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Gear Up | |

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Focus Problem, Step 1: Understand the Problem | |

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Exposure to an open-ended problem on a medical error | |

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Previews the use of rates and units and Polya's problem solving process | |

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Getting Started: Syllabus | |

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Group activity to learn course policies | |

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Develops critical reading skills | |

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Getting Started: Skills | |

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Venn diagrams are used to explore prerequisite knowledge | |

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Reviews prerequisite skills | |

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Develops Venn diagrams | |

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Getting Started: Groups | |

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Personality test to improve group dynamics | |

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Develops knowledge of the Cartesian coordinate system | |

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Develops the ability to plot and read ordered pairs | |

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Exposes students to the term variable | |

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A Tale of Two Numbers (FP) | |

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Exploration of ratios and rates used in daily life | |

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Previews scaling fractions | |

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Develops ratio and rates concepts including notation | |

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Part and Whole | |

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Conceptual review of fraction operations | |

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Reviews fraction concepts and operations | |

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Develops the skill of drawing a picture | |

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The Elusive A in Math | |

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Assess traits necessary to success in mathematics | |

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Develops pie and bar graphs | |

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Connects equivalent fractions and scaling | |

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Previews working with axes and increments on them | |

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Two by Two | |

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Visualizing situations with scatterplots | |

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Develops scatterplots | |

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Applies pie graphs and plotting points | |

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Multiply or Divide? (FP) | |

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Daily situations that involve unit conversions by multiplying or dividing | |

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Develops unit conversions | |

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Applies student success knowledge from 1.7 | |

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Recap | |

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Shift Gears | |

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Focus Problem, Step 2: Devise a Plan | |

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Revisit focus problem and develop a plan to solve it | |

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Applies knowledge gained to date | |

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Higher or Lower? (FP) | |

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Compare two pay structures with graphs, tables, and Excel | |

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Previews integers, equations, like terms, and the commutative property | |

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Develops percent calcuations, the concept of a function, and generalizing a calculation | |

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Applies scaling | |

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The X Factor | |

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Important algebraic vocabulary | |

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Develops the terms equation, expression, constant, variable, term | |

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Applies Venn diagrams | |

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Reviews pi | |

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Take Two and Call Me… | |

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Interpreting a graph that accompanies a medicine | |

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Connects scaling with units and rates | |

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Develops understanding of rates and units | |

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Applies independent/dependent variables, function concepts, and reading ordered pairs | |

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Good Eats (FP) | |

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Understanding nutrition labels and nutrition guidelines | |

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Develops the concept of proportionality | |

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Applies fraction and percent skills | |

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General Number | |

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Generalizing patterns with variables | |

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Exposes students to Fibonacci sequence | |

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Develops generalizing a pattern, inductive and deductive reasoning | |

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Previews simplifying expressions | |

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Up and Down (FP) | |

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Percent situations from daily life | |

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Previews integers | |

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Develops the concept of percent change | |

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Applies the skills of finding the percent of a number and increasing or decreasing a number by a percent | |

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The Social Network | |

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Exploration of viral growth on the internet | |

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Previews order of operations and slope concepts | |

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Develops the concepts of linear and exponential growth | |

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Applies the idea of generalizing a pattern | |

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Exposes students to building a mathematical model | |

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Connects exponential growth and percent of increase | |

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Recap | |

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Wind Down | |

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Focus Problem, Step 3: Carry Out the Plan | |

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Revisit focus problem and solve it | |

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Applies knowledge gained to date | |

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Cookie Monster | |

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Recipe conversion to decrease its size | |

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Connects conversions with scaling | |

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Applies fraction skills | |

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Applies unit conversion skills | |

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Picture This | |

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Matching scenarios with graphs | |

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Exposes students to fitting data with a curve | |

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Connects scatterplots and types of change | |

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Infinity and Beyond | |

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Exploration of Sierpinski triangles and their patterns | |

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Connects area and perimeter to generalizing a pattern | |

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Applies concepts of area and perimeter | |

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Exposes students to Sierpinski triangles | |

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Connects proportionality to similar triangles | |

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Error and Estimation: Liquid Medicine | |

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Impact of being inaccurate with liquid medicine | |

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Exposes students to volume concepts | |

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Applies the concepts of constant and variable | |

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Applies the concepts of independent and dependent variables | |

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Applies unit conversions | |

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Previews order of operations | |

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Focus Problem, Step 4: Look Back | |

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Reflect on focus problem and cycle as a whole | |

