1: The student understands and applies the concepts and procedures of mathematics.

1.1: Understand and apply concepts and procedures from number sense.

1.1.1: Understand the concept and symbolic representations of integers as the set of natural numbers, their additive inverses, and 0.

1.1.1.c: Locate the additive inverse of a given integer on a number line.

Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.1.2: Understand the relative values of integers and non-negative fractions, decimals, and percents.

1.1.2.a: Order different representations of fractions, decimals, and/or percents.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.2.b: Show and determine equivalence between non-negative integers, fractions, decimals, and percents using words, pictures, models, and symbols.

Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals

1.1.2.c: Order integers, fractions, decimals, and/or percents and explain why one number is greater than, less than, or equal to another.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.2.d: Explain when a fraction, decimal, or percent of one whole is not the same as the same fraction, decimal, or percent of a different whole.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.4: Understand the concepts of ratio and percent.

1.1.4.a: Write or show and explain ratios in part/part and part/whole relationships using words, objects, pictures, models, and/or symbols.

Part:Part and Part:Whole Ratios

1.1.4.b: Represent equivalent ratios using objects, pictures, or symbols.

Part:Part and Part:Whole Ratios
Percents, Fractions and Decimals
Polling: Neighborhood

1.1.4.c: Represent equivalent percentages using objects, pictures, and symbols.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions
Percents, Fractions and Decimals

1.1.4.d: Express or represent percent as a ratio based on 100 equal size parts of a set.

Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

1.1.4.e: Explain ratio and percents and give examples of each.

Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

1.1.4.f: Create a ratio equivalent to a given ratio to determine an unknown value for a dimension or a number of events or objects.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

1.1.5: Understand the meaning of multiplication and division of non-negative decimals and fractions.

1.1.5.a: Explain or show the meaning of multiplying and dividing non-negative fractions and decimals using words, pictures, or models.

Dividing Fractions
Multiplying Fractions
Multiplying with Decimals

1.1.5.b: Explain the effect of multiplying a whole number by a decimal number.

Multiplying with Decimals

1.1.5.c: Explain why multiplication of fractions involves multiplying denominators.

Multiplying Fractions
Multiplying Mixed Numbers

1.1.5.d: Demonstrate how multiplication and division with decimals affects place value.

Multiplying with Decimals

1.1.5.f: Translate a picture or illustration into an equivalent symbolic representation of multiplication and division of non-negative fractions and decimals.

Dividing Fractions
Multiplying Fractions
Multiplying with Decimals

1.1.5.g: Select and/or use an appropriate operation to show understanding of addition, subtraction, multiplication, or division of non-negative rational numbers.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

1.1.6: Apply strategies or uses computational procedures to add and subtract non-negative decimals and fractions.

1.1.6.a: Find the sums or differences of non-negative fractions or decimals.

Fractions with Unlike Denominators
Sums and Differences with Decimals

1.1.6.b: Find sums or differences of decimals or fractions in real-world situations.

Fractions with Unlike Denominators
Sums and Differences with Decimals

1.1.6.d: Calculate sums of two numbers with decimals to the thousandths or three numbers with decimals to hundredths.

Sums and Differences with Decimals

1.1.6.e: Calculate difference between numbers with decimals to thousandths.

Sums and Differences with Decimals

1.1.6.f: Complete multiple-step computations requiring addition and/or subtraction.

Adding Real Numbers
Sums and Differences with Decimals

1.1.7: Apply strategies and uses tools appropriate to tasks involving addition and subtraction of non-negative decimals and fractions.

1.1.7.c: Describe strategies for mentally adding and/or subtracting non-negative decimals and fractions.

Fractions with Unlike Denominators
Sums and Differences with Decimals

1.1.8: Apply estimation strategies involving addition and subtraction of non-negative decimals and fractions to predict results or determine reasonableness of answers.

1.1.8.a: Explain whether estimation or exact calculation is appropriate in situations involving addition and subtraction of non-negative decimals and fractions.

Estimating Sums and Differences
Fractions with Unlike Denominators
Sums and Differences with Decimals

1.1.8.b: Use a variety of estimation strategies prior to computation to predict an answer.

Estimating Population Size
Estimating Sums and Differences

1.1.8.e: Explain an appropriate adjustment when an estimate and a computation do not agree.

Estimating Sums and Differences

1.1.8.f: Explain or describe a strategy for estimation involving addition and subtraction of non-negative decimals and fractions.

Estimating Population Size
Estimating Sums and Differences
Fractions with Unlike Denominators
Sums and Differences with Decimals

1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Understand the concepts of surface area and volume of rectangular prisms.

1.2.1.a: Represent the volume for given rectangular prisms using pictures or models.

Prisms and Cylinders - Activity A

1.2.1.b: Describe and provide examples of surface area and volume.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.1.c: Explain and give examples of how area and surface area are related.

Perimeter, Circumference, and Area - Activity B
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

1.2.1.d: Describe the relationship between surface area and volume of a rectangular prism.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.2.1.e: Label measurements of rectangular prisms to show understanding of the relationships among linear dimensions, surface area, and volume of rectangular prisms.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.2.2: Understand the differences between area (square) units and volume (cubic) units.

