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Parent Guide 1
HISTOGRAMS AND BAR GRAPHS 1.1.
Histograms and bar graphs are visual ways to represent data. Both consist of vertical bars
(called bins ) with heights that represent the number of data points (called the frequency ) in each
bin. In a histogram each bar represents the number of data elements within a certain range of
values. Values at the left side of a bin’s range are included in that bin. Each range of values
should have the same width. In a bar graph each bar represents the number of data elements in
a certain category. All the bars are the same width and are separated from each other. For
additional information and examples, see the Math Notes box on page 8 in the text.
Example 1
The scores for a 25-point quiz are listed below arranged from
least to greatest.
Using intervals of five points, create a histogram for the class.
See histogram at right. Scores on the right end of the interval
are included in the next interval. The interval between 10 and
15 only includes the two scores of 12 and 13. The interval between
15 and 20 only includes the six scores of 15, 16, 16, 16, 18, and 19.
Example 2
Ms. Lim asked each of her students about their favorite kind of pet.
Based on their responses, she drew the bar graph at right. Use the
bar graph to answer each question.
a. What is the favorite pet?
b. How many students chose a bird as their favorite pet?
c. What was the least favorite pet?
d. If every student voted once, how many students are
in the class?
Answers: a. dog b. 6 c. fish d. 28
0
Score
Frequency
0
Favorite pet
Frequency
cat dog fish bird
2 Making Connections : Course 1
Problems
- Mr. Diaz surveyed his employees on the time it takes them
to get to work. The results are shown in the histogram at
right.
a. How many employees completed the survey?
b. How many employees get to work in less than 20 minutes?
c. How many employees get to work in less than 40 minutes?
d. How many employees take 60 minutes to get to work?
- The two sixth grade classes at Vista Middle School voted
for their favorite dessert. The results are shown in the bar
graph at right for the five favorite choices.
a. What was the favorite dessert and how many students
made that choice?
b. How many students selected cake as their favorite dessert?
c. How many students selected yogurt as their favorite?
d. How many more students selected ice cream than pudding?
- Mr. Fernandez asked 30 people at work how many pets they owned. The results are shown
below. Make a histogram to display this data. Use intervals of one pet.
0 pets 5 people
1 pet 8 people
2 pets 10 people
3 pets 3 people
4 pets 2 people
5 pets 1 person
9 pets 1 person
- During the fist week of school Ms. Chan asked her students to name the county where they
were born. There were so many different countries she grouped them by continent:
North America: 14 students, South America: 2 students, Europe: 3 students,
Asia: 10 students, Africa: 1 student, Australia: 0 students.
Make a bar graph to display this information.
0
Minutes to work
Frequency
0
Favorite dessert
Frequency
yogurt puddin
g
cake fruit ice
cream
4 Making Connections : Course 1
EXTENDING PATTERNS 1.1.
Students are asked to use their powers of observation and pattern recognition skills to extend
patterns and predict the number of dots that will be in a figure that is too large to draw. Later in
the course, variables will be used to describe the patterns.
Example
Examine the dot pattern at right. Assuming the pattern continues:
a. Draw figure 4.
b. How many dots will be in Figure 10?
Solution:
The horizontal dots are one
more than the figure number
and the vertical dots are even
numbers (or, twice the figure
number).
Figure 1 has 3 dots, Figure 2 has 6 dots, and
Figure 3 has 9 dots. The number of dots is the
figure number multiplied by three.
Figure 10 has 30 dots.
Problems
For each dot pattern, draw the next figure and determine the number of dots in Figure 10.
Figure 1 Figure 2 Figure 3
Figure 1 Figure 2 Figure 3 Figure 1 Figure 2 Figure 3 Figure 4
Figure 1 Figure 2 Figure 3 Figure 1 Figure 2 Figure 3
Figure 1 Figure 2 Figure 3 Figure 1 Figure 2 Figure 3
Figure 4
Parent Guide 5
X 5 {
} x 5
Answers
- 50 dots 2. 31 dots 3. 110 dots
- 22 dots 5. 40 dots 6. 142 dots
PROPORTIONAL RELATIONSHIPS 1.1.
Students solve proportional reasoning (ratio) problems in a variety of ways. They may find the
number or cost for one unit and they multiply by the number of units. They may also organize
work in a table. Later in the course students will use ratio equations or proportions to solve this
kind of problem.
Example 1
If three boxes of cereal weigh 36 ounces, how much will 10 boxes weigh?
36 ÷ 3 = 12 ounces per box
12! 10 = 120 ounces
Example 2
If 10 pencils weigh 34 grams, how much will 50 pencils weigh?
pencils ounces
10 34
50?
34! 5 = 170 ounces
Figure 4 Figure 5 Figure 4
Figure 4 Figure 5
Figure 4
Parent Guide 7
Pile #
9
15
15
15
15
15
15
Pile #
6 6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
REPRESENTING QUANTITIES 1.2.1 – 1.2.
