### 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 rational numbers.

1.1.1.c: Explain the meaning of square root of a whole number and provide examples.

1.1.2: Understand the relative values of rational numbers.

1.1.2.a: Order rational numbers including integers, whole number powers, and square roots, and explain why one rational number is greater than, equal to, or less than another.

1.1.2.b: Order rational numbers including integers, whole number powers, and square roots based on a picture of a real world model, locations on a number line, or symbolic representation.

1.1.2.c: Explain why one given rational number including integers, whole-number powers, and square roots is greater than, equal to, or less than another rational number.

1.1.3: Understand and use the distributive property and the properties of addition and multiplication on rational numbers.

1.1.3.b: Use the distributive property to simplify expressions that include integers.

1.1.3.c: Use the distributive property to factor expressions.

1.1.3.e: Use the addition and multiplication properties, including the distributive property, to assist with computations.

1.1.4: Apply the concepts of ratio, percent, and direct proportion.

1.1.4.a: Determine an unknown value for a dimension or a number of events or objects using ratio or proportion.

1.1.4.b: Determine an unknown value for a dimension or a number of events or objects using percents.

1.1.4.c: Select and use the most advantageous representation of ratios or percents in a given situation.

1.1.4.d: Determine a ratio or percent in a given situation.

1.1.5: Understand the meaning of addition, subtraction, multiplication, division, powers, and square roots on rational numbers.

1.1.5.b: Explain the meaning of taking whole number powers of integers or square roots of whole numbers using words, pictures, or models.

1.1.5.c: Represent a situation involving multiplication or division of integers, whole number powers of integers, or square roots of whole numbers.

1.1.5.d: Explain how the result of dividing a rational number by a fraction between 0 and 1 is different from the result of dividing the same number by a fraction greater than 1.

1.1.5.e: Translate a given situation, picture, or illustration into a numeric expression or equation involving decimals, fractions, integers, whole number powers, and square roots of whole numbers.

1.1.5.f: Select and/or use an appropriate operation to show understanding of whole number powers and square roots.

1.1.5.g: Convert between equivalent forms of rational numbers including whole number powers and square roots of perfect squares.

1.1.6: Apply strategies or uses computational procedures using order of operations and addition, subtraction, multiplication, division, powers, and square roots on rational numbers.

1.1.6.a: Compute with rational numbers using order of operations.

1.1.6.b: Compute using whole number powers and/or square roots of perfect squares.

1.1.6.d: Complete multi-step computations using two or more different operations with rational numbers.

1.1.7: Apply strategies and uses tools to complete tasks involving computation of rational numbers.

1.1.7.c: Describe strategies for mental computation with integers using powers and square roots.

1.1.8: Apply estimation strategies involving computation of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict results or determine reasonableness of answers.

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

1.1.8.c: Use a variety of estimation strategies to verify the reasonableness of calculated results.

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 decimals, fractions, and integers, using +, -, x, Ö, powers, and square roots.

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

1.2.1: Understand how a change in one linear dimension affects surface area and volume of rectangular prisms and cylinders and how changes in two linear dimensions affect perimeter and area of rectangles.

1.2.1.a: Determine and/or describe the impact that a change in one dimension has on volume and surface area in right cylinders and rectangular prisms.

1.2.1.b: Determine and/or describe a change in a linear dimension given a change in volume and/or surface area of rectangular prisms and cylinders.

1.2.1.c: Determine and/or describe the impact on perimeter and/or area of a rectangle caused by a change in two dimensions.

1.2.2: Understand and use rate, slope, and other derived units of measurement.

1.2.2.a: Explain the concept of a rate or slope in a given situation.

1.2.2.c: Calculate a rate of change or slope in a situation.

1.2.3: Explain why different situations require different levels of precision.

1.2.3.a: Describe or explain why different situations require different levels of precision.

1.2.3.b: Compare situations that require different levels of precision.

1.2.3.c: Select and describe an appropriate unit of measure for the precision needed in a given situation.

1.2.5: Use formulas, including the Pythagorean Theorem, to determine measurements related to triangles, rectangular prisms, and right cylinders.

1.2.5.a: Explain how to use a formula to calculate and label the surface area and volume of a prism or cylinder.

1.2.5.b: Use the Pythagorean Theorem to determine and label a missing dimension of a right triangle or prism.

1.2.5.c: Determine and label surface areas of right cylinders and right prisms.

1.2.5.d: Determine and label dimensions of a triangle, prism, or cylinder based on a given perimeter, circumference, area, and/or volume.

1.2.6: Apply strategies to obtain reasonable estimates of surface area and volume of right cylinders and rectangular prisms, and the lengths of sides of right triangles.

1.2.6.b: Use estimation to determine and label volume and surface area for right cylinders and right prisms and explain why an approximation is appropriate.

1.2.6.c: Use estimation strategies to determine and label the approximate length of the third side of a right triangle given the lengths of two sides.

1.2.6.d: Use estimation strategies to determine and labels the approximate distance or height in a situation using similar triangles or the Pythagorean Theorem.

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

1.3.1: Understand properties of cylinders, cones, and pyramids.

1.3.1.a: Identify or describe cylinders, cones, or pyramids.

