.
Interquartile Range – The difference between the upper quartile and the lower quartile.
Examples:
Lower half of data
4
6
7
8
Upper half of data
9
Lower
Quartile
12
16
17
19
24
28
Upper
Quartile
Median
Interquartile Range = 19 – 7 = 12
So half of the numbers (approximately) are between 7 and 19.
4
6
8
7
Lower
Quartile
12
16
18
24
14
2
Median
Upper
Quartile
28
Interquartile Range = 21 – 7 = 14
So half of the numbers are between 7 and 21.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-3: Skew & MAD
Name:
Symmetric – A symmetric graph typically has a high point or peak in the middle of the data set. The
mean and median are or about equal. The mean is the best measure of center.
Skewed right – A right-skewed graph has much of its data to the left with only a few data values on the
right. The mean of the data set is greater than the median. The median is the best measure of center.
Skewed left – A left-skewed graph has much of its data to the right with only a few data values on the
left. The mean of the data set is less than the median. The median is the best measure of center.
Our principal asks every math teacher to estimate the amount of time our students spend studying each
week. Mr. Mangham decides to estimate the amount of time by taking a sample of 8 students in his
math class. Then, he can determine the mean amount of time students spend studying each week.
In the situation the population the entire group of students that Mr. Mangham could collect data from.
The sample will be the 8 students that Mr. Mangham random chooses to get data from. You would say
that the sample size is 8.
Mr. Mangham gets the following data: 60, 120, 50, 150, 150, 50, 100, and 200.
The distribution of the data is called its variability. The variability of data describes how spread out the
data is. This can also be described as the spread of data. One measure of variability or spread is the
range. Another measure is called the mean absolute deviation. The mean absolute deviation is the
average of the absolute values of the deviations of each data value from the mean.
Data
60
120
50
150
150
50
100
200
Mean
Mean =
880
= 110
8
Absolute value of
difference from
mean
50
10
60
40
40
60
10
90
MAD
MAD =
360
= 45
8
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-3: Data Displays
Name:
Bar Graph
• A display in which numbers are represented by bars whose heights or lengths correspond to the
magnitude of the numbers being represented.
• Compares data from several situations.
Line Graph
• A line drawn through pairs of associated numbers on a coordinate grid.
• Time is graphed on the horizontal axis.
• Used to show changes over time.
Circle Graph
• A display in which parts of a whole are represented by sectors that show the fraction of the
whole taken up by each part.
• Often called a pie chart.
• Allows you to visually compare a part of the data to the whole set of data.
Line Plot
• A display of data that uses stacked Xs to show how many times each data value occurs.
• The values are listed on a horizontal number line.
Stem-and-Leaf Plot
• Displays a collection of numbers in which the digits in certain place values are designated as the
stems and the digits in lower place values are designated as the leaves.
• Leaves are placed side-by-side next to the stems.
Venn Diagram
• A visual aid that uses circles to represent sets and the relationships between them.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-4: Box-and-Whisker Plots & Scatter Plots
Name:
A box-and-whisker plot summarizes the data using the median, the upper and lower quartiles, and the
highest and lowest, or extreme values.
Directions to construct a box-and-whisker plot:
1. Draw a number line at least as long as the range of the data.
2. Place vertical lines above the number line to represent the lowest value, lower quartile, median,
upper quartile, and highest value. The lowest and highest values are called the extremes.
3. Draw a box containing the quartile values. Draw a vertical line through the median. Extend the
whiskers from each quartile to the extreme values.
Example:
216
223
Lowest
229
LQ
240
247
254
255
Median
257
271
311
UQ
320
Highest
200 210 220 230 240 250 260 270 280 290 300 310 320 330
Note that all the numbers on the line are evenly spaced.
This is very important for a box-and-whisker plot.
When you graph two sets of data as ordered pairs, you form a scatter plot.
If the points trend upward to the right, there is a positive relationship.
If the points trend downward to the right, there is a negative relationship.
If no trend is evident, there is no relationship.
Positive relationship
For example, the more
passes you throw the
more yards you will get.
Negative relationship
For example, the more
points you score the
fewer games you will
lose.
No relationship
For example, the amount
of times you win the coin
flip does not affect how
many games you win.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-5: Titanic Team Project
Name:
“How could we have saved more people aboard the Titanic?”
Create an exciting, entertaining, and informative Titanic Survival display
Assumptions:
You left for New York at the same time with all the same passengers and equipment aboard.
You will still encounter the iceberg along the way.
Main question to answer:
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How could we have saved an additional ________ people?
You goal is to prove your answer to this question MATHEMATICALLY.
Display Requirements
Each group will be given one piece of posterboard. Your display must be on one side only.
•
•
Use the mean, median, mode, and range of a set of data (at least 8 numbers) to make a
conclusion
Find the quartiles of the same set of data to make a conclusion
Create a box-and-whisker plot of the same set of data to educate the reader
•
•
Create at least one graph to display important data to your reader (graph paper)
Create a table of the data used in your graphs (optional)
•
As part of your description on how to save more people show at least one unit conversions in
each category below:
o Customary units
2. Metric units
3. Rates (ex. ft/sec to mi/min)
•
Demonstrate your knowledge of rates, unit rates, and ratios in some fashion to help the reader
understand a topic.
•
Hints of advice for getting a maximum grade:
Creative approaches to solving the problem are welcome. Make sure to use real data about the
Titanic to support your approach.
The more you demonstrate your math knowledge, the better.
Neatness matters, however your grade is not based on the most colorful. It is mostly based on
the math.
You are responsible for completing the math, not a computer or calculator. Do not show
calculations on your display - use a separate sheet of paper.
Feel free to add any “extras” to make your display more appealing. Cite any sources you use.
