### 1: The student understands and applies the concepts and procedures of mathematics.

#### 1.1: Understand and apply concepts and procedures from number sense.

1.1.2: Understand the relative values of integers and non-negative rational numbers.

1.1.2.a: Compare different representations of non-negative rational numbers by implementing strategies (e.g., like denominators, changing to the same form).

1.1.2.b: Identify equivalence between non-negative integers, fractions, percents, and decimals.

1.1.2.c: Compare and order integer values and explain which is greater and why (e.g., place the integers on a number line).

1.1.2.d: Represent and identify integers on a model (e.g., number line, fraction line, or decimal grid).

1.1.4: Understand the concepts of ratio and percent.

1.1.4.a: Write ratios in part/part and part/whole relationships using objects, pictures, and symbols (e.g., using /, :, or “to” as representations for ratios).

1.1.4.b: Represent equivalent ratios using objects, pictures, or symbols.

1.1.4.c: Represent equivalent percentages using objects, pictures, and symbols.

1.1.4.d: Identify percent as 100 equal-size parts of a set (e.g., 1% of 200 items is 2 items).

1.1.4.e: Explain ratio and percents and give examples of each.

1.1.5: Understand the meaning of multiplication and division on non-negative rational numbers.

1.1.5.a: Explain the meaning of multiplying and dividing non-negative fractions and decimals using words or visual or physical models (e.g., sharing a restaurant bill, cutting a board into equal-sized pieces, drawing a picture of an equation or situation).

1.1.5.b: Explain why multiplication of fractions can be done by multiplying denominators while addition of fractions requires finding common denominators.

1.1.5.c: Use technology to demonstrate how multiplication and division with decimals affects place value.

1.1.6: Apply computational procedures with fluency for addition and subtraction on non-negative rational numbers.

1.1.6.a: Find the sums or differences of nonnegative fractions or decimals.

1.1.6.b: Write and solve real-world problem situations to find sums or differences of decimals or fractions.

1.1.6.d: Use addition and subtraction to solve real-world problems involving non-negative rational numbers.

1.1.7: Understand and apply strategies and tools to complete tasks involving addition and subtraction on non-negative rational numbers.

1.1.7.c: Use calculators to add and subtract with decimal numbers with precision to the thousandths place and beyond.

1.1.8: Apply estimation strategies to predict or determine the reasonableness of answers in situations involving addition and subtraction on non-negative rational numbers.

1.1.8.b: Apply estimation strategies prior to computation on whole numbers, decimals, and fractions to approximate an answer.

1.1.8.e: Describe various strategies used during estimation involving fractions and decimals.

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

1.2.1: Understand the concepts of volume and extend the concept of area to surface area of rectangular prisms.

1.2.1.b: Represent the volume for given rectangular prisms using pictures or models.

1.2.1.c: Compare the surface area of two different rectangular prisms.

1.2.1.d: Describe and provide examples for surface area measurement (e.g., gift wrapping, painting a room, amount of material needed to build a box).

1.2.1.e: Explain and give examples of how the area and surface area are related (e.g., surface area is the sums of the areas of all the sides of a rectangular prism).

1.2.1.f: Describe and compare the use of area and volume (e.g., covering and filling).

1.2.2: Understand the differences between square and cubic units.

1.2.2.d: Explain why volume is measured in cubic units.

1.2.2.e: Explain how the selected unit of length affects the size of cubic units (e.g., centimeter versus inch).

1.2.4: Understand and apply systematic procedures to measure volume and capacity for solid shapes.

1.2.4.c: Select and use tools that match the unit.

1.2.4.d: Count or compute to obtain the volume or capacity and label the measurement.

1.2.4.e: Use volume and capacity to describe and compare figures (e.g., fill containers with cubes to find which has a greater volume).

1.2.4.f: Measure the capacity of containers using appropriate tools and label (e.g., graduated cylinders, measuring cups, tablespoons).

1.2.6: Understand and apply strategies to obtain reasonable estimates of volume or capacity.

1.2.6.b: Estimate volume or capacity.

1.2.6.c: Use estimation to justify reasonableness of a volume of a rectangular prism.

1.2.6.d: Estimate a measurement of volume or capacity using standard or non-standard units (e.g., estimate the capacity of a bowl in cups and handfuls).

1.2.6.e: Use or describe a process to find a reasonable estimate of volume or capacity (e.g., fill a container with rice or popcorn).

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

1.3.1: Understand the characteristics of circles and rectangular prisms.

1.3.1.a: Name and sort circles or rectangular prisms according to their attributes (faces, edges, radii, base, parallel faces).

1.3.1.b: Draw a figure with given characteristics (e.g., the set of points equidistant from a given point).

1.3.1.c: Identify lines of symmetry in rectangular prisms.

1.3.1.d: Explain lines of symmetry for circles.

1.3.2: Apply understanding of angles and polygons.

