Download 6.9A Plan24.tree.diagrams - Texarkana Independent School

Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
4th Six Weeks
PLAN CODE:
Tipton
Course/subject:
Mathematics
Grade(s):
6
Time allotted
for instruction:
1 – 1 ½ hour
Title:
Working with Tree Diagrams
Lesson TOPIC:
Tree Diagrams
TAKS Objective:
Objective 5: The student will demonstrate an understanding of
probability and statistics.
FoCUS TEKS and
Student Expectation:
(9) Probability and statistics. The student uses experimental and
theoretical probability to make predictions. The student is expected to:
(A) construct sample spaces using lists, tree diagrams, and
combinations
(11) Underlying processes and mathematical tools. The student
applies Grade 6 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and
outside of school. The student is expected to:
(C) select or develop an appropriate problem-solving strategy from a
variety of different types, including drawing a picture, looking for a
pattern, systematic guessing and checking, acting it out, making a
table, working a simpler problem, or working backwards to solve a
problem
Supporting TEKS and
Student Expectations:
Concepts
Enduring Understandings/Generalizations/Principles
The student will understand that
A tree diagram shows all the possible outcomes of an event.
Tree Diagram
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
After the class is seated, give them the following scenario:
Anna went shopping for clothes to wear to the Texas High football games on Friday nights. She bought
five pieces of clothing. She bought an orange t-shirt, a black t-shirt, a white t-shirt, orange wind pants, and
black wind pants.
Next ask the class: How many different outfits do you predict Anna can come up with using these items?
B.
Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active
learning experience, art, music, modeling, discussion, reading, listening, viewing,
etc.)
The teacher will list the shirts in one column and the wind pants in another column. Tell the class that
they are going to learn to use tree diagrams to find all possible ways to choose from two sets. Write the
choices of wind pants on the board with options available (orange wind pants with an orange t-shirt,
orange wind pants with a black t-shirt, orange wind pants with a white t-shirt) Go through the same
process with the black wind pants. Tell the class that tree diagrams enable us to check our organized
lists. Go through the steps of how to set up a tree diagram with the class. Tell the class to write down one
of the category choices in one column, leaving enough space for the tree branches. Emphasize that an
example of a category in the introductory scenario would be “pants” or “shirts.” Let the class know that
each item in the category needs to be used. Demonstrate how to connect the orange wind pants with
each choice of shirt by drawing a straight line.
Category
Orange t-shirt
Orange wind pants
Black t-shirt
White t-shirt
Do the same illustration with the black wind pants. Show the class that there is another way to check for
possible choices by using multiplication. Show your students how to multiply your number of category
choices by each other. For example, there are two pant choices and three shirt choices in the
introductory scenario. If you multiply 2 x 3, you get a total of six possibilities for the outfit choices.
C.
Guided activity or strategy
Have each student get out a piece of scratch paper. Place the following scenario on the board/overhead:
Tyler is going to get a choice of what he wants for lunch. He may choose a
hotdog, hamburger, or pizza. He may also choose chips, fruit, or salad to go
with it. How many different choices does he have?
Have the class make a tree diagram showing the number of possible choices. Also have them write the
multiplication problem that would solve for the number of possible choices. Monitor as students are
working. After students have had time to complete the guided activity, go over the correct answers with
the class.
D.
Accommodations/modifications
Students requiring modifications may work with a peer to complete the guided activity.
E.
Enrichment
Students requiring enrichment may reteach the lesson in a small group setting for students requiring
assistance.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
II.
STUDENT PERFORMANCE
A.
Description
Students may complete the Working with Tree Diagrams Worksheet individually or with a partner.
B.
Accommodations/modifications
Students requiring modifications may work with a peer to complete the Working with Tree Diagrams
Worksheet.
C.
iii.
Enrichment
Assessment of Activities
A.
Description
Individual student grades may be taken on the Working with Tree Diagrams Worksheet.
B.
Rubrics/grading criteria
Grades may be taken based on the Working with Tree Diagrams Worksheet Answer Key and Grading
Rubric.


IV.
C.
Accommodations/modifications
D.
Enrichment
E.
Sample discussion questions
What real world situation would require you to know the number of possible choices?
Do you think tree diagrams help with organization? Why or why not?
TAKS Preparation
A.
Transition to TAKS context
The teacher will lead the students in a discussion of how tree diagram or possible choice problems may
look in test format by placing the TAKS questions below on the board/overhead.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
B.
Sample TAKS questions
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
V.
Key Vocabulary
Tree Diagram
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
VI.
Resources
A.
Textbook
Math Advantage ~ Middle School I
Chapter 14: Probability
 Account for All Possibilities, pp. 270-271
Student Handbook
 Lesson 14.1, pp. H62
B.


C.
VII.
Supplementary materials
Working with Tree Diagrams Worksheet
Working with Tree Diagrams Worksheet Answer Key and Grading Rubric
Technology
follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
This lesson may be followed by the following topics:

Conditional Probability

Probability of Simultaneous Events

Combinations
VIII.
Teacher Notes
In order to be successful with tree diagrams, students need to be somewhat systematic in drawing them.
Stress that tree diagrams need to be made as neatly and uniformly as possible. This will make drawing
conclusions from them easier and more accurate.
It is not uncommon for students to find a short cut in drawing the tree diagram. The example below is one
type of common short cut:
In a seemingly harmless attempt to save himself or herself some writing, the student has lopped off a
branch of the tree by writing tuna once and drawing a branch from bean soup and chicken noodle. When
he or she went to count the items at the bottom, he or she ends up with five instead of six. For a larger
tree diagram, an error like this in one of the initial branches would result in missing even more
combinations.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District