### 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 decimals in money and fractions.

1.1.1.a: Represent parts of a whole or parts of a set as fractions with common denominators.

1.1.1.c: Illustrate fractions as parts of a whole object, number, or set.

1.1.1.d: Explain or show how a fraction can be decomposed as a sum of smaller fractions.

1.1.2: Understand the relative values of decimals in money and fractions.

1.1.2.a: Describe or show equivalent fractions using models, including pictures, paper folding, geoboards, and parallel number lines.

1.1.2.b: Approximate halves, thirds, and fourths in relationship to whole units on a number line.

1.1.2.c: Order fractions with like-denominators using numbers, pictures, and objects.

1.1.2.e: Explain how to order fractions and/or decimals related to money.

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

1.1.3: Understand and use the associative property of addition and multiplication and the commutative, identity, and zero properties of multiplication on whole numbers.

1.1.3.a: Explain the commutative property of multiplication and give examples.

1.1.3.b: Explain the identity property of addition and multiplication and give examples.

1.1.3.c: Explain why equations are true or false based on one of the properties of addition or multiplication.

1.1.3.d: Illustrate and demonstrate the use of the commutative, associative, or identity property of addition or multiplication using words, pictures, numbers, or objects.

1.1.3.e: Use addition or multiplication properties to replicate a computational strategy when given an example.

1.1.3.f: Illustrate and demonstrate the use of the zero property of multiplication on whole numbers.

1.1.5: Understand the meaning of addition and subtraction of like-denominator fractions.

1.1.5.a: Represent addition and subtraction of fractions with like-denominators using numbers, pictures, and models including everyday objects, fraction circles, number lines, and geoboards.

1.1.5.b: Use joining, separating, part-part-whole, and comparison situations to add and subtract like-denominator fractions.

1.1.5.c: Translate a given picture or illustration into an equivalent symbolic representation of addition and subtraction of like denominator fractions.

1.1.5.d: Select and/or use an appropriate operation to show understanding of addition and subtraction of like-denominator fractions.

1.1.6: Use computational procedures for multiplication and division of whole numbers.

1.1.6.a: Select and develop strategies that help with recall of multiplication and division through 12s.

1.1.6.b: Select and test algorithms used in computational situations that involve multiplication and division of whole numbers and explain strategies.

1.1.6.e: Appropriately apply and explain the concept of remainder in a given context.

1.1.8: Apply estimation strategies involving multiplication and division of whole numbers to predict or determine the reasonableness of answers in situations.

1.1.8.b: Apply a variety of estimation strategies, including multiples of 10 and 100, rounding, and compatible numbers, to predict an answer prior to computation.

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

1.2.1: Understand the concept of area.

1.2.1.a: Demonstrate how area covers a figure and perimeter encloses an area.

1.2.1.b: Illustrate the difference between perimeter and area with drawings.

1.2.4: Apply a procedure to measure length, perimeter, and area.

1.2.4.b: Measure length and perimeter using the suggested procedure.

1.2.4.c: Measure area using the suggested procedure with manipulatives or grid paper and counting the square units.

1.2.6: Understand and apply strategies to obtain reasonable estimates of area measurements for irregular figures.

1.2.6.a: Describe situations in which estimated measurements are appropriate.

1.2.6.b: Explain a process that can be used to find a reasonable estimate of the area measurement of an irregular figure.

1.2.6.d: Use estimation to determine the area of a rectangle and record the number of units with a label.

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

1.3.1: Understand the concepts of parallel and perpendicular lines and line symmetry in 2-dimensional shapes and figures.

1.3.1.c: Draw one or more lines of symmetry in a given 2-dimensional figure.

1.3.1.d: Describe properties of 2-dimensional figures including parallel and perpendicular lines or lines of symmetry.

1.3.3: Locate or plot points in the first quadrant on a coordinate grid.

1.3.3.a: Locate points or objects in the first quadrant on a coordinate grid in terms of horizontal and vertical position.

1.3.3.b: Plot a given set of ordered pairs in the first quadrant of a coordinate grid.

1.3.3.c: Use ordered pairs to name the location of points or objects in the first quadrant of a coordinate grid.

1.3.4: Understand the change made to the position of a 2-dimensional shape or figure by a single translation (slide) or reflection (flip) with or without a grid.

1.3.4.a: Show and explain a translation or reflection using a 2-dimensional shape or figure.

1.3.4.b: Record results of a translation or a reflection on a grid by listing the ordered pairs of the new vertices.

1.3.4.c: Demonstrate or draw and describe a single translation or a single reflection.

