The main goals for the first two weeks of class are to complete preliminary assessment activities and set the tone for the class in terms of procedures and expectations. There are no specific assessment goals listed which are correlated to the CA Mathematics Standards because of the pre-assessment activities. Various Mathematical Reasoning standards may be addressed depending on the introductory activities chosen by individual teachers.

Preliminary Assessment:

• STAR Math testing
• MDTP testing
• open-ended assessment

Class Arrangements:

• set-up notebooks
• classroom rules
• assignment journals
• set-up portfolios
• mathematics journals
• problem solving techniques - diagram/process/solution
• review Standards expectations

Some Possible Introductory Collaborative Group Activities:

• The First Twelve Days of School

  Texas Instruments Problem
  Explanation by Dr. Math

• The Prisoners' Dilemma

  The Prisoners' Dilemma
  Potential Solutions of The Prisoner's Dilemma

• The Rope Activity

  Clear the classroom so that there is a large area in the center or go out to a spot with some space to complete the activity. Have four students hold a rope with one on each vertex of the square. Have other students get into the space created by rope.

  Question for the class: If we make a different shape with the rope, can more students fit into the space?

  Add in more students to hold the rope.

  Question for the class: What shape will fit in the most students?

  Isoperimetric Theorem and Inequality by Alexander Bogomolny
  Isoperimetric Theorem and Its Variants by Alexander Bogomolny
  Area, What's a Square Foot? by The Energy Conservation Enhancement Project
  

Preliminary Technology Training:

• Geometer's Sketchpad
• Claris Works - intro to word processing, intro to spreadsheets
• SimCalc
• Internet - introduction (AUP training)

The main focus for these two weeks will be addressing Mathematical Reasoning standards all of which are considered Key Standards for the seventh grade. The listed Algebra and Functions standards may be met as a result of the activity but they are not intended to be the main focus.

Main Activity
Interactive Mathematics Text
        p. 4 Hop, Skip and Jump Activity
           This activity includes patterns, mathematical reasoning, and generalizing algebraically. It can be used as a vehicle for the introduction of algebraic thinking, vocabulary and the use of algebraic expressions.

Traffic Jam Activity

Alignment to CA Mathematics Standards:
Algebra and Functions
1.1 use variables and appropriate operations to write an expression, equation, inequality, or system of equations or inequalities which represent a verbal description (e.g., three less than a number, half as large as area A)
Mathematical Reasoning
1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns
1.2 formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed
1.3 determine when and how to break a problem into simpler parts
2.6 express the solution clearly and logically using appropriate mathematical notation and terms and clear language, and support solutions with evidence, in both verbal and symbolic work

Extensions
MAC Text
        pp. 32-35 - Powers and Exponents
        pp. 136-139 - Sequences
        pp. 24-32 - Variables and Expressions

Alignment to CA Mathematics Standards:
Algebra and Functions
1.2 use order of operations correctly to evaluate algebraic expressions such as 3(2x+5)^2
1.4 use algebraic terminology correctly (e.g., variable, equation, term, coefficient, inequality, expression, constant)
2.1 interpret positive whole number powers as repeated multiplication and negative whole numbers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
Mathematical Reasoning
1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns

Resources

• What is an exponent? - Dr. Math Archives
• Understanding Exponents - Dr. Math Archives
• Exponents in the Real World - Dr. Math Archives
• 0 Power - Dr. Math Archives
• Scientific Notation - Dr. Math Archives
• Tower of Hanoi - Dr. Math Archives

• Detecting Patterns - RHL School
• Detecting More Patterns - RHL School

• Addition and Multiplication Tables in Various Bases by Alexander Bogomolny
  

• Video -- The Power of Algebra - Words Into Symbols
  Explains how expressions or sentences in words can be translated into algebraic expressions or sentences and introduces several problem-solving strategies.

Assessment

• Students will be given the problem for 15 pairs of people. They will be able to explain their answer using the generalized formula n(n+2) equals the minimum number of moves to complete the problem.