1.2.2.a: Select appropriate units for area and volume in given situations.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.2.b: Explain why volume is measured in cubic units.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.2.c: Explain how the selected unit of length affects the size of cubic units.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.2.d: Explain why area is measured in square units and volume is measured in cubic units.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.4: Use a systematic procedure to measure and describe the volume of rectangular prisms.

1.2.4.a: Suggested Procedure:

1.2.4.a.3: Select a tool that matches the unit chosen.

Triple Beam Balance

1.2.4.a.4: Use the selected tool to determine the number of units.

Triple Beam Balance

1.2.4.b: Select and describe the appropriate units and/or tools for measuring length, area, and/or volume.

Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.4.c: Measure the volume of rectangular prisms using manipulatives or pictures and counts the number of units as part of the measurement procedure.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.6: Understand and apply strategies to obtain reasonable estimates of volume using manipulatives and/or drawings.

1.2.6.b: Estimate and label volume or capacity.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.6.c: Use estimation to determine reasonableness of a volume of a rectangular prism.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.2.6.d: Describe a procedure to find a reasonable estimate of volume or capacity.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Understand the properties of circles and rectangular prisms.

1.3.1.a: Describe circles or rectangular prisms using geometric properties.

Circles
Classifying Triangles
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.3.1.b: Draw a figure given properties that describe a circle or rectangular prism.

Circles
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

1.3.1.c: Explain lines of symmetry for 2-dimensional figures including circles.

Classifying Triangles
Holiday Snowflake Designer

1.3.2: Use the attributes of angles and polygons.

1.3.2.a: Use, sort, classify, and label geometric figures in illustrations, nature, and art.

Classifying Quadrilaterals - Activity A
Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

1.3.2.b: Sort and classify 2-dimensional shapes and/or figures according to their properties including number of sides, number of vertices, types of angles, parallel sides, perpendicular sides, symmetry, and/or congruence.

Classifying Quadrilaterals - Activity A
Classifying Triangles
Holiday Snowflake Designer
Triangle Angle Sum - Activity A

1.3.2.d: Find the missing angle given two angles of a triangle.

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

1.3.2.e: Describe or draw lines of symmetry for angles and/or polygons.

Holiday Snowflake Designer

1.3.2.f: Identify, describe, or draw angles or polygons using geometric properties.

Classifying Triangles

1.3.3: Understand the relative location of points with integer coordinates on a number line.

1.3.3.a: Plot integers and non-negative fractions and/or decimals on a number line.

Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.3.3.b: Locate the point of final destination given directions for movement on an integer number line.

Comparing and Ordering Integers
Real Number Line - Activity A

1.3.3.c: Determine and describe the distance between any two integers on a number line.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Real Number Line - Activity A

1.3.3.d: Describe the relative location of points and objects on a number line with both positive and negative numbers.

Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.3.3.e: Locate objects on a number line based on given numeric locations.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.3.3.f: Identify or name the location of points on a number line using coordinates or labels.

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.3.4: Understand and apply rotations to a 2-dimensional figure about its center or a vertex.

1.3.4.a: Describe a 90¡ or 180¡ rotation of a figure about its center or a vertex.

Rotations, Reflections and Translations

1.3.4.b: Describe a rotation so that another person could draw it.

Rotations, Reflections and Translations

1.3.4.c: Describe whether an object has been translated or rotated on a coordinated grid.

Rotations, Reflections and Translations

1.3.4.d: Draw a design using a 90¡, 180¡, 270¡, or 360¡ rotation of a shape or figure.

Rotations, Reflections and Translations

1.3.4.e: Plot the points and write the coordinates of an object or figure that has been rotated 90¡, 180¡, or 270¡ about its center or a vertex on a coordinate grid.

Rotations, Reflections and Translations

1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.1: Understand probability as a number between 0 and 1 inclusive.

1.4.1.a: Represent the probability of a simple event as a number between 0 and 1 inclusive.

Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

1.4.1.b: Express probabilities as fractions or decimals between 0 and 1 inclusive, and percents between 0 and 100 inclusive.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

1.4.1.c: Translate between representations of probability including fractions, decimals, and percents.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Percents, Fractions and Decimals
Probability Simulations
Theoretical and Experimental Probability

1.4.2: Use procedures to determine outcomes and/or the probabilities of events or situations.

1.4.2.a: Determine the probability of a simple event as a ratio, decimal, or percent.

Compound Independent Events
Compound Independent and Dependent Events
Estimating Population Size
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

1.4.2.b: Represent all possible outcomes of an experiment in a variety of ways including an organized list, a table, or a tree diagram.

Permutations and Combinations

1.4.4: Understand and use measures of central tendency to describe a set of data.

1.4.4.a: Use mean, median and mode, to describe or explain a set of data in familiar and new situations

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.b: Determine mean, median, and mode of a set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.c: Explain why the mean, median, and mode may not be the same for a given set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.d: Explain why the mean, median, or mode best describes a set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.4.e: Explain what the mean, median, and mode indicate about a set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

1.4.5: Read and interpret data presented in diagrams, single line graphs, and histograms.

