| |
| |
| |
| |
| |
| |
| Gear Up | |
| |
| |
| |
| Focus Problem, Step 1: Understand the Problem | |
| |
| |
| Exposure to an open-ended problem on a medical error | |
| |
| |
| Previews the use of rates and units and Polya's problem solving process | |
| |
| |
| |
| Getting Started: Syllabus | |
| |
| |
| Group activity to learn course policies | |
| |
| |
| Develops critical reading skills | |
| |
| |
| |
| Getting Started: Skills | |
| |
| |
| Venn diagrams are used to explore prerequisite knowledge | |
| |
| |
| Reviews prerequisite skills | |
| |
| |
| Develops Venn diagrams | |
| |
| |
| |
| Getting Started: Groups | |
| |
| |
| Personality test to improve group dynamics | |
| |
| |
| Develops knowledge of the Cartesian coordinate system | |
| |
| |
| Develops the ability to plot and read ordered pairs | |
| |
| |
| Exposes students to the term variable | |
| |
| |
| |
| A Tale of Two Numbers (FP) | |
| |
| |
| Exploration of ratios and rates used in daily life | |
| |
| |
| Previews scaling fractions | |
| |
| |
| Develops ratio and rates concepts including notation | |
| |
| |
| |
| Part and Whole | |
| |
| |
| Conceptual review of fraction operations | |
| |
| |
| Reviews fraction concepts and operations | |
| |
| |
| Develops the skill of drawing a picture | |
| |
| |
| |
| The Elusive A in Math | |
| |
| |
| Assess traits necessary to success in mathematics | |
| |
| |
| Develops pie and bar graphs | |
| |
| |
| Connects equivalent fractions and scaling | |
| |
| |
| Previews working with axes and increments on them | |
| |
| |
| |
| Two by Two | |
| |
| |
| Visualizing situations with scatterplots | |
| |
| |
| Develops scatterplots | |
| |
| |
| Applies pie graphs and plotting points | |
| |
| |
| |
| Multiply or Divide? (FP) | |
| |
| |
| Daily situations that involve unit conversions by multiplying or dividing | |
| |
| |
| Develops unit conversions | |
| |
| |
| Applies student success knowledge from 1.7 | |
| |
| |
| |
| 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 | |
| |
| |
| |
| Higher or Lower? (FP) | |
| |
| |
| Compare two pay structures with graphs, tables, and Excel | |
| |
| |
| Previews integers, equations, like terms, and the commutative property | |
| |
| |
| Develops percent calcuations, the concept of a function, and generalizing a calculation | |
| |
| |
| Applies scaling | |
| |
| |
| |
| The X Factor | |
| |
| |
| Important algebraic vocabulary | |
| |
| |
| Develops the terms equation, expression, constant, variable, term | |
| |
| |
| Applies Venn diagrams | |
| |
| |
| Reviews pi | |
| |
| |
| |
| Take Two and Call Me… | |
| |
| |
| Interpreting a graph that accompanies a medicine | |
| |
| |
| Connects scaling with units and rates | |
| |
| |
| Develops understanding of rates and units | |
| |
| |
| Applies independent/dependent variables, function concepts, and reading ordered pairs | |
| |
| |
| |
| Good Eats (FP) | |
| |
| |
| Understanding nutrition labels and nutrition guidelines | |
| |
| |
| Develops the concept of proportionality | |
| |
| |
| Applies fraction and percent skills | |
| |
| |
| |
| General Number | |
| |
| |
| Generalizing patterns with variables | |
| |
| |
| Exposes students to Fibonacci sequence | |
| |
| |
| Develops generalizing a pattern, inductive and deductive reasoning | |
| |
| |
| Previews simplifying expressions | |
| |
| |
| |
| Up and Down (FP) | |
| |
| |
| Percent situations from daily life | |
| |
| |
| Previews integers | |
| |
| |
| Develops the concept of percent change | |
| |
| |
| Applies the skills of finding the percent of a number and increasing or decreasing a number by a percent | |
| |
| |
| |
| The Social Network | |
| |
| |
| Exploration of viral growth on the internet | |
| |
| |
| Previews order of operations and slope concepts | |
| |
| |
| Develops the concepts of linear and exponential growth | |
| |
| |
| Applies the idea of generalizing a pattern | |
| |
| |
| Exposes students to building a mathematical model | |
| |
| |
| Connects exponential growth and percent of increase | |