1.3.2.a: Identify geometric figures and concepts in nature and art (e.g., triangle in architecture, rhombus in beadwork, culturally relevant textiles, quilts).

1.3.2.c: Create a three-dimensional shape given its net or draw the net of a given threedimensional shape.

1.3.2.d: Find the missing measure of an angle using the properties of parallel lines, perpendicular lines, vertical and corresponding angles.

1.3.3: Understand the relative location of integers on a number line.

1.3.3.a: Show the order of a given set of integers on a number line.

1.3.3.b: Identify the point of final destination given directions for movement on a number line including positive and negative numbers (vertical or horizontal) (e.g., temperature variation at different times of the day, bank accounts, gain and loss of weight).

1.3.3.c: Determine the distance between any two integers on a number line.

1.3.3.d: Describe relative location of points and objects on a number line with both positive and negative numbers.

1.3.3.e: Identify objects on a number line based on given numeric locations.

1.3.4: Apply understanding of rotations (turns) to two-dimensional figures.

1.3.4.a: Apply rotations (turns) of 900 or 1800 to a simple two-dimensional figure.

1.3.4.b: Create a design using (900, 1800, 2700, 3600) rotations (turns) of a shape.

1.3.4.c: Show how a shape has been rotated by 900 or 1800.

1.3.4.d: Describe a rotation so that another person could draw it

1.3.4.e: Identify the coordinates of objects that have been rotated 900, 1800, or 2700 on a coordinate grid.

1.3.4.f: Determine whether an object has been translated or rotated on a coordinate grid.

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

1.4.1: Understand probability as a ratio between and including 0 and 1.

1.4.1.b: Express probabilities as fractions or decimals between 0 and 1 and percents between 0 and 100.

1.4.2: Understand various ways to determine outcomes of events or situations.

1.4.2.a: Determine and use the probabilities of the outcome of a single event.

1.4.2.c: Calculate probability for an event (e.g., pulling colored or numbered balls from a bag, drawing a card, rolling a six on a number cube, spinning a spinner, etc.).

1.4.3: Analyze how data collection methods affect the data collected.

1.4.3.d: Compare data collection methods for a given situation to determine fairness of the method (e.g., compare a phone survey, a web survey, and a personal interview survey).

1.4.4: Apply measures of central tendency to interpret a set of data.

1.4.4.a: Determine when it is appropriate to use mean, median, or mode and why a specific measure provides the most useful information in a given context.

1.4.4.b: Use mean, median, and mode to explain familiar situations (e.g., the heights of students in the class, the hair color of students in the class).

1.4.4.c: Find the missing number given a mean for a data set with a missing element (e.g., given a set of homework scores and the desire to earn an average score of 80%, determine what score the student must earn on the next assignment).

1.4.5: Understand how to organize, display, and interpret data in text from single line graphs and scatter plots.

1.4.5.a: Justify a choice of a graph type for a given situation using information about the type of data.

1.4.5.b: Read and interpret data from single line graphs and scatter plots, and determine when the use of these graphs is appropriate.

1.4.5.c: Use an appropriate representation to display data (e.g., table, graphs) given a particular situation and audience.

1.4.5.f: Use technology to generate bar graphs, line graphs, and scatter plots from tables of data.

1.4.6: Evaluate a data set to determine how it can be, or has been, used to support a point of view.

1.4.6.a: Compare graphs to data sets (e.g., given unlabeled graphs and data sets, match the appropriate data to a graph).

1.4.6.d: Explain whether the scale on a graph accurately represents the data.

1.4.6.e: Compare or evaluate two or more interpretations of the same set of data for accuracy.

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

1.5.1: Apply rules for number patterns based on two arithmetic operations.

1.5.1.a: Recognize or extend patterns and sequences using operations that alternate between terms.

1.5.1.b: Create, explain, or extend number patterns involving two related sets of numbers and two operations including addition, subtraction, multiplication, or division.

1.5.1.c: Use rules for generating number patterns (e.g., Fibonacci sequence, bouncing ball) to model real-life situations.

1.5.1.e: Supply missing elements in a pattern based on two operations.

1.5.1.f: Select or create a pattern that is equivalent to a given pattern.

1.5.2: Apply understanding of patterns involving two arithmetic operations to develop a rule.

1.5.2.a: Describe the rule for a pattern with combinations of two arithmetic operations in the rule.

1.5.2.b: Identify patterns involving combinations of operations in the rule, including exponents (e.g., 2, 5, 11, 23).

1.5.2.c: Represent a situation with a rule involving a single operation (e.g., presidential elections occur every four years; when will the next three elections occur after a given year?).

1.5.3: Apply understanding of equalities and inequalities to interpret and represent relationships between quantities.

1.5.3.a: Express relationships between quantities (decimals, percents, and integers) using =, not equal to, <, >, less than or equal to, and greater than or equal to.

1.5.3.b: Match a given situation to the correct inequality or equality.

