S.1: Number Sense, Properties, and Operations

S.1.GLE.1: Quantities can be expressed and compared using ratios and rates

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

S.1.GLE.1.IQ.1: How are ratios different from fractions?

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Proportions and Common Multipliers

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

S.1.GLE.1.RA.1: Knowledge of ratios and rates allows sound decision-making in daily life such as determining best values when shopping, creating mixtures, adjusting recipes, calculating car mileage, using speed to determine travel time, or making saving and investing decisions.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

S.1.GLE.1.RA.3: Rates and ratios are used in mechanical devices such as bicycle gears, car transmissions, and clocks.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

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

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

Estimating Population Size

S.1.GLE.1.N.3: Mathematicians reason abstractly and quantitatively.

Biconditional Statements
Conditional Statements

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

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

S.1.GLE.2.IQ.1: Why might estimation be better than an exact answer?

Estimating Sums and Differences
Multiplying Decimals (Area Model)

S.1.GLE.2.IQ.2: How do operations with fractions and decimals compare to operations with whole numbers?

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Fractions Greater than One (Fraction Tiles)
Multiplying Decimals (Area Model)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

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

S.1.GLE.2.RA.1: Rational numbers are an essential component of mathematics. Understanding fractions, decimals, and percentages is the basis for probability, proportions, measurement, money, algebra, and geometry.

Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values

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

S.1.GLE.2.N.1: Mathematicians envision and test strategies for solving problems.

Estimating Population Size

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

Estimating Population Size

S.1.GLE.3: In the real number system, rational numbers have a unique location on the number line and in space

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

S.1.GLE.3.IQ.1: Why are there negative numbers?

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values

S.1.GLE.3.IQ.2: How do we compare and contrast numbers?

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

S.1.GLE.3.RA: Relevance and Application:

S.1.GLE.3.RA.2: Negative numbers can be used to represent quantities less than zero or quantities with an associated direction such as debt, elevations below sea level, low temperatures, moving backward in time, or an object slowing down.

Integers, Opposites, and Absolute Values

S.1.GLE.3.N: Nature of Mathematics:

S.1.GLE.3.N.1: Mathematicians use their understanding of relationships among numbers and the rules of number systems to create models of a wide variety of situations.

Solving Algebraic Equations I
Solving Algebraic Equations II

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

Biconditional Statements

S.2: Patterns, Functions, and Algebraic Structures

S.2.GLE.1: Algebraic expressions can be used to generalize properties of arithmetic

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

S.2.GLE.1.IQ.1: If we didn't have variables, what would we use?

Solving Algebraic Equations I

S.2.GLE.1.IQ.2: What purposes do variable expressions serve?

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Equations on the Number Line
Using Algebraic Equations

S.2.GLE.1.IQ.4: Why does the order of operations exist?

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

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

S.2.GLE.1.RA.1: The simplification of algebraic expressions allows one to communicate mathematics efficiently for use in a variety of contexts.

Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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

S.2.GLE.1.N.3: Mathematicians reason abstractly and quantitatively.

Biconditional Statements
Conditional Statements

S.2.GLE.2: Variables are used to represent unknown quantities within equations and inequalities

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

S.2.GLE.2.IQ.1: Do all equations have exactly one unique solution? Why?

Absolute Value Equations and Inequalities
Solving Equations on the Number Line
Using Algebraic Equations

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

S.2.GLE.2.N.1: Mathematicians use graphs and equations to represent relationships among variables. They use multiple representations to gain insights into the relationships between variables.

Solving Equations on the Number Line
Using Algebraic Equations

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

Estimating Population Size

S.3: Data Analysis, Statistics, and Probability

S.3.GLE.1: Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge

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

S.3.GLE.1.IQ.2: When is one data display better than another?

Box-and-Whisker Plots
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

S.3.GLE.1.IQ.4: What makes a good statistical question?

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

S.3.GLE.1.RA: Relevance and Application:

S.3.GLE.1.RA.1: Comprehension of how to analyze and interpret data allows better understanding of large and complex systems such as analyzing employment data to better understand our economy, or analyzing achievement data to better understand our education system.

Box-and-Whisker Plots
Polling: City
Real-Time Histogram

S.3.GLE.1.RA.2: Different data analysis tools enable the efficient communication of large amounts of information such as listing all the student scores on a state test versus using a box plot to show the distribution of the scores.

Polling: City

S.3.GLE.1.N: Nature of Mathematics:

S.3.GLE.1.N.1: Mathematicians leverage strategic displays to reveal data.

Polling: City
Real-Time Histogram

S.3.GLE.1.N.2: Mathematicians model with mathematics.

Estimating Population Size
Using Algebraic Expressions

S.4: Shape, Dimension, and Geometric Relationships

S.4.GLE.1: Objects in space and their parts and attributes can be measured and analyzed

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

S.4.GLE.1.IQ.3: What does area tell you about a figure?

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

S.4.GLE.1.IQ.4: What properties affect the area of figures?

Chocomatic (Multiplication, Arrays, and Area)
Perimeter and Area of Rectangles

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

S.4.GLE.1.RA.1: Knowledge of how to find the areas of different shapes helps do projects in the home and community. For example how to use the correct amount of fertilizer in a garden, buy the correct amount of paint, or buy the right amount of material for a construction project.

Area of Parallelograms
Perimeter and Area of Rectangles

S.4.GLE.1.RA.2: The application of area measurement of different shapes aids with everyday tasks such as buying carpeting, determining watershed by a center pivot irrigation system, finding the number of gallons of paint needed to paint a room, decomposing a floor plan, or designing landscapes.

Area of Parallelograms
Perimeter and Area of Rectangles

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

S.4.GLE.1.N.3: Mathematicians make sense of problems and persevere in solving them.

Estimating Population Size

S.4.GLE.1.N.4: Mathematicians reason abstractly and quantitatively.

Biconditional Statements
Conditional Statements
Estimating Population Size