### 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.

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.

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

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.

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.

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.

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

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

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

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

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.

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.

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

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

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

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

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.

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

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

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

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

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.

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.

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

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

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

#### 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.

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

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

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

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.

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.

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

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

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

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.

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

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

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.

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.

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

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

#### 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.

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

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

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.

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.

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

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

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

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.

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

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

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

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

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

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.

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

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

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

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.

#### 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.

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

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

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.

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.

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

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

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

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

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

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.

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

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

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

#### 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.

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

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

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.

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

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".

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

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

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".

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

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.

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

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

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.

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.

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

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

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

### 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.

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

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

#### 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.

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.

### 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.

#### 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.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.