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Debriefs the focus problem solution | |

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Cycle Wrap-up | |

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Active test preparation exercises | |

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Reviews topics, skills, and concepts from the cycle | |

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Connects cycle skills and concepts to apply them to new problems | |

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Gear Up | |

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Focus Problem, Step 1: Understand the Problem | |

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Exposure to an open-ended problem on baseball's magic number | |

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Previews the use of expressions, formulas, and integers | |

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It's All Relative (FP) | |

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Work with atoms and ions to develop integer concepts | |

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Develops integer concepts | |

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Previews integer operations | |

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Sign and Size, Part 1 (FP) | |

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Real-life situations to develop signed number addition/subtraction rules | |

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Develops integer operations of addition and subtraction | |

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Applies integer concepts and operations to realistic scenarios | |

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Sign and Size, Part 2 | |

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Use of patterns to develop signed number multiplication/division rules | |

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Develops integer operations multiplication and division | |

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Defines real numbers | |

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Exposes students to imaginary numbers | |

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Reviews the concept of square roots | |

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An Ounce of Prevention | |

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Grades situations to understand means | |

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Develops means conceptually and numerically | |

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Previews order of operations | |

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Measure Up | |

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Geometric formulas with units to develop exponent rules | |

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Develops whole number exponent properties | |

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Applies geometric formulas | |

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Applies the use of units in calculations | |

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Count Up (FP) | |

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Common situations with like terms | |

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Develops like terms | |

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Applies knowledge of formulas | |

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Exposes students to polynomial terminology and addition/subtraction | |

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Recap | |

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Shift Gears | |

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Focus Problem, Step 2: Devise a Plan | |

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Revisit focus problem and develop a plan to solve it | |

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Applies knowledge gained to date | |

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Order Up | |

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Order of operations and their use in formulas | |

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Develops the order of operations | |

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Applies order of operations to evaluating formulas | |

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Previews inverse operations necessary for equation solving | |

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Does Order Matter? | |

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Uses of the commutative and associative properties in algebra and mental math | |

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Develops the commutative and associative properties | |

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Develops mental math skills | |

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Applies percent skills and adding like terms | |

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Fair Share | |

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Development and application of the distributive property | |

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Develops the distributive property and mental math skills | |

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Applies the commutative property | |

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Applies the distributive property to multiplying polynomials | |

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Reviews like terms and whole number exponent properties | |

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Seat Yourself (FP) | |

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Pattern recognition using a tables and chairs situation | |

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Applies the distributive property and connects it to like terms | |

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Develops the ability to write expressions | |

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Punt, Pass, Kick | |

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Pythagorean Theorem off a grid | |

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Develops the Pythagorean Theorem | |

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Develops conceptual and numeric approaches to equation solving | |

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Previews concepts related to solving equations | |

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Connects Pythagorean triples to similar triangles | |

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Ramp Up | |

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Slope on and off a grid | |

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Develops slope concepts and calculations | |

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Connects slope to linearity | |

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Applies Pythagorean Theorem and unit conversions | |

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Shortest Distance (Optional) | |

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Pythagorean Theorem on a grid to measure distances | |

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Applies Pythagorean Theorem, slope, and the order of operations | |

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Develops the distance formula and measurement skills | |

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Connects slope and the distance formula | |

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Recap | |

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Wind Down | |

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Focus Problem, Step 3: Carry Out the Plan | |

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Revisit focus problem and solve it | |

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Applies knowledge gained to date | |

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Parts of Speech | |

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Operations vs. operators | |

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Applies the distributive property | |

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Develops understanding of operations | |

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In the Swing of Things (Optional) | |

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Investigation of a pendulum formula | |

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Applies the order of operations | |

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Connects functions to the order of operations | |

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Applies function concepts | |

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Error and Estimation: Rounding (Optional) | |

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Impact of being inaccurate with a financial formulas | |

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Applies the order of operations | |

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Develops understanding of the role of accuracy and precision | |

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Focus Problem, Step 4: Look Back | |

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Reflect on focus problem and cycle as a whole | |

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Debriefs the focus problem solution | |

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| |

Cycle Wrap-up | |

| |

| |

Active test preparation exercises | |

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| |

Reviews topics, skills, and concepts from the cycle | |

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Connects cycle skills and concepts to apply them to new problems | |

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Gear Up | |

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| |

Focus Problem, Step 1: Understand the Problem | |

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Exposure to an open-ended problem about comparing e-readers | |

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Previews the use of linear equations | |

