### 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 the concepts and symbolic representations of mixed numbers, proper and improper fractions, and decimals.

1.1.1.a: Represent mixed numbers, proper and improper fractions, and decimals using words, pictures, models, and/or numbers.

1.1.1.b: Make a model when given a symbolic representation or write a fraction or decimal when given a number line, picture, or model.

1.1.1.c: Explain how the value of a fraction changes in relationship to the size of the whole.

1.1.1.d: Explain the value for a given digit and/or show how to read and write decimals to at least the thousandths place.

1.1.2: Understand the relative values of non-negative fractions or decimals.

1.1.2.a: Order decimals, proper and improper fractions, and/or mixed numbers with denominators 2, 3, 4, 5, 6, 10, 12, and/or 15 using symbolic representations, number lines, or pictures.

1.1.2.c: Explain why one fraction is greater than, less than, or equal to another fraction.

1.1.2.d: Explain why one decimal is greater than, less than, or equal to another decimal.

1.1.2.e: Show how factors and multiples can be used to name equivalent fractions.

1.1.3: Understand and apply the concept of divisibility including primes, composites, factors, and multiples.

1.1.3.b: Illustrate prime or composite numbers by creating a physical model.

1.1.3.c: Identify prime or composite numbers between 1 and 100 and explain why a whole number is prime or composite.

1.1.3.e: Use factors, multiples, and prime and composite numbers in a variety of situations.

1.1.3.f: Factor a number into its prime factorization or into factor pairs.

1.1.3.g: Explain or show whether one number is a factor of another number.

1.1.3.h: Explain or demonstrate why a number is prime or composite.

1.1.5: Understand the meaning of addition and subtraction of non-negative decimals and fractions.

1.1.5.a: Represent addition and subtraction of fractions with denominators of 2, 4, 8 or 2, 3, 6, 12 or 2, 5, 10.

1.1.5.b: Represent or explain addition and subtraction of non-negative decimals through thousandths using words, pictures, models, or numbers.

1.1.5.c: Explain a strategy for adding and subtracting fractions.

1.1.5.d: Select and/or use an appropriate operation(s) to show understanding of addition and subtraction of non-negative decimals and/or fractions.

1.1.5.e: Explain the relationship between addition and subtraction of non-negative decimals and fractions.

1.1.5.f: Translate a picture or illustration into an equivalent symbolic representation of addition and subtraction of non-negative fractions and decimals.

1.1.6: Apply strategies or uses computational procedures to add and subtract non-negative decimals and like-denominator fractions.

1.1.6.a: Add and subtract non-negative decimals and like-denominator fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and/or 15.

1.1.6.b: Find sums or differences of decimals or like-denominator fractions in given situations.

1.1.6.c: Calculate sums of two numbers with decimals to the thousandths or three numbers with decimals to hundredths.

1.1.6.d: Calculate difference of numbers with decimals to thousandths.

1.1.7: Apply strategies and uses tools appropriate to tasks involving addition and subtraction of non-negative decimals or like-denominator fractions.

1.1.7.c: Describe strategies for mentally adding or subtracting non-negative decimals and/or like-denominator fractions.

1.1.8: Apply estimation strategies involving addition and subtraction of non-negative decimals and like-denominator fractions to predict results or determine reasonableness of answers.

1.1.8.f: Explain or describe a strategy used for estimation involving addition and subtraction of non-negative decimals and like-denominator fractions.

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

1.2.3: Understand how measurement units of capacity, mass, and length are organized in the metric system.

1.2.3.c: Convert between units in the metric system:

1.2.3.c.1: Length - millimeter, centimeter, meter, kilometer

1.2.4: Use a systematic procedure to measure and describe the area of rectangles or triangles.

1.2.4.b: Select and describe the appropriate units and/or tools for measuring length, perimeter, and/or area.

1.2.4.c: Demonstrate a procedure for measuring the area of a rectangle or right triangle.

1.2.4.d: Use procedures to measure length, perimeter, and/or area.