Created by Lance Mangham, 6th grade math, Carroll ISD
TITANIC PROJECT GRADES
TEAM: ______________________________________________
Topic
Points Possible
Mean, Median, Mode, Range Found
9
Mean, Median, Mode, Range used to make a
conclusion
6
Quartiles Found
9
Quartiles used to make a conclusion
6
Box-and-Whisker Plot created and explained
10
At least one graph of important data
10
Customary unit conversion
5
Metric unit conversion
5
Rate conversion
5
Demonstration of rates, unit rates, ratios
10
Method of saving passengers is well explained
and creative
15
Overall project well explained to readers
10
TOTAL
100
Points
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-6: Mean, Median, Mode, and Range
Name:
For this section use the numbers listed in “Loading the Titanic” section.
Find the mean, median, mode, and range using the data above (nearest whole number).
Mean
Median
Mode
Range
1.
Cutlery – Left column
2.
Cutlery – Right column
3.
Cutlery – Both columns
4.
Linens – Left column
5.
Linens – Right column
Votes for your favorite year – 144 people surveyed
1912
1913
1914
1915
1916
1917
1918
1919
12
15
17
18
20
32
18
12
Find the mean, median, mode, and range using the data above (nearest hundredth).
Mean
Median
Mode
6.
First 4 years
7.
First 5 years
8.
First 6 years
9.
First 7 years
10.
All 8 years
Range
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-6B: Mean, Median, Mode, and Range
Name:
11.
{12, 8, 6, 14, 18, 8, 300} Why is the mean of the set above not a good
representation of the set of numbers?
12.
{2, 4, 4, 6, 84, 88, 92, 98} Why is the median of the set above not a good
representation of the set of numbers?
13.
{1, 1, 4, 5, 6, 7, 8, 9, 10, 90, 90} Why is the mode of the set above not a
good representation of the set of numbers?
14. {3, 3, 6, 6, 9, 9} What is the mode of this set of numbers?
15.
A set of 5 different positive integers has a mean of 33 and a median of 40.
How large can the greatest number be?
16.
Research the winning and losing scores of the last 11 Super Bowls. What
is the median winning score and the median losing score?
For each description below make a different data set. All the data sets should have:
7 values and a mean of 21
In each data set circle the median and put a square around the mode (if there is one).
A. Mean is larger than median.
D. Median is larger than mode.
B. Median is larger than mean.
E. Mode is larger than median.
C. Mean is larger than mode.
F. Mean, median, and mode are equal.
G. Mode is larger than mean.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-6C: Mean Absolute Deviation
Name:
MAD (mean absolute deviation) is another measure of variability (like range) in a data set. The mean
absolute deviation (MAD) is the average of the absolute values of the differences between each data
value in a data set and the set's mean. In other words, it is the average distance that each value is away
from the mean.
If a data set has a small mean absolute deviation, then this means that the data values are relatively close
to the mean. If the mean absolute deviation is large, then the values are spread out and far from the
mean.
To find the MAD:
1. Find the mean
2. Subtract each data value from the mean
3. Take the absolute value of each value from step #2.
4. Add up all values from step #3.
5. Divide by the number of data values.
Mean
1.
Find the mean absolute deviation:
{10, 7, 13, 10, 8}
MAD
Mean
2.
Find the mean absolute deviation:
{110,114, 104, 108, 106}
Find the mean absolute deviation:
{87, 75, 85, 77, 74, 82, 90, 88, 79, 81}
Find the mean absolute deviation:
{15, 17, 15, 17, 21, 17, 15, 23, 20, 18}
Sum of absolute values from mean
MAD
Mean
4.
Sum of absolute values from mean
MAD
Mean
3.
Sum of absolute values from mean
Sum of absolute values from mean
MAD
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-6D: Mean Absolute Deviation
Name:
1.
Find the mean absolute deviation for the set. S = {85, 90, 68, 75, 79}
2.
Sherrie just registered for her wedding. So far 6 items have been fulfilled on her registry. Find the
mean price of the fulfilled items. $29, $58, $15, $129, $75, $22
3.
Find the mean absolute deviation of the fulfilled items on Sherrie's registry. $29, $58, $15, $129,
$75, $22
Family A and Family B both have 8 people in their family. The ages of each member is listed
below. Which statement is correct about the variability of the two families?
Family A: 35, 5, 42, 9, 16, 3, 8, 12
Family B: 1, 5, 29, 3, 7, 35, 6, 9
4.
A. The variability is the same for both Family A and Family B because they have the same mean
absolute deviation.
B. The variability for Family A is greater because the mean is greater for Family A.
C. The variability for Family B is greater because the mean absolute deviation is greater for
Family B.
D. There is not enough information to determine the variability.
5.
Find the mean absolute deviation for the set. S = {65, 90, 85, 70, 70, 95, 55}
6.
Answer the following questions using the following data set of the oldest family member of each
person in April’s class. S = {55, 72, 100, 45, 66, 71, 58, 62}
7.
Mean =
8.
Median =
9.
IQR =
10. MAD =
11. Which measure of central tendency best describes the data (Mean, Median) and Why?
12. Which measure of variability describe the data best (IQR, MAD) and Why?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-7: Graphs
Name:
2.
CIRCLE GRAPHS – Titanic Passengers & Titanic Survivors
Which two categories of passengers made up about three-fourths of the
people sailing on the Titanic?
What is the sum of the percentages on any circle graph?
3.
Were there more third class passengers or more “higher class” passengers?
4.
Did more crew survive or first class passengers survive?
5.
Which categories of survivors add up to nine-twentieths?
Just looking at the survivor circle graph, it appears that the crew and third
class did well with 55% of the survivors coming from these two categories.
Why is this misleading?
1.
6.
7.
BAR GRAPH – Titanic Adult Passengers & Survivors
Which class had the most female passengers?
8.
About what fraction of the male crew survived?
9.
Did more male adults or female adults survive?
