### 1: Number, Number Sense and Operations

#### 1.B: Compare, order and convert among fractions, decimals and percents.

1.B.1: Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation.

1.B.3: Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and other (irrational) as non-terminating and non-repeating decimals.

#### 1.E: Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

1.E.4: Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals.

#### 1.G: Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations.

1.G.9: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares).

#### 1.H: Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

1.H.8: Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use.

#### 1.I: Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

1.I.6: Simplify numerical expressions involving integers and use integers to solve real-life problems.

1.I.7: Solve problems using the appropriate form of a rational number (fraction, decimal or percent).

1.I.9: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares).

### 2: Measurement

#### 2.B: Convert units of length, area, volume, mass and time within the same measurement system.

2.B.2: Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters.

#### 2.C: Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.

2.C.6: Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms.

2.C.7: Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors.

#### 2.E: Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature.

2.E.4: Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system.

2.E.5: Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems.

#### 2.F: Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

2.F.9: Describe what happens to the surface area and volume of a three-dimensional object when the measurements of the object are changed; e.g., length of sides are doubled.

#### 2.G: Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

2.G.8: Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas.

### 3: Geometry and Spatial Sense

#### 3.D: Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

3.D.2: Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:

3.D.2.b: Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent.

#### 3.E: Use proportions to express relationships among corresponding parts of similar figures.

3.E.1: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures.

3.E.6: Determine and use scale factors for similar figures to solve problems using proportional reasoning.

#### 3.F: Describe and use the concepts of congruence, similarity and symmetry to solve problems.

3.F.7: Identify the line and rotation symmetries of two-dimensional figures to solve problems.

#### 3.G: Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.

3.G.3: Use and demonstrate understanding of the properties of triangles. For example:

3.G.3.a: Use Pythagorean Theorem to solve problems involving right triangles.

3.G.3.b: Use triangle angle sum relationships to solve problems.

3.G.5: Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures.

#### 3.H: Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.

3.H.8: Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).

#### 3.I: Identify and draw three-dimensional objects from different views (top, side, front and perspective).

3.I.9: Draw representations of three-dimensional geometric objects from different views.

#### 3.J: Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.

3.J.6: Determine and use scale factors for similar figures to solve problems using proportional reasoning.

### 4: Patterns, Functions and Algebra

#### 4.B: Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

4.B.1: Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.

4.B.2: Generalize patterns by describing in words how to find the next term.

#### 4.D: Use symbolic algebra to represent and explain mathematical relationships.

4.D.9: Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula.

#### 4.E: Use rules and variables to describe patterns, functions and other relationships.

4.E.3: Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, 16... is nonlinear.

#### 4.F: Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.

4.F.5: Represent linear equations by plotting points in the coordinate plane.

4.F.6: Represent inequalities on a number line or a coordinate plane.

#### 4.G: Write, simplify and evaluate algebraic expressions.

4.G.1: Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.

4.G.7: Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified; e.g., 4m = m + m + m + m or a [dot] 5 + 4 = 5a + 4.

#### 4.K: Graph linear equations and inequalities.

4.K.5: Represent linear equations by plotting points in the coordinate plane.

4.K.6: Represent inequalities on a number line or a coordinate plane.

### 5: Data Analysis and Probability

#### 5.A: Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

5.A.1: Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.

#### 5.D: Compare increasingly complex displays of data, such as multiple sets of data on the same graph.

5.D.5: Compare data from two or more samples to determine how sample selection can influence results.

#### 5.E: Collect, organize, display and interpret data for a specific purpose or need.

5.E.2: Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph.

#### 5.F: Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

5.F.3: Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures.

#### 5.I: Describe the probability of an event using ratios, including fractional notation.

5.I.7: Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models.

#### 5.K: Make and justify predictions based on experimental and theoretical probabilities.

5.K.8: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences.

### 6: Mathematical Processes

#### 6.K: Recognize and use mathematical language and symbols when reading, writing and conversing with others.

Correlation last revised: 8/29/2016

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