### 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 representation of fractions, decimals, and integers.

1.1.1.b: Convert between equivalent forms of fractions, decimals, or percents.

1.1.1.d: Explain or demonstrate that decimals may have multiple equivalent representations.

1.1.2: Understand the relative values of decimals, fractions, or integers.

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

1.1.2.b: Order decimals, fractions and/or integers based on a picture of a real world model, locations on a number line, or symbolic representation.

1.1.2.c: Explain why one integer, fraction, decimal, or percent is greater than, less than, or equal to another given number.

1.1.3: Understand and use the inverse property of addition on integers (W) and the inverse property of multiplication on non-negative decimals or fractions.

1.1.3.a: Use the inverse relationship between multiplication and division to simplify computations.

1.1.4: Understand the concept of direct proportion.

1.1.4.a: Explain or illustrate the meaning of a ratio, percent or proportion.

1.1.4.b: Express proportional relationships using objects, pictures, and symbols.

1.1.4.c: Complete or write a proportion for a given situation.

1.1.4.d: Predict a future situation using direct proportion

1.1.4.e: Represent equivalent ratios and/or percents using pictures, diagrams, or symbols.

1.1.4.f: Determine or use a ratio, percent, or proportion in a given situation.

1.1.5: Understand the meaning of addition and subtraction of integers.

1.1.5.a: Explain or show the meaning of addition and subtraction of integers using words, pictures, or real-world models.

1.1.5.b: Translate a symbolic addition or subtraction of integers into a real-life situation.

1.1.5.c: Show addition and subtraction of integers using technology.

1.1.5.d: Translate a given picture or illustration representing addition or subtraction of integers into an equivalent symbolic representation.

1.1.5.e: Explain why multiplication of fractions involves multiplying denominators while addition of fractions requires finding common denominators.

1.1.5.f: Select and/or use an appropriate operation to show understanding of addition and subtraction of integers.

1.1.6: Apply strategies or uses computational procedures using order of operations to add, subtract, multiply, and divide non-negative decimals and fractions.

1.1.6.a: Find the product or quotient using non-negative decimals and fractions.

1.1.6.b: Use multiplication and division in real world situations involving non-negative rational numbers.

1.1.6.c: Multiply non-negative decimals and fractions.

1.1.6.e: Compute with non-negative rational numbers using order of operations.

1.1.6.g: Complete multi-step calculations requiring two or more operations with non-negative decimals and fractions.

1.1.7: Apply strategies and uses tools to complete tasks involving addition and subtraction of integers and the four basic operations on non-negative decimals and fractions.

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

1.1.8: Apply estimation strategies involving addition and subtraction of integers and the four basic operations on non-negative decimals and fractions to predict results or determine reasonableness of answers.

1.1.8.a: Determine and explain when an approximation, estimation, or exact computation is appropriate and selects or illustrates a real-life situation where estimation is sufficient.

1.1.8.b: Use estimation strategies to predict an answer prior to operations on non-negative rational numbers.

1.1.8.d: Compute to check the reasonableness of estimated answers for a given situation.

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 computation with non-negative decimals and fractions.

#### 1.2: Understand and apply concepts and procedures from measurement.

1.2.1: Understand how changes in one linear dimension affect other linear measurements and area of rectangles, triangles, and circles.

1.2.1.a: Determine and/or describe the impact on the perimeter, circumference, and/or area of a rectangle, triangle, and/or circle caused by a change in one dimension.

1.2.1.b: Determine and/or describe the impact on one dimension caused by a change in perimeter, circumference and/or area of a rectangle, triangle, and/or circle.

1.2.3: Understand how the unit of measure affects the precision of measurement.

1.2.3.a: Identify, describe, or explain how the unit selected for a situation can affect the precision of the measurement.

1.2.3.b: Explain why measurement systems have different size units and how that allows for different levels of precision.

1.2.4: Understand and use a systematic procedure to measure and describe angles.

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.

1.2.5: Use formulas to determine measurements related to circles, triangles, and rectangular prisms.

1.2.5.a: Use formulas to determine and label missing measurements for circles, including radius, diameter, circumference, and area, in given situations.

1.2.5.b: Use formulas to determine and label missing measurements for rectangular prisms, including length, width, height, volume, and surface area, in given situations.

1.2.5.c: Use formulas to determine and label missing measurements for triangles, including base, height, perimeter, and area, in given situations.

1.2.5.d: Demonstrate or explain how to use a formula for finding the area and circumference of a circle.

1.2.5.e: Calculate and label dimensions of rectangular prisms with given volumes and/or surface areas.

1.2.5.f: Determine the surface area of a rectangular prism.

1.2.6: Understand and apply strategies to obtain a reasonable estimate of measurements related to circles, right triangles, and surface area of rectangular prisms.

1.2.6.b: Estimate and label circle, right triangle, and rectangular prism measurements.

1.2.6.c: Use common approximations of pi to estimate and label the circumference and the area of circles.

1.2.6.e: Explain why estimation or precise measurement is appropriate in a given situation.

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

1.3.1: Understand the concept of similarity and its relationship to congruence.

1.3.1.a: Identify or describe congruence in figures.

1.3.1.b: Explain how two figures are similar and/or congruent using definitions or real-world examples.

1.3.1.c: Produce a sample scale drawing and explains how it is an example of similarity.

1.3.2: Use the attributes of rectangular prisms, polygons, angles, and circles.