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Rule of Thumb | |

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Explore weighted means with grade situations | |

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Applies means and rates in a new context | |

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Develops weighted means | |

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| |

Working Hard for the Money (FP) | |

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Correlation between profession and income, unemployment rate | |

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Applies means and weighted means | |

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Applies making scatterplots | |

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Develops correlation, median, and mode | |

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Previews finding the trend line | |

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| |

Previews slope-intercept form | |

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| |

Applies scaling concepts | |

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| |

Connects measures of center to geometry | |

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A Fine Balance (Optional) | |

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| |

Using chemical equations to understand solutions to equations | |

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Connects algebraic ideas with chemistry notation | |

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Develops the concept of solutions to equations | |

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Previews algebraic identities | |

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Just a Pinch | |

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Measuring natural variation using standard deviation | |

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| |

Develops standard deviation concepts and calculations | |

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Applies means, order of operations, and signed numbers | |

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| |

Previews equation solving concepts | |

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| |

Separate but Equal (FP) | |

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| |

Real-life scenarios that can be solved numerically and with one-step equations | |

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Develops one-step equations and understanding of equation solving | |

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Connects algebraic and numeric methods of equation solving | |

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On the Rise | |

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Analyze an article about food packaging using algebra, geometry, and statistics | |

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Applies mean, median, standard deviation, and bar graphs | |

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| |

Develops Pareto charts | |

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| |

Applies writing and solving one-step equations | |

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Recap | |

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| |

Shift Gears | |

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| |

Focus Problem, Step 2: Devise a Plan | |

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| |

Revisit focus problem and develop a plan to solve it | |

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| |

Applies knowledge gained to date | |

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| |

Game On (FP) | |

| |

| |

Use pictures and algebra to solve two-step and multi-step equations | |

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| |

Develops solving of linear equations | |

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Develops identities and contradictions | |

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| |

Quarter Wing Night (FP) | |

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| |

Determine the number of buffalo wings in varying scenarios | |

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| |

Applies equation solving techniques | |

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| |

Applies percent concepts | |

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| |

Eastbound and Down (FP) | |

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| |

Analyzing gas price scenarios with and without a car wash | |

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| |

Applies equation solving techniques | |

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| |

Connects linear equation solving and graphing | |

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| |

Reviews linearity, slope, and rate of change | |

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| |

Previews systems of equations | |

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Get in Line (FP) | |

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| |

Explore linear situations algebraically and on a graph | |

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| |

Develops slope-intercept form and its uses in graphing | |

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| |

Connects linearity between tables, graphs, and equations | |

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| |

Exposes students to the concept of domain | |

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| |

Gas Up and Go (Optional) | |

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| |

Study Distance = Rate x Time to explore variation | |

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| |

Develops direct and inverse variation | |

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| |

Exposes students to combined variation | |

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| |

Applies equation solving | |

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| |

Recap | |

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| |

Wind Down | |

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| |

Focus Problem, Step 3: Carry Out the Plan | |

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| |

Revisit focus problem and solve it | |

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| |

Applies knowledge gained to date | |

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Value of a Dollar (Optional) | |

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| |

Determine the amount of time worked to pay for a tank of gas | |

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| |

Develops rational functions | |

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| |

Applies direct and inverse variation | |

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When is the Algebra Worth It? (Optional) | |

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Assess when algebra is useful | |

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| |

Applies and extends equation solving techniques | |

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| |

Exposes students to non-linear equation solving | |

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| |

Error and Estimation: Volume | |

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| |

Revisit and quantify liquid medicine overfilling error | |

| |

| |

Applies slope-intercept form and graphing | |

| |

| |

Applies percent of change and unit conversions | |

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| |

Focus Problem, Step 4: Look Back | |

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| |

Reflect on focus problem and cycle as a whole | |

| |

| |

Debriefs the focus problem solution | |

| |

| |

Cycle Wrap-up | |

| |

| |

Active test preparation exercises | |

| |

| |

Reviews topics, skills, and concepts from the cycle | |

| |

| |

Connects cycle skills and concepts to apply them to new problems | |

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| |

Gear Up | |

| |

| |

| |

Focus Problem, Step 1: Understand the Problem | |

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| |

Exposure to an open-ended problem about making sense of a large number | |

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| |

Previews dimensional analysis | |

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| |

A Matter of Change (FP) | |

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| |

Work with more involved conversion problems | |

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| |

Develops dimensional analysis | |

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| |

Previews scientific notation | |

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| |

Little Giants (FP) | |

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Explores very large and very small numbers | |

