#### S.1: Number Sense, Properties, and Operations

S.1.GLE.1: Proportional reasoning involves comparisons and multiplicative relationships among ratios

S.1.GLE.1.IQ: Inquiry Questions:

S.1.GLE.1.IQ.1: What information can be determined from a relative comparison that cannot be determined from an absolute comparison?

S.1.GLE.1.IQ.2: What comparisons can be made using ratios?

S.1.GLE.1.IQ.3: How do you know when a proportional relationship exists?

S.1.GLE.1.IQ.5: When is it better to use an absolute comparison?

S.1.GLE.1.IQ.6: When is it better to use a relative comparison?

S.1.GLE.1.RA: Relevance and Application:

S.1.GLE.1.RA.1: The use of ratios, rates, and proportions allows sound decision-making in daily life such as determining best values when shopping, mixing cement or paint, adjusting recipes, calculating car mileage, using speed to determine travel time, or enlarging or shrinking copies.

S.1.GLE.1.RA.3: Proportional reasoning is used extensively in geometry such as determining properties of similar figures, and comparing length, area, and volume of figures.

S.1.GLE.1.N: Nature of Mathematics:

S.1.GLE.1.N.2: Mathematicians reason abstractly and quantitatively.

S.1.GLE.1.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

S.1.GLE.2: Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently

S.1.GLE.2.IQ: Inquiry Questions:

S.1.GLE.2.IQ.1: How do operations with rational numbers compare to operations with integers?

S.1.GLE.2.RA: Relevance and Application:

S.1.GLE.2.RA.1: The use and understanding algorithms help individuals spend money wisely. For example, compare discounts to determine best buys and compute sales tax.

S.1.GLE.2.RA.2: Estimation with rational numbers enables individuals to make decisions quickly and flexibly in daily life such as estimating a total bill at a restaurant, the amount of money left on a gift card, and price markups and markdowns.

S.1.GLE.2.RA.3: People use percentages to represent quantities in real-world situations such as amount and types of taxes paid, increases or decreases in population, and changes in company profits or worker wages.

S.1.GLE.2.N: Nature of Mathematics:

S.1.GLE.2.N.2: Mathematicians make sense of problems and persevere in solving them.

S.1.GLE.2.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

#### S.2: Patterns, Functions, and Algebraic Structures

S.2.GLE.1: Properties of arithmetic can be used to generate equivalent expressions

S.2.GLE.1.IQ: Inquiry Questions:

S.2.GLE.1.IQ.1: How do symbolic transformations affect an equation or expression?

S.2.GLE.1.IQ.2: How is it determined that two algebraic expressions are equivalent?

S.2.GLE.1.N: Nature of Mathematics:

S.2.GLE.1.N.1: Mathematicians abstract a problem by representing it as an equation. They travel between the concrete problem and the abstraction to gain insights and find solutions.

S.2.GLE.1.N.2: Mathematicians reason abstractly and quantitatively.

S.2.GLE.2: Equations and expressions model quantitative relationships and phenomena

S.2.GLE.2.IQ: Inquiry Questions:

S.2.GLE.2.IQ.1: Do algebraic properties work with numbers or just symbols? Why?

S.2.GLE.2.IQ.2: Why are there different ways to solve equations?

S.2.GLE.2.IQ.4: Why might estimation be better than an exact answer?

S.2.GLE.2.IQ.5: When might an estimate be the only possible answer?

S.2.GLE.2.RA: Relevance and Application:

S.2.GLE.2.RA.1: Procedural fluency with algebraic methods allows use of linear equations and inequalities to solve problems in fields such as banking, engineering, and insurance. For example, it helps to calculate the total value of assets or find the acceleration of an object moving at a linearly increasing speed.

S.2.GLE.2.RA.3: Estimation with rational numbers enables quick and flexible decision-making in daily life. For example, determining how many batches of a recipe can be made with given ingredients, how many floor tiles to buy with given dimensions, the amount of carpeting needed for a room, or fencing required for a backyard.

S.2.GLE.2.N: Nature of Mathematics:

S.2.GLE.2.N.1: Mathematicians model with mathematics.

#### S.3: Data Analysis, Statistics, and Probability

S.3.GLE.1: Statistics can be used to gain information about populations by examining samples

S.3.GLE.1.IQ: Inquiry Questions:

S.3.GLE.1.IQ.1: How might the sample for a survey affect the results of the survey?

S.3.GLE.1.IQ.2: How do you distinguish between random and bias samples?

S.3.GLE.1.IQ.3: How can you declare a winner in an election before counting all the ballots?

S.3.GLE.2: Mathematical models are used to determine probability

S.3.GLE.2.IQ: Inquiry Questions:

S.3.GLE.2.IQ.1: Why is it important to consider all of the possible outcomes of an event?

S.3.GLE.2.IQ.3: What are situations in which probability cannot be used?

S.3.GLE.2.RA: Relevance and Application:

S.3.GLE.2.RA.1: The ability to efficiently and accurately count outcomes allows systemic analysis of such situations as trying all possible combinations when you forgot the combination to your lock or deciding to find a different approach when there are too many combinations to try; or counting how many lottery tickets you would have to buy to play every possible combination of numbers.

S.3.GLE.2.RA.2: The knowledge of theoretical probability allows the development of winning strategies in games involving chance such as knowing if your hand is likely to be the best hand or is likely to improve in a game of cards.

S.3.GLE.2.N: Nature of Mathematics:

S.3.GLE.2.N.2: Mathematicians construct viable arguments and critique the reasoning of others.

S.3.GLE.2.N.3: Mathematicians model with mathematics.

#### S.4: Shape, Dimension, and Geometric Relationships

S.4.GLE.1: Modeling geometric figures and relationships leads to informal spatial reasoning and proof

S.4.GLE.1.IQ: Inquiry Questions:

S.4.GLE.1.IQ.2: How does scale factor affect length, perimeter, angle measure, area and volume?

S.4.GLE.1.RA: Relevance and Application:

S.4.GLE.1.RA.2: Proportional reasoning is used extensively in geometry such as determining properties of similar figures, and comparing length, area, and volume of figures.

S.4.GLE.1.N: Nature of Mathematics:

S.4.GLE.1.N.3: Mathematicians look for relationships that can be described simply in mathematical language and applied to a myriad of situations. Proportions are a powerful mathematical tool because proportional relationships occur frequently in diverse settings.

S.4.GLE.2: Linear measure, angle measure, area, and volume are fundamentally different and require different units of measure

S.4.GLE.2.IQ: Inquiry Questions:

S.4.GLE.2.IQ.5: How are surface area and volume like and unlike each other?

S.4.GLE.2.IQ.6: What do surface area and volume tell about an object?

S.4.GLE.2.IQ.8: Why is pi an important number?

S.4.GLE.2.RA: Relevance and Application:

S.4.GLE.2.RA.1: The ability to find volume and surface area helps to answer important questions such as how to minimize waste by redesigning packaging, or understanding how the shape of a room affects its energy use.

S.4.GLE.2.N: Nature of Mathematics:

S.4.GLE.2.N.3: Mathematicians make sense of problems and persevere in solving them.

S.4.GLE.2.N.4: Mathematicians construct viable arguments and critique the reasoning of others.

Correlation last revised: 9/22/2020

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