1.2.4.e: Measure the area in figures composed of rectangles and triangles.

1.2.5: Use formulas to determine perimeter and area of rectangles and right triangles.

1.2.5.a: Explain how to find the perimeter or area of any rectangle using a rule.

1.2.5.d: Determine and label right triangles and all rectangles with whole number dimensions and a given perimeter or area.

1.2.6: Understand and apply strategies to obtain reasonable estimates of angle measurements and areas of rectangles and right triangles.

1.2.6.b: Estimate and label areas of rectangles and right triangles.

1.2.6.c: Explain an appropriate process for estimating perimeter or area of a rectangle or right triangle or an angle measurement.

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

1.3.2: Use the properties of parallel and perpendicular lines and line of symmetry.

1.3.2.a: Describe parallel and perpendicular lines and/or lines of symmetry.

1.3.2.b: Draw, describe, and/or label a figure or design that includes a given set of properties including parallel or perpendicular lines and/or line of symmetry.

1.3.2.c: Draw, describe, and/or label angles, quadrilaterals, parallel and/or perpendicular lines, lines of symmetry, and congruent 2-dimensional shapes or figures.

1.3.2.d: Sort, classify, and label shapes and figures using the properties of parallel lines, perpendicular lines, and lines of symmetry.

1.3.2.e: Complete a picture or design using a line of symmetry.

1.3.2.f: Complete pictures or designs from a variety of cultures that incorporate parallel line(s), perpendicular line(s), and/or a line(s) of symmetry.

1.3.3: Locate or plot points with whole number, fraction, and/or decimal coordinates on a positive number line.

1.3.3.b: Describe the relative position of fractions and/or decimals on a positive number line.

1.3.3.c: Identify or move the coordinates of points on an incomplete number line involving fractional or decimal increments.

1.3.4: Understand and apply translations or reflections to a 2-dimensional shape or figure.

1.3.4.a: Draw a translation or reflection of a given figure on a grid.

1.3.4.b: Use translations or reflections to describe patterns in art, architecture, or nature.

1.3.4.c: Describe whether a figure has been translated or reflected.

1.3.4.d: Create designs using translations and/or reflections.

1.3.4.e: Identify a picture or diagram of a particular translation or reflection.

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

1.4.1: Understand the likelihood of simple events occurring.

1.4.1.a: Predict and test how likely it is that a certain outcome will occur.

1.4.1.e: Explain why some outcomes are equally likely or more or less likely to happen than others.

1.4.1.f: Determine whether a real-life event has zero probability, 50% probability, or 100% probability of occurring.

1.4.3: Understand how different collection methods or different questions can affect the data collected.

1.4.3.b: Explain how different data collection methods, including phone survey, internet search, and person-to-person survey, affect the data set for a given question.

1.4.4: Understand and use the mean, median, and mode to describe a set of data.

1.4.4.a: Explain how to determine the mean of a set of data and explain the significance of the mean.

1.4.4.b: Determine the mean of a given set of data using objects or pictures.

1.4.4.c: Determine and explain whether mean, median, or mode is the most appropriate measure of central tendency in a given situation.

1.4.4.d: Explain why the mean, median, or mode may be greater than or less than the other measures for a given set of data.

1.4.4.e: Determine the mean for two samples from the same population and explain why they may not be the same.

1.4.5: Read data presented in text and circle graphs.

1.4.5.a: Read and interpret data from text and circle graphs in terms of patterns.

1.4.5.b: Explain the completeness and accuracy of data presented in circle graphs.

1.4.5.c: Explain whether line plots, pictographs, tables, charts, bar or circle graphs are more appropriate for a given set of data, particular situation, or purpose, or answers a question most effectively.

1.4.5.d: Summarize data presented in a circle graph or text.

1.4.5.e: Describe trends or patterns in data represented in a line plot or pictograph.

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

1.5.1: Recognize, extend, and/or create patterns of objects or shapes or patterns of numbers with a single arithmetic operation between terms.