1.3.4.d: Describe translations and/or reflections in designs.

1.3.4.e: Draw the figure resulting from a particular translation or reflection on a grid.

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

1.4.1: Understand when events are certain, impossible, possible, more likely, less likely, or equally likely.

1.4.1.a: Predict the likelihood of events and use the vocabulary of probability.

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

1.4.1.c: Explain why events are certain or uncertain.

1.4.1.d: Place events in order based on their likelihood of occurrence.

1.4.1.e: Identify and describe possible and impossible events.

1.4.1.f: Determine and explain which events are more likely, less likely, or equally likely to happen, given an area model.

1.4.3: Understand how to use appropriate questions and samples to collect information about a specific topic.

1.4.3.c: Select data collection methods, including conducting a survey, using observations, or measuring.

1.4.3.d: Make and explain a plan to collect, record, and organize data.

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

1.4.4.a: Explain what the median represents and how to find it for a set of data.

1.4.4.b: Determine the mode and median for a set of data.

1.4.4.c: Explain whether the mode or median better describes a set of data.

1.4.4.d: Determine data points that would result in a given median.

1.4.4.e: Use pictures to illustrate median.

1.4.4.f: Complete a set of data based on a given mode or median and a partial set of data.

1.4.5: Read and understand data from line plots and pictographs.

1.4.5.a: Read and interpret data from line plots.

1.4.5.b: Describe a trend from a given line plot.

1.4.5.c: Summarize text and data in a given table, chart, line plot, pictograph, or bar graph.

1.4.5.d: Describe the completeness and accuracy of data in a graph, given a set of data.

1.4.5.e: Explain whether the components of a graph are appropriate.

1.4.5.f: Explain whether a line plot, pictograph, table, chart, or bar graph is more appropriate for a given situation or to answer a question most effectively.

1.4.5.g: Read and interpret data from a pictograph where the scale is more than one unit.

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

1.5.1: Recognize, understand, and extend a pattern of shapes and/or objects or a pattern of numbers with a single addition, subtraction, or multiplication between terms.

1.5.1.a: Extend, describe, or construct patterns of numbers, using addition, subtraction, or multiplication, based on a single operation between terms.

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

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

1.5.1.d: Construct a number pattern and explain what makes it a pattern.

1.5.1.e: Determine missing elements in the beginning, middle, and/or end of a pattern.

1.5.2: Describe a rule for a pattern with a single arithmetic operation.

1.5.2.a: Identify or generate a rule for a pattern with a single arithmetic operation in order to extend or fill in parts of the pattern.

1.5.2.b: Show growing patterns using objects or pictures and explain the rule.

1.5.2.c: Determine the operation that changes the elements of one set of numbers into the elements of another set of numbers such as using a function machine.

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

1.5.4: Use a single variable to write expressions and equations that represent situations involving multiplication and division of whole numbers.

1.5.4.a: Read formulas, expressions, and equations involving a single variable.

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

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

1.5.6.a: Solve a simple equation using addition, subtraction, multiplication, or division.

1.5.6.b: Write and solve a one-step equation for a given situation.

### 2: The student uses mathematics to define and solve problems.

#### 2.2: Construct solutions.

2.2.2: Select and use appropriate concepts and procedures from number sense, measurement, geometric sense, and/or statistics to construct solutions.

2.2.2.a: Use addition, subtraction, multiplication, and/or division of whole numbers to construct a solution.

2.2.2.b: Use measurements related to length, perimeter, time, money value, weight/mass, capacity, temperature, or area to construct a solution.

2.2.2.c: Use properties of 2-dimensional figures, congruence, location, translation, or reflection in the first quadrant of a grid to construct a solution.

2.2.2.d: Use median and/or mode to construct a solution.

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

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

3.1.1.a: Compare mathematical information and results represented in tables, charts, pictographs, bar graphs, line plots, text, diagrams, figures, or pictures.

3.1.1.c: Differentiate between a valid and invalid comparison of mathematical information or results.

#### 3.3: Verify results.

3.3.3: Understand how to validate thinking about numerical, measurement, geometric, and/or statistical ideas.

3.3.3.a: Explain and support thinking about numerical, measurement, geometric, and/or statistical ideas using patterns and relationships.

### 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 one or two different sources for a given purpose.

4.1.2.a: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, models, pictographs, bar graphs, or line plots for a specific 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 in pictures, tables, charts, pictographs, bar graphs, line plots, drawings, or other appropriate forms and include title, labels, appropriate and consistent scales, and accurate data display.

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.