# Title of Event: Intermediate Technology Refresh Training: Broward

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Trainer Notes for
5-9 FTCE Course

Title of Event: Math Content for 5-9 Math FTCE
Block: Session 1
Description: This course will focus on the math content from the Florida 5-9 middle grades mathematics competencies
Delivery Method: Classroom Instruction with online tutorials
Target Audience: Teachers
Session Duration: Session 1 of 10
Prerequisites: None
Specific Objectives:
Participants will be able solve real-world problems using appropriate problem-solving strategies.
Participants will be able to identify appropriate mathematical representations or models of real-world problems.
Participants will be able to identify and analyze mathematical errors.
Participants will be able to identify elements and subsets of the real number system.
Participants will be able to use estimation strategies.
Participants will be able to simplify & evaluate radical expressions and order of operations.
Participants will be able to factor and find GCF & LCM.

Standards:
4 Knowledge of mathematical connections
1. Identify prerequisite skills for a given topic.
2. Identify common misconceptions in mathematics (e.g., area and perimeter).
3. Identify the relationship between mathematical concepts (e.g., repeated addition and multiplication).
4. Identify mathematical errors, including computation, algebraic, data analysis, and geometric errors.
5. Analyze mathematical errors, including computation, algebraic, data analysis, and geometric errors.
6. Identify fundamental ideas that connect middle grades mathematics to advanced mathematics (e.g., trigonometry, number theory, pre-calculus, calculus).
5 Knowledge of number sense, concepts, and operations
1. Identify elements and subsets of the real number system.
2. Compare the relative size of real numbers expressed in a variety of forms, including fractions, decimals, percents, and scientific notation.
3. Identify estimation strategies.
4. Simplify expressions using the laws of exponents.
5. Identify equivalent forms of rational exponents and radicals.
7. Determine the prime factorization of composite numbers.
8. Identify the greatest common factor (GCF) and least common multiple (LCM) of sets of numbers.
9. Evaluate numerical expressions using order of operations.
10. Solve real-world problems using proportions.
11. Solve real-world problems that involve real numbers.

Time           Content       Process/                                                                            Participant                  Materials/
Frame                        Product                                                                             Evaluation                   Resources
Duration       Course        Script for each Content Area                                                        Assessment of Specific       Training Materials for Activities
Of Activity)   Outline                                                                                           Objectives
Introductio   The instructor provide participants:                                                About the course
30 minutes     n to                1. Information about instructor                                                                            5-9 syllabus.pdf
Course                         a. background                                                                                   5-9 objectives.pdf
b. how to be reached
2. Information about the course & objectives hand-out objectives.pdf)
a. Course objectives
b. Participant obligations – reinforce the need to complete all
assignments PRIOR to the next class. Success is
dependent on their active participation.
3. Syllabus hand-out and discuss syllabus (syllabus.pdf)
a. Assignment that needs to be completed before each class
4. Course Online Support: http://www.interactmath.com/
a. Opening page – hit ENTER
Course (hit SUBMIT)                                                                         Comp 4/5 pretest
c. Select Chapter 1: Real Numbers and Algebraic
Expressions. Five sections will appear.
d. Select Section 1:Real Numbers. 29 exercises will
appear.
e. Select Section 3: Exponents, Square Roots, and the
Order of Operations. 78 exercises will appear.
5. Pretest for Competency 4 & 5

30 minutes     Competen       The instructor will start with Competency 4 – Knowledge of Mathematics             Participants will
cy 4           Connections                                                                        understand and solve         1_Competency 4/5 notes.docx
a. Talk about Misconceptions & Identifying Math Errors on Notes Sheet          problems dealing with        Slides 1 to 17 from Comp_4.ppt
for Competency 4                                                         competency 4 topics:
b. Using LCD w/PowerPoint or Flip Chart work Comp_4.ppt                         Math misconceptions        comp 4-errors and
c. Practice problems (odds) from worksheet                                       strategies                 misconceptions.pdf
comp 4-errors and misconceptions.pdf                                 Identifying math
errors
Trainer Notes for
5-9 FTCE Course

40 minutes   Competen     3.   The instructor will continue with Competency 5 – Knowledge of number         Participants will         Slides 1 to 8 from Comp_5.ppt
cy 5              sense, concepts, and operations                                              understand and solve
4.   The instructor will discuss the number sense                                 problems dealing with
5.   The instructor will continue with Competency 4/5 Notes, a study sheet for    competency 5 topics:
concepts from this competency.                                                Real numbers
6.   Instructor will use Competency 5 PowerPoint/FlipChart to work on topics       Converting
from this competency and solve problems with participants                      between/among
7.   The instructor will discuss the following concepts:                            fractions, decimals &
a. Number Systems (Venn Diagram of real numbers system)                        percents
b. Decimal, fraction, percent equivalencies
8.   Practice problems(evens) from
a. Comp_5_Fractions_Decimals_Percents.pdf
b. Comp_5_Fractions_Decimals.pdf

10 minutes                BREAK
65 minutes   Competen     7. The instructor will continue with Competency 4/5 Notes, a study sheet for      Participants will         Slides 9 to 24 from Comp_5.ppt
cy 5 con’t        concepts from this competency.                                               understand and solve
8. Instructor will use Competency 5 PowerPoint/FlipChart to work on topics        problems dealing with     Worksheets:
from this competency and solve problems with participants                    competency 5 topics:       Comp_5_Factors_Factorization.p
9. The instructor will discuss the following concepts:                             Scientific notation       df
c. Scientific notation                                                 Laws of exponents        Comp_5_GCF.pdf
d. Laws of exponent                                                    Working with radicals    Comp_5_LCM.pdf
e. Radical expressions, radicals and exponents                         Factoring, GCF &         Comp_5_Scientific_Notation.pdf
f.    Factorization, GCF, LCM                                           LCM                      Comp_5_Exponent_mult.pdf
g. Order of Operations                                                 Order of operations      Comp_5_Exponents_Div.pdf
10.Instructor will show participants the following problems on the board/screen                              Comp_5_Square_Roots.pdf
and ask for volunteers to work the problem: Section 1:Real Numbers.                                      Comp_5_Powers_prod.pdf
Problems 2, 6, 10, 14, 18, 22 Section 3: Exponents, Square Roots, and                                    Comp_5_Order_of_Operations.p
the Order of Operations Problems 3, 9, 17, 25, 31, 37, 45, 55, 61, 67, 73                                 df
11.Practice problems(EOE) from                                                                               Comp_5_Percent_Word_Proble
a. Comp_5_Factors_Factorization.pdf                                                                      ms.pdf
b. Comp_5_GCF.pdf                                                                                       Comp_5_Proportion_Word_Probl
c. Comp_5_LCM.pdf                                                                                        ems.pdf
d. Comp_5_Scientific_Notation.pdf                                                                       Comp_5_Markup_Discount_Tax.
e. Comp_5_Exponent_mult.pdf                                                                              pdf
f.   Comp_5_Exponents_Div.pdf
g. Comp_5_Square_Roots.pdf
h. Comp_5_Powers_prod.pdf
i.   Comp_5_Order_of_Operations.pdf
j.   Comp_5_Percent_Word_Problems.pdf
k. Comp_5_Proportion_Word_Problems.pdf
l.   Comp_5_Markup_Discount_Tax.pdf

15           Session 1    1.   Instructor will again review how to access Interact Math.                    Participants will be
wrap-up/     2.   Instructor will give participants a homework assignment (session 1           fluent with topics in     Session 1 assignment
Homework          assignment.doc) from http://www.interactmath.com/                            competency 4 & 5

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