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You are in : Home Room : Units : PD-ROM 1.1
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MODULE 1 INTRODUCT...
Unit 1.1 Introduct...
Resource Index
Math Content Strand
Instructional Stra...
Special Education ...
Lesson Plan Project
Unit 1.1 Reflection
Unit 1.1 Conclusion

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Overview

Welcome to the Unit 1.1 Tree Trunk Problem!

 This unit focuses on the CAHSEE problem:

The diameter of a tree trunk varies directly with the age of the tree. A 45-year-old tree has a trunk diameter of 18 inches. What is the age of a tree that has a trunk diameter of 20 inches?

A.  47 years
B.  50 years
C.  63 years
D.  90 years

This question has challenged up to 65% of students who have taken the CAHSEE exam. As you progress through this unit, you will deepen your content knowledge on approaches to proportional reasoning and develop instructional strategies to assist students in mastering these kinds of problems.

The major California Mathematics Content standards addressed in this question include:

Number Sense (6th) 1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.

Algebra and Functions (6th) 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.

Algebra and Functions (7th) 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs.

Prerequisites

Successful completion of PD-ROMi is a prerequisite to this unit.

Objectives

In Unit 1.1: The Tree Trunk Problem, you will

  • Deepen your understanding of mathematical concepts in Algebra, including:
    • Using unit rate, ratios, and proportions; and
    • Solving direct variation problems through unit rates and proportions.

  • Develop skills in new instructional strategies, including
    • The importance of the flow of the lesson;
    • Use of poetry and literature to support teaching and learning of mathematics; and
    • Teaching vocabulary.

  • Apply your new knowledge and skills in the Lesson Plan Project.

How to Take this Unit

What you will see:

  • This unit is organized around a highly-missed question from the California High School Exit Examination
  • The unit presents lessons taught by middle school teachers.
  • These teachers designed the lessons with input from Drs. Harris Shultz and Marty Bonsangue. 
  • You will work through three separate strands on math content and instructional strategies, including strategies for supporting students with special needs.

What you will do:

  • As you move through the unit, you will read text, view videoclips of classroom teaching, and respond to reflection and assessment questions.
  • You will submit your responses to the assessment questions as you move through the unit.
  • Once you submit a response, comments from Drs. Shultz, Bonsangue, and Costa will "pop-up" for your viewing.
    In addition, your Online Facilitator will be checking your responses for accuracy and completion.
  • At the end of each strand, you will be asked to post your reflection on the Discussion Board. You will also respond to a colleague's posting.
  • At the end of the unit, you will also be asked to reflect on the entire learning experience.
  • Finally, at the end of each unit, you also apply what you've learned to a lesson plan project.  

Unit Duration

Unit 1.1 The Tree Trunk Problem should take approximately 10-15 hours, depending on your technology skills and knowledge of instructional strategies.  You may complete this unit on your own time, but each strand is expected to be completed by a specific deadline. This will allow your Online Facilitator to provide collective support and will facilitate your collaboration with your colleagues. It will also insure that you complete the unit by the course endpoint.


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