Teaching the
Next Generation SSS
(2007)

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 engage in activities and in depth discussions that promote higher level thinking skills.
connect standards in relation to solving equations with examples.
analyze items that prior grade levels have learned.

 Problem Solving
– Developing perseverance and critical thinking
– Allow students think time to reach a solution
 Reasoning and Proof
– Mathematical conjectures
– Examples and counter examples
 Communication
– Read, write, listen, think, and discuss
– Increase the use of appropriate math vocabulary

 Connections
– Integers, expressions, and equations
– Other content areas, science
– Real-world contexts
 Representation
– Useful tools for building understanding
– Concrete - Representational - Abstract
– Tables, describe in words, draw a picture, write and solve equations


Rigor is quality instruction that focuses on the depth of the learning not the breadth. It’s not more work; it’s meaningful, respectful work that requires the student to think deeply and critically to accomplish the assigned tasked.
Eric Bergholm, Hillsborough County Public Schools, Florida

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Collaborate vertical and horizontal teaching
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Use cooperative learning (Kagan) strategies to introduce or remediate equations
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Represent equations using models, vocabulary, pictures, and real world situations

Grade Level Old GLE’s
K
1 st
2 nd
3 rd
4 th
5 th
6 th
7 th
8 th
67
78
84
88
89
77
78
89
93
New
Benchmarks
11
14
21
17
21
23
19
22
19

MA.
912.
A.
Subject Grade
Level
3.
1
Body of
Knowledge
Big Idea/
Supporting
Idea
Benchmark
MA.912.A.3.1

Grade Level/Course Benchmark
4
Describe mathematical relationships using expressions, equations, and visual representations
6
7
Write, solve and graph one- and two-step linear equations and inequalities.
Formulate and use different strategies to solve one- and two-step linear equations including equations with rational coefficients.
8 Solve literal equations for a specific variable.
Algebra 1
Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.
Geometry Solve real world problems using right triangles.
Algebra 2
Pre-Calculus
Solve logarithmic and exponential equations
Solve trigonometric equations and real-world problems involving applications of trigonometric equations using technology when appropriate.

NGSSS: Equations(6 th )
MA.6.A.3.2 Write, solve, and graph one and two step linear equations and inequalities

Example : The height of a tree was 7 inches in the year 2000. Each year the same tree grew an additional 10 inches. Write an equation to show the height the year 2000. h of the tree in y years. Let y be the number of years after
12

th
y = 10x + 7
10 is the slope (amount that the tree grows each year)
7 is the y intercept
(the starting year 2000)

NGSSS: Equations(7 th )
MA.7.A.3.3 - Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational expressions.

Example : Which steps would solve ⅔ x – 4 = 10
A. Add 4 to both sides of the equation, then multiply both sides by
2/3.
B. Add 4 to both sides of the equation, then multiply both sides by 3/2.
C. Subtract 4 from both sides of the equation, then multiply both sides by 2/3.
D. Subtract 4 from both sides of the equation, then multiply both sides by 3/2.
14

NGSSS: Equations(8 th )
MA.8.A.4.1 - Solve literal equations for a specified variable.

Example : The following equation tells you how much simple interest you will earn if you invest an amount of money (P) at a specified rate (r), for a given amount of time (t): I = Prt. Solve for P.
15

th
I = Prt. Solve for P rt
I = Prt rt
P = I_ rt

A
NGSSS: Equations - Algebra
MA.912.A.3.1 Solve linear equations with one variable that include simplifying algebraic expressions.
B
3(2x+5) = 10x-3+2x x + 5(x-1) = 7
C D
10x + 12=2(5x + 6) 5(x + 4)= x +2x +6
17

A. 3(2x + 5) = 10x – 3 + 2x
6x + 15 = 12 x – 3
Distributive & combine like terms
-6x -6x
15 = 6x – 3
+3 +3
18 = 6x
6 6 x = 3

B. x + 5(x – 1) = 7 Distributive property x + 5x – 5 = 7 Combine like terms
6x – 5 = 7
+5 +5
6x = 12
6 6 x = 2

C. 10x + 12 = 2(5x + 6)
10x + 12 = 10x + 12
All real numbers or infinite solutions

D. 5(x + 4) = x + 2x + 6
5x + 20 = 3x + 6
Distributive and combine like terms
-3x -3x
2x + 20 = 6
-20 -20
2x = - 14
2 2 x = -7

NGSSS: Equations - Geometry
MA.912.G.5.4 Solve real-world problems involving right triangles

Example :
The distance of the base of a ladder from the wall it leans against should be at least 1/3 of the ladder's total length. Suppose a 12-ft ladder is placed according to these guidelines. Give the minimum distance of the base of the ladder from the wall. How far up the wall will the ladder reach?
22

One third of the ladder is the base
1/3(ladder) = base
1/3(12) = 4 = base
The base is at least 4 feet.

