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 concepts and symbolic representations of mixed numbers, proper and improper fractions, and decimals.

1.1.1.a: Represent mixed numbers, proper and improper fractions, and decimals using words, pictures, models, and/or numbers.

Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)

1.1.1.b: Make a model when given a symbolic representation or write a fraction or decimal when given a number line, picture, or model.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)

1.1.1.c: Explain how the value of a fraction changes in relationship to the size of the whole.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)

1.1.1.d: Explain the value for a given digit and/or show how to read and write decimals to at least the thousandths place.

Cannonball Clowns (Number Line Estimation)
Modeling Decimals (Base-10 Blocks)
Subtracting Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

1.1.2: Understand the relative values of non-negative fractions or decimals.

1.1.2.a: Order decimals, proper and improper fractions, and/or mixed numbers with denominators 2, 3, 4, 5, 6, 10, 12, and/or 15 using symbolic representations, number lines, or pictures.

Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)

1.1.2.c: Explain why one fraction is greater than, less than, or equal to another fraction.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

1.1.2.d: Explain why one decimal is greater than, less than, or equal to another decimal.

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Treasure Hunter (Decimals on the Number Line)

1.1.2.e: Show how factors and multiples can be used to name equivalent fractions.

Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)

1.1.3: Understand and apply the concept of divisibility including primes, composites, factors, and multiples.

1.1.3.b: Illustrate prime or composite numbers by creating a physical model.

Factor Trees (Factoring Numbers)

1.1.3.c: Identify prime or composite numbers between 1 and 100 and explain why a whole number is prime or composite.

Factor Trees (Factoring Numbers)

1.1.3.e: Use factors, multiples, and prime and composite numbers in a variety of situations.

Factor Trees (Factoring Numbers)

1.1.3.f: Factor a number into its prime factorization or into factor pairs.

Factor Trees (Factoring Numbers)

1.1.3.g: Explain or show whether one number is a factor of another number.

Factor Trees (Factoring Numbers)

1.1.3.h: Explain or demonstrate why a number is prime or composite.

Factor Trees (Factoring Numbers)

1.1.5: Understand the meaning of addition and subtraction of non-negative decimals and fractions.

1.1.5.a: Represent addition and subtraction of fractions with denominators of 2, 4, 8 or 2, 3, 6, 12 or 2, 5, 10.

Adding Fractions (Fraction Tiles)

1.1.5.b: Represent or explain addition and subtraction of non-negative decimals through thousandths using words, pictures, models, or numbers.

Adding Decimals (Base-10 Blocks)
Subtracting Decimals (Base-10 Blocks)

1.1.5.c: Explain a strategy for adding and subtracting fractions.

Adding Fractions (Fraction Tiles)

1.1.5.d: Select and/or use an appropriate operation(s) to show understanding of addition and subtraction of non-negative decimals and/or fractions.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Subtracting Decimals (Base-10 Blocks)

1.1.5.e: Explain the relationship between addition and subtraction of non-negative decimals and fractions.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Subtracting Decimals (Base-10 Blocks)

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

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Subtracting Decimals (Base-10 Blocks)

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

1.1.6.a: Add and subtract non-negative decimals and like-denominator fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and/or 15.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Subtracting Decimals (Base-10 Blocks)

1.1.6.b: Find sums or differences of decimals or like-denominator fractions in given situations.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Subtracting Decimals (Base-10 Blocks)

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

Adding Decimals (Base-10 Blocks)

1.1.6.d: Calculate difference of numbers with decimals to thousandths.

Subtracting Decimals (Base-10 Blocks)

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

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

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Subtracting Decimals (Base-10 Blocks)

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

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

Fraction Artist 2 (Area Models of Fractions)

1.2: Understand and apply concepts and procedures from measurement.

1.2.3: Understand how measurement units of capacity, mass, and length are organized in the metric system.

1.2.3.c: Convert between units in the metric system:

1.2.3.c.1: Length - millimeter, centimeter, meter, kilometer

Measuring Trees

1.2.4: Use a systematic procedure to measure and describe the area of rectangles or triangles.

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

Fido's Flower Bed (Perimeter and Area)

1.2.4.c: Demonstrate a procedure for measuring the area of a rectangle or right triangle.

Fido's Flower Bed (Perimeter and Area)

1.2.4.d: Use procedures to measure length, perimeter, and/or area.

Fido's Flower Bed (Perimeter and Area)

1.2.4.e: Measure the area in figures composed of rectangles and triangles.

Fido's Flower Bed (Perimeter and Area)

1.2.5: Use formulas to determine perimeter and area of rectangles and right triangles.

1.2.5.a: Explain how to find the perimeter or area of any rectangle using a rule.