1.5.1.a: Extend, describe, or create patterns of numbers using division based on a single operation between terms.

1.5.1.b: Extend, describe, or create patterns of shapes or objects.

1.5.1.c: Extend and represent patterns using words, tables, numbers, models, and pictures.

1.5.1.d: Extend a pattern by supplying missing elements in the beginning, middle, and/or end of the pattern.

1.5.2: Develop a rule for patterns, which may include combinations of two arithmetic operations.

1.5.2.a: Generate a rule for a pattern to extend or fill in parts of the pattern.

1.5.2.b: Determine a rule for a pattern of alternating operations and explains the rule.

1.5.2.c: Identify a rule for a pattern with two operations between terms.

1.5.2.d: Explain why a given rule with a single operation fits a given pattern.

1.5.2.e: Describe or write a rule for a pattern based on a single operation.

1.5.2.f: Explain why a given rule fits a pattern based on a single arithmetic operation in the rule.

1.5.3: Understand the concept of mathematical equality and inequality and uses the symbols =, "not equal to", <, and >.

1.5.3.a: Express relationships between like denominator fractions and decimal quantities using <, >, =, or "not equal to".

1.5.3.b: Describe a situation represented by an equation or inequality involving like denominator fractions and/or decimals.

1.5.3.c: Write a simple equation or inequality using non-negative decimals or like-denominator fractions to represent a given situation.

1.5.4: Use variables to write expressions and equations that represent situations involving addition and subtraction of non-negative decimals and like-denominator fractions.

1.5.4.a: Read expressions and equations involving variables.

1.5.4.b: Write an expression or equation using a variable to represent a given situation.

1.5.4.c: Describe a situation that represents a given expression or equation that includes a variable.

1.5.4.e: Write or illustrate expressions or equations using manipulatives, models, pictures, and symbols for given situations.

1.5.5: Apply algebraic properties to evaluate expressions using manipulatives, pictures, and/or symbols.

1.5.5.b: Determine the value of simple expressions or formulas involving addition and subtraction of non-negative decimals and like denominator fractions and/or multiplication and division of whole numbers given the values of the variables.

1.5.6: Apply properties to solve equations involving multiplication and division.

1.5.6.a: Solve a one-step equation involving multiplication or division using manipulatives, pictures, and/or symbols.

1.5.6.b: Write and solve an equation in a given situation.

1.5.6.c: Explain or show the meaning of the solution to an equation.

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

3.1.1: Analyze numerical, measurement, geometric, and/or statistical information in familiar situations.

3.1.1.a: Analyze mathematical information or results represented in tables, charts, graphs, text, diagrams, figures, or pictures.

3.1.1.b: Compare mathematical information represented in tables, charts, graphs, text, diagrams, figures, or pictures.

3.1.1.d: Differentiate between valid and invalid analysis of mathematical information or results.

#### 3.2: Conclude.

3.2.1: Draw and support conclusions.

3.2.1.b: Use data or examples as evidence to support or contradict a given conclusion.

3.2.1.c: Identify a valid conclusion based on given information.

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

#### 4.1: Gather information.

4.1.2: Extract numerical, measurement, geometric, and/or statistical information from multiple sources for a given purpose.

4.1.2.a: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, bar graphs, line plots, pictographs, circle graphs, and/or models for a purpose.

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

4.2.1: Understand how to organize numerical, measurement, geometric, and/or statistical information to communicate for a given purpose.

4.2.1.a: Select a useful format and organize mathematical information for a given purpose.

4.2.2: Understand how to represent numerical, measurement, geometric, and/or statistical information in graphs or other appropriate forms.

4.2.2.a: Represent mathematical information using tables, charts, pictographs, bar graphs, line plots, circle graphs, pictures, models, drawings, or other forms including titles, labels, appropriate and consistent scales, and accurate display of data.

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

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

5.2.1: Use mathematical thinking, modeling, patterns, and ideas in other disciplines.

5.2.1.a: Give examples of mathematical patterns and ideas in other disciplines.

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.