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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

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teaching to the next generation sss 2007
Teaching to the Next Generation SSS(2007)

Mathematics Pre-School Inservice (6 – 8) August 18, 2010

in today s training we will
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
how do we make sense of teaching deeply
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

  • 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 rigor is not
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.


Eric Bergholm, Hillsborough County Public Schools, Florida

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.

what are the nctm process standards
What are the NCTM Process Standards?
  • Problem Solving
  • Reasoning and Proof
  • Connections
  • Communication
  • Representation


nctm process standards
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


Read, write, listen, think, and discuss

Increase the use of appropriate math vocabulary

nctm process standards14
NCTM Process Standards


Integers, expressions, and equations

Other content areas, science

Real-world contexts


Useful tools for building understanding

Concrete - Representational - Abstract

Tables, describe in words, draw a picture, write and solve equations

6 th grade equation strategies

6th Grade Equation Strategies

Solving one-step

algebraic equations

ngsss equations 6 th
NGSSS: Equations(6th)


  • 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.

Dynamic Classroom Interactive Scale--Big Ideas website

Human Equations

Algebra Tiles

Magic Square

dynamic classroom
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
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
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
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
Algebra Tile Example

Try x – 4 = 8.

magic squares
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 higher-level critical thinking skills.

ngsss 7 th grade ma 7 a 3 3
NGSSS: 7th gradeMA.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 5-mile trip?

systems of equations
Systems of Equations

Big Ideas Math Textbook

Aligned to the Next Generation SSS


ngsss 8 th grade
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
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 equations30
Systems of Equations


  • 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.  


  • 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
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 equations32
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/games/game_14.pdf
systems of equations33
Systems of Equations

Lesson Objective: To solve systems of linear equations using three different techniques


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

think pair share
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.


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
Where do they go from here?
  • AlgebraMA.912.A.3.1 :3(2x+5) = 10x-3+2x
  • GeometryMA.912.G.5.4 : Are these equations parallel, perpendicular, or intersecting.Y = 3 (x - 3) + 9 y = 2.1 (x + 2) - 4
  • Algebra IIMA.912.A.6.5 : 3 log x = 4
  • Pre-CalculusMA.912.T.3.4 : Solve 2 sin(x) +1=0 on the interval [0, 2p)

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
Curriculum & Staff Development CenterRequires a Course Evaluation!

Don’t forget to complete your online evaluation!

food for thought
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