Fido's Flower Bed (Perimeter and Area)

1.2.5.d: Determine and label right triangles and all rectangles with whole number dimensions and a given perimeter or area.

Fido's Flower Bed (Perimeter and Area)

1.2.6: Understand and apply strategies to obtain reasonable estimates of angle measurements and areas of rectangles and right triangles.

1.2.6.b: Estimate and label areas of rectangles and right triangles.

Fido's Flower Bed (Perimeter and Area)

1.2.6.c: Explain an appropriate process for estimating perimeter or area of a rectangle or right triangle or an angle measurement.

Fido's Flower Bed (Perimeter and Area)
Measuring Motion

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

1.3.2: Use the properties of parallel and perpendicular lines and line of symmetry.

1.3.2.a: Describe parallel and perpendicular lines and/or lines of symmetry.

Quilting Bee (Symmetry)

1.3.2.b: Draw, describe, and/or label a figure or design that includes a given set of properties including parallel or perpendicular lines and/or line of symmetry.

Quilting Bee (Symmetry)

1.3.2.c: Draw, describe, and/or label angles, quadrilaterals, parallel and/or perpendicular lines, lines of symmetry, and congruent 2-dimensional shapes or figures.

Quilting Bee (Symmetry)

1.3.2.d: Sort, classify, and label shapes and figures using the properties of parallel lines, perpendicular lines, and lines of symmetry.

Quilting Bee (Symmetry)

1.3.2.e: Complete a picture or design using a line of symmetry.

Quilting Bee (Symmetry)

1.3.2.f: Complete pictures or designs from a variety of cultures that incorporate parallel line(s), perpendicular line(s), and/or a line(s) of symmetry.

Quilting Bee (Symmetry)

1.3.3: Locate or plot points with whole number, fraction, and/or decimal coordinates on a positive number line.

1.3.3.b: Describe the relative position of fractions and/or decimals on a positive number line.

Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

1.3.3.c: Identify or move the coordinates of points on an incomplete number line involving fractional or decimal increments.

Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

1.3.4: Understand and apply translations or reflections to a 2-dimensional shape or figure.

1.3.4.a: Draw a translation or reflection of a given figure on a grid.

Quilting Bee (Symmetry)
Rock Art (Transformations)

1.3.4.b: Use translations or reflections to describe patterns in art, architecture, or nature.

Quilting Bee (Symmetry)
Rock Art (Transformations)

1.3.4.c: Describe whether a figure has been translated or reflected.

Quilting Bee (Symmetry)
Rock Art (Transformations)

1.3.4.d: Create designs using translations and/or reflections.

Quilting Bee (Symmetry)
Rock Art (Transformations)

1.3.4.e: Identify a picture or diagram of a particular translation or reflection.

Quilting Bee (Symmetry)
Rock Art (Transformations)

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

1.4.1: Understand the likelihood of simple events occurring.

1.4.1.a: Predict and test how likely it is that a certain outcome will occur.

Spin the Big Wheel! (Probability)

1.4.1.e: Explain why some outcomes are equally likely or more or less likely to happen than others.

Spin the Big Wheel! (Probability)

1.4.1.f: Determine whether a real-life event has zero probability, 50% probability, or 100% probability of occurring.

Spin the Big Wheel! (Probability)

1.4.3: Understand how different collection methods or different questions can affect the data collected.

1.4.3.b: Explain how different data collection methods, including phone survey, internet search, and person-to-person survey, affect the data set for a given question.

Mascot Election (Pictographs and Bar Graphs)

1.4.4: Understand and use the mean, median, and mode to describe a set of data.

1.4.4.a: Explain how to determine the mean of a set of data and explain the significance of the mean.

Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

1.4.4.b: Determine the mean of a given set of data using objects or pictures.

Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

1.4.4.c: Determine and explain whether mean, median, or mode is the most appropriate measure of central tendency in a given situation.

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

1.4.4.d: Explain why the mean, median, or mode may be greater than or less than the other measures for a given set of data.

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

1.4.4.e: Determine the mean for two samples from the same population and explain why they may not be the same.

Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

1.4.5: Read data presented in text and circle graphs.

1.4.5.a: Read and interpret data from text and circle graphs in terms of patterns.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

1.4.5.b: Explain the completeness and accuracy of data presented in circle graphs.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

1.4.5.c: Explain whether line plots, pictographs, tables, charts, bar or circle graphs are more appropriate for a given set of data, particular situation, or purpose, or answers a question most effectively.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

1.4.5.d: Summarize data presented in a circle graph or text.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

1.4.5.e: Describe trends or patterns in data represented in a line plot or pictograph.

Mascot Election (Pictographs and Bar Graphs)

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

1.5.1: Recognize, extend, and/or create patterns of objects or shapes or patterns of numbers with a single arithmetic operation between terms.

