### 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 and use scientific notation.

1.1.1.b: Express and/or use equivalents among fractions, decimals, percents, integers, positive integer exponents, square roots, and/or numbers written in scientific notation.

1.1.4: Understand the concept of inverse proportion and apply direct and inverse proportion.

1.1.4.a: Explain, illustrate, or describe examples of inverse proportion.

1.1.4.b: Determine whether a real-world problem involves direct or inverse proportion.

1.1.4.c: Use direct or inverse proportion to determine an unknown number of objects or an unknown value in a given situation.

1.1.6: Complete multi-step computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots.

1.1.6.a: Calculate using order of operations on rational numbers.

1.1.8: Apply estimation strategies in situations involving multi-step computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers.

1.1.8.b: Use a variety of estimation strategies to predict or to verify the reasonableness of calculated results.

1.1.8.c: Describe a strategy used for estimation using multi-step computations.

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

1.2.1: Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume.

1.2.1.a: Determine and/or describe the impact of a change in two linear dimensions on perimeter, area, surface area, and/or volume.

1.2.1.b: Describe how changes in one or more linear dimensions affect perimeter, area, and/or volume in real world situations.

1.2.1.c: Determine the change in one or more linear dimensions given a change in perimeter, area, surface area, and/or volume.

1.2.3: Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision.

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

1.2.5: Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids.

1.2.5.a: Use formulas to determine and label the volume of a compound figure.

1.2.5.b: Use formulas to determine and label the surface area of a compound figure.

1.2.6: Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision.

1.2.6.a: Determine when approximate measurements are sufficient and estimate a reasonable measurement at an appropriate level of precision.

1.2.6.d: Select and use a procedure to find a reasonable estimate for and label the volumes of prisms and cylinders.

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

1.3.1: Understand the properties of and the relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures.

1.3.1.a: Make and test conjectures about 2-dimensional and 3-dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models.

1.3.1.b: Use the relationship between similar figures to determine the scale factor.

1.3.1.c: Match or draw a 3-dimensional figure that could be formed by folding a given net.

1.3.2: Use the properties of and relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures including prisms, cylinders, cones, and pyramids.

1.3.2.a: Match or draw 3-dimensional objects from different views using the same properties and relationships.

1.3.2.b: Sort, classify, and label prisms, cylinders, cones, and pyramids.

1.3.2.c: Sort, classify, and label 2-dimensional and 3-dimensional shapes according to characteristics including faces, edges, and vertices, using actual and virtual modeling.

1.3.2.d: Construct geometric figures, including angle bisectors, perpendicular bisectors, and triangles given specific characteristic, using a variety of tools and technologies.

1.3.2.f: Create a three-dimensional scale drawing with particular geometric properties.

1.3.3: Use geometric properties to determine and plot points on a coordinate grid.

1.3.3.a: Determine geometric properties of two-dimensional objects using coordinates on a grid.

1.3.4: Apply multiple transformations - translations, reflections, and/or rotations to 2-dimensional figures. Apply single dilations to 2-dimensional figures.

1.3.4.a: Use multiple translations, reflections, and/or rotations to create congruent figures on a coordinate grid.

1.3.4.b: Use dilation of a given figure to form a similar figure.

1.3.4.c: Determine the final coordinates of a point after multiple transformations.

1.3.4.d: Describe a combination of two translations, reflections, and/or rotations to transform one figure to another figure with or without a coordinate grid.

1.3.4.e: Determine rotational symmetry of a figure.

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

1.4.1: Understand the concepts of dependent and independent events.

1.4.1.a: Describe whether the outcome of a first event affects the probability of a later event.

1.4.1.b: Describe the difference between dependent and independent events.

1.4.1.c: Describe the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.

1.4.2: Use procedures to compute the probability of dependent and independent events.

1.4.2.a: Determine the sample space for independent or dependent events.

1.4.2.b: Determine probabilities of dependent and independent events.

1.4.2.c: Determine the outcomes and probability of multiple independent or dependent events.

1.4.2.d: Modify or revise a simple game based on independent probabilities so that all players have an equal probability of winning.

1.4.3: Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled.

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

1.4.5: Use bivariate data in tables and displays to predict mathematical relationships.

1.4.5.b: Determine whether an equation for a line is appropriate for a given set of data and supports the judgment with data.

1.4.5.c: Match an equation with a set of data or a graphic display.

1.4.5.d: Identify trends in a set of data in order to make a prediction based on the information.

1.4.6: Determine and explain how the same set of data can support different points of view.

1.4.6.a: Explain how the same set of data can support different points of view.

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

1.5.1: Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions.

1.5.1.a: Represent, extend, or create a pattern or sequence between sets of numbers representing a linear function.

1.5.1.b: Identify, extend, or create a geometric sequence or pattern.

1.5.1.c: Translate among equivalent numerical, graphical, and algebraic forms of a linear function.

1.5.1.e: Describe or represent linear and exponential patterns in words or algebraic symbols.

1.5.2: Determine an equation or rule for a linear function represented in a pattern, table, graph, or model.

1.5.2.a: Determine an equation of a line from a set of ordered pairs.

1.5.2.c: Write an equation or rule to describe a sequence.

1.5.2.d: Write an equation for a line given a graph of the line.

1.5.2.e: Write a rule for a recursive geometric pattern.

1.5.2.f: Write an expression, equation, or inequality with two variables representing a linear and/or non-linear model of a real-world problem.

1.5.2.g: Write an equation for a reasonable line to describe a set of bivariate data from a table or scatter plot.

1.5.4: Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots. Uses variables to write non-linear equations.

1.5.4.a: Use variables to write expressions and equations to represent situations that can be described using repeated addition or repeated multiplication.

1.5.4.b: Write equations in recursive form for additive or multiplicative models.

1.5.4.c: Match an expression or equation to a given real-world situation and explain the meaning of a variable.

1.5.4.d: Differentiate between and explain correct vs. incorrect representations of algebraic situations.

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

1.5.5: Apply algebraic properties to simplify expressions involving whole number exponents.

1.5.5.a: Write and/or simplify expressions including applying the distributive property.

1.5.5.b: Simplify an expression involving exponents.

1.5.6: Apply properties to solve multi-step equations and systems of equations.

1.5.6.a: Rearrange formulas to solve for a particular variable.

1.5.6.b: Determine the solution to a system of linear equations using tables, graphs, and/or symbols.

1.5.6.c: Interpret solutions of systems of equations.

1.5.6.d: Solve, or write and solve, multi-step equations.

1.5.6.e: Solve, or write and solve, linear inequalities.

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

3.1.1: Analyze, compare, and integrate mathematical information from multiple sources.

3.1.1.a: Analyze mathematical information or results.

3.1.1.b: Integrate information from two or more sources.

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 inductive or deductive reasoning.

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

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.

3.3.3: Validate thinking about mathematical ideas.

3.3.3.a: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning

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

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

4.2.2: Represent mathematical information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2- or 3-dimensional drawings, or other appropriate 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.