Main Activity
Interactive Mathematics Text
        p. 23 Apple Sacks
           This activity includes working with combinations and probability.

This will be available as an ESCOT Runner problem.

Alignment to CA Mathematics Standards:
Data, Statistics and Probability
SAT9 - "predict outcomes"
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
2.4 make and test conjectures using both inductive and deductive reasoning

Extensions
MAC Text
        pp. 521-525 - Combinations
        pp. 157-160 - Probability/Simple Events

Alignment to CA Mathematics Standards:
Data, Statistics and Probability
SAT9 - "Determine combinations"

Resources

• Selected Probability Readings - Dr. Math Archives
  
• Probability and Statistics - Dr. Math Archives
  
• Changing Colors - Cut-The-Knot
  
• Looping Chips Puzzle - Cut-The-Knot
  
• Northcott's Game - Cut-The-Knot
  
• Squares and Circles - Cut-The-Knot
  
• Fif - Cut-The-Knot
  
• Scoring - Cut-The-Knot
  

Assessment

• Students will demonstrate ability to justify how to predict an outcome.

Main Activity CHANGE
        Exploring Mathematical Concepts
           A variety of short lessons to reinforce standards-based concepts.

MAC Text
        pp. 426-429 - Scale Drawings
        pp. 301-302 - Constructing Perpendicular Lines
        pp. 311-312 - Constructing Angle Bisectors and Segments
        pp. 343 - Pythagorean Theorem
        pp. 344-350 - The Pythagorean Theorem

Alignment to CA Mathematics Standards:
Measurement and Geometry
1.2 construct and read scale drawings and models
3.1 identify and construct basic elements of geometric figures, (e.g., altitudes, midpoints, diagonals, angle bisectors and perpendicular bisectors; and central angles, radii, diameters and chords of circles) using compass and straight-edge
3.3 know and understand the Pythagorean Theorem and use it to find the length of the missing side of a right triangle and lengths of other line segments, and, in some situations, empirically verify the Pythagorean Theorem by direct measurement
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
2.4 make and test conjectures using both inductive and deductive reasoning
2.7 indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy

Resources

• Pythagorean Theorem - Cut-the-Knot
  
• Animated Proof of the Pythagorean Theorem
  
• Pythagorean Theorem Investigation using GSP
  

Assessment

• Students will demonstrate understanding of increases and decreases.
• Students will solve problems that involve discounts, markups, commissions, profit and simple compound interest with decimals and money.