Transcript Instructor Materials

GED® MATHEMATICS INSTITUTE
FOUNDATIONS OF
QUANTITATIVE
PROBLEM
SOLVING FOR ADULT
EDUCATORS
1
Quantitative
Reasoning To
Calculate Measures
of Central
Tendency
2
Lesson Goals:
• Calculate the mean, median, mode, and
range. (Q.7.a)
• Calculate a missing data value given
the average and all the missing data
values but one, as well as calculating
the average, given the frequency
counts of all the data values, and
calculating a weighted average. (Q.7.a)
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
What you will do in this lesson:
Think, Pair, Share
Think & work alone
Cooperative
Learning in
Small
Groups
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
4
Basic Measures of
Central Tendency
http://hippocampus.org/HippoCa
mpus/?user=leahfelcher&playlist=
Measures+of+Central+Tendency
5
Reviewing in Pairs…
McGraw Hill Common Core Achieve
Student Text
p. 260, Vocabulary Review # 1-5
p. 260, Skill Review # 1-4
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
6
Calculating Missing Data
A web site had 12,000 hits the first day and 16,000
hits the second day. How many hits must it have
on the third day to average 20,000 hits a day for
the three days?
12,000 + 16,000 + n = 20,000
3
(28,000 + n) = (20,000)3
28,000 + n = 60,000
n = 32,000
Therefore, the site would need to have 32,000 hits
the third day.
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
7
Multiple Choice Problem
Suppose you scored 91 on one quiz and
89 on a second quiz. How many points
out of 100 must you score on the third
quiz to average 96 for the three quizzes?
A. 90
B. 96
C.100
D. There is no way.
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
8
Multiple Choice Problem
91 + 89 + n = 96
3
180 + n = 288
n = 108
Thus, the correct answer is D because
the maximum number of points on the
quiz is 100 and you need 108 to achieve
the given average.
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
9
Calculating the Average
Using Frequency Counts
https://www.youtube.com/watch
?v=AUtuOQ205dA
10
Parking Spaces per House
Given the frequency table, find the mean number of
parking spaces to two decimal places.
Isabella went up and down Hampton Street to find out how
many parking spaces each house had. Here are her
results:
Parking Spaces
Frequency
1
15
2
27
3
8
4
5
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
11
Parking Spaces per House
Given the frequency table, find the mean number of
parking spaces to two decimal places.
Mean = 15×1 + 27×2 + 8×3 + 5×4
15 + 27 + 8 + 5
= 15 + 54 + 24 + 20
55
= 2.05…
The Mean is 2.05 (to 2 decimal places)
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
12
Questions to Ponder…
• How do you think calculating a “weighted
average” differs from calculating just a regular
average (mean)?
• When do you think you would find a weighted
average instead of a regular average?
• If you have 4 test scores and one of them counts
double, how would you find the average of the
scores? Is this a weighted average or a regular
average? Justify your answer.
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
13
Think about Math, problem 1
McGraw Hill Common Core Achieve, Student Text, p.259
A carwash station sold 80 regular carwashes
at $8 and 20 premium carwashes at $10.
What was the average price of a carwash
sold?
A.
B.
C.
D.
$8.00
$8.40
$9.00
$10.00
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
14
Think about Math, problem 1
McGraw Hill Common Core Achieve, Student Text, p.259
A carwash station sold 80 regular carwashes at $8 and
20 premium carwashes at $10. What was the average
price of a carwash sold?
Average = 80 ($8) + 20 ($10)
= $640 + $200 = $840 (Sum of all the carwashes sold)
$840 ÷ 100 = $8.40
(divide the sum by the total number of carwashes)
Thus, B is the answer.
INSTRUCTIONAL BEST PRACTICES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
15