| |
| |
| |
| Recap | |
| |
| |
| |
| Wind Down | |
| |
| |
| |
| Focus Problem, Step 3: Carry Out the Plan | |
| |
| |
| Revisit focus problem and solve it | |
| |
| |
| Applies knowledge gained to date | |
| |
| |
| |
| Cookie Monster | |
| |
| |
| Recipe conversion to decrease its size | |
| |
| |
| Connects conversions with scaling | |
| |
| |
| Applies fraction skills | |
| |
| |
| Applies unit conversion skills | |
| |
| |
| |
| Picture This | |
| |
| |
| Matching scenarios with graphs | |
| |
| |
| Exposes students to fitting data with a curve | |
| |
| |
| Connects scatterplots and types of change | |
| |
| |
| |
| Infinity and Beyond | |
| |
| |
| Exploration of Sierpinski triangles and their patterns | |
| |
| |
| Connects area and perimeter to generalizing a pattern | |
| |
| |
| Applies concepts of area and perimeter | |
| |
| |
| Exposes students to Sierpinski triangles | |
| |
| |
| Connects proportionality to similar triangles | |
| |
| |
| |
| Error and Estimation: Liquid Medicine | |
| |
| |
| Impact of being inaccurate with liquid medicine | |
| |
| |
| Exposes students to volume concepts | |
| |
| |
| Applies the concepts of constant and variable | |
| |
| |
| Applies the concepts of independent and dependent variables | |
| |
| |
| Applies unit conversions | |
| |
| |
| Previews order of operations | |
| |
| |
| |
| 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 | |
| |
| |
| |
| |
| |
| |
| Gear Up | |
| |
| |
| |
| Focus Problem, Step 1: Understand the Problem | |
| |
| |
| Exposure to an open-ended problem on baseball's magic number | |
| |
| |
| Previews the use of expressions, formulas, and integers | |
| |
| |
| |
| It's All Relative (FP) | |
| |
| |
| Work with atoms and ions to develop integer concepts | |
| |
| |
| Develops integer concepts | |
| |
| |
| Previews integer operations | |
| |
| |
| |
| Sign and Size, Part 1 (FP) | |
| |
| |
| Real-life situations to develop signed number addition/subtraction rules | |
| |
| |
| Develops integer operations of addition and subtraction | |
| |
| |
| Applies integer concepts and operations to realistic scenarios | |
| |
| |
| |
| Sign and Size, Part 2 | |
| |
| |
| Use of patterns to develop signed number multiplication/division rules | |
| |
| |
| Develops integer operations multiplication and division | |
| |
| |
| Defines real numbers | |
| |
| |
| Exposes students to imaginary numbers | |
| |
| |
| Reviews the concept of square roots | |
| |
| |
| |
| An Ounce of Prevention | |
| |
| |
| Grades situations to understand means | |
| |
| |
| Develops means conceptually and numerically | |
| |
| |
| Previews order of operations | |
| |
| |
| |
| Measure Up | |
| |
| |
| Geometric formulas with units to develop exponent rules | |
| |
| |
| Develops whole number exponent properties | |
| |
| |
| Applies geometric formulas | |
| |
| |
| Applies the use of units in calculations | |
| |
| |
| |
| Count Up (FP) | |
| |
| |
| Common situations with like terms | |
| |
| |
| Develops like terms | |
| |
| |
| Applies knowledge of formulas | |
| |
| |
| Exposes students to polynomial terminology and addition/subtraction | |
| |
| |
| |
| 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 | |
| |
| |
| |
| Order Up | |
| |
| |
| Order of operations and their use in formulas | |
| |
| |
| Develops the order of operations | |
| |
| |
| Applies order of operations to evaluating formulas | |
| |
| |
| Previews inverse operations necessary for equation solving | |
| |
| |
| |
| Does Order Matter? | |
| |
| |
| Uses of the commutative and associative properties in algebra and mental math | |
| |
| |
| Develops the commutative and associative properties | |
| |
| |
| Develops mental math skills | |
| |
| |
| Applies percent skills and adding like terms | |
| |
| |
| |
| Fair Share | |
| |
| |
| Development and application of the distributive property | |
| |
| |
| Develops the distributive property and mental math skills | |
| |
| |
| Applies the commutative property | |
| |
| |
| Applies the distributive property to multiplying polynomials | |
