Data
Analysis and Probability
Overview
of Lesson
Using
data analysis and probability, students track food inventory and
look at options available for creating special offers.
Students
will work in groups and use a tree diagram to determine how
many combinations can be created from a given set of selections.
Objectives
- Students
will use a tree diagram to provide possible combinations.
Ohio Academic
Content Standards
Mathematics
Data Analysis and Probability
Benchmark
H:
Find all possible outcomes of simple experiments or problem-solving
situations, using methods such as lists, arrays and tree diagrams.
Indicators
Data Collection
4. Determine appropriate data to be collected to answer questions
posed by students or teacher, collect and display data and clearly
communicate findings.
5. Modify
initial conclusions, propose and justify new interpretations and
predictions as additional data are collected.
Probability
7. List and explain all possible outcomes in a given situation.
Materials
Procedure
Scenario:
The manager must determine the appropriate inventory
of staples to maintain for a pizzeria. Most restaurants and cafeterias
use a spreadsheet program that enables them to track food movement.
This helps them recognize trends such as which items are most
popular and what specials they might offer.
-
Survey
students to decide which pizza options for toppings and crusts
should be used to create the classroom tree diagram. Make
a list of the suggestions and then take a vote of the top
four topping choices and top three types of crust. This part
of the exercise helps students get enthused about the activity.
-
Ask the
students to determine how many combinations can be created
from the selections. Allow them to offer suggestions on how
to proceed.
-
Divide
the students into small groups to solve the problem. After
15 to 20 minutes, check on their progress. Facilitate a discussion
on processes employed to solve the problem.
-
Suggest
that a tree diagram could be used to solve the problem. Demonstrate
how to make a tree diagram.
-
Ask students
to share observations about this procedure. Ask if there is
a way students could anticipate how many choices there would
be. How many choices would there be if two more toppings were
available?
Tree Diagram
Example
4 toppings
— pepperoni, mushroom, sausage, hot peppers
3 crusts — thin, medium, deep dish
| Sample
Space (the number of possibilities) |
| 1.
Pepperoni — thin |
7.
Sausage — thin |
| 2.
Pepperoni — medium |
8.
Sausage — medium |
| 3.
Pepperoni — deep dish |
9.
Sausage — deep dish |
| 4.
Mushroom — thin |
10.
Hot peppers — thin |
| 5.
Mushroom — medium |
11.
Hot peppers — medium |
| 6.
Mushroom — deep dish |
12.
Hot peppers — deep dish |
4 x 3 = 12 possible pizzas
Evaluation
Working
in small groups, the students can use the tree diagram to solve
a new problem. This time, they are working with three topping
choices and three sizes of pizza. The teacher might consider whether
or not the students could solve the problem without a blank tree.
The fourth grade teacher could determine whether or not the students
need a partial tree to complete the task. Comprehension by 75
to 80 percent of the students indicates that the lesson was successful.
Answer
(to evaluation question)
Sizes
— small, medium, large
Toppings — pepperoni, sausage, mushroom
| 1.
Small — pepperoni |
6.
Large — mushroom |
| 2.
Medium — pepperoni |
7.
Small — sausage |
| 3.
Large — pepperoni |
8.
Medium — sausage |
| 4.
Small — mushroom |
9.
Large — sausage |
| 5.
Medium — mushroom |
|
3 x 3 = 9 possible pizzas
|