10. About what percent of first class male passengers survived?
11. Did more third class males or first class males survive?
12. Was the number of surviving males more or less than 400?
BAR GRAPH – Titanic Children Passengers & Survivors
13. Which class of children had the most survivors?
14. Which class of children had the smallest percentage of survivors?
15. Were there more male or female children aboard the Titanic?
16. About what percent of third class male children survived?
Were the more second class female or male children aboard the
17.
Titanic?
Third class male children made up about what percent of all the male
18.
children aboard the Titanic?
LINE GRAPH – Titanic Lifeboats % Occupied
19. Which lifeboat(s) were the least percent occupied?
Why do you think earlier lifeboats were generally not as occupied as
20.
later lifeboats?
21. What was the median percentage occupied of the first five lifeboats?
22. What was the first lifeboat that was more than three-fourths full?
What was the approximate mean percentage occupied of the first 10
23.
lifeboats?
Based on the trend, make a prediction for the percent occupied of 11th
24.
lifeboat launched. 12th lifeboat? 13th lifeboat?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-8: Graphs
1.
2.
Name:
SCATTER PLOT – Yearly North Atlantic Iceberg Total
Which year(s) had the highest total number of icebergs?
4.
Which year had about twice as many icebergs as 1906?
Just looking at the graph, what would be a good estimate of the mean
number of icebergs per year?
What is the median number of icebergs per year?
5.
Which two years combine for 1000 icebergs?
6.
Does the scatter plot show a positive, negative, or no relationship?
3.
7.
8.
9.
HISTOGRAM – April North Atlantic Iceberg Total
What would be a good estimate of the median number of icebergs
each April?
Why would the mean not be a good representation of the entire set of
data?
How many years were there 50 or less April icebergs?
10. Is there a better chance of having 75 icebergs or 375 icebergs?
1-50
6
11. Create the frequency table for the histogram.
LINE PLOT – Titanic Lifeboat Capacities
12. What is the mode of the lifeboat capacities?
13. How many lifeboats had a capacity of 47?
14. Approximate the mean of the lifeboat capacities.
What is the total capacity of all lifeboats which can hold less than
15.
50 passengers?
16. What is the median of the lifeboat capacities?
VENN DIAGRAM – Titanic Passengers
17. How many men passengers were aboard the Titanic?
18. How many first class passengers were aboard the Titanic?
19. How many passengers were men traveling first class?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-9: Appropriate Graph/Stem-and-Leaf
Name:
Determine which kind of graph (line, bar, circle) is the most appropriate.
Show the number of students enrolled in each grade at a particular
1.
high school.
2. Compare the cost of a telephone call with the length of the call.
3.
Show the number of winning games for different soccer teams
during a season.
4. Show your height between ages 6 and 13.
5. Show the monthly sales of all the departments in a store.
6.
Compare the increase in typing speed with the number of hours of
practice.
7. Show the amount of federally owned land in each state in the south.
Stem-and-Leaf Plot
Create a stem-and-leaf plot for the occupants of the 20 lifeboats. Let the stem represent the tens
place and the leaves the ones place. Make sure to include a key.
8.
Create a stem-and-leaf plot for the percentage of Titanic survivors by nationality (just the 6 nations
listed). Make sure to include a key.
9.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-10: Quartiles/Box-and Whisker Plots
Name:
Complete the table below.
Extreme
Low
Value
Statistics
a.
April iceberg count
b.
Lifeboat occupants
c.
Food supplies
(only the ones listed
in pounds)
Lower
Quartile
Upper
Quartile
Median
Extreme
High
Value
Interquartile
Range
(Difference)
4. Construct a box-and-whisker plot on a separate sheet of paper for letter a above.
Use the box-and-whisker plot below to answer each question.
75
80
85 90 95 100 105 110 115 120 125 130 135
5.
What is the median?
6.
What is the range?
7.
What is the lower quartile?
8.
What is the upper quartile?
9.
What is the interquartile range?
10.
What are the extremes?
Use the data at the right to answer each question.
11.
What is the median?
12.
What is the range?
13.
What is the upper quartile?
14.
What is the lower quartile?
15.
What is the interquartile range?
16.
What are the extremes?
30, 34, 40, 44,
48, 52, 54, 56,
57, 61, 62, 66,
67, 70, 75
17.
Make a box-and-whisker plot of the data.
18.
What does it mean if a B&W plot has one long whisker?
19.
What does it mean if a B&W plot has a long box?
20.
What does it mean if a B&W plot has a median toward
the left of the box?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-10: Quartiles/Box-and Whisker Plots
Name:
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-10: Darth Vader Raiders
Name:
Below is a stem-and-leaf plot of the points scored by the Darth Vader Raiders football team in 2013 and
2014.
Darth Vader Raider Raiders
Points in 2013
Points in 2014
7 3 0
0
7 4 4 2 0
1
4 7 7
9 8
2
4 7 8 8
5
3
5 8
4
2 5
Key = 0 | 3 means 3 points
1.
Which year did the Darth Vader Raiders football team score more points?
2.
Describe the distribution of the stem-and-leaf plots for each year.
3.
You can also use a dot plot to represent the data.
4.
How does the shape of the stem-and-leaf plot distribution compare with the shape of the dot plot
distributions?
Complete the table below for the Darth Vader Raiders.
2013 Team
2014 Team
Minimum score
Lower quartile (Q1)
Median
Upper Quartile (Q3)
Maximum
IQR
MAD
Mean
Complete a box-and-whisker plot for the 2013 season and another one for the 2014 season.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-11: Scatter Plots
Name:
Determine whether a scatter plot of the data below would show a positive, negative, or no
relationship or correlation.
1.
The selling price of a calculator and the number of advanced features it contains
2.
The number of miles walked in a pair of shoes and the thickness of the heel
3.
A child’s age and the child’s height
4.