1.3.2.a: Sort, classify, and label circles according to their properties.

1.3.2.b: Sort, classify, and describe rectangular prisms according to their properties including vertices, edges, faces, bases, and parallel faces.

1.3.2.c: Draw rectangular prisms and circles with specified properties.

1.3.2.d: Explain and use the relationship between radius, diameter, and circumference.

1.3.2.e: Find the missing angle given all but one of the angles of a triangle or quadrilateral.

1.3.2.f: Sort, classify, and label figures according to their geometric properties.

1.3.3: Describe the location of points on a coordinate grid in any of the four quadrants.

1.3.3.a: Plot and label ordered pairs in any of the four quadrants.

1.3.3.b: Name the coordinates of a given point in any of the four quadrants.

1.3.3.c: Describe the location of objects on a coordinate grid using coordinates or labels.

1.3.4: Apply a combination of translations and/or reflections to 2-dimensional figures.

1.3.4.a: Explain the result of two or more translations or reflections of a figure with or without a grid.

1.3.4.b: Plot a combination of two translations and/or reflections of a simple figure with a coordinate grid.

1.3.4.c: Explain the transformation of one figure to another on a two-dimensional coordinate grid in terms of a combination of two translations or two reflections.

1.3.4.d: Describe a combination of two translations and/or reflections so that another person could draw them.

1.3.4.e: Explain a series of transformations in a given diagram or picture.

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

1.4.2: Use procedures to determine the probabilities of complementary and mutually exclusive events.

1.4.2.c: Determine, interpret, or express probabilities in the form of a fraction, decimal, or percent.

1.4.2.e: Predict the probability of future events based on empirical data.

1.4.4: Determine and use range and the measures of central tendency of a set of data.

1.4.4.a: Explain the effects of extreme values on the mean of a set of data.

1.4.4.b: Describe how additional data added to data sets may affect the measures of central tendency.

1.4.4.c: Explain the relationship between the range and measures of central tendency.

1.4.4.d: Complete a set of data based on a given mean, median, or mode and a partial set of data.

1.4.4.e: Explain why the mean, median, and mode may not be the same and what each indicates as a measure of central tendency in a given situation.

1.4.4.f: Determine and/or use the mean, median, mode, and/or range for a set of data.

1.4.5: Read and interpret data presented in diagrams, stem-and-leaf plots, scatter plots, and box-and-whisker plots.

1.4.5.a: Describe the accuracy and completeness of the data in a Venn diagram, stem-and-leaf plot, box-and-whisker plot, and/or scatter plot.

1.4.5.b: Read and interpret the data in Venn Diagrams, stem-and-leaf plots, box-and-whisker- plots, and/or scatter plots.

1.4.5.c: Select and explain which graph type is the most appropriate representation for a given set of data.

1.4.5.d: Interpret and describe trends and patterns represented in data and data displays.

1.4.5.e: Explain statistical information, including median, range, inter-quartile range, for a given box-and-whisker plot.

1.4.5.f: Use data from a sample or data display to make an inference.

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

1.5.1: Apply knowledge of linear relationships to recognize, extend, and/or create patterns in tables and graphs.

1.5.1.a: Select a linear relationship that has the same pattern as another linear relationship.

1.5.1.b: Use technology to generate graphic representations of linear relationships.

1.5.1.c: Select, extend, or represent patterns and sequences using tables, graphs, or expressions.

1.5.1.d: Use technology to generate graphic representations of linear and non-linear relationships.

1.5.1.e: Describe the relationship between a term in a sequence and its position in the sequence.

1.5.1.f: Identify patterns that are linear relations and provides missing terms in the beginning, middle, and/or end of the pattern.

1.5.2: Determine a rule for linear patterns and sequences with combinations of two operations in the rule.

1.5.2.b: Use an equation or graph to describe a linear relationship.

1.5.2.c: Use technology to determine the rule for a linear pattern or sequence.

1.5.3: Express relationships between quantities using equality and inequality symbols.

1.5.3.a: Express relationships between quantities including integers, and non-negative decimals and fractions 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 integers and/or non-negative decimals and fractions.

1.5.3.c: Write a simple equation or inequality using rational numbers and integers to represent a given situation.

1.5.4: Use variables to write expressions, linear equations, and inequalities that represent situations involving integers and non-negative decimals and fractions.

1.5.4.a: Write an expression, equation, or inequality using variables to represent a given situation.

1.5.4.b: Describe a situation that corresponds to a given expression, equation, or inequality.

1.5.4.c: Describe a situation involving a linear relationship that matches a given graph.

1.5.4.d: Translate among different representations of linear equations, using symbols, graphs, tables, diagrams, or written descriptions.

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

1.5.5: Apply algebraic properties to evaluate expressions and formulas using order of operations.

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 and two-step equations with one variable.

1.5.6.a: Solve single variable one-step or two-step equations and checks the solution.

1.5.6.b: Write and solve a single-variable one- or two-step equation for a given situation.

1.5.6.c: 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, statistical, and/or algebraic information from a variety of sources.

3.1.1.a: Analyze mathematical information or results.

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, statistical, and/or algebraic 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, scatter plots, stem-and-leaf plots, box-and-whisker plots, diagrams, and/or models for a purpose.

#### 4.2: Organize, represent, and share information.

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

4.2.2.a: Represent mathematical information using tables, charts, histograms, scatter plots, stem-and-leaf plots, box-and-whisker plots, 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.