1.5.1.a: Extend, describe, or create patterns of numbers using division based on a single operation between terms.

Pattern Flip (Patterns)

1.5.1.b: Extend, describe, or create patterns of shapes or objects.

Pattern Flip (Patterns)

1.5.1.c: Extend and represent patterns using words, tables, numbers, models, and pictures.

Pattern Flip (Patterns)

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

Pattern Flip (Patterns)

1.5.2: Develop a rule for patterns, which may include combinations of two arithmetic operations.

1.5.2.a: Generate a rule for a pattern to extend or fill in parts of the pattern.

Pattern Flip (Patterns)

1.5.2.b: Determine a rule for a pattern of alternating operations and explains the rule.

Pattern Flip (Patterns)

1.5.2.c: Identify a rule for a pattern with two operations between terms.

Pattern Flip (Patterns)

1.5.2.d: Explain why a given rule with a single operation fits a given pattern.

Pattern Flip (Patterns)

1.5.2.e: Describe or write a rule for a pattern based on a single operation.

Pattern Flip (Patterns)

1.5.2.f: Explain why a given rule fits a pattern based on a single arithmetic operation in the rule.

Pattern Flip (Patterns)

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

1.5.3.a: Express relationships between like denominator fractions and decimal quantities using <, >, =, or "not equal to".

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Treasure Hunter (Decimals on the Number Line)

1.5.3.b: Describe a situation represented by an equation or inequality involving like denominator fractions and/or decimals.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Road Trip (Problem Solving)
Treasure Hunter (Decimals on the Number Line)

1.5.3.c: Write a simple equation or inequality using non-negative decimals or like-denominator fractions to represent a given situation.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Road Trip (Problem Solving)
Treasure Hunter (Decimals on the Number Line)

1.5.4: Use variables to write expressions and equations that represent situations involving addition and subtraction of non-negative decimals and like-denominator fractions.

1.5.4.a: Read expressions and equations involving variables.

Road Trip (Problem Solving)

1.5.4.b: Write an expression or equation using a variable to represent a given situation.

Road Trip (Problem Solving)

1.5.4.c: Describe a situation that represents a given expression or equation that includes a variable.

Road Trip (Problem Solving)

1.5.4.e: Write or illustrate expressions or equations using manipulatives, models, pictures, and symbols for given situations.

Modeling Decimals (Base-10 Blocks)
Road Trip (Problem Solving)
Toy Factory (Set Models of Fractions)

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

1.5.5.b: Determine the value of simple expressions or formulas involving addition and subtraction of non-negative decimals and like denominator fractions and/or multiplication and division of whole numbers given the values of the variables.

Fraction, Decimal, Percent (Area and Grid Models)

1.5.6: Apply properties to solve equations involving multiplication and division.

1.5.6.a: Solve a one-step equation involving multiplication or division using manipulatives, pictures, and/or symbols.

Road Trip (Problem Solving)

1.5.6.b: Write and solve an equation in a given situation.

Road Trip (Problem Solving)

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

Road Trip (Problem Solving)

3: The student uses mathematical reasoning.

3.1: Analyze information.

3.1.1: Analyze numerical, measurement, geometric, and/or statistical information in familiar situations.

3.1.1.a: Analyze mathematical information or results represented in tables, charts, graphs, text, diagrams, figures, or pictures.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

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

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

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

Reaction Time 2 (Graphs and Statistics)

3.2: Conclude.

3.2.1: Draw and support conclusions.

3.2.1.b: Use data or examples as evidence to support or contradict a given conclusion.

Reaction Time 2 (Graphs and Statistics)

3.2.1.c: Identify a valid conclusion based on given information.

Reaction Time 2 (Graphs and Statistics)

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

4.1: Gather information.

4.1.2: Extract numerical, measurement, geometric, and/or statistical information from multiple sources for a given purpose.

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

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2: Organize, represent, and share information.

4.2.1: Understand how to organize numerical, measurement, geometric, and/or statistical information to communicate for a given purpose.

4.2.1.a: Select a useful format and organize mathematical information for a given purpose.

Reaction Time 1 (Graphs and Statistics)

4.2.2: Understand how to represent numerical, measurement, geometric, and/or statistical information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using tables, charts, pictographs, bar graphs, line plots, circle graphs, pictures, models, drawings, or other forms including titles, labels, appropriate and consistent scales, and accurate display of data.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-world situations.

5.2: Relate mathematical concepts and procedures to other disciplines.

5.2.1: Use mathematical thinking, modeling, patterns, and ideas in other disciplines.

5.2.1.a: Give examples of mathematical patterns and ideas in other disciplines.

Pattern Flip (Patterns)