Hair color and how fast you can run a mile
5.
The number of minutes a candle burns and the candle’s height
6.
The length of a taxi ride and the amount of the fare
7.
Gender and the year of your birth
8.
How much you read and the number of words you know
9.
How fast you type and how long it takes you to type a book report for LA class
10.
The number of words written and amount of ink remaining in a pen
11.
The number of letters in first name and height in centimeters
12.
The outside temperature and cost of air conditioning
13.
The number of pages you have read in a book and the number of pages
remaining.
14.
The day of the month and the wind speed.
15.
The age of a car and its selling price.
16.
The weight of a vehicle and its gas mileage.
17.
The outside temperature and the number of people in attendance at the beach.
18.
The month of the year and the number of birthdays in a certain month.
19.
The population of a state and the number of senators.
20.
The length of your hair and the number of days since your last haircut.
21.
The number of hours spent studying and the test score received.
Determine whether each scatter plot shows a positive, negative, or no correlation.
22.
23.
24.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-11B: Scatter Plots
Name:
When data points are not completely linear, a trend line is used to allow us to make predictions from the
data. A trend line indicates the general course of data.
A scatterplot is a graph that displays bivariate data on a coordinate plane and may be used to show a
relationship between two variables.
Bivariate data shows the relationship between two variables. Example: Ice cream sales versus the
temperature on that day. The two variables are Ice Cream Sales and Temperature.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-11C: Scatter Plots
Name:
Trend lines, slope, rate of change, y-intercept, predictions of future, equation of trend line, as x increases
what happens to y,
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-11D: Scatter Plots
Name:
Since it is often impossible to sample an entire population, a random sample can be used to estimate
the traits of the entire population.
Association is the degree to which two variables are related.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-11E: Scatter Plots
Name:
Two variables are related in a positive association when values for one variable tend to increase as
values for the other variable also increase.
Two variables are related in a negative association when values for one variable tend to decrease as
values for the other variable increase.
When a linear pattern, such as one of the form y = mx + b , describes the essential nature of the
relationship between two variables, they have a linear association.
When a non-linear pattern, such as a curve, describes the essential nature of the relationship between
two variables, they have a non-linear association.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-11F: Scatter Plots
Name:
John made a scatterplot below showing the relationship between his typing accuracy and his typing
speed.
John's Typing
100
Accuracy (percetn)
95
90
85
80
75
70
65
60
40
50
60
70
80
90
100
Speed (words per minute)
Which statement best describes the relationship shown in this scatterplot?
A.
B.
C.
D.
There is no relationship between John’s typing speed and his typing accuracy.
As John’s typing speed increased, his accuracy remained constant.
As John’s typing speed increased, his accuracy increased.
As John’s typing speed increased, his accuracy decreased.
Created by Lance Mangham, 6th grade math, Carroll ISD
Name:
Accelerated Mathematics Formula Chart
Linear Equations
Slope-intercept form
y = mx + b
Constant of proportionality
k=
y
x
y = kx (8th grade)
Slope of a line
m=
y2 − y1 th
(8 grade)
x2 − x1
C = 2π r or C = π d
Circle
Circumference
Direct Variation
Area
1
(b1 + b2 ) h
2
Rectangle
A = bh
Trapezoid
A=
Parallelogram
A = bh
Circle
A = π r2
Triangle
A=
bh
1
or A = bh
2
2
Surface Area (8th grade)
Prism
Cylinder
Lateral
Total
S = Ph
S = Ph + 2 B
S = 2π rh
S = 2π rh + 2π r 2
Volume
Triangular prism
V = Bh
Cylinder
Rectangular prism
V = Bh
Cone
Pyramid
1
V = Bh
3
Sphere
V = π r 2 h or V = Bh (8th grade)
1
1
V = Bh or π r 2 (8th grade)
3
3
4
V = π r 3 (8th grade)
3
22
7
Pi
π ≈ 3.14 or π ≈
Distance
d = rt
Compound Interest
A = P (1 + r )t
Simple Interest
I = prt
Pythagorean Theorem
a 2 + b 2 = c 2 (8th grade)
Customary – Length
1 mile = 1760 yards
1 yard = 3 feet
1 foot = 12 inches
Metric – Length
1 kilometer = 1000 meters
1 meter = 100 centimeters
1 centimeter = 10 millimeters
Customary – Volume/Capacity
1 pint = 2 cups
1 cup = 8 fluid ounces
1 quart = 2 pints
1 gallon = 4 quarts
Metric – Volume/Capacity
1 liter = 1000 milliliters
Customary – Mass/Weight
1 ton = 2,000 pounds
1 pound = 16 ounces
Metric – Mass/Weight
1 kilogram = 1000 grams
1 gram = 1000 milligrams
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-12B: Measurement
Name:
Length
1 in = 2.54 cm
Mass
1 oz = 28.35 g
Capacity
1 pt = 0.47 L
1 cm = 0.39 in
1 g = 0.035 oz
1 L = 2.11 pt
1 ft = 30.48 cm
1 lb = 0.45 kg
1 qt = 0.95 L
1 m = 3.28 ft
1 kg = 2.2 lb
1 L = 1.06 qt
1 mi = 1.61 km
1 gal = 3.79 L
1 km = 0.62 mi
1 L = 0.26 gal
1 m = 39.37 in
1 in = 0.0254 m
1 m = 1.09 yd
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-13: Measurement Comparisons
Name:
Name
Abbreviation
inch
in
foot
ft
Approximate Comparison
length of half a thumb
length of a paper clip
length of an adult male foot
yard
yd
length from nose to outstretched fingertip
mile
mi
length of 14 football fields
ounce
oz
weight of a birthday card
pound
lb
weight of three apples
quart
qt
amount in a medium container of milk
gallon
gal
amount in a small bucket
kilometer
km
meter
m
centimeter
cm
millimeter
mm
kilogram
kg
gram
g
milligram
mg
liter
L
milliliter
mL
9 football fields
a little more than half a mile
half the height of a door
a meter stick
a little bit more than 3 feet
the width of a door
length of a raisin
the width of your pinky
the width of an M&M
the width of a paper clip
width of a period at the end of a sentence
the width of a dime
the point of a pencil
mass of a cantaloupe
the mass of a few apples
the mass of a hammer
mass of a raisin
the weight of a paperclip
the weight of a Cheerio
the weight of a marshmallow
the weight of a grain of sand
the weight of a grain of rice
half of a large bottle of soda
half an eyedropper
a raindrop
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-14: Measurement Conversions
Name:
There are several different ways to convert between units of measurement. One way to convert metric
units is to memorize the sentence:
King(Kilo) Henry(Hecto) Died(Deka) [base units, gram, liter, meter] Drinking(deci) Chocolate(centi)
Milk(milli)
Another way is to use proportions:
Example
14 gallons = x qt.
