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
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.
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.
6. Simplify radical expressions.
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
b. Use pull down menu to find ADP: Algebra 1 Online
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
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
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
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
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