A: Number and Operations

A.1: Students will understand numerical concepts and mathematical operations

A.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

A.1.1.1: Compare and order rational numbers.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

A.1.1.2: Use equivalent representations for rational numbers (e.g., integers, decimals, fractions, percents, ratios, numbers with whole-number exponents).

Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)
Modeling Fractions (Area Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

A.1.1.3: Use appropriate representations of positive rational numbers in the context of real-life applications.

Integers, Opposites, and Absolute Values

A.1.1.5: Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

A.1.2: Understand the meaning of operations and how they relate to one another.

A.1.2.1: Calculate multiplication and division problems using contextual situations.

Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

A.1.2.2: Factor a whole number into a product of its primes.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

A.1.2.3: Demonstrate the relationship and equivalency among ratios and percents.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

A.1.2.4: Use proportions to solve problems.

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

A.1.2.5: Explain and perform:

A.1.2.5.b: addition, subtraction, multiplication, and division with decimals

Adding Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Subtracting Decimals (Base-10 Blocks)
Sums and Differences with Decimals

A.1.2.5.c: addition and subtraction with integers

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

A.1.2.5.d: addition, subtraction, and multiplication with fractions and mixed numerals

Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Fractions
Multiplying Mixed Numbers

A.1.3: Compute fluently and make reasonable estimates.

A.1.3.1: Estimate quantities involving rational numbers using various estimations.

Estimating Sums and Differences
Multiplying Decimals (Area Model)

A.1.3.2: Use estimates to check reasonableness of results and make predictions in situations involving rational numbers.

Estimating Sums and Differences
Multiplying Decimals (Area Model)

A.1.3.4: Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

Rational Numbers, Opposites, and Absolute Values

A.1.3.5: Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

Modeling Decimals (Area and Grid Models)
Percents, Fractions, and Decimals

A.1.3.6: Interpret and use ratios in different contexts.

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)

A.1.3.7: Compute and perform multiplication and division of fractions and decimals and apply these procedures to solving problems.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Square Roots

B: Algebra

B.1: Students will understand algebraic concepts and applications.

B.1.1: Understand patterns, relations, and functions.

B.1.1.1: Solve problems involving proportional relationships.

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

B.1.1.2: Graph ordered pairs in the coordinate plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

B.1.1.3: Explain and use symbols to represent unknown quantities and variable relationships.

Solving Algebraic Equations I
Using Algebraic Expressions

B.1.1.4: Explain and use the relationships among ratios, proportions, and percents.

Percent of Change
Percents, Fractions, and Decimals

B.1.1.5: Make generalizations based on observed patterns and relationships.

Pattern Finder

B.1.2: Represent and analyze mathematical situations and structures using algebraic symbols.

B.1.2.1: Solve problems involving proportional relationships.

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

B.1.2.2: Use letters to represent an unknown in an equation.

Solving Equations on the Number Line
Using Algebraic Equations

B.1.2.3: Solve one-step linear equations and inequalities in one variable with positive whole-number solutions.

Absolute Value with Linear Functions
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable

B.1.3: Use mathematical models to represent and understand quantitative relationships.

B.1.3.1: Develop and use mathematical models to represent and justify mathematical relationships found in a variety of situations.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

B.1.3.2: Create, explain, and use mathematical models such as:

B.1.3.2.a: Venn diagrams to show the relationships between the characteristics of two or more sets

Compound Inequalities

B.1.3.2.b: equations and inequalities to model numerical relationships

Absolute Value Equations and Inequalities
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Using Algebraic Equations

B.1.4: Analyze changes in various contexts.

B.1.4.3: Use ratios to predict changes in proportional situations.

Geometric Probability

B.1.4.4: Use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences, and perimeter.

Percents, Fractions, and Decimals

B.1.4.5: Generate formulas to represent relationships involving changes in perimeter.

Perimeter and Area of Rectangles

C: Geometry

C.1: Students will understand geometric concepts and applications.

C.1.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

C.1.1.1: Identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:

C.1.1.1.b: understand that the sum of angles of any triangle is 180 degrees and the sum of the angles of any quadrilateral is 360 degrees and use this information to solve problems

Polygon Angle Sum
Triangle Angle Sum

C.1.1.1.c: visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids

Surface and Lateral Areas of Prisms and Cylinders

C.1.1.3: Describe the properties of geometric figures that include regular polygons, circles, ellipses, cylinders, cones, spheres, and cubes.

Circles
Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones

C.1.1.5: Classify triangles as scalene, isosceles, or equilateral and by angles (i.e., right, acute, and obtuse).

Classifying Triangles

C.1.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

C.1.2.1: Use coordinate geometry to describe location on a plane.

Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

C.1.2.2: Recognize skewed lines in space.

Parallel, Intersecting, and Skew Lines

C.1.3: Apply transformations and use symmetry to analyze mathematical situations.

C.1.3.1: Identify line of symmetry with rotation and scaling.

Rock Art (Transformations)

D: Measurement

D.1: Students will understand measurement systems and applications.

D.1.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

D.1.1.1: Perform multi-step conversions of measurement units to equivalent units within a given system (e.g., 36 inches equals 3 feet or 1 yard).

Unit Conversions

D.1.1.3: Select and use units of appropriate size and type to measure angles (e.g., degrees, radians), perimeter, area, and capacity in both U.S. customary and metric systems.

Fido's Flower Bed (Perimeter and Area)

D.1.2: Apply appropriate techniques, tools, and formulas to determine measurements.

D.1.2.1: Apply various measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational number representations for length, liquid, weight, perimeter, temperature, and time.

Measuring Trees

D.1.2.2: Select and use formulas for perimeters of squares and rectangles.

Perimeter and Area of Rectangles

E: Data Analysis and Probability

E.1: Students will understand how to formulate questions, analyze data, and determine probabilities.

E.1.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

E.1.1.1: Use statistical representations to analyze data.

Box-and-Whisker Plots

E.1.1.2: Draw and compare different graphical representations of the same data.

Box-and-Whisker Plots
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

E.1.1.3: Use mean, median, mode, and range to describe data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

E.1.1.4: Sketch circle graphs to display data.

Graphing Skills

E.1.1.5: Solve problems by collecting, organizing, displaying and interpreting data

Describing Data Using Statistics
Estimating Population Size
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)

E.1.1.6: Compare different samples of a population with the entire population and determine the appropriateness of using a sample.

Polling: City
Polling: Neighborhood
Populations and Samples

E.1.1.7: Conduct and explain sampling techniques such as observations, surveys, and random sampling for gathering data.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

E.1.1.8: Determine the median for a rational number data set containing an odd number of data points.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

E.1.1.9: Calculate and explain the median for a whole number data set containing an even number of data points.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

E.1.1.11: Formulate and solve problems by collecting, organizing, displaying, and interpreting data.

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

E.1.2: Select and use appropriate statistical methods to analyze data.

E.1.2.1: Choose an appropriate graphical format to organize and represent data.

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

E.1.2.2: Describe the effects of missing or incorrect data.

Polling: City
Polling: Neighborhood

E.1.2.3: Compute and analyze statistical measurements for data sets:

E.1.2.3.a: understand how additional data added to data sets may affect the computations of central tendency

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

E.1.2.3.b: understand how the inclusion or exclusion of outliers affects measures of central tendency

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

E.1.2.3.c: know why a specific measure of central tendency provides the most useful information in a given context

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

E.1.2.4: Use data samples of a population and describe the characteristics and limitations of the sample.

Polling: City
Polling: Neighborhood
Populations and Samples

E.1.2.5: Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

Polling: City
Polling: Neighborhood

E.1.2.6: Explain how the way a question is asked in a survey might influence the results obtained.

Polling: Neighborhood

E.1.2.7: Identify data that represent sampling errors and explain why the sample and the display might be biased.

Polling: City
Populations and Samples

E.1.2.8: Identify claims based on statistical data and, in sample cases, evaluate the validity and usefulness of the claims.

Polling: City

E.1.3: Develop and evaluate inferences and predictions that are based on data.

E.1.3.2: Conduct observations, surveys, experiments and/or simulations, record the results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.

Describing Data Using Statistics
Mascot Election (Pictographs and Bar Graphs)
Polling: City
Reaction Time 2 (Graphs and Statistics)

E.1.3.3: Find all possible combinations in a given set (e.g., the number of ways a set of books can be arranged on a shelf).

Permutations and Combinations

E.1.3.4: Compare expected results with actual results in a simple experiment.

Independent and Dependent Events
Polling: Neighborhood

E.1.4: Understand and apply basic concepts of probability.

E.1.4.1: List all possible outcomes for a compound event composed of two independent events and recognize whether an outcome is certain, impossible, likely, or unlikely.

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

E.1.4.2: Determine and compare experimental (empirical) and mathematical (theoretical) probabilities (e.g., flipping two color counters).

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

E.1.4.3: Determine theoretical and experimental probabilities and use them to make predictions about events.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

E.1.4.4: Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.

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

E.1.4.5: Use data to estimate the probability of future events (e.g., batting averages).

Independent and Dependent Events

E.1.4.7: Describe the difference between independent and dependent events and identify situations involving independent or dependent events.

Independent and Dependent Events