NGSSS: Equations – Algebra 2
MA.912.A.6.5 – Solve equations that contain radical expressions.

Example :
Solve the following equation for x:
24

Solve
+5 +5
3x 2 + 10x = 5 square both sides
3x 2 + 10x = 25
-25 -25
3x 2 + 10x – 25 = 0 Factor
(3x – 5)(x +5) = 0 Solve for x.
3x – 5 = 0 x + 5 = 0 x = 5/3 x = - 5

NGSSS: Equations – Pre-Calculus
MA.912.T.3.4 – Solve trigonometric equations and real-world problem s involving applications of trigonometric equations using technology when appropriate.

Example :
Solve 2 sin(x) +1=0 on the interval [0, 2 p
)
26

2sin(x) + 1 = 0
-1 -1
2sin(x) = -1
2 2
Sin(x) = -1/2
X = 7 π/6, 11π/6

NGSSS: Equations – Calculus
MA.912.C.3.8 – Solve optimization problems.

Example :
You want to enclose a rectangular field with an area of 5,000 m^2. Find the shortest length of fencing you can use.

The minimum perimeter (length of the fencing) would be if the rectangular field is a square.
Therefore:
If x is the side of the square, then x 2 = 5000 (area) x = 5000 m
The shortest length of fencing is the perimeter of the square, 4 times x or approximately 282.843 m

Prentice Hall Website www.pearsonsuccessnet.com
Access Codes for Florida courses 2011
Algebra 1
Geometry
Algebra 2
PHMADP11FLENA1B
PHMADP11FLENGB
PHMADP11FLENA2B
* Then create your own username and password.
Holt/Larson Website http://my.hrw.com
User Name: JRUTTER26
Password: z7d8w
Glencoe Website www.connectED.mcgraw-hill.com
Username: florida02
Password: math2011

MA.912.A.3.12 Graph linear equations/inequalities with and without graphing technology.
MA.912.A.4.9 Find approximate solutions for polynomial equations.
MA.912.A.7.1
Graph quadratic equations with and without graphing technology.
MA.912.A.7.10 Find approximate solutions of quadratic equations
MA.912.A.9.2 Graph conic sections with and without using graphing technology.


Investigating application of equations

Through TI-Nspire





Select Holt McDougal Florida Larson textbook
Select Videos and Activities tab
Select TI-Nspire activities
Select TI-Nspire Larson Algebra 1 activities






Select Holt McDougal Florida edition
Algebra 1 (2011)
– Scroll down to locate
Select All TI products
Choose Lesson HM.1.1.4
– Materials correlated to this standard
Select Applications of equations
Print teacher and student worksheets
– Either pdf or doc




Solving an equation with a real-world application
Creating an equation to represent a real-world problem
Recognize values of the variable that would not make sense for a real-world problem


Equation

Variable



Need TI-Nspire Teacher Edition installed on your computer
– See your tech specialist
Applications_of_equations.tns




Introduce student worksheet
Introduce parallel teacher notes
Work through student worksheet using
TI-Nspire


Investigating application of equations

Activity/game






Mathematics FL Algebra 2
Select Teacher resources
Select Chapter 1
Select Activities, games, and puzzles
Select Lesson 1-4 activities, games, and puzzles





To identify properties of equality
To solve single- and multi-step equations
To identify sometimes, always, or never statements
To solve literal equations






Identity
Solution of an equation
Inverse operations
Equation
Literal equation

Next Generation Sunshine State
Standards www.floridastandards.org
Academic
Plan http://acadplan.leeschools.net/forms/index.htm
Webb’s Depth of
Knowledge http://deannasheets.com/questioning/Blooms_DOK.p
df

www.FloridaStandards.org
Select Basic and Adult Education,
Secondary Grades 9 -12, Mathematics, select your general subject, select your specific class.

Algebra 1 Academic Plan
Quarter 1
 Chapter 1 Sec. 1-1 to 1-7
 Chapter 2 Sec. 2-1 to 2-8
 Chapter 3 Sec. 3-1 to 3-8
Quarter 1 District Common Exam

Algebra 1 Academic Plan
Quarter 2
 Chapter 4 Sec. 4-1 to 4-7
 Chapter 5 Sec. 5-1 to 5-7 Skip 5-2
 Chapter 6 Sec. 6-1 to 6-6
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Algebra 1 Academic Plan
Quarter 3
 Chapter 7 Sec. 7-1 to 7-5
 Chapter 8 Sec. 8-1 to 8-8
Quarter 3 District Common Exam
From Q1 to Q3 but the emphasis is on Q3.