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| |

Develops scientific notation | |

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| |

Connects dimensional analysis to scientific notation | |

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| |

Applies Pareto charts and medians | |

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| |

Previews negative exponents and compound inequalities | |

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| |

Outwit and Outlast (FP) | |

| |

| |

Situations with proportionality, explored numerically and algebraically | |

| |

| |

Develops solving proportions algebraically | |

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| |

Connects scaling with algebraic methods of solving | |

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| |

Applies rates | |

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| |

Exposes students to concepts of apportionment | |

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| |

| |

Chances Are (Optional) | |

| |

| |

Simple probability situations from daily life | |

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| |

Develops theoretical and experimental probabilities | |

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| |

Connects area to probability | |

| |

| |

Applies scientific notation | |

| |

| |

Previews compound inequalities | |

| |

| |

| |

A Model Approach (FP) | |

| |

| |

Working with numbers in scientific notations from science scenarios | |

| |

| |

Develops negative exponents | |

| |

| |

Connects scientific notation to exponent rules | |

| |

| |

Applies exponent rules, unit conversions, and solving proportions algebraically | |

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| |

Recap | |

| |

| |

| |

Shift Gears | |

| |

| |

| |

Focus Problem, Step 2: Devise a Plan | |

| |

| |

Revisit focus problem and develop a plan to solve it | |

| |

| |

Applies knowledge gained to date | |

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| |

| |

Chain, Chain, Chain | |

| |

| |

Linear relationships in alkanes | |

| |

| |

Exposes students to domain | |

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| |

Develops writing linear models using y = mx + b | |

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| |

Connects equation solving to linear models | |

| |

| |

| |

Hot and Cold | |

| |

| |

Analyzing and developing temperature formulas | |

| |

| |

Develops factoring the greatest common factor | |

| |

| |

Develops solving equations for a variable | |

| |

| |

Applies slope-intercept form and equation solving | |

| |

| |

| |

Going Viral | |

| |

| |

Statistics and models of viral marketing in social media | |

| |

| |

Exposes students to solving an exponential equation | |

| |

| |

Develops exponential models | |

| |

| |

Connects functions to exponential growth | |

| |

| |

Connects slope, growth, and statistics | |

| |

| |

Develops understanding of the concept of size | |

| |

| |

Applies factoring the GCF | |

| |

| |

| |

The Cost of College (Optional) | |

| |

| |

Comparing tuition and fee structures | |

| |

| |

Develops solving systems with graphing and substitution | |

| |

| |

Connects graphing and algebraic methods of solving systems | |

| |

| |

Applies solving literal equations, solving equations, graphing lines | |

| |

| |

Applies writing equations of lines | |

| |

| |

| |

Tuition Increases (Optional) | |

| |

| |

Exploring the effects of a tuition increase on revenue | |

| |

| |

Develops quadratic function modeling | |

| |

| |

Connects linear, exponential, and quadratic functions | |

| |

| |

Applies systems of equations | |

| |

| |

Applies multiplying binomials | |

| |

| |

| |

Recap | |

| |

| |

| |

Wind Down | |

| |

| |

| |

Focus Problem, Step 3: Carry Out the Plan | |

| |

| |

Revisit focus problem and solve it | |

| |

| |

Applies knowledge gained to date | |

| |

| |

| |

Outliers (Optional) | |

| |

| |

Modeling height using belly button height | |

| |

| |

Exposes students to residuals, the Golden ratio, and compound inequalities | |

| |

| |

Develops z-scores | |

| |

| |

Connects issues of size and scale to statistics | |

| |

| |

Applies standard deviation and mean | |

| |

| |

| |

A Little Less (FP) | |

| |

| |

Large scale effects of plastic saving measures | |

| |

| |

Applies dimensional analysis | |

| |

| |

Develops concepts of size and scale | |

| |

| |

| |

Error and Estimation: Order of Magnitude Optional | |

| |

| |

A new scale to make sense of size | |

| |

| |

Develops order of magnitude | |

| |

| |

Applies scientific notation and exponent rules | |

| |

| |

| |

Focus Problem, Step 4: Look Back | |

| |

| |

Reflect on focus problem and cycle as a whole | |

| |

| |

Debriefs the focus problem solution | |

| |

| |

Cycle Wrap-up | |

| |

| |

Active test preparation exercises | |

| |

| |

Reviews topics, skills, and concepts from the cycle | |

| |

| |

Connects cycle skills and concepts to apply them to new problems | |