K-8 Mathematics Standards - Lee County Public Schools

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Transcript K-8 Mathematics Standards - Lee County Public Schools

Teaching the
Next Generation SSS
(2007)
Equations Threading
Through Grades 6-12
In today’s inservice training,
we will…
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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.
NCTM Process Standards
 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
NCTM Process Standards
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
What is Rigor?
Rigor
 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
Strategies for
Teaching In Depth
 Collaborate
teaching
vertical and horizontal
 Use
cooperative learning (Kagan)
strategies to introduce or remediate
equations
 Represent
equations using models,
vocabulary, pictures, and real world
situations
Comparison of Standards
Grade Level
Old GLE’s
New
Benchmarks
K
1st
2nd
3rd
4th
5th
6th
7th
8th
67
78
84
88
89
77
78
89
93
11
14
21
17
21
23
19
22
19
Coding Scheme for NGSSS
MA.
912.
Subject
Grade
Level
A.
3.
1
Body of
Big Idea/ Benchmark
Knowledge Supporting
Idea
MA.912.A.3.1
Identify the threading
standards for solving
equations.
The Common Thread
Grade Level/Course
4
6
7
Benchmark
Describe mathematical relationships using expressions,
equations, and visual representations
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
Solve logarithmic and exponential equations
Pre-Calculus
Solve trigonometric equations and real-world problems
involving applications of trigonometric equations using
technology when appropriate.
NGSSS: Equations(6th)
MA.6.A.3.2 - Write, solve, and graph one and
two step linear equations and inequalities
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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 h of the tree in
y years. Let y be the number of years after
the year 2000.
12
6th grade
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(7th)
MA.7.A.3.3 - Formulate and use different
strategies to solve one-step and two-step linear
equations, including equations with rational
expressions.
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Example: Which steps would solve ⅔x – 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(8th)
MA.8.A.4.1 - Solve literal equations for a specified
variable.
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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
8th grade
I = Prt. Solve for P
I = Prt
rt
rt
P = I_
rt
NGSSS: Equations - Algebra
MA.912.A.3.1 - Solve linear equations with one
variable that include simplifying algebraic
expressions.
A
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
Algebra 1
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
Algebra 1
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
Algebra 1
C. 10x + 12 = 2(5x + 6)
10x + 12 = 10x + 12
All real numbers or infinite solutions
Algebra 1
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
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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
Geometry
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.
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Example: Solve the following equation for x:
24
Algebra 2
Solve
+5
+5
3x2 + 10x = 5 square both sides
3x2 + 10x
= 25
-25 -25
3x2 + 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.
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Example: Solve 2 sin(x) +1=0 on the
interval [0, 2p)
26
Pre Calculus
2sin(x) + 1 = 0
-1 -1
2sin(x) = -1
2
2
Sin(x) = -1/2
X = 7π/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.
Calculus
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
x2 = 5000 (area)
x = 5000 m
The shortest length of fencing is the
perimeter of the square, 4 times x or
approximately 282.843 m
Textbook
Prentice Hall Website
www.pearsonsuccessnet.com
Access Codes for Florida courses 2011
Algebra 1
PHMADP11FLENA1B
Geometry
PHMADP11FLENGB
Algebra 2
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
Graphing Technology
Standards (New)
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.
Algebra 1 Pre-AP Activity
Holt McDougal Larson
Florida textbook
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Investigating application of equations
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Through TI-Nspire
Accessing the textbook
website
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Select Holt McDougal Florida Larson
textbook
Select Videos and Activities tab
Select TI-Nspire activities
Select TI-Nspire Larson Algebra 1
activities
Accessing the textbook
website
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Select Holt McDougal Florida edition
Algebra 1 (2011)
– Scroll down to locate
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Select All TI products
Choose Lesson HM.1.1.4
– Materials correlated to this standard
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Select Applications of equations
Print teacher and student worksheets
– Either pdf or doc
Math Objectives
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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
Vocabulary
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Equation
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Variable
Download TI-Nspire files

Need TI-Nspire Teacher Edition
installed on your computer
– See your tech specialist
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Applications_of_equations.tns
Student worksheet and
Teacher notes
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Introduce student worksheet
Introduce parallel teacher notes
Work through student worksheet using
TI-Nspire
Algebra 2 Activity
Pearson Prentice Hall
Florida textbook
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Investigating application of equations
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Activity/game
Accessing the textbook
website
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Mathematics FL Algebra 2
Select Teacher resources
Select Chapter 1
Select Activities, games, and puzzles
Select Lesson 1-4 activities, games,
and puzzles
Math Objectives
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To identify properties of equality
To solve single- and multi-step
equations
To identify sometimes, always, or
never statements
To solve literal equations
Vocabulary
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Identity
Solution of an equation
Inverse operations
Equation
Literal equation
Websites
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
Websites Continued
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
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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
2nd 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
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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
2nd 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
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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
2nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.
Geometry Academic Plan
Quarter 3
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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
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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
2nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.
Geometry H Academic Plan
Quarter 3
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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
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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
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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
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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
2nd Semester District Common Exam
From Q1 to Q2 but the emphasis is on Q2.
Liberal Arts Academic Plan
Quarter 3 PH Geometry
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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
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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
2nd 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
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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
2nd 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
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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
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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
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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
2nd 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
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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.