| |
| |
| Reviews like terms and whole number exponent properties | |
| |
| |
| |
| Seat Yourself (FP) | |
| |
| |
| Pattern recognition using a tables and chairs situation | |
| |
| |
| Applies the distributive property and connects it to like terms | |
| |
| |
| Develops the ability to write expressions | |
| |
| |
| |
| Punt, Pass, Kick | |
| |
| |
| Pythagorean Theorem off a grid | |
| |
| |
| Develops the Pythagorean Theorem | |
| |
| |
| Develops conceptual and numeric approaches to equation solving | |
| |
| |
| Previews concepts related to solving equations | |
| |
| |
| Connects Pythagorean triples to similar triangles | |
| |
| |
| |
| Ramp Up | |
| |
| |
| Slope on and off a grid | |
| |
| |
| Develops slope concepts and calculations | |
| |
| |
| Connects slope to linearity | |
| |
| |
| Applies Pythagorean Theorem and unit conversions | |
| |
| |
| |
| Shortest Distance (Optional) | |
| |
| |
| Pythagorean Theorem on a grid to measure distances | |
| |
| |
| Applies Pythagorean Theorem, slope, and the order of operations | |
| |
| |
| Develops the distance formula and measurement skills | |
| |
| |
| Connects slope and the distance formula | |
| |
| |
| |
| Recap | |
| |
| |
| |
| Wind Down | |
| |
| |
| |
| Focus Problem, Step 3: Carry Out the Plan | |
| |
| |
| Revisit focus problem and solve it | |
| |
| |
| Applies knowledge gained to date | |
| |
| |
| |
| Parts of Speech | |
| |
| |
| Operations vs. operators | |
| |
| |
| Applies the distributive property | |
| |
| |
| Develops understanding of operations | |
| |
| |
| |
| In the Swing of Things (Optional) | |
| |
| |
| Investigation of a pendulum formula | |
| |
| |
| Applies the order of operations | |
| |
| |
| Connects functions to the order of operations | |
| |
| |
| Applies function concepts | |
| |
| |
| |
| Error and Estimation: Rounding (Optional) | |
| |
| |
| Impact of being inaccurate with a financial formulas | |
| |
| |
| Applies the order of operations | |
| |
| |
| Develops understanding of the role of accuracy and precision | |
| |
| |
| |
| 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 | |
| |
| |
| |
| |
| |
| |
| Gear Up | |
| |
| |
| |
| Focus Problem, Step 1: Understand the Problem | |
| |
| |
| Exposure to an open-ended problem about comparing e-readers | |
| |
| |
| Previews the use of linear equations | |
| |
| |
| |
| Rule of Thumb | |
| |
| |
| Explore weighted means with grade situations | |
| |
| |
| Applies means and rates in a new context | |
| |
| |
| Develops weighted means | |
| |
| |
| |
| Working Hard for the Money (FP) | |
| |
| |
| Correlation between profession and income, unemployment rate | |
| |
| |
| Applies means and weighted means | |
| |
| |
| Applies making scatterplots | |
| |
| |
| Develops correlation, median, and mode | |
| |
| |
| Previews finding the trend line | |
| |
| |
| Previews slope-intercept form | |
| |
| |
| Applies scaling concepts | |
| |
| |
| Connects measures of center to geometry | |
| |
| |
| |
| A Fine Balance (Optional) | |
| |
| |
| Using chemical equations to understand solutions to equations | |
| |
| |
| Connects algebraic ideas with chemistry notation | |
| |
| |
| Develops the concept of solutions to equations | |
| |
| |
| Previews algebraic identities | |
| |
| |
| |
| Just a Pinch | |
| |
| |
| Measuring natural variation using standard deviation | |
| |
| |
| Develops standard deviation concepts and calculations | |
| |
| |
| Applies means, order of operations, and signed numbers | |
| |
| |
| Previews equation solving concepts | |
| |
| |
| |
| Separate but Equal (FP) | |
| |
| |
| Real-life scenarios that can be solved numerically and with one-step equations | |
| |
| |
| Develops one-step equations and understanding of equation solving | |
| |
| |
| Connects algebraic and numeric methods of equation solving | |
| |
| |
| |
| On the Rise | |
| |
| |
| Analyze an article about food packaging using algebra, geometry, and statistics | |
| |
| |
| Applies mean, median, standard deviation, and bar graphs | |