1.4.5.a: Explain which graph type is most appropriate for a given situation and data.

Box-and-Whisker Plots
Line Plots
Stem-and-Leaf Plots

1.4.5.b: Read and interpret data from Venn diagrams, single line graphs, and/or histograms; and explains the use of these graphs.

Histograms
Populations and Samples

1.4.5.e: Explain the completeness and accuracy of data presented in single line graphs and histograms.

Histograms
Populations and Samples

1.4.5.f: Describe trends or patterns in data represented in single line graphs and histograms.

Histograms
Populations and Samples

1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Recognize, extend, and/or create patterns and sequences that use two different arithmetic operations alternating between terms.

1.5.1.a: Create a pattern and explain what makes it a pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.1.c: Identify and describe a number pattern for a given table, graph, rule, or words,

Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Finding Patterns
Geometric Sequences
Using Tables, Rules and Graphs

1.5.1.e: Extend a pattern by supplying missing elements in the beginning, middle, and/or end of the pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2: Develop a rule for patterns involving combinations of two arithmetic operations.

1.5.2.b: Identify, describe, or write a rule for a given pattern involving two different alternating operations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

1.5.2.d: Determine a rule in order to supply missing elements in the beginning, middle, or end of a pattern or sequence.

Arithmetic Sequences

1.5.3: Understand the concept of mathematical equality and inequality and uses the symbols =, "not equal to", <, >, "less than or equal to" and "greater than or equal to".

1.5.3.a: Express relationships between quantities including non-negative fractions, decimals, percents, and integers using =, "not equal to", <, >, "less than or equal to" and "greater than or equal to".

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.5.3.b: Describe a situation represented by an equation or inequality involving non-negative fractions, decimals, percents, and/or integers.

Using Algebraic Equations

1.5.3.c: Write a simple equation or inequality using non-negative fractions, decimals, percents, and integers to represent a given situation.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4: Use variables to write expressions, equations, and inequalities that represent situations involving two arithmetic operations on whole numbers and/or non-negative decimals and fractions.

1.5.4.a: Translate a situation involving two arithmetic operations into algebraic form involving variables and using =, "not equal to", >, <, "less than or equal to", or "greater than or equal to".

Using Algebraic Equations

1.5.4.b: Describe a situation involving two arithmetic operations that matches a given equation with variables.

Using Algebraic Equations

1.5.4.c: Write an equation, expression, or inequality using a variable to represent a given situation and explains the meaning of the variable.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.d: Describe a situation that corresponds to a given expression, equation, or inequality that includes variables.

Using Algebraic Equations
Using Algebraic Expressions

1.5.4.e: Explain the meaning of variables in a formula, expression, or equation.

Using Algebraic Equations
Using Algebraic Expressions

1.5.5: Apply algebraic properties to evaluate expressions and formulas using pictures and/or symbols.

1.5.5.c: Write an expression with a variable that represents a given situation and determine the value of the expression given a value for the variable.

Using Algebraic Equations
Using Algebraic Expressions

1.5.6: Apply a variety of properties to solve one-step equations.

1.5.6.a: Solve one-step equations involving non-negative rational numbers using manipulatives, pictures, and/or symbols.

Modeling One-Step Equations - Activity A

1.5.6.b: Solve one-step single variable equations.

Modeling One-Step Equations - Activity A

1.5.6.c: Write and solve one-step single variable equations for a given situation.

Modeling One-Step Equations - Activity A
Using Algebraic Equations
Using Algebraic Expressions

1.5.6.d: Explain or show the meaning of the solution to an equation.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Analyze numerical, measurement, geometric, probability, and/or statistical information from a variety of sources.

3.1.1.a: Analyze mathematical information or results represented in single line graphs and scatter plots.

Biconditional Statement
Conditional Statement
Scatter Plots - Activity A

3.1.1.b: Compare mathematical information represented in tables, charts, graphs, text, diagrams, figures, or pictures.

Biconditional Statement
Conditional Statement
Populations and Samples

3.1.1.d: Differentiate between valid and invalid analysis of mathematical information or results.

Biconditional Statement
Conditional Statement

3.3: Verify results.

3.3.1: Justify results using evidence.

3.3.1.a: Justify results using evidence and information from the problem situation and/or known facts, patterns, and relationships.

Introduction to Functions

3.3.2: Evaluate reasonableness of results.

3.3.2.b: Verify that the solution to a real-world problem makes sense in relation to the situation.

Biconditional Statement
Conditional Statement

4: The student communicates knowledge and understanding in both everyday and mathematical language.

4.1: Gather information.

4.1.2: Extract numerical, measurement, geometric, probability, and/or statistical information from multiple sources.

4.1.2.a: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, line graphs, circle graphs, histograms, Venn diagrams, and/or models for a purpose.

Histograms

4.2: Organize, represent, and share information.

4.2.2: Represent numerical, measurement, geometric, probability, and/or statistical information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using tables, charts, line graphs, circle graphs, histograms, Venn diagrams, pictures, models, drawings, or other appropriate forms including title, labels, appropriate and consistent scales, and accurate display of data.

Describing Data Using Statistics
Histograms