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?

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

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

Rational Numbers, Opposites, and Absolute Values

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

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

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

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

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

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

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.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers
Road Trip (Problem Solving)

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.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

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

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

Biconditional Statements
Conditional Statements

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

Biconditional Statements

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?

Adding and Subtracting Integers
Adding on the Number Line

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.

Percent of Change

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.

Estimating Sums and Differences

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.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram

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

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

Estimating Population Size

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

Biconditional Statements

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?

Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations
Using Algebraic Equations

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

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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.

Solving Equations on the Number Line
Using Algebraic Equations

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

Biconditional Statements
Conditional Statements

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?

Compound Interest
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Algebraic Equations II
Using Algebraic Equations

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

Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

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

Estimating Sums and Differences

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

Estimating Sums and Differences

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.

Solving Two-Step Equations

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.

Estimating Population Size

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

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

Estimating Population Size

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?

Polling: City
Polling: Neighborhood

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

Polling: Neighborhood
Populations and Samples

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

Polling: City

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?

Independent and Dependent Events
Spin the Big Wheel! (Probability)

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

Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

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.

Independent and Dependent Events
Permutations and Combinations
Spin the Big Wheel! (Probability)

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.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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

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

Biconditional Statements

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

Estimating Population Size

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?

Dilations
Similar Figures

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.

Beam to Moon (Ratios and Proportions)

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.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

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?

Surface and Lateral Areas of Prisms and Cylinders

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

Prisms and Cylinders
Pyramids and Cones

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

Circumference and Area of Circles

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.

Prisms and Cylinders

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

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

Estimating Population Size

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

Biconditional Statements