1.3.1.b: Classify and label cylinders, cones, or pyramids.

1.3.1.c: Draw nets of cylinders, prisms, and pyramids.

1.3.1.d: Identify and label rays, lines, end points, line segments, vertices, and angles in three-dimensional shapes and figures.

1.3.2: Use the properties of similarity; uses the Pythagorean Theorem to determine if a triangle is a right triangle.

1.3.2.a: Sort, classify, and label similar and congruent figures.

1.3.2.b: Use properties of similarity to draw, describe, sort, classify, and/or label two-dimensional figures in illustrations or real life.

1.3.2.c: Draw a shape similar to a given complex shape.

1.3.2.e: Use the Pythagorean Theorem to determine if a triangle is a right triangle.

1.3.3: Describe the relative position of points on a coordinate grid.

1.3.3.a: Locate a missing vertex given the coordinates of the vertices of a polygon.

1.3.3.b: Explain a method for finding the missing side of a triangle in a real-world setting.

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

1.3.4.a: Use any combination of rotations, reflections, and/or translations to draw or locate congruent figures on a grid.

1.3.4.b: Use ordered pairs or labels to describe the location of a picture or an object transformed by any combination of translations, reflections, and/or rotations on a coordinate grid.

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

1.4.1: Understand the concept of compound events.

1.4.1.a: Determine and explain when events are compound.

1.4.1.b: Describe the difference between compound events involving "and" or "or".

1.4.1.c: Describe or represent compound events.

1.4.2: Use procedures to determine the probability of compound events.

1.4.2.a: Determine the sample space for simple experiments involving independent or compound events.

1.4.2.b: Calculate the probability of two independent events occurring simultaneously using various methods including organized lists, tree diagrams, counting procedures, and area models.

1.4.2.c: Explain the relationship between theoretical and empirical probability of compound events.

1.4.2.d: Predict the probability of outcomes of experiments and relates the predictions to empirical results.

1.4.2.e: Design a situation that would produce a given probability.

1.4.2.f: Design a game using compound probabilities with equal chances of winning for all players.

1.4.3: Describe how different samples of a population may affect the data collected.

1.4.3.a: Describe bias in population samples and explains a procedure for selecting an unbiased representative sample.

1.4.3.c: Determine whether claims made about results are based on biased data due to sampling.

1.4.4: Identify clusters and outliers in data and determine effects on the measures of central tendency.

1.4.4.a: Identify clusters and outliers and determine how they may affect measures of central tendency.

1.4.4.b: Modify a set of data so that the median is a more reasonable measure of central tendency than the mean.

1.4.4.c: Examine variations in data, including clusters and outliers, to select the most appropriate measure of central tendency to describe a given set of data.

1.4.4.d: 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, tables of ordered pairs, and scatter plots and makes predictions based on the data.

1.4.5.a: Describe trends or patterns in data presented in a table of ordered pairs or a scatter plot.

1.4.5.b: Read and interpret the data in Venn Diagrams, tables of ordered pairs, and/or scatter plots.

1.4.5.d: Draw trend lines with or without technology and makes predictions about real-world situations.

1.4.5.e: Explain whether stem-and-leaf plot, box-and-whisker plot, or scatter plot is more appropriate for a given set of data, a particular situation, or purpose, or answers a question most effectively.

1.4.5.f: Determine whether claims made about results are based on biased representations of data.

1.4.5.g: Predict an outcome given a linear relationship involving non-negative rational numbers.

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

1.5.1: Apply knowledge of linear and non-linear relationships to recognize, extend, and create patterns and sequences in tables and graphs.

1.5.1.a: Extend, represent, or create linear and non-linear patterns and sequences using tables and graphs.

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

1.5.1.d: Extend a pattern by supplying missing terms in the beginning, middle, or end of a linear or non-linear pattern.

1.5.2: Determine a rule for linear and non-linear functions represented in tables, graphs, patterns or situations.

1.5.2.a: Determine a rule, developed from a table, graph, or situation, using words or algebraic symbols.

1.5.2.b: Develop a rule that describes a recursive pattern in terms of current and previous values such as the Fibonacci sequence.

1.5.2.c: Describe a rule and/or construct a table to represent a pattern.

1.5.2.d: Use technology to develop a table or graph from a given rule.

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

1.5.3.a: Express relationships between quantities including whole number exponents and square roots 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 whole number exponents and/or square roots.

1.5.3.c: Use equality and inequality symbols to express relationships between rational numbers using square roots and powers in a given situation.

1.5.4: Use variables to write expressions, linear equations, and inequalities that represent situations involving relationships with rational numbers.

1.5.4.a: Use variables to write an expression, equation, or inequality 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.

1.5.6: Apply a variety of properties to solve multi-step equations and one-step inequalities with one variable.

1.5.6.a: Solve multi-step single-variable equations involving parentheses, like terms, or variables on both sides of the equal sign.

1.5.6.b: Write and solve multi-step single variable equations involving parentheses, like terms, or variables on both sides of the equal sign.

1.5.6.c: Solve, or write and solve, one-step inequalities.

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, 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, diagrams, models, and graphs including scatter plots, stem-and-leaf plots, and box-and-whisker plots 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, 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.