Use the fact that 1 gal = 4 qt.
Example #2
14 qt. = x gal.
1 gallon x gallons
=
4 quart 14 quarts
1 • 14 4 x
=
4
4
3.5 gal = x
1 gallon 14 gallons
=
4 quart
x quarts
1 • q = 4 • 14
q = 56 quarts
In accelerated math we are going to also introduce dimensional analysis. This method will better
prepare you for advanced math and science classes in the future.
Example
14 gallons = x qt.
14 gallons 4 quarts
•
= 56 quarts
1
1 gallon
Let’s say you want to convert 55 miles per hour to feet per second.
Example #2
55 miles 5280 feet 1 hour 1 min. 80.7 ft.
•
•
•
≈
1 hour
1 mile
60 min. 60 sec. 1 sec.
The units cancel each other out leaving just feet per second left. This tells you that your answer is in the
correct units.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-15: Customary Measurement
Name:
Solve all problems with dimensional analysis or proportions and show all steps.
1. How many inches wide was the Titanic?
2.
How many pounds did the Titanic weigh fully loaded?
3.
How many yards high was the rudder?
4.
How many inches high was the crow’s nest?
5.
How many cups of drinking water were on board the Titanic per day?
6.
How many ounces of fresh fish were on the Titanic?
7.
How many tons of poultry were on the Titanic?
8.
How many quarts of fresh milk were on the Titanic?
9.
If one-fourth of the ice cream was eaten, how many pints of ice cream
were eaten?
10. How many tons of fresh meat was on the Titanic?
11. What is the maximum height of a medium size iceberg in inches?
12. Very large icebergs are over how many yards tall?
By 2:00am on the night of the sinking the Titanic had taken on how many
pounds of water?
What is the maximum number of minutes of expected survival in water
14.
between 50 and 60 degrees?
13.
15. How many yards deep does the Titanic lie?
16. 13 yd. =
in.
17.
12 qt. =
19. 5 c. =
fl. oz.
20.
16 fl. oz. =
22. 7 c. =
pt.
23.
25. 3 gal. =
qt.
28. 5 mi. =
31. 11 c. =
gal.
18. 10 c. =
pt.
c.
21. 12 pt. =
qt.
24 pt. =
c.
24. 53 qt. =
gal.
26.
20 qt. =
gal.
27. 3.5 c. =
fl. oz.
ft.
29.
12 qt. =
pt.
30.
1
c. =
2
fl. oz.
pt.
32.
6 pt. =
c.
33. 0.5 qt. =
pt.
3
The sign before a bridge says maximum weight 5 tons. Joe’s truck weighs 7,350 pounds. Can
the bridge support his weight?
Kroger is selling 16 ounces of cream cheese for $2.79. Costco is selling 4 pounds of cream
35.
cheese for $7.99. Which store has the best price on cream cheese?
Recipe: 1 quart apple juice, 2.75 cups of lemon-lime soda, 64 ounces pineapple juice, 2 quarts
36. cold water, 0.25 cups lemon juice
What is the smallest container that will hold all of this punch? 4, 5, 6, or 7 quart
34.
37. How long will it take the students at DIS to drink 1,000,000 pints of milk?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-16: Customary Measurement
Name:
Use a ruler to measure the following lines to the nearest quarter of an inch.
1
2
3
4
5
6
7
8
9
10
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-17: Measurement – Time
Name:
1.
2 hours and 45 minutes plus 3 hours and 35 minutes equals…
2.
My clock shows that it is 8:40 am. What time will it be in six and onehalf hours?
3.
How many minutes are in 3.5 hours?
4.
It is now 6:30 am. What time was it 8.5 hours ago?
5.
25 min + 55 min =
6.
7.
Find the elapsed time:
From 4:15am to 11:00am
Find the elapsed time:
From 9:59am to 7:46am
Find the elapsed time.
8.
6:45pm to 9:20pm
9.
9:57am to 11:50am
10. 5:45am to 11:30am
11. 3:11pm to 10:40am
12. 8:15am to 10:09pm
13. 1:35am to 7:28pm
14.
Martha ran at a pace of 8 miles per hour from 9:30am to 1:00pm. How
far did she run?
15. 8 hours equals how many minutes?
16. 2 weeks equals how many days?
17. 300 minutes equals how many hours?
18. 28 days equals how many weeks?
19. 600 minutes equals how many hours?
20. 120 seconds equals how many minutes?
21. How many seconds are in a day?
Write an equation that can be used to find m, the number of minutes in
h hours.
A grandfather clock takes 30 seconds to strike six. How long does it
23.
take to strike twelve?
22.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-18: Metric System
Name:
The metric system is a decimal system of physical units based on its unit of length, the meter.
Introduced and adopted by law in France in the 1790s, the metric system was subsequently adopted as
the common system of weights and measures by a majority of countries, and by all countries as the
system used in scientific work.
