Transcript K-8 Mathematics Standards

Teaching to the
Next Generation SSS
(2007)
Mathematics Pre-School Inservice (6 – 8)
August 18, 2010
In today’s training, we will…
•engage in activities and in-depth
discussions that promote higher
level thinking skills
•connect each standard in relation
to equations with an example
•be aware of items that prior grade
levels have learned
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
How do we make sense of teaching deeply?
Provide a “focused” curriculum.
Collaboration of vertical and
horizontal teaching
Explore deeper content-based
knowledge. Think of a swimming
pool. Most people stay in the
shallow end…we now need to
venture to the unknown depths
of knowledge.
Develop connections from 6th
grade math through pre-calculus
Emphasis on higher level
thinking- analysis, evaluation
and synthesis
Teaching For Depth

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Equations as an example standard linked through
the grade levels
Fair game review through models and visuals
Use cooperative learning strategies to introduce or
remediate equations
Represent equations using models, vocabulary,
pictures, and real world situations
Lead students to mastery level not memorization
What is Rigor?
What Rigor is Not:
a measure of the quantity of
content to be covered.
a special program or curriculum
for select students.
about severity or hardship.
only about higher-order thinking.
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
Coding Scheme for NGSSS
MA.
6.
A.
3.
1
Subject
Grade
Level
Body of
Knowledge
Big Idea/
Supporting
Idea
Benchmark
MA.6.A.3.1
Identify the threading standards for
solving equations.
The Common Thread
Grade Level/Course
Benchmark
4
Describe mathematical relationships using
expressions, equations, and visual
representations.
6
Write solve and graph one- and two-step linear
equations and inequalities.
7
Formulate and use different strategies to solve
one and two step linear equations including
equations with rational coefficients.
8
Use tables, graphs, and models to represent,
analyze, and solve problems related to systems of
linear equations.
Algebra 1
Solve and graph simple and compound inequalities in
one variable and be able to justify each step in a
solution.
Geometry
Use coordinate geometry to find slopes,
perpendicular lines, parallel lines and equations
of lines.
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.
What are the
NCTM Process Standards?
– Problem Solving
– Reasoning and Proof
– Connections
– Communication
– Representation
12
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
Focus on Equations!
6th Grade Equation Strategies
Solving one-step
algebraic equations
NGSSS: Equations(6th)
MA.6.A.3.2
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. The most
literal equation might be 7 + 10y = h.
STRATEGIES
Dynamic Classroom Interactive
Scale--Big Ideas website
Human Equations
Algebra Tiles
Magic Square
Dynamic Classroom
Interactive Scale
This strategy gives students a visual
opportunity to see an algebraic
equation solved using a scale. This
demonstrates how equations must be
balanced.
Benefits: It allows the students to
enhance computer skills and provides a
high interest activity with graphics.
Human Equations
This is a kinesthetic activity that
provides the students with an
opportunity to move throughout the
classroom while modeling how to
solve one-step equations.
Benefits: Allows students to
cooperate in a group activity while
moving throughout the room .
How do I do this?
Students are given cards with numbers,
variables and symbols on them.
An equation is placed on the board.
X + 7 = 10 d – 8 = 9 a + 2 = 11
Students will model the equation with their
cards in the front of the class.
Students in the class are called on to solve
the problem by moving the cardholders as
they go through the steps of solving the
problem.
Algebra Tiles
They are used to solve algebraic
equations using colors and shapes.
Benefits: Students see positive and
negative integers in colors. It allows
them to see constants and variables
in different shapes.
Algebra Tile Example
Try x – 4 = 8.
Magic Squares
This is an enrichment option from
page 289 of the 6th grade textbook.
Benefits: This provides a
cooperative learning activity for
students to explore and expand their
comprehension of one-step
equations and encourages higherlevel critical thinking skills.
Magic Square…Your Turn!
Use equations to solve the magic square.
Hint: all lines horizontal, vertical and diagonal have
the same sum.
16
a
2
13
b
10
11
8
9
6
7
c
4
15
d
1
NGSSS: 7th grade
MA.7.A.3.3
Example: It costs an initial fixed cost of $2
plus an additional $1.50 per mile to rent a
taxi. Write an equation that represents the
method for calculating the total cost of a
taxi ride? What is the total cost for a 5mile trip?
Systems of Equations
Big Ideas Math Textbook
Aligned to the Next Generation SSS
www.floridastandards.org
NGSSS: 8th grade
Example: Jan decided to save some money.
She already had $25. She received and
saved $5 on Friday each week for 8
weeks. Make a table and a graph of the
money she would have each week. If she
continues with this same savings plan,
how much money will she have after 2
years?
Lesson: Systems of Equations
Essential Question: How can you
solve a system of linear equations?
Chapter: 2
Section: 5
Topic: Linear Systems
Next Generation Standard : MA.8.A.1.3 &
MA.8.A.1.4
Systems of Equations
MA.8.A.1.3
