### 1: Calculations and Estimations

#### 1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.1: Model, and compare rational numbers with an emphasis on integers

1.1.3: Use rates, ratios, and percents to solve problems

1.1.4: Locate rational numbers (with an emphasis on integers) on a number line

1.1.5: Interpret, model, and use percents greater than 100 and less than 1 to solve problems

1.1.6: Determine the prime factorization of a number less than 1000 and express the prime factorization using exponents when applicable

#### 1.2: Compute fluently and make reasonable estimates

1.2.1: Develop and analyze algorithms and compute with integers

1.2.2: Multiply and divide fractions and mixed numbers

1.2.3: Compute with squares and cubes, with an emphasis on finding area, surface area, and volume

1.2.4: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, and part-whole relationships)

1.2.5: Apply order of operations including exponents, to simplify calculations and evaluate expressions

1.2.6: Develop and use strategies to estimate the results of integer computations and judge the reasonableness of results

1.2.7: Use referent numbers in estimating answers to calculations with fractions and percents (e.g., 12 x 3/8 < 6, since 3/8 < 1/2 and 1/2 of 12 is 6)

#### 1.3: Understand meanings of operations and how they relate to one another

1.3.2: Use inverse operations (addition and subtraction, multiplication and division) to solve problems and check solutions involving calculations with integers

1.3.3: Apply the associative, commutative, and distributive properties to simplify computations with rational numbers (with an emphasis on integers)

1.3.5: Apply the property of additive inverses to determine solutions of equations

### 2: Statistics and Probability

#### 2.1: Select and use appropriate statistical methods to analyze data

2.1.1: Find, use, and interpret measures of center and spread, including mean and interquartile range for given or derived data

#### 2.2: Understand and apply basic concepts of probability

2.2.1: Compute experimental probabilities from a set of data and theoretical probabilities for single and simple compound events, using various methods (e.g., organized lists, tree diagrams, area models)

2.2.2: Determine probabilities of simple independent and dependent events

2.2.3: Compare experimental probability of an event with the theoretical probability and explain any difference

2.2.4: Determine all possible outcomes of a particular event or all possible arrangements of objects in a given set by applying various methods including tree diagrams and systematic lists

#### 2.3: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

2.3.2: Identify situations in which it makes sense to sample and identify methods for selecting a sample (e.g., convenience sampling, responses to survey, random sampling) that are representative of a population

2.3.3: Distinguish between random and biased samples and identify possible sources of bias in sampling

2.3.4: Represent and interpret data using frequency distribution tables, box-and whisker-plots, stem-and-leaf plots, and single- and multiple- line graphs

2.3.5: Determine the graphical representation of a set of data that best shows key characteristics of the data

#### 2.4: Develop and evaluate inferences and predictions that are based on data

2.4.1: Analyze data from frequency distribution tables, box-and whisker-plots, stem-and-leaf plots using measures of center and spread and draw conclusions

2.4.2: Predict and evaluate how adding data to a set of data affect measures of center

### 3: Algebraic Relationships

#### 3.1: Understand patterns, relations, and functions

3.1.1: Represent, analyze and determine rules for finding patterns involving integers with tables, graphs, words, and when possible, symbolic rules

#### 3.2: Represent and analyze mathematical situations and structures using algebraic symbols

3.2.1: Algebraically represent situations and solve problems involving linear equations and inequalities

3.2.3: Interpret algebraic relationships represented by two-column tables, number lines and coordinate graphs (four quadrants)

3.2.4: Graph linear equations on a coordinate grid by making a table using integer coordinates

#### 3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model situations, make predictions and inferences, and solve problems using linear equations

3.3.2: Recognize and represent direct variation using tables, graphs, and equations

3.3.3: Identify and sketch a graph that models a given situation

#### 3.4: Analyze change in various contexts

3.4.1: Identify and describe how a change in one variable relates to a change in a second variable

### 4: Measurement

#### 4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.1: Select the most appropriate unit to measure surface area and volume

4.1.2: Convert from a measurement expressed in one unit within a system to another using a different unit within the same system to measure surface and volume

#### 4.2: Apply appropriate techniques, tools, and formulas to determine measurements

4.2.1: Develop and use strategies and formulas for calculating surface area and volume of right prisms, pyramids, and cylinders

4.2.2: Develop strategies for determining approximate volumes of irregular shapes

4.2.3: Determine surface area and volume of three-dimensional block constructions, given a two-dimensional representation

4.2.4: Compare and contrast the formulas for surface area and volume of prisms and pyramids

4.2.5: Create examples of rectangular prisms having the same volume, but different surface areas

4.2.6: Describe what happens to the surface area and volume of a solid when its shape is changed

4.2.7: Use referents to make estimates of surface area and volume and evaluate the reasonableness of the estimate

### 5: Geometry

#### 5.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

5.1.1: Determine defining properties that characterize classes of quadrilaterals including side and angle measurements and their component parts (e.g., altitudes, medians, diagonals, bisectors)

5.1.2: Identify parallel and intersecting lines and pairs of angles formed (right, vertical, adjacent) by parallel lines cut by a transversal and determine their measure

5.1.3: Use proportional reasoning, drawings, models or technology to demonstrate congruence and similarity of polygons with an emphasis on quadrilaterals

5.1.4: Determine the measures of missing sides and angles in congruent quadrilaterals and their component parts

#### 5.2: Use visualization, spatial reasoning, and geometric modeling to solve problems

5.2.1: Model, sketch, and label prisms, pyramids, cylinders, and quadrilaterals with specified side lengths or angle measures

5.2.2: Use two-dimensional representation of three-dimensional objects, including nets, to solve problems involving surface area and volume

#### 5.3: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

5.3.1: Identify properties of quadrilaterals and their component parts on a coordinate graph

#### 5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Determine the image of a point (with integer coordinates) on a graph under translations and reflections

Correlation last revised: 10/24/2008

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