The meter (m), which is approximately 39.37 in., was originally defined as one ten-millionth of the
distance from the equator to the North Pole on a line running through Paris. Between 1792 and 1799,
French scientists measured part of this distance. Treating the earth as a perfect sphere, they then
estimated the total distance and divided it into ten-millionths.. The measurements of modern science
required greater precision, however, and in 1983 the meter was defined as the length of the path traveled
by light in a vacuum during a time interval of 1/299,792,458 of a second .
All metric units were originally derived from the meter, but by 1900 the metric system began to be
based on the mks (meter-kilogram-second) system, by which the unit of mass, the gram, was redefined
as the kilogram, and the unit of time, the second, was added. Because of the need of science for small
units, the cgs (centimeter-gram-second) system also came into use. The unit of volume, the liter, was
originally defined as 1 cubic decimeter (cdm3), but in 1901 it was redefined as the volume occupied by a
kilogram of water at 4° C at 760 mm of mercury; in 1964 the original definition (cdm3) was restored.
A series of Greek decimal prefixes is used to express multiples; a similar series of Latin decimal
prefixes is used to express fractions. These prefixes have been adopted by and expanded in the
International System of Units.
The U.S., Great Britain, and other English-speaking countries use inches, feet, miles, pounds, tons, and
gallons as units of length, weight, and volume for common measurements. Today, however, within the
framework of the International System of Units, these English-system units are legally based on metric
standards.
In the U.S. several attempts were made to bring the metric system into general use. In 1821 Secretary of
State John Quincy Adams, in a report to Congress, advocated the adoption of the metric system. In 1866
Congress legalized the use of the metric system, and from that time this system was increasingly
adopted, notably in medicine and science, as well as in certain sports, such as track. In 1893 the National
Bureau of Standards of the U.S. adopted the metric system in legally defining the yard and the pound.
In 1965 Great Britain became the first of the English-speaking countries to begin an organized effort to
abandon the older units of measurement. Canada, Australia, New Zealand, and South Africa quickly
followed and soon exceeded the speed of change in Great Britain. In 1971, after an extensive study, the
U.S. secretary of commerce recommended that the U.S. convert to metric units under a ten-year
voluntary plan. On Dec. 23,1975, President Gerald R. Ford signed the Metric Conversion Act of 1975. It
defines the metric system as being the International System of Units as interpreted in the U.S. by the
secretary of commerce. The act coordinates the metric effort, but does not specify a conversion
schedule.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-19: Metric Measurement
Name:
Choose an appropriate metric unit of mass for each.
1.
a grain of rice
2.
a bag of groceries
3.
a feather
4.
a cat
5.
a leaf
6.
an eraser
Choose an appropriate metric unit of capacity for each.
7.
a gasoline tank
8.
a coffee mug
9.
6 raindrops
10.
a pitcher of juice
11.
a swimming pool
12.
a can of paint
State whether each of the following is best measured in terms of mass or capacity.
13.
a bag of potatoes
14.
water in a birdbath
15.
an apple
16.
a puppy
17.
a cup of hot cider
18.
the inside of the
refrigerator
19.
juice in a baby’s bottle
20.
water in a fish tank
22.
Jason drank 5.8 L of juice
at breakfast.
24.
A penny is about 3 kg.
26.
A textbook is about 1 kg.
Write true or false.
The mass of a horse is
21.
about 500 kg.
A mug holds 250 mL of
23.
hot chocolate.
A teaspoon holds about 5
25.
L.
Choose the most reasonable measurement.
About how tall would your friend be?
27.
A. 1.5 mm
B. 1,500 cm
About how wide would your desk be?
28.
A. 50 mm
B. 50 m
A tree is about how tall?
29.
A. 20 km
B. 20 m
An envelope is about how long?
30.
A. 24 cm
B. 2.4 cm
C. 1.5 km
D. 1,500 mm
C. 5 m
D. 50 cm
C. 20 cm
D. 2 km
C. 24 mm
D. 2.4 m
A beaker contains 62 milliliters of solution. When full it holds 1.5 liters. Which
expression shows how much you can still add?
31.
a. 0.0015-62 mL
b. 1500-62 mL
c. 1.5-.62 L
d. 1.5-62000L
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-20: Metric Measurement
Name:
Solve all problems with dimensional analysis or proportions and show all steps.
1. How many kilometers long was the Titanic?
2.
How many millimeters did the Titanic travel from Southampton to
Cherbourg? Write your answer in scientific notation.
3.
How many kilometers high is very large iceberg?
4.
What is the maximum height of a bergy bit in millimeters?
5.
What is the sum of the lengths of slits 2 through 5 on the Titanic in
centimeters?
6.
3.72 L =
9.
0.018 kg =
mL
7.
9.75 m =
cm
g
10.
149 cm =
m
g
13.
3 mm =
cm
14. 14 L =
mL
15. 6.7 g =
mg
16.
9.3 L =
mL
17. 0.89 m =
cm
18. 0.085 g =
mg
19.
4,600 mm =
m
20. 3.904 L =
mL
21. 205 g =
kg
22.
609 mg =
g
23. 0.0019 m =
mm
24. 38 mL =
L
25.
720 m =
26. 150 cm =
mm
12. 0.56 kg =
km
8.
6.8 g =
11. 524 cm =
kg
m
What unit of measure would you use to measure each item?
the height of an office building
27.
A. km
B. cm
C. m
D. mm
the width of a page of text
28.
A. km
B. cm
C. m
D. mm
the length of an ant
29.
A. km
B. cm
C. m
D. mm
the depth of a lake
30.
A. km
B. cm
C. m
D. mm
Suzy wants to build a doghouse for Buster. She wants the doghouse to be 4 meters by 3 meters.