Algebra 1 Academic Plan
Quarter 4
 Chapter 9 Sec. 9-1 to 9-6 Skip 9-5
 Chapter 10 Sec. 10-1 to 10-3
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Algebra 1H Academic Plan
Quarter 1
 Chapter 1 Sec. 1-1 to 1-6 Skip 1-5
 Chapter 2 Sec. 2-1 to 2-7
 Chapter 3 Sec. 3-1 to 3-8
 Chapter 4 Sec. 4-1 to 4-5
Quarter 1 District Common Exam

Algebra 1H Academic Plan
Quarter 2
 Chapter 4 Sec. 4-1 to 4-7
 Chapter 5 Sec. 5-1 to 5-7
 Chapter 6 Sec. 6-1 to 6-7 Skip 6-5 to 6-6
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Algebra 1H Academic Plan
Quarter 3
 Chapter 7 Sec. 7-1 to 7-6
 Chapter 8 Sec. 8-1 to 8-4
 Chapter 9 Sec. 9-1 to 9-8
 Chapter 10 Sec. 10-1 to 10-8 Skip 10-5
Quarter 3 District Common Exam
From Q1 to Q3 but the emphasis is on Q3.

Algebra 1H Academic Plan
Quarter 4
 Chapter 11 Sec. 11-1 to 11-2
 Chapter 12 Sec. 12-1 to 12-4
 Chapter 6 Sec. 6-5 to 6-6
 Chapter 8 Sec. 8-5 to 8-6
 Chapter 11 Sec. 11-3 to 11-5
 Chapter 12 Sec. 12-5 to 12-7
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Geometry Academic Plan
Quarter 1
 Chapter 1 Sec. 1-1 to 1-8 Skip 1-6
 Chapter 2 Sec. 2-1 to 2-6 Skip 2-4
 Chapter 3 Sec. 3-1 to 3-8 Skip 3-6
Quarter 1 District Common Exam

Geometry Academic Plan
Quarter 2
 Chapter 4 Sec. 4-1 to 4-7
 Chapter 5 Sec. 5-1 to 5-7
 Chapter 6 Sec. 6-1 to 6-7
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Geometry Academic Plan
Quarter 3
 Chapter 7 Sec. 7-1 to 7-5
 Chapter 8 Sec. 8-1 to 8-4
 Chapter 10 Sec. 10-1 to 10-8 Skip 10-5
 Chapter 12 Sec. 12-3
 Chapter 11 Sec. 11-1 to 11-3
Quarter 3 District Common Exam
From Q1 to Q3 but the emphasis is on Q3.

Geometry Academic Plan
Quarter 4
 Chapter 11 Sec. 11-4 to 11-7
 Chapter 12 Sec. 12-1 to 12-5
 Chapter 9 Sec. 9-1 to 9-7 Skip 9-4
 Chapter 1 Sec. 1-6 If you have the time
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Geometry H Academic Plan
Quarter 1
 Chapter 1 Sec. 1-1 to 1-7
 Chapter 2 Sec. 2-1 to 2-7
 Chapter 3 Sec. 3-1 to 3-6
Quarter 1 District Common Exam

Geometry H Academic Plan
Quarter 2
 Chapter 4 Sec. 4-1 to 4-8
 Chapter 5 Sec. 5-1 to 5-6
 Chapter 6 Sec. 6-1 to 6-7
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Geometry H Academic Plan
Quarter 3
 Chapter 7 Sec. 7-1 to 7-7
 Chapter 8 Sec. 8-1 to 8-7
 Chapter 9 Sec. 9-1
 Chapter 11 Sec. 11-1 to 11-6
Quarter 3 District Common Exam
From Q1 to Q3 but the emphasis is on Q3.