 Big Idea 1 - Analyze and represent linear functions,
and solve linear equations and systems of linear
equations.
 Benchmark: Use tables, graphs, and models to
represent, analyze, and solve real-world problems
related to systems of linear equations.
MA.8.A.1.4
 Big Idea 1 - Analyze and represent linear functions,
and solve linear equations and systems of linear
equations.
 Benchmark: Identify the solution to a system of
linear equations using graphs
Vocabulary 2-5
System of Linear Equations – two or more
linear equations placed together
Solution of the System of Linear Equations –
any ordered pair in a system that makes all of
the equations true.
No solution – when two lines are parallel there
are no points of intersection. Since the two
lines do not share a common point, there is no
solution for parallel lines.
Infinite solutions – a system of linear
equations has no limit to the pairs of solutions
Systems of Equations
Activities:
–Taking Math Deeper TE pg. T-81
Incorporates Kagan strategy, Think-Pair-Share
–Game Closet: Tic-Tac-Toe
http://www.bigideasmath.com/uploads/game
s/game_14.pdf
Systems of Equations
Lesson Objective: To solve systems of linear
equations using three different techniques
http://www.bigideasmath.com/protected/content/ipe/grade%20
8/02/g8_02_05.pdf
Vocabulary: system of linear equations, solution
of a system of linear equations
Previous Learning: In Section 1.3n 8th grade
textbook, students learned how to solve
equations with variables on both sides
TIC – TAC – TOE
Y=x+4
Y = 3x - 1
Y = 1.5x - 2
Y = -x + 13
Y = 2/3x -3
Y = -2x + 5
Y = 2x + 9
Y=6–x
Y = -x – 4
Y = 3/5x + 4
Y = 2x + 5
Y = 1/2x - 1
Y + x = 27
Y=x+3
Y = 2x + 3
Y=x+8
X–y=7
0.5x + y = 5
Think – Pair - Share
Setup: Six note cards with the solving methods
below: (2 cards per a method)
1. Solve Using Algebra.
2. Solve Using A Graph.
3. Solve Using A Table.
The teacher will give examples to the class, such
as: A middle school yearbook committee has 35
members. There are 7 more girls than boys. Use
the models to write a system of linear equations.
Then solve the system to find the number of boy
x and the number of girls y.
Procedure
Students will be in teams of 4. A stack of note cards
will be in each team. Each team will choose a note
card from the note card pile. Each student will allow
2-3 minutes to think and solve individually with the
method that is shown on their card. When time is up,
the students will share and check each others work
and come up with a consensus before they share with
the entire team. The teacher will then pick and review
answers and methods from 2 groups before moving on
to another example.
Where do they go from here?
Algebra
MA.912.A.3.1 :
3(2x+5) = 10x-3+2x
Geometry
MA.912.G.5.4 : Are these equations
parallel, perpendicular, or intersecting. Y = 3 (x - 3) +
9 y = 2.1 (x + 2) - 4
Algebra II
MA.912.A.6.5 : 3 log x = 4
Pre-Calculus
the interval [0, 2p)
MA.912.T.3.4 : Solve 2 sin(x) +1=0 on
Where do I find the Next Generation
Sunshine State Standards (NGSSS)?
Textbook – Front of Text
Each Section
www.FloridaStandards.org – Standards by Grade
level
• Step 1 – Subject: Mathematics
• Step 2 - Grade Level: 6,7, or 8
www.bigideasmath.com – Standards listed as
NGSSS correlations
• Step 1 – Teacher Resources Tab
• Step 2 – NGSSS Correlations
What does the School District of Lee County
mandate I teach and when?
You will need to check your Academic Plan by grade level
and subject (intensive, regular, advanced).
Go to…
- Learn Page
- District Resources - Academic Plans
- Click on Navigation Bar on left
- Scroll down to your grade/subject and click
Once the plan is loaded, you have three choices:
• 1st Tab – Quarterly Guides
• 2nd Tab – Complete Plan
• 3rd Tab – Vocabulary Key Terms (also located
on Bigideasmath.com, Teacher Resources,
Glossary flash cards)
What Materials will I receive?
- Teacher Edition
- Student Textbook
- Record and Practice Journal and Answer Key
- Advance Topics Book for Advanced Courses
(store extras for next year – not consumable!)
- Assessment Book (6th and 7th)
- Online Resources
- Math Resources by Chapter TE book
Available on CD Rom
- TE CD
- Lesson Planning Tools
- Lesson Tutorials
- Dynamic Assessment
- Dynamic Teaching
- Editable Ancillary can be edited from CD
What do I do if a student is
absent or needs extra help?
- Have students go to www.bigideasmath.com
- Student Resources

Lesson Tutorial (podcast of lesson)

Graphic Organizer

Progress Check

Vocabulary Check

Chapter Test
What can Parents do to help
students at home?
Go to www.BigIdeasmath.com and click on Parent tab
 Help with Homework
(English, Spanish, Haitian-Creole)
 Parent Letters
 Basic Skills Handbook
 Skills Review Handbook
Planning Time!
- Get with your grade level / subject
counterpart
- Using resources you have been given,
talk about and plan a section from
Chapter 1
Curriculum & Staff Development Center
Requires a Course Evaluation!
Don’t forget to complete your
online evaluation!
Thank You!
Food For Thought
Liping Ma (1999) used this exact problem with
teachers in the U.S. and in China.
Of 23 U.S. teachers:
– 6 could not create a story problem
– 16 created story problems with misconceptions
-Confusing dividing by 1/2 with dividing by 2
-Confusing dividing by 1/2 with multiplying by 1/2
– 1 provided a conceptually correct representation,
but it contained pedagogical problems
-Fractional number of children
90% of Chinese teachers created a correct
representation