31. When she arrives at the lumber store, the clerk tells her the lumber is measured in centimeters.
What are the dimensions for Buster’s doghouse in centimeters?
Sammy needs to replace all the strings on his kite collection. George’s Hobby Shop sells kite
string for $15.00/meter. Hobby Depot sells kite string for $13.50/50 centimeters. Sammy needs
32.
8 meters of kite string. How much would Sammy pay for the string at George’s Hobby Shop?
How much would Sammy pay for the string at Hobby Depot?
Sarah is trying to determine which container to use for her leftovers. She has 2 liters of soup
33. leftover. One of her containers can hold 1000 milliliters of a liquid and the other container can
hold 0.1 kiloliters. Which container should she use?
If a zilch is equal to 13 milches and a milch is equal to 23 pilches, would you accept 8000 pilches
34.
for 26 zilches?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-21: Measurement
Name:
Solve all problems with dimensional analysis or proportions and show all steps. You may use a
calculator, however you must show all other work.
1.
At top speed, how many feet per minute could the Titanic travel?
2.
At maximum usage, how many pounds of coal were used each hour?
3.
A glacier can flow toward the sea at how many yards per hour?
4.
5.
At impact water began rushing into the hull at how many pounds per
minute?
At sea level what is the water pressure in ounces per square foot (144
square inches = 1 square foot)?
6.
18 m/min to cm/sec
7.
5.7 gal/hr to c/min
8.
264 yd/sec to mi/hr
9.
2 qt/min to gal/hr
10.
99 in/sec to mi/day
11.
154 mi/hr to in/sec
12.
7.7 ft/sec to mi/hr
13.
20 cm/sec to m/min
14.
5 L/hr to mL/min
15.
10 c/min to pt/hr
16.
20 yd/sec to ft/min
17.
100 L/min to mL/sec
18.
Alex can run the 50-yard dash in 17 seconds. Andy can run 600-feet in 49 seconds. Which
runner is faster?
19.
Kim has 4 windows that are 22 inches long and 4 that are 5 feet long. The fabric store sells fabric
by the yard. How many yards of fabric will Kim need if she makes all 8 window toppers?
Jonathon wants to surprise his wife with ice cream. Georgia’s Ice Cream Store sells his wife’s
20. favorite flavor in two different sizes. He can buy a pint for $5.17 or he can buy a half gallon for
$16.00. Which ice cream should Jonathon buy?
21.
Kelli is having a party. She is serving 14 gallons of ice tea. At the party supply store, they have
pitchers that can hold 2 quarts. How many pitchers should Kelli buy to serve her ice tea?
22.
Buster the dog weighs 5 kilograms. Last year he weighed 5,500 grams. Did he lose weight or
gain weight this year? How much?
23.
Sally thinks she found the biggest rock; her rock weighs 23 grams. Bobby’s rock weighs 2,300
milligrams. Which rock weighs the most?
24.
A jeweler bought 2 meters of silver chain. She used 20 centimeters for a bracelet and 60
centimeters for a necklace. How many meters of silver did she have left?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-22: Metric Measurement
Name:
Use a ruler to measure the following lines to the nearest centimeter and the nearest millimeter.
1
2
3
4
5
6
7
8
9
10
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Which weighs more: an ounce of water or an ounce of lead?
Surprise! The water weighs more because it is measured by volume, while lead is measured by weight.
If you set a cup with a fluid ounce of water on a balance scale across from an ounce of lead in an
identical cup, the scale will tip toward the water.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-23: Measurement Scavenger Hunt
Name:
Find three objects or activities that you estimate are close to each measurement below. Write the names
of the objects or activities next to the appropriate measure.
1.
weighs 2 pounds
2.
is 16 inches in diameter
3.
holds 2 pints when full
4.
takes 25 seconds to complete
5.
is 8 feet long
6.
requires 2 cups to fill
7.
can be recited in 12 minutes
8.
is 6 centimeters wide
9.
weighs 7 ounces
10.
is half a yard long
11.
takes 5 minutes to walk to
12.
is one meter long
13.
holds 10 gallons when full
14.
can drive to in half an hour
15.
weighs 5 grams
16.
holds 5 liters when full
17.
weighs 10 kilograms
18.
takes 5 seconds to do
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-24: Measurement
Name:
“Let’s see how old you weigh. Hmm…five till.”
Attributes That Can Be Measured
Time/Age
Weight/Mass
Temperature
Length – height, distance, depth, perimeter, circumference, width
Density
Capacity/Volume
Speed/Velocity
Area/Surface Area
Value/Money
Energy/Light/Heat
Economy
Central Tendency
Sound
Force
Acceleration
Momentum
Inertia
Viscosity
IQ
Pressure
Buoyancy
Probability
Gravity
Radiation
Strength
Acidity
Memory
Power/Work
Magnetism
Humidity
Angles
Solubility
Ductility
Malleability
Did you know: No measurement can be 100% accurate. It is impossible.
Did you know: Absolute zero is -459.67 degrees Fahrenheit.
Numbers are ADJECTIVES. The label (or the unit of measure) is the NOUN.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-25: Unfamiliar Units of Measure
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
cord
hogshead
peck
carat
karat
watt
bolt
barrel
calorie
rod
furlong
hand
acre
board foot
ream
hertz
gross tonnage
Mach 1
light year
jigger
gill
Troy pound
knot
quire
gross
bit
nose
magnum
lux
volume of firewood
capacity of liquid
volume of dry items
weight of precious stones
amount of gold
electric work capability
length of cloth or paper
capacity, wet or dry
heat energy or fuel value-food
length – land
length – land
length – horse height
area – land
volume – lumber
amount of paper
frequency –light wave
volume – ship
speed – ships and planes
length – space
capacity – liquid
capacity – liquid
weight – precious metals
speed – ships and planes
amount of paper
amount of items
capacity – computer memory
length – horse racing
capacity – liquid
illumination
30
horsepower
work capability – engine
Name:
8 ft. by 4 ft. by 4 ft. stack
63 gallons
537.61 cu. in.
one-fifth of a gram
24k = 100%
based on current, resistance
varies
31.5 gallons
energy to raise temperature
16.5 ft.
