BIG IDEA: PROBLEM -SOLVING USING THE 3 CENTRAL TENDENCIES:
Mean Median ,Mode and Range.
LESSON PLAN
Tuesday November 24, 2015
Real Life Problem-Solving Using
Median and Mode
Big Idea: Real -Life Problems using Mean,
Median and Mode
Arithmetic Mean,
Student Learning Goal(s):
1. To use arithmetic mean, median and mode to
compare sets of data.
2. To further develop students' learning skills
(e.g. collaboration) while solving real -life
problems involving the 3 central tendencies
(arithmetic mean, median and mode).
3. To use mathematical language while solving and
communicating word problem. (s).
Materials:
Chart paper
Markers
Word problems
On-line:
Interactive on-line quizzes Nelson Math
www.socrative.org
Essential Questions:
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What are the measures of central tendency?
What are their definitions?
How do I calculate them (steps involved)?
How do I relate them to real life?
How can they be used in or with real life
numbers.
Success Criteria: B.U.C.K. Or I.D.E.A.S
(Box, Underline , Circle , Knock out information)
Use BUMP IT strategy
1. Getting Started (approx. 10-15 minutes):
Instructions:Teacher will review through a power-point
the three central tendencies including Arithmetic
Mean vs. Geometric Mean, Median and Mode.
Provide two ways of calculating each central
tendency.
Before or Activation task:
Arithmetic Mean =
Sum of all data values
Number of data values
By the end of the Getting Started, students will
be able to:
-Identify the 3 Measures of Central Tendencies
(Arithmetic Mean, Median and Mode)
-Use 3 central tendencies (Arithmetic Mean, Median
and Mode) to compare sets of data.
- Apply the four step problem-solving model;
-Use multiple strategies
-Apply the 4 step problem-solving model (e.g.
BUCK);
-Use real life problems.
- To use self-checking strategies like : Guess and
check.
a+ b+ c
3
Example:
5 , 14 24, 10 15
70/5 = 14
1
Before or Activation Task (Powerpoint):
Problem #1:
A student achieved the following percentage
grades on his tests: 87, 95, 76, and 88. He would like
an 85 or better overall. What is the minimum grade he
must get on the test in order to achieve the average?
The unknown is x
(87+95+76+88+ x) divided by 5 = 85
Using algebraic statements and simplifying:
Solve by inspection
87 +95+76+88 + x=425
346 +x =425
X= 98
For example:
Geometric Mean
The geometric mean is calculated by taking the
nth root of the product of a set of data.
Find the Geometric Mean:
6
54
1. Recall
2. Multiply
6 x 54 =324
3. Square Root
is 18 (a perfect square)
Take one number and squaring it.
Median:
The median refers to the mid-point in a series of
numbers.
To find the median, arrange the numbers in order from
smallest to largest. If there is an odd number of
values, the middle value is the median. If there is an
even number of values the average of the two middle
values is the median.
Example #1- Find the median of 19, 29, 36, 15, and
20
In order: 15, 19 20 29 36 sincere there are 5 values
(odd number) , 20 is the median middle number.
Example #2- Find the median of 67, 28, 92, 37, 81, 75
In order: 28 , 378, 67,75, 81, 92 sincere there are 6
values (even number) we must average those two
middle numbers to get the median value
Average: 67 + 75
= 142/ 2= 71
Finding the Mode
The mode of a set of values is the value that occurs
most often. A set of values may have more than one
mode or no mode.
2
Example #115, 21, 26, 25, 21 , 23, 28, 21
The mode is 21 since it occurs three times and the
other values occur only once.
2. Working On It (approx. 10-20 minutes)
Lesson Problems During:
1. Each of the 6 tables will be given a word problem
involving the 3 central tendencies. Students will be
able to read and interpret data while solving for
arithmetic mean, median and mode.
2.See attached Appendix of collaborative group
work.
See 6 different real life word problems.
Sam receives the following scores on his English
tests: 63, 84, 96. What average score does he need
on the last two tests in order to maintain an 85
average?
Thinking Strategies or Tools:
-BUCK
-Apply the 3 Central Tendencies while solving Word
Problems.
-Guess and check
-Use BUMP IT strategy.
Modifications:
Extra time
Math peer group buddy
Repeat and review written instructions.
Model and provide student exemplars
The average of the last two scores is x.
63 + 84 + 96 + x + x =
63
+ 84 +96 + x + x
(5) 63 + 84 + 96 + 2x = 85 x 5
5
243 + 2x = 425
243 + 2x -243 = 425-243
2x = 182
2
2
Assessment and Evaluation:
Tasks:
Students will present their presentations
Listening (Powerpoint)
Interactive (Group work)
Tic-Tac Toe Activity consolidation
KICA (Knowledge, Inquiry, Communication,
Application).
-Thermometer Student Rubric
3. Consolidation: Summary and Closure:
Students will present their word problems applying the
3 Central Tendencies. Students will evaluate each
other's work by providing immediate and descriptive
feedback and next steps.
At Home:
-on-line videos
-www.socrative.org
Take up each of the word problems on-line.
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