| |
| |
| Develops Pareto charts | |
| |
| |
| Applies writing and solving one-step equations | |
| |
| |
| |
| 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 | |
| |
| |
| |
| Game On (FP) | |
| |
| |
| Use pictures and algebra to solve two-step and multi-step equations | |
| |
| |
| Develops solving of linear equations | |
| |
| |
| Develops identities and contradictions | |
| |
| |
| |
| Quarter Wing Night (FP) | |
| |
| |
| Determine the number of buffalo wings in varying scenarios | |
| |
| |
| Applies equation solving techniques | |
| |
| |
| Applies percent concepts | |
| |
| |
| |
| Eastbound and Down (FP) | |
| |
| |
| Analyzing gas price scenarios with and without a car wash | |
| |
| |
| Applies equation solving techniques | |
| |
| |
| Connects linear equation solving and graphing | |
| |
| |
| Reviews linearity, slope, and rate of change | |
| |
| |
| Previews systems of equations | |
| |
| |
| |
| Get in Line (FP) | |
| |
| |
| Explore linear situations algebraically and on a graph | |
| |
| |
| Develops slope-intercept form and its uses in graphing | |
| |
| |
| Connects linearity between tables, graphs, and equations | |
| |
| |
| Exposes students to the concept of domain | |
| |
| |
| |
| Gas Up and Go (Optional) | |
| |
| |
| Study Distance = Rate x Time to explore variation | |
| |
| |
| Develops direct and inverse variation | |
| |
| |
| Exposes students to combined variation | |
| |
| |
| Applies equation solving | |
| |
| |
| |
| Recap | |
| |
| |
| |
| Wind Down | |
| |
| |
| |
| Focus Problem, Step 3: Carry Out the Plan | |
| |
| |
| Revisit focus problem and solve it | |
| |
| |
| Applies knowledge gained to date | |
| |
| |
| |
| Value of a Dollar (Optional) | |
| |
| |
| Determine the amount of time worked to pay for a tank of gas | |
| |
| |
| Develops rational functions | |
| |
| |
| Applies direct and inverse variation | |
| |
| |
| |
| When is the Algebra Worth It? (Optional) | |
| |
| |
| Assess when algebra is useful | |
| |
| |
| Applies and extends equation solving techniques | |
| |
| |
| Exposes students to non-linear equation solving | |
| |
| |
| |
| Error and Estimation: Volume | |
| |
| |
| Revisit and quantify liquid medicine overfilling error | |
| |
| |
| Applies slope-intercept form and graphing | |
| |
| |
| Applies percent of change and unit conversions | |
| |
| |
| |
| 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 | |
| |
| |
| |
| |
| |
| |
| Gear Up | |
| |
| |
| |
| Focus Problem, Step 1: Understand the Problem | |
| |
| |
| Exposure to an open-ended problem about making sense of a large number | |
| |
| |
| Previews dimensional analysis | |
| |
| |
| |
| A Matter of Change (FP) | |
| |
| |
| Work with more involved conversion problems | |
| |
| |
| Develops dimensional analysis | |
| |
| |
| Previews scientific notation | |
| |
| |
| |
| Little Giants (FP) | |
| |
| |
| Explores very large and very small numbers | |
| |
| |
| Develops scientific notation | |
| |
| |
| Connects dimensional analysis to scientific notation | |
| |
| |
| Applies Pareto charts and medians | |
| |
| |
| Previews negative exponents and compound inequalities | |
| |
| |
| |
| Outwit and Outlast (FP) | |
| |
| |
| Situations with proportionality, explored numerically and algebraically | |
| |
| |
| Develops solving proportions algebraically | |
| |
| |
| Connects scaling with algebraic methods of solving | |
| |
| |
| Applies rates | |
| |
| |
| Exposes students to concepts of apportionment | |
| |
| |
| |
| Chances Are (Optional) | |
| |
| |
| Simple probability situations from daily life | |
| |
| |
| Develops theoretical and experimental probabilities | |
| |
| |
| 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 | |
| |
| |
| |
| 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 | |
| |
| |
| |
| Chain, Chain, Chain | |
| |
| |
| Linear relationships in alkanes | |
| |
| |
| Exposes students to domain | |
| |
| |
| Develops writing linear models using y = mx + b | |
| |
| |
| 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 | |