200 yd.
about 4 in
43,560 sq. ft.
1 in. by 12 in. by 12 in.
about 500 sheets
waves per second
100 cu. ft.
speed of sound
about 6 trillion miles
2 mouthfuls
one-fourth pint
12 oz.
1.852 mph
25 sheets
12 dozen
8 bits
small distance
2 quarts
light 1m from candle source
energy for one horse to life 33,000 lbs. 1 ft. in
1 min.
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-26: Problem Solving
Name:
1. There are 12 coins that are numbered 1 through 12. Eleven weigh the same and one is either lighter
or heavier than the others. Using just three weighings with a balance scale, devise a scheme that will
find the counterfeit coin AND determine whether it is lighter or heavier.
2. A prison guard and his bloodhound are chasing an escaped prisoner. The prisoner has a 10 mile head
start but the guard is walking 1 mph faster than the prisoner. The bloodhound is trained to run to the
prisoner, run back to the guard, and then continue running back and forth between them. If the
bloodhound runs 10 mph, how far does the bloodhound run before the guard finally catches up to the
prisoner?
3. If one has already driven one mile at 30 mph, how fast must one drive the second mile so that the
average speed for the trip equals 60 mph? (Hint: The answer is not 90 mph.)
Suppose you want to invent a metric clock using the system below.
1 day = 10 metric hours, 1 metric hour = 10 metric minutes
1 metric minutes = 10 metric seconds, 1 metric second = 10 metric miniseconds
If you start a standard clock and a metric clock together (midnight or metric 0), what is the time in our
standard system when the metric clock registers 4 metric hours, 5 metric minutes, 6 metric seconds, and
7 metric miniseconds.
Suppose a metric calendar uses the system below.
1 day = 1 metric day, 1 metric week = 10 metric days
1 metric month = 10 metric weeks, 1 metric year = 10 metric months
If both calendars begin at 0 B.C., what was the metric calendar date on January 1, 2005?
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-27: Who Finished When?
Name:
(Taken from Algebraic Thinking: Grades 6-8, Lawrence & Hennessy)
Allie’s walking rate is 2.5 meters per second. Her younger brother, Matt, walks 1.5 meters per second.
Because Allie’s rate is faster the Matt’s, Matt gets to start the race at the 25-meter mark. If race is 100
meters long, what happens in the race?
There are numerous ways to solve this problem (rates, tables, graphs, proportions, pictures, and more).
Explain your strategy for solving this problem and give evidence to support your answer. Show your
solution step by step with an explanation of how you arrived at your answer. Do all this work on a
separate sheet of paper and then answer the following questions.
1.
Who wins the race?
2.
What was the winning person’s time?
3.
By how many seconds did the winning person win?
4.
By how many meters did the winning person win?
5.
If Allie won the race, at what point in time and at what distance
did she catch up to Matt?
6.
What if there was no head start? By how many meters and by
how seconds would Allie have won?
7.
Where would Matt need to start to make the race end in as close
to a tie as possible?
Time:
Distance:
Time:
Distance:
8. Create a line graph of the original race. Place meters on the y-axis and seconds on the x-axis. Draw
a line representing Allie’s race and another line representing Matt’s race. Use graph paper.
9. Create your own race amongst five runners. State each runner’s speed and the amount of head start
he or she should get if the race must end in a five-way tie. None of the five speeds may be a multiple
of any of the others.
Time to finish
Time to finish
Race
Person’s
Speed
Head Start
(with no head
(with head
distance:
Name
(m/sec)
given
start)
start)
Created by Lance Mangham, 6th grade math, Carroll ISD
Activity 8-28: Pickles Will Kill You!
Name:
Numbers are all around us. People can use numbers in misleading ways. All of the numbers below are
true, so does that mean pickles will kill you?
Every pickle you eat brings you nearer to death. Amazingly, the "thinking man" has failed to grasp the
terrifying significance of the term "in a pickle." Although leading horticulturists have long known that
Cucumis sativus possesses an indehiscent pepo, the pickle industry continues to expand.
Pickles are associated with all the major diseases of the body. Eating them breeds war and communism.
They can be related to most airline tragedies. Auto accidents are caused by pickles. There exists a
positive relationship between crime waves and consumption of this fruit of the cucurbit family.
For example ...
•
•
•
•
•
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Nearly all sick people have eaten pickles. The effects are obviously cumulative.
99.9% of all people who die from cancer have eaten pickles.
99.8% of all soldiers have eaten pickles.
96.8% of all communist sympathizers have eaten pickles.
99.7% of the people involved in air and auto accidents ate pickles within 14 days preceding the
accident.
93.1% of all juvenile delinquents come from homes where pickles are served frequently.
Evidence points to the long-term effects of pickle eating:
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•
Of all the people born in 1869 who later dined on pickles, there has been a 100% mortality.
All pickle eaters born between 1879 and 1899 have wrinkled skin, have lost most of their teeth,
have brittle bones and failing eyesight -- if the ills of eating pickles have not already caused their
death.
Even more convincing is the report of a noted team of medical specialists: rats force-fed with 20 pounds
of pickles per day for 30 days developed bulging abdomens. Their appetites for wholesome food were
destroyed.
In spite of all the evidence, pickle growers and packers continue to spread their evil. More than 120,000
acres of fertile U.S. soil are devoted to growing pickles.
Eat orchid petal soup. Practically no one has as many problems from eating orchid petal soup as they do
with eating pickles.
Created by Lance Mangham, 6th grade math, Carroll ISD