1.5.3.c: Express relationships between nonnegative rational numbers using symbols.

1.5.3.d: Write an inequality with a single variable to match a particular situation.

1.5.4: Apply understanding of tables, graphs, expressions, equations, or inequalities to represent situations involving two arithmetic operations.

1.5.4.a: Translate a situation involving multiple arithmetic operations into algebraic form using equations, tables, and graphs.

1.5.4.b: Identify or describe a situation involving two arithmetic operations that matches a given graph.

1.5.4.c: Represent an equation, expression, or inequality using a variable in place of an unknown number.

1.5.4.e: Represent an equation or expression using a variable in place of an unknown number.

1.5.4.f: Identify a situation that corresponds to a given equation or expression.

1.5.6: Understand and apply a variety of strategies to solve one-step equations.

1.5.6.a: Solve one-step equations using pictures and symbols.

1.5.6.b: Solve one-step single variable equations using any strategy (e.g., what number goes in the mystery box?).

1.5.6.c: Solve real-world situations involving single variable equations.

1.5.6.d: Explain a strategy for solving a single variable equation.

1.5.6.e: Write and solve one-step single variable equations for a given situation.

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

3.1.1: Analyze information from a variety of sources to interpret and compare information.

3.1.1.b: Read and interpret data from single line graphs and scatter plots and determine when the use of these graphs is appropriate.

3.1.1.c: Use volume and capacity to describe and compare figures (e.g., fill containers with cubes to find which has a greater volume).

#### 3.2: Make predictions, inferences, conjectures, and draw conclusions.

3.2.1: Apply prediction and inference skills to make or evaluate conjectures.

3.2.1.b: Predict a future element in a relation (e.g., find the fifteenth term in a pattern).

3.2.2: Apply the skills of drawing conclusions and support those conclusions using evidence.

3.2.2.a: Draw conclusions from displays, texts, or oral discussions and justify those conclusions with logical reasoning or other evidence (e.g., read a newspaper article or ad; draw a conclusion and support that conclusion with evidence from the article or elsewh

#### 3.3: Verify results.

3.3.1: Analyze procedures and information used to justify results using evidence.

3.3.1.a: Find and compare rectangular prisms that have a given volume (e.g., if two rectangular prisms have the same volume and one has twice the height of the other, determine how the areas of their bases compare).

3.3.1.b: Apply estimation strategies prior to computation of whole numbers, decimals, and fractions to determine reasonableness of answers.

3.3.1.c: Identify different ways of selecting a sample (e.g., convenience sampling, response to a survey, random sampling) and which method makes a sample more representative for a population.

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

#### 4.1: Gather information.

4.1.1: Apply a planning process to collect information for a given purpose.

4.1.1.a: Use mean, median, and mode to explain familiar situations (e.g., the heights of students in the class; the hair color of students in the class).

4.1.2: Understand how to extract information from multiple sources using reading, listening, and observation.

4.1.2.a: Use mean, median, and mode to explain situations (e.g., the heights of students in the class; hair color of students in the class; favorite movie of students in the class; most watched movie in a specific time frame).

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

4.2.1: Apply organizational skills for a given purpose.

4.2.1.a: Show the order of the set of integers on a number line with both positive and negative numbers (e.g., organize the given birth years of the following Arabic kings on a number line).

4.2.2: Apply communication skills to clearly and effectively express or present ideas and situations using mathematical language or notation.

4.2.2.a: Articulate various strategies used during estimation involving fractions and decimals.

4.2.2.c: Use an appropriate representation to display data (e.g., table, graphs) given a particular situation and audience.

### 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

#### 5.1: Relate concepts and procedures within mathematics.

5.1.1: Apply concepts and procedures from a variety of mathematical areas in a given problem or situation.

5.1.1.a: Translate a situation involving multiple arithmetic operations into algebraic form using equation, table, and graphs.

5.1.1.b: Given a set of data, compare various representations (e.g., table, graph, rule) for a given situation.

5.1.2: Apply different mathematical models and representations to the same situation.

5.1.2.a: Represent equivalent ratios or given percentages using objects, pictures, and symbols.

#### 5.2: Relate mathematical concepts procedures to other disciplines.

5.2.1: Analyze mathematical patterns and ideas to extend mathematical thinking and modeling to other disciplines.

5.2.1.b: Show the order of the set of integers on a number line with both positive and negative numbers (e.g., organize and graph on a number line the given birth years of the given Arabic kings).

5.2.1.c: Read a micrometer to the nearest hundredth of an inch or centimeter, depending on the tool.

#### 5.3: Relate mathematical concepts and procedures to real-world situations.

5.3.1: Understand that mathematics is used in daily life and extensively outside the classroom.

5.3.1.a: Write and solve real-world problem situations to find sums or differences of decimals or fractions (e.g., explain how to find the change received from a \$50.00 bill when a given amount of CD's and tapes with prices are bought).

Correlation last revised: 11/13/2008

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