### 1: Number, Number Sense and Operations

#### 1.C: Develop meaning for percents, including percents greater than 100 and less than 1.

1.C.4: Describe what it means to find a specific percent of a number, using real-life examples.

1.C.5: Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.

#### 1.D: Use models and pictures to relate concepts of ratio, proportion and percent.

1.D.3: Explain why a number is referred to as being "rational," and recognize that the expression [a/b] can mean a parts of size [1/3] each, a divided by b, or the ratio of a to b.

1.D.5: Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.

#### 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.6: Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions.

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

1.G.1: Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 25), and explain why "squared" means "second power" and "cubed" means "third power."

1.G.2: Find and use the prime factorization of composite numbers. For example:

1.G.2.c: Apply the prime factorization to solve problems and explain solutions.

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

1.H.8: Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take [2 2/3 divided by 1/6].

1.H.12: Develop and analyze algorithms for computing with fractions and decimals, 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.11: Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning.

1.I.13: Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., [7/8 + 12/13] [approximation] and 4.23 x 5.8 [approximation] 25.

1.I.14: Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.

1.I.15: Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was \$140, and the sale price is \$100.

### 2: Measurement

#### 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.3: Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by:

2.C.3.b: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.

#### 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.6: Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape 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.5: Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.

### 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.1: Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides.

3.D.4: Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting.

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

3.G.3: Use multiple classification criteria to classify triangles; e.g., right scalene triangle.

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

3.H.5: Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.

### 4: Patterns, Functions and Algebra

#### 4.A: Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

4.A.1: Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.

4.A.2: Use words and symbols to describe numerical and geometric patterns, rules and functions.

#### 4.C: Use variables to create and solve equations and inequalities representing problem situations.

4.C.6: Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations.

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

4.E.2: Use words and symbols to describe numerical and geometric patterns, rules and functions.

#### 4.H: Solve linear equations and inequalities symbolically, graphically and numerically.

4.H.4: Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.

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

4.K.4: Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.

#### 4.L: Analyze functional relationships, and explain how a change in one quantity results in a change in the other.

4.L.7: Identify and describe situations with constant or varying rates of change, and compare them.

### 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, construct and interpret line graphs, circle graphs and histograms.

#### 5.B: Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.

5.B.5: Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers.

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

5.D.3: Compare representations of the same data in different types of graphs, such as a bar graph and circle graph.

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

5.E.2: Select, create and use graphical representations that are appropriate for the type of data collected.

#### 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.4: Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).

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

5.K.7: Design an experiment to test a theoretical probability and explain how the results may vary.

### 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.