When counting large numbers of one item or comparing two quantities of the same item, it is
helpful to have the items arranged in a way that is easy to count. In comparing two quantities,
they may be described as equal ( = ), or one is greater than ( > ), or less than ( < ) the other.
Example 1
Write an expression that represents the total
number of items and give the total.
Example 2
Write expressions to present the total number
of items in each pile and then compare the
totals using =, <, or >.
Problems
Write an expression that represents the total number of items and give the total.
20 20 20
8 Making Connections : Course 1
Write expressions to present the total number of items in each pile and then compare the totals
using =, <, or >.
Answers
Pile #
6
12
12
12
12
12
12
Pile #
8
8
8
8
8
8
8
8
8
8
Pile #
9
15
15
15
15
15
15
Pile #
6 6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
10 Making Connections : Course 1
STEM-AND-LEAF PLOTS 1.3.
A s tem-and-leaf plot is a way to display data that shows each individual value from a set of
numbers and how they are distributed. The vertical “stem” part of the graph represents all of
the digits in a number except the last one and the horizontal “leaves” represent the last digit of
the number. For an additional example, see the Math Notes box on page 48 in the text.
Example 1 Example 2
Make a stem-and-leaf plot of this set of data:
34, 31, 37, 44, 38, 29, 34, 42, 43, 34, 52, and 41.
Solution:
Make a stem-and-leaf plot of this set of
data: 192, 182, 180, 192, 178, 175, 195,
177, and 177.
Solution:
Problems
Make a stem-and-leaf plot of each set of data.
- 29, 28, 34, 30, 33, 26, 18, and 34. 2. 2.5, 3.4, 2.7, 2.5, 1.9, 3.1, 4.2, and 3.0.
89, 81, and 123.
113, 101, 108, 109, 105, 103, and 91.
- 45, 47, 52, 85, 46, 32, 83, 80, and 75. 6. 475, 462, 456, 480, 472, 455, 454, and
73, 61, 67, and 68.
74, 85, 91, 88, and 97.
Parent Guide 11
Answers
Parent Guide 13
The mode is the value in a data set that occurs most often. Data sets may have more than one
mode or no mode.
Example 3
Find the mode of this set of data: 34, 31, 37,
44, 34, 42, 34, 43, and 41.
- The mode of this data set is 34 since there
are three 34’s and only one of each of the
other numbers.
Example 4
Find the mode of this set of data: 92, 82, 80,
92, 78, 75, 95, 77, and 77.
- The modes of this set of data are 77 and
92 since there are two of each of these
numbers and only one of each of the other
numbers. This data set is said to be
bimodal since it has two modes.
Problems
Find the mode of each set of data.
- 29, 28, 34, 30, 33, 26, and 34. 6. 25, 34, 35, 27, 25, 31, and 30.
89, 81, and 123.
113, 101, 108, 109, 105, 103, and 91.
The median is the middle number in a set of data arranged in numerical order. If there are an
even number of values, the median is the mean (average) of the two middle numbers.
Example 5
Find the median of this set of data: 34, 31, 37,
44, 38, 34, 43, and 41.
- Arrange the data in order: 31, 34, 34, 34,
37, 38, 41, 43, and 44.
- Find the middle value(s): 37 and 38.
- Since there are two middle values, find
their mean: 37 + 38 = 75, 75 ÷ 2 = 37.5.
Therefore, the median of this data set is
Example 6
Find the median of this set of data: 92, 82, 80,
92, 78, 75, 95, 77, and 77.
- Arrange the data in order: 75, 77, 77, 78,
80, 82, 92, 92, and 95.
- Find the middle value(s): 80. Therefore,
the median of this data set is 80.
14 Making Connections : Course 1
Problems
Find median of each set of data.
- 29, 28, 34, 30, 33, 26, and 34. 10. 25, 34, 27, 25, 31, and 30.
92, 89, 81, and 123.
113, 101, 108, 109, 105, 103, and 91.
The range of a set of data is the difference between the highest value and the lowest value.
Example 7
Find the range of this set of data: 114, 109,
131, 96, 140, and 128.
- The highest value is 140.
- The lowest value is 96.
- The range of this set of data is 44.
Example 8
Find the range of this set of data: 37, 44, 36,
29, 78, 15, 57, 54, 63, 27, and 48.
- The highest value is 78.
- The lowest value is 27.
- The range of this set of data is 51.
Problems
Find the range of each set of data in problems 9 through 12.
Outliers are numbers in a data set that are either much higher or much lower that the other
numbers in the set.
Example 9
Find the outlier of this set of data: 88, 90 96,
93, 87, 12, 85, and 94.
Example 10
Find the outlier of this set of data: 67, 54, 49,
76, 64, 59, 60, 72, 123, 44, and 66.