Geometry H Academic Plan
Quarter 4
 Chapter 10 Sec. 10-1 to 10-7
 Chapter 12 Sec. 12-1 to 12-7
 Chapter 9 Sec. 9-2 to 9-7
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Liberal Arts Academic Plan
Quarter 1 PH Algebra 1
 Skill Handbook Line Plot







Chapter 2 Sec. 2-7
Chapter 1 Sec. 1-2 to 1-8
Chapter 8 Sec. 8-2 to 8-5
Chapter 5 Sec. 5-2
Chapter 2 Sec. 2-1 to 2-5
Chapter 3 Sec. 3-4 to 3-6
Chapter 6 Sec. 6-1 to 6-5
Quarter 1 District Common Exam

Liberal Arts Academic Plan
Quarter 2 PH Geometry
 Chapter 1 Sec. 1-6
 Chapter 3 Sec. 3-1
 Chapter 5 Sec. 5-2 to 5-3
 Chapter 4 Sec. 4-1 to 4-3
 Chapter 8 Sec. 8-3 to 8-4
 Chapter 7 Sec. 7-2 to 7-3
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Liberal Arts Academic Plan
Quarter 3 PH Geometry
 Chapter 3 Sec. 3-4
 Chapter 6 Sec. 6-1 to 6-5
 Chapter 7 Sec. 7-1, 7-4, and 7-5
 Chapter 4 Sec. 4-1
 Chapter 8 Sec. 8-1 and 8-2
 Chapter 10 Sec. 10-3 to 10-8
Quarter 3 District Common Exam
From Q1 to Q3 but the emphasis is on Q3.

Liberal Arts Academic Plan
Quarter 4
PH Geometry
 Chapter 7 Sec. 7-6 and 7-7
 Chapter 11 Sec. 11-2

PH Algebra 1
Chapter 10 Sec. 10-5 to 10-7
 Chapter 7 Sec. 7-1, 7-5, and 7-6
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Algebra 2 Academic Plan
Quarter 1
 Chapter 1 Sec. 1-1 to 1-6
 Chapter 2 Sec. 2-1 to 2-8
 Chapter 3 Sec. 3-1
Quarter 1 District Common Exam

Algebra 2 Academic Plan
Quarter 2
 Chapter 3 Sec. 3-2, 3-3 and 3-6
 Chapter 4 Sec. 4-1 to 4-5 (part 1)
 Chapter 4 Sec. 4-6 to 4-8
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Algebra 2 Academic Plan
Quarter 3
 Chapter 5 Sec. 5-1 to 5-9
 Chapter 6 Sec. 6-1 to 6-8
Quarter 3 District Common Exam
From Q1 to Q3 but the emphasis is on Q3.

Algebra 2 Academic Plan
Quarter 4
 Chapter 7 Sec. 7-1 to 7-5
 Chapter 8 Sec. 8-1 to 8-6
 Chapter 9 Sec. 9-1 to 9-5
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Algebra 2H Academic Plan
Quarter 1
 Chapter 1 Sec. 1-2
 Chapter 2 Sec. 2-1, 2-3, 2-5 and 2-7 to 2-9
 Chapter 3 Sec. 3-1 to 3-5
 Chapter 4 Sec. 4-1 to 4-10 Skip 4-5
Quarter 1 District Common Exam

Algebra 2H Academic Plan
Quarter 2
 Chapter 5 Sec. 5-1 to 5-9
 Chapter 6 Sec. 6-1 to 6-6
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Algebra 2H Academic Plan
Quarter 3
 Chapter 7 Sec. 7-1 to 7-7
 Chapter 8 Sec. 8-1 to 8-3
Quarter 3 District Common Exam

Algebra 2H Academic Plan
Quarter 4
 Chapter 9 Sec. 9-2 to 9-7
 Chapter 12 Sec. 10-1 to 10-6 Skip 10-5
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.

Pre-Calculus Academic Plan
Quarter 1
 Chapter 0 Formal Rules of Algebra
 Chapter 1 Sec. 1-1 to 1-7
 Chapter 2 Sec. 2-3 to 2-6
 Chapter 4 Sec. 4-1 to 4-5
Quarter 1 District Common Exam

Pre-Calculus Academic Plan
Quarter 2
 Chapter 4 Sec. 4-6 to 4-7
 Chapter 5 Sec. 5-1 to 5-5
 Chapter 7 Sec. 7-1 to 7-5 Skip 7-4
2 nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.

Pre-Calculus Academic Plan
Quarter 3
 Chapter 8 Sec. 8-1 to 8-5
 Chapter 9 Sec. 9-1 to 9-5 Skip 9-4
 Chapter 10 Sec. 10-1 to 10-5
Quarter 3 District Common Exam

Pre-Calculus Academic Plan
Quarter 4
 Chapter 12 Sec. 12-1 to 12-6
 Chapter 3 Sec. 3-1 to 3-4
Final Exam District Common Exam
From Q1 